Refs #324. Upgrade LAPACK to 3.5.0 version.

lapack-netlib/CMakeLists.txt

@@ -188,6 +188,7 @@ else()
     CACHE STRING "Linker flags for shared libs" FORCE)
 endif( NOT LATESTLAPACK_FOUND )
 
+message(STATUS "BUILD TESTING : ${BUILD_TESTING}" )
 if(BUILD_TESTING)
   add_subdirectory(TESTING)
 endif(BUILD_TESTING)
@@ -200,7 +201,7 @@ option(LAPACKE "Build LAPACKE" OFF)
 # if LAPACKE_WITH_TMG is selected, we need to add those routines to LAPACKE
 option(LAPACKE_WITH_TMG "Build LAPACKE with tmglib routines" OFF)
 if (LAPACKE_WITH_TMG)
-  option(LAPACKE "Build LAPACKE" ON)
+  set(LAPACKE ON)
   if(NOT BUILD_TESTING)
      add_subdirectory(TESTING/MATGEN)
    endif(NOT BUILD_TESTING)

lapack-netlib/DOCS/Doxyfile

@@ -647,7 +647,7 @@ INPUT_ENCODING         = UTF-8
 # *.hxx *.hpp *.h++ *.idl *.odl *.cs *.php *.php3 *.inc *.m *.mm *.dox *.py 
 # *.f90 *.f *.for *.vhd *.vhdl
 
-FILE_PATTERNS          = *.f
+FILE_PATTERNS          = *
 
 # The RECURSIVE tag can be used to turn specify whether or not subdirectories 
 # should be searched for input files as well. Possible values are YES and NO. 

lapack-netlib/DOCS/psfig.tex

@@ -1,391 +0,0 @@
-% Psfig/TeX Release 1.2
-% dvi2ps-li version
-%
-% All software, documentation, and related files in this distribution of
-% psfig/tex are Copyright 1987, 1988 Trevor J. Darrell
-%
-% Permission is granted for use and non-profit distribution of psfig/tex 
-% providing that this notice be clearly maintained, but the right to
-% distribute any portion of psfig/tex for profit or as part of any commercial
-% product is specifically reserved for the author.
-%
-% $Header$
-% $Source$
-%
-% Thanks to Greg Hager (GDH) and Ned Batchelder for their contributions
-% to this project.
-%
-\catcode`\@=11\relax
-\newwrite\@unused
-\def\typeout#1{{\let\protect\string\immediate\write\@unused{#1}}}
-\typeout{psfig/tex 1.2-dvi2ps-li}
-
-%% Here's how you define your figure path.  Should be set up with null
-%% default and a user useable definition.
-
-\def\figurepath{./}
-\def\psfigurepath#1{\edef\figurepath{#1}}
-
-%
-% @psdo control structure -- similar to Latex @for.
-% I redefined these with different names so that psfig can
-% be used with TeX as well as LaTeX, and so that it will not 
-% be vunerable to future changes in LaTeX's internal
-% control structure,
-%
-\def\@nnil{\@nil}
-\def\@empty{}
-\def\@psdonoop#1\@@#2#3{}
-\def\@psdo#1:=#2\do#3{\edef\@psdotmp{#2}\ifx\@psdotmp\@empty \else
-    \expandafter\@psdoloop#2,\@nil,\@nil\@@#1{#3}\fi}
-\def\@psdoloop#1,#2,#3\@@#4#5{\def#4{#1}\ifx #4\@nnil \else
-       #5\def#4{#2}\ifx #4\@nnil \else#5\@ipsdoloop #3\@@#4{#5}\fi\fi}
-\def\@ipsdoloop#1,#2\@@#3#4{\def#3{#1}\ifx #3\@nnil 
-       \let\@nextwhile=\@psdonoop \else
-      #4\relax\let\@nextwhile=\@ipsdoloop\fi\@nextwhile#2\@@#3{#4}}
-\def\@tpsdo#1:=#2\do#3{\xdef\@psdotmp{#2}\ifx\@psdotmp\@empty \else
-    \@tpsdoloop#2\@nil\@nil\@@#1{#3}\fi}
-\def\@tpsdoloop#1#2\@@#3#4{\def#3{#1}\ifx #3\@nnil 
-       \let\@nextwhile=\@psdonoop \else
-      #4\relax\let\@nextwhile=\@tpsdoloop\fi\@nextwhile#2\@@#3{#4}}
-% 
-%
-\def\psdraft{
-	\def\@psdraft{0}
-	%\typeout{draft level now is \@psdraft \space . }
-}
-\def\psfull{
-	\def\@psdraft{100}
-	%\typeout{draft level now is \@psdraft \space . }
-}
-\psfull
-\newif\if@prologfile
-\newif\if@postlogfile
-\newif\if@noisy
-\def\pssilent{
-	\@noisyfalse
-}
-\def\psnoisy{
-	\@noisytrue
-}
-\psnoisy
-%%% These are for the option list.
-%%% A specification of the form a = b maps to calling \@p@@sa{b}
-\newif\if@bbllx
-\newif\if@bblly
-\newif\if@bburx
-\newif\if@bbury
-\newif\if@height
-\newif\if@width
-\newif\if@rheight
-\newif\if@rwidth
-\newif\if@clip
-\newif\if@verbose
-\def\@p@@sclip#1{\@cliptrue}
-
-%%% GDH 7/26/87 -- changed so that it first looks in the local directory,
-%%% then in a specified global directory for the ps file.
-
-\def\@p@@sfile#1{\def\@p@sfile{null}%
-	        \openin1=#1
-		\ifeof1\closein1%
-		       \openin1=\figurepath#1
-			\ifeof1\typeout{Error, File #1 not found}
-			\else\closein1
-			    \edef\@p@sfile{\figurepath#1}%
-                        \fi%
-		 \else\closein1%
-		       \def\@p@sfile{#1}%
-		 \fi}
-\def\@p@@sfigure#1{\def\@p@sfile{null}%
-	        \openin1=#1
-		\ifeof1\closein1%
-		       \openin1=\figurepath#1
-			\ifeof1\typeout{Error, File #1 not found}
-			\else\closein1
-			    \def\@p@sfile{\figurepath#1}%
-                        \fi%
-		 \else\closein1%
-		       \def\@p@sfile{#1}%
-		 \fi}
-
-\def\@p@@sbbllx#1{
-		%\typeout{bbllx is #1}
-		\@bbllxtrue
-		\dimen100=#1
-		\edef\@p@sbbllx{\number\dimen100}
-}
-\def\@p@@sbblly#1{
-		%\typeout{bblly is #1}
-		\@bbllytrue
-		\dimen100=#1
-		\edef\@p@sbblly{\number\dimen100}
-}
-\def\@p@@sbburx#1{
-		%\typeout{bburx is #1}
-		\@bburxtrue
-		\dimen100=#1
-		\edef\@p@sbburx{\number\dimen100}
-}
-\def\@p@@sbbury#1{
-		%\typeout{bbury is #1}
-		\@bburytrue
-		\dimen100=#1
-		\edef\@p@sbbury{\number\dimen100}
-}
-\def\@p@@sheight#1{
-		\@heighttrue
-		\dimen100=#1
-   		\edef\@p@sheight{\number\dimen100}
-		%\typeout{Height is \@p@sheight}
-}
-\def\@p@@swidth#1{
-		%\typeout{Width is #1}
-		\@widthtrue
-		\dimen100=#1
-		\edef\@p@swidth{\number\dimen100}
-}
-\def\@p@@srheight#1{
-		%\typeout{Reserved height is #1}
-		\@rheighttrue
-		\dimen100=#1
-		\edef\@p@srheight{\number\dimen100}
-}
-\def\@p@@srwidth#1{
-		%\typeout{Reserved width is #1}
-		\@rwidthtrue
-		\dimen100=#1
-		\edef\@p@srwidth{\number\dimen100}
-}
-\def\@p@@ssilent#1{ 
-		\@verbosefalse
-}
-\def\@p@@sprolog#1{\@prologfiletrue\def\@prologfileval{#1}}
-\def\@p@@spostlog#1{\@postlogfiletrue\def\@postlogfileval{#1}}
-\def\@cs@name#1{\csname #1\endcsname}
-\def\@setparms#1=#2,{\@cs@name{@p@@s#1}{#2}}
-%
-% initialize the defaults (size the size of the figure)
-%
-\def\ps@init@parms{
-		\@bbllxfalse \@bbllyfalse
-		\@bburxfalse \@bburyfalse
-		\@heightfalse \@widthfalse
-		\@rheightfalse \@rwidthfalse
-		\def\@p@sbbllx{}\def\@p@sbblly{}
-		\def\@p@sbburx{}\def\@p@sbbury{}
-		\def\@p@sheight{}\def\@p@swidth{}
-		\def\@p@srheight{}\def\@p@srwidth{}
-		\def\@p@sfile{}
-		\def\@p@scost{10}
-		\def\@sc{}
-		\@prologfilefalse
-		\@postlogfilefalse
-		\@clipfalse
-		\if@noisy
-			\@verbosetrue
-		\else
-			\@verbosefalse
-		\fi
-
-}
-%
-% Go through the options setting things up.
-%
-\def\parse@ps@parms#1{
-	 	\@psdo\@psfiga:=#1\do
-		   {\expandafter\@setparms\@psfiga,}}
-%
-% Compute bb height and width
-%
-\newif\ifno@bb
-\newif\ifnot@eof
-\newread\ps@stream
-\def\bb@missing{
-	\if@verbose{
-		\typeout{psfig: searching \@p@sfile \space  for bounding box}
-	}\fi
-	\openin\ps@stream=\@p@sfile
-	\no@bbtrue
-	\not@eoftrue
-	\catcode`\%=12
-	\loop
-		\read\ps@stream to \line@in
-		\global\toks200=\expandafter{\line@in}
-		\ifeof\ps@stream \not@eoffalse \fi
-		%\typeout{ looking at :: \the\toks200 }
-		\@bbtest{\toks200}
-		\if@bbmatch\not@eoffalse\expandafter\bb@cull\the\toks200\fi
-	\ifnot@eof \repeat
-	\catcode`\%=14
-}	
-\catcode`\%=12
-\newif\if@bbmatch
-\def\@bbtest#1{\expandafter\@a@\the#1%%BoundingBox:\@bbtest\@a@}
-\long\def\@a@#1%%BoundingBox:#2#3\@a@{\ifx\@bbtest#2\@bbmatchfalse\else\@bbmatchtrue\fi}
-\long\def\bb@cull#1 #2 #3 #4 #5 {
-	\dimen100=#2 bp\edef\@p@sbbllx{\number\dimen100}
-	\dimen100=#3 bp\edef\@p@sbblly{\number\dimen100}
-	\dimen100=#4 bp\edef\@p@sbburx{\number\dimen100}
-	\dimen100=#5 bp\edef\@p@sbbury{\number\dimen100}
-	\no@bbfalse
-}
-\catcode`\%=14
-%
-\def\compute@bb{
-		\no@bbfalse
-		\if@bbllx \else \no@bbtrue \fi
-		\if@bblly \else \no@bbtrue \fi
-		\if@bburx \else \no@bbtrue \fi
-		\if@bbury \else \no@bbtrue \fi
-		\ifno@bb \bb@missing \fi
-		\ifno@bb \typeout{FATAL ERROR: no bb supplied or found}
-			\no-bb-error
-		\fi
-		%
-		\count203=\@p@sbburx
-		\count204=\@p@sbbury
-		\advance\count203 by -\@p@sbbllx
-		\advance\count204 by -\@p@sbblly
-		\edef\@bbw{\number\count203}
-		\edef\@bbh{\number\count204}
-		%\typeout{ bbh = \@bbh, bbw = \@bbw }
-}
-%
-% \in@hundreds performs #1 * (#2 / #3) correct to the hundreds,
-%	then leaves the result in @result
-%
-\def\in@hundreds#1#2#3{\count240=#2 \count241=#3
-		     \count100=\count240	% 100 is first digit #2/#3
-		     \divide\count100 by \count241
-		     \count101=\count100
-		     \multiply\count101 by \count241
-		     \advance\count240 by -\count101
-		     \multiply\count240 by 10
-		     \count101=\count240	%101 is second digit of #2/#3
-		     \divide\count101 by \count241
-		     \count102=\count101
-		     \multiply\count102 by \count241
-		     \advance\count240 by -\count102
-		     \multiply\count240 by 10
-		     \count102=\count240	% 102 is the third digit
-		     \divide\count102 by \count241
-		     \count200=#1\count205=0
-		     \count201=\count200
-			\multiply\count201 by \count100
-		 	\advance\count205 by \count201
-		     \count201=\count200
-			\divide\count201 by 10
-			\multiply\count201 by \count101
-			\advance\count205 by \count201
-			%
-		     \count201=\count200
-			\divide\count201 by 100
-			\multiply\count201 by \count102
-			\advance\count205 by \count201
-			%
-		     \edef\@result{\number\count205}
-}
-\def\compute@wfromh{
-		% computing : width = height * (bbw / bbh)
-		\in@hundreds{\@p@sheight}{\@bbw}{\@bbh}
-		%\typeout{ \@p@sheight * \@bbw / \@bbh, = \@result }
-		\edef\@p@swidth{\@result}
-		%\typeout{w from h: width is \@p@swidth}
-}
-\def\compute@hfromw{
-		% computing : height = width * (bbh / bbw)
-		\in@hundreds{\@p@swidth}{\@bbh}{\@bbw}
-		%\typeout{ \@p@swidth * \@bbh / \@bbw = \@result }
-		\edef\@p@sheight{\@result}
-		%\typeout{h from w : height is \@p@sheight}
-}
-\def\compute@handw{
-		\if@height 
-			\if@width
-			\else
-				\compute@wfromh
-			\fi
-		\else 
-			\if@width
-				\compute@hfromw
-			\else
-				\edef\@p@sheight{\@bbh}
-				\edef\@p@swidth{\@bbw}
-			\fi
-		\fi
-}
-\def\compute@resv{
-		\if@rheight \else \edef\@p@srheight{\@p@sheight} \fi
-		\if@rwidth \else \edef\@p@srwidth{\@p@swidth} \fi
-}
-%		
-% Compute any missing values
-\def\compute@sizes{
-	\compute@bb
-	\compute@handw
-	\compute@resv
-}
-%
-% \psfig
-% usage : \psfig{file=, height=, width=, bbllx=, bblly=, bburx=, bbury=,
-%			rheight=, rwidth=, clip=}
-%
-% "clip=" is a switch and takes no value, but the `=' must be present.
-\def\psfig#1{\vbox {
-	% do a zero width hard space so that a single
-	% \psfig in a centering enviornment will behave nicely
-	%{\setbox0=\hbox{\ }\ \hskip-\wd0}
-	%
-	\ps@init@parms
-	\parse@ps@parms{#1}
-	\compute@sizes
-	%
-	\ifnum\@p@scost<\@psdraft{
-		\if@verbose{
-			\typeout{psfig: including \@p@sfile \space }
-		}\fi
-		%
-		\special{ pstext="\@p@swidth \space 
-			\@p@sheight \space
-			\@p@sbbllx \space \@p@sbblly \space 
-			\@p@sbburx  \space 
-			\@p@sbbury \space startTexFig" \space}
-		\if@clip{
-			\if@verbose{
-				\typeout{(clip)}
-			}\fi
-			\special{ pstext="doclip \space"}
-		}\fi
-		\if@prologfile
-		    \special{psfile=\@prologfileval \space } \fi
-		\special{psfile=\@p@sfile \space }
-		\if@postlogfile
-		    \special{psfile=\@postlogfileval \space } \fi
-		\special{pstext=endTexFig \space }
-		% Create the vbox to reserve the space for the figure
-		\vbox to \@p@srheight true sp{
-			\hbox to \@p@srwidth true sp{
-				\hss
-			}
-			\vss
-		}
-	}\else{
-		% draft figure, just reserve the space and print the
-		% path name.
-		\vbox to \@p@srheight true sp{
-		\vss
-			\hbox to \@p@srwidth true sp{
-				\hss
-				\if@verbose{
-					\@p@sfile
-				}\fi
-				\hss
-			}
-		\vss
-		}
-	}\fi
-}}
-\def\psglobal{\typeout{psfig: PSGLOBAL is OBSOLETE; use psprint -m instead}}
-\catcode`\@=12\relax
-

lapack-netlib/INSTALL/dlamch.f

@@ -72,6 +72,10 @@
       CHARACTER          CMACH
 *     ..
 *
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION   A, B
+*     ..
+*
 * =====================================================================
 *
 *     .. Parameters ..

lapack-netlib/INSTALL/ilaver.f

@@ -41,14 +41,14 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date September 2012
+*> \date November 2013
 *
 *> \ingroup auxOTHERauxiliary
 *
 *  =====================================================================
       SUBROUTINE ILAVER( VERS_MAJOR, VERS_MINOR, VERS_PATCH )
 *
-*  -- LAPACK computational routine (version 3.4.2) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     September 2012
@@ -58,8 +58,8 @@
       INTEGER VERS_MAJOR, VERS_MINOR, VERS_PATCH
 *  =====================================================================
       VERS_MAJOR = 3
-      VERS_MINOR = 4
-      VERS_PATCH = 2
+      VERS_MINOR = 5
+      VERS_PATCH = 0
 *  =====================================================================
 *
       RETURN

lapack-netlib/INSTALL/make.inc.ALPHA

@@ -1,7 +1,7 @@
 ####################################################################
 #  LAPACK make include file.                                       #
-#  LAPACK, Version 3.4.1                                           #
-#  April 2012                                                      #
+#  LAPACK, Version 3.5.0                                           #
+#  November 2013                                                   #
 ####################################################################
 #
 SHELL = /bin/sh

lapack-netlib/INSTALL/make.inc.HPPA

@@ -1,7 +1,7 @@
 ####################################################################
 #  LAPACK make include file.                                       #
-#  LAPACK, Version 3.4.1                                           #
-#  April 2012                                                      #
+#  LAPACK, Version 3.5.0                                           #
+#  November 2013                                                   #
 ####################################################################
 #
 SHELL = /bin/sh

lapack-netlib/INSTALL/make.inc.IRIX64

@@ -1,7 +1,7 @@
 ####################################################################
 #  LAPACK make include file.                                       #
-#  LAPACK, Version 3.4.1                                           #
-#  April 2012                                                      #
+#  LAPACK, Version 3.5.0                                           #
+#  November 2013                                                   #
 ####################################################################
 #
 SHELL = /sbin/sh

lapack-netlib/INSTALL/make.inc.O2K

@@ -1,7 +1,7 @@
 ####################################################################
 #  LAPACK make include file.                                       #
-#  LAPACK, Version 3.4.1                                           #
-#  April 2012                                                      #
+#  LAPACK, Version 3.5.0                                           #
+#  November 2013                                                   #
 ####################################################################
 #
 SHELL = /sbin/sh

lapack-netlib/INSTALL/make.inc.SGI5

@@ -1,7 +1,7 @@
 ####################################################################
 #  LAPACK make include file.                                       #
-#  LAPACK, Version 3.4.1                                           #
-#  April 2012                                                      #
+#  LAPACK, Version 3.5.0                                           #
+#  November 2013                                                   #
 ####################################################################
 #
 SHELL = /sbin/sh

lapack-netlib/INSTALL/make.inc.SUN4

@@ -1,7 +1,7 @@
 ####################################################################
 #  LAPACK make include file.                                       #
-#  LAPACK, Version 3.4.1                                           #
-#  April 2012                                                      #
+#  LAPACK, Version 3.5.0                                           #
+#  November 2013                                                   #
 ####################################################################
 #
 SHELL = /bin/sh

lapack-netlib/INSTALL/make.inc.SUN4SOL2

@@ -1,7 +1,7 @@
 ####################################################################
 #  LAPACK make include file.                                       #
-#  LAPACK, Version 3.4.1                                           #
-#  April 2012                                                      #
+#  LAPACK, Version 3.5.0                                           #
+#  November 2013                                                   #
 ####################################################################
 #
 SHELL = /bin/sh

lapack-netlib/INSTALL/make.inc.XLF

@@ -1,7 +1,7 @@
 ####################################################################
 #  LAPACK make include file.                                       #
-#  LAPACK, Version 3.4.1                                           #
-#  April 2012                                                      #
+#  LAPACK, Version 3.5.0                                           #
+#  November 2013                                                   #
 ####################################################################
 #
 SHELL = /bin/sh

lapack-netlib/INSTALL/make.inc.gfortran

@@ -1,7 +1,7 @@
 ####################################################################
 #  LAPACK make include file.                                       #
-#  LAPACK, Version 3.4.1                                           #
-#  April 2012                                                      #
+#  LAPACK, Version 3.5.0                                           #
+#  November 2013                                                   #
 ####################################################################
 #
 SHELL = /bin/sh
@@ -13,9 +13,9 @@ SHELL = /bin/sh
 #  desired load options for your machine.
 #
 FORTRAN  = gfortran 
-OPTS     = -O2
+OPTS     = -O2 -frecursive
 DRVOPTS  = $(OPTS)
-NOOPT    = -O0
+NOOPT    = -O0 -frecursive
 LOADER   = gfortran
 LOADOPTS =
 #

lapack-netlib/INSTALL/make.inc.gfortran_debug

@@ -1,7 +1,7 @@
 ####################################################################
 #  LAPACK make include file.                                       #
-#  LAPACK, Version 3.4.1                                           #
-#  April 2012                                                      #
+#  LAPACK, Version 3.5.0                                           #
+#  November 2013                                                   #
 ####################################################################
 #
 SHELL = /bin/sh
@@ -12,10 +12,10 @@ SHELL = /bin/sh
 #  selected.  Define LOADER and LOADOPTS to refer to the loader
 #  and desired load options for your machine.
 #
-FORTRAN  = gfortran -fimplicit-none -g
+FORTRAN  = gfortran -fimplicit-none -g -frecursive
 OPTS     =
 DRVOPTS  = $(OPTS)
-NOOPT    = -g -O0
+NOOPT    = -g -O0 -frecursive
 LOADER   = gfortran -g
 LOADOPTS =
 #

lapack-netlib/INSTALL/make.inc.ifort

@@ -1,7 +1,7 @@
 ####################################################################
 #  LAPACK make include file.                                       #
-#  LAPACK, Version 3.4.1                                           #
-#  April 2012                                                      #
+#  LAPACK, Version 3.5.0                                           #
+#  November 2013                                                   #
 ####################################################################
 #
 SHELL = /bin/sh

lapack-netlib/INSTALL/make.inc.pgf95

@@ -1,7 +1,7 @@
 ####################################################################
 #  LAPACK make include file.                                       #
-#  LAPACK, Version 3.4.1                                           #
-#  April 2012                                                      #
+#  LAPACK, Version 3.5.0                                           #
+#  November 2013                                                   #
 ####################################################################
 #
 SHELL = /bin/sh

lapack-netlib/INSTALL/make.inc.pghpf

@@ -1,7 +1,7 @@
 ####################################################################
 #  LAPACK make include file.                                       #
-#  LAPACK, Version 3.4.1                                           #
-#  April 2012                                                      #
+#  LAPACK, Version 3.5.0                                           #
+#  November 2013                                                   #
 ####################################################################
 #
 SHELL = /bin/sh

lapack-netlib/README

@@ -20,6 +20,7 @@ VERSION 3.3.1 : April 2011
 VERSION 3.4.0 : November 2011
 VERSION 3.4.1 : April 2012
 VERSION 3.4.2 : September 2012
+VERSION 3.5.0 : November 2013
 
 LAPACK is a library of Fortran 90 with subroutines for solving
 the most commonly occurring problems in numerical linear algebra.
@@ -40,8 +41,8 @@ very much on the efficiency of the BLAS.
 
 =================
 LAPACK INSTALLATION:
- - LAPACK can be installed with make. Configuration haev to be set in the
- make.inc file. A make.inc.example for a Linux mahcine running GNU compilers
+ - LAPACK can be installed with make. Configuration have to be set in the
+ make.inc file. A make.inc.example for a Linux machine running GNU compilers
  is given in the main directory. Some specific make.inc are also available in
  the INSTALL directory
  - LAPACK includes also the CMAKE build. You will need to have CMAKE installed

lapack-netlib/SRC/CMakeLists.txt

@@ -113,7 +113,7 @@ set(SLASRC
    slaqtr.f slar1v.f slar2v.f ilaslr.f ilaslc.f 
    slarf.f  slarfb.f slarfg.f slarfgp.f slarft.f slarfx.f slargv.f 
    slarrv.f slartv.f 
-   slarz.f  slarzb.f slarzt.f slaswp.f slasy2.f slasyf.f 
+   slarz.f  slarzb.f slarzt.f slaswp.f slasy2.f slasyf.f slasyf_rook.f 
    slatbs.f slatdf.f slatps.f slatrd.f slatrs.f slatrz.f slatzm.f 
    slauu2.f slauum.f sopgtr.f sopmtr.f sorg2l.f sorg2r.f 
    sorgbr.f sorghr.f sorgl2.f sorglq.f sorgql.f sorgqr.f sorgr2.f 
@@ -134,6 +134,8 @@ set(SLASRC
    ssygst.f ssygv.f  ssygvd.f ssygvx.f ssyrfs.f ssysv.f  ssysvx.f 
    ssytd2.f ssytf2.f ssytrd.f ssytrf.f ssytri.f ssytri2.f ssytri2x.f
    ssyswapr.f ssytrs.f ssytrs2.f ssyconv.f 
+   ssytf2_rook.f ssytrf_rook.f ssytrs_rook.f
+   ssytri_rook.f ssycon_rook.f ssysv_rook.f
    stbcon.f 
    stbrfs.f stbtrs.f stgevc.f stgex2.f stgexc.f stgsen.f 
    stgsja.f stgsna.f stgsy2.f stgsyl.f stpcon.f stprfs.f stptri.f 
@@ -144,7 +146,8 @@ set(SLASRC
    stfttr.f stpttf.f stpttr.f strttf.f strttp.f 
    sgejsv.f  sgesvj.f  sgsvj0.f  sgsvj1.f 
    sgeequb.f ssyequb.f spoequb.f sgbequb.f
-   sbbcsd.f slapmr.f sorbdb.f sorcsd.f 
+   sbbcsd.f slapmr.f sorbdb.f sorbdb1.f sorbdb2.f sorbdb3.f sorbdb4.f
+   sorbdb5.f sorbdb6.f sorcsd.f sorcsd2by1.f
    sgeqrt.f sgeqrt2.f sgeqrt3.f sgemqrt.f
    stpqrt.f stpqrt2.f stpmqrt.f stprfb.f
   )
@@ -176,15 +179,17 @@ set(CLASRC
    checon.f cheev.f  cheevd.f cheevr.f cheevx.f chegs2.f chegst.f 
    chegv.f  chegvd.f chegvx.f cherfs.f chesv.f  chesvx.f chetd2.f 
    chetf2.f chetrd.f 
-   chetrf.f chetri.f chetri2.f  chetri2x.f cheswapr.f
-   chetrs.f chetrs2.f chgeqz.f chpcon.f chpev.f  chpevd.f 
+   chetrf.f chetri.f chetri2.f chetri2x.f cheswapr.f
+   chetrs.f chetrs2.f 
+   chetf2_rook.f chetrf_rook.f chetri_rook.f chetrs_rook.f checon_rook.f chesv_rook.f
+   chgeqz.f chpcon.f chpev.f  chpevd.f 
    chpevx.f chpgst.f chpgv.f  chpgvd.f chpgvx.f chprfs.f chpsv.f  
    chpsvx.f 
    chptrd.f chptrf.f chptri.f chptrs.f chsein.f chseqr.f clabrd.f 
    clacgv.f clacon.f clacn2.f clacp2.f clacpy.f clacrm.f clacrt.f cladiv.f 
    claed0.f claed7.f claed8.f 
    claein.f claesy.f claev2.f clags2.f clagtm.f 
-   clahef.f clahqr.f 
+   clahef.f clahef_rook.f clahqr.f 
    clahrd.f clahr2.f claic1.f clals0.f clalsa.f clalsd.f clangb.f clange.f clangt.f 
    clanhb.f clanhe.f 
    clanhp.f clanhs.f clanht.f clansb.f clansp.f clansy.f clantb.f 
@@ -195,7 +200,7 @@ set(CLASRC
    clarf.f  clarfb.f clarfg.f clarfgp.f clarft.f 
    clarfx.f clargv.f clarnv.f clarrv.f clartg.f clartv.f 
    clarz.f  clarzb.f clarzt.f clascl.f claset.f clasr.f  classq.f 
-   claswp.f clasyf.f clatbs.f clatdf.f clatps.f clatrd.f clatrs.f clatrz.f 
+   claswp.f clasyf.f clasyf_rook.f clatbs.f clatdf.f clatps.f clatrd.f clatrs.f clatrz.f 
    clatzm.f clauu2.f clauum.f cpbcon.f cpbequ.f cpbrfs.f cpbstf.f cpbsv.f  
    cpbsvx.f cpbtf2.f cpbtrf.f cpbtrs.f cpocon.f cpoequ.f cporfs.f 
    cposv.f  cposvx.f cpotf2.f cpotrf.f cpotri.f cpotrs.f cpstrf.f cpstf2.f 
@@ -207,6 +212,8 @@ set(CLASRC
    csyr.f   csyrfs.f csysv.f  csysvx.f csytf2.f csytrf.f csytri.f 
    csytri2.f csytri2x.f csyswapr.f
    csytrs.f csytrs2.f csyconv.f 
+   csytf2_rook.f csytrf_rook.f csytrs_rook.f
+   csytri_rook.f csycon_rook.f csysv_rook.f
    ctbcon.f ctbrfs.f ctbtrs.f ctgevc.f ctgex2.f 
    ctgexc.f ctgsen.f ctgsja.f ctgsna.f ctgsy2.f ctgsyl.f ctpcon.f 
    ctprfs.f ctptri.f 
@@ -219,7 +226,8 @@ set(CLASRC
    chfrk.f ctfttp.f clanhf.f cpftrf.f cpftri.f cpftrs.f ctfsm.f ctftri.f 
    ctfttr.f ctpttf.f ctpttr.f ctrttf.f ctrttp.f 
    cgeequb.f cgbequb.f csyequb.f cpoequb.f cheequb.f
-   cbbcsd.f clapmr.f cunbdb.f cuncsd.f  
+   cbbcsd.f clapmr.f cunbdb.f cunbdb1.f cunbdb2.f cunbdb3.f cunbdb4.f
+   cunbdb5.f cunbdb6.f cuncsd.f cuncsd2by1.f
    cgeqrt.f cgeqrt2.f cgeqrt3.f cgemqrt.f
    ctpqrt.f ctpqrt2.f ctpmqrt.f ctprfb.f)
 
@@ -261,7 +269,7 @@ set(DLASRC
    dlaqtr.f dlar1v.f dlar2v.f iladlr.f iladlc.f 
    dlarf.f  dlarfb.f dlarfg.f dlarfgp.f dlarft.f dlarfx.f dlargv.f 
    dlarrv.f dlartv.f 
-   dlarz.f  dlarzb.f dlarzt.f dlaswp.f dlasy2.f dlasyf.f 
+   dlarz.f  dlarzb.f dlarzt.f dlaswp.f dlasy2.f dlasyf.f dlasyf_rook.f 
    dlatbs.f dlatdf.f dlatps.f dlatrd.f dlatrs.f dlatrz.f dlatzm.f dlauu2.f 
    dlauum.f dopgtr.f dopmtr.f dorg2l.f dorg2r.f 
    dorgbr.f dorghr.f dorgl2.f dorglq.f dorgql.f dorgqr.f dorgr2.f 
@@ -283,6 +291,8 @@ set(DLASRC
    dsysv.f  dsysvx.f 
    dsytd2.f dsytf2.f dsytrd.f dsytrf.f dsytri.f dsytrs.f dsytrs2.f 
    dsytri2.f dsytri2x.f dsyswapr.f dsyconv.f
+   dsytf2_rook.f dsytrf_rook.f dsytrs_rook.f
+   dsytri_rook.f dsycon_rook.f dsysv_rook.f
    dtbcon.f 
    dtbrfs.f dtbtrs.f dtgevc.f dtgex2.f dtgexc.f dtgsen.f 
    dtgsja.f dtgsna.f dtgsy2.f dtgsyl.f dtpcon.f dtprfs.f dtptri.f 
@@ -294,7 +304,8 @@ set(DLASRC
    dtfttr.f dtpttf.f dtpttr.f dtrttf.f dtrttp.f 
    dgejsv.f  dgesvj.f  dgsvj0.f  dgsvj1.f 
    dgeequb.f dsyequb.f dpoequb.f dgbequb.f
-   dbbcsd.f dlapmr.f dorbdb.f dorcsd.f 
+   dbbcsd.f dlapmr.f dorbdb.f dorbdb1.f dorbdb2.f dorbdb3.f dorbdb4.f
+   dorbdb5.f dorbdb6.f dorcsd.f dorcsd2by1.f
    dgeqrt.f dgeqrt2.f dgeqrt3.f dgemqrt.f
    dtpqrt.f dtpqrt2.f dtpmqrt.f dtprfb.f )
 
@@ -324,14 +335,16 @@ set(ZLASRC
    zhegv.f  zhegvd.f zhegvx.f zherfs.f zhesv.f  zhesvx.f zhetd2.f 
    zhetf2.f zhetrd.f 
    zhetrf.f zhetri.f zhetri2.f zhetri2x.f zheswapr.f
-   zhetrs.f zhetrs2.f zhgeqz.f zhpcon.f zhpev.f  zhpevd.f 
+   zhetrs.f zhetrs2.f
+   zhetf2_rook.f zhetrf_rook.f zhetri_rook.f zhetrs_rook.f zhecon_rook.f zhesv_rook.f
+   zhgeqz.f zhpcon.f zhpev.f  zhpevd.f 
    zhpevx.f zhpgst.f zhpgv.f  zhpgvd.f zhpgvx.f zhprfs.f zhpsv.f  
    zhpsvx.f 
    zhptrd.f zhptrf.f zhptri.f zhptrs.f zhsein.f zhseqr.f zlabrd.f 
    zlacgv.f zlacon.f zlacn2.f zlacp2.f zlacpy.f zlacrm.f zlacrt.f zladiv.f 
    zlaed0.f zlaed7.f zlaed8.f 
    zlaein.f zlaesy.f zlaev2.f zlags2.f zlagtm.f 
-   zlahef.f zlahqr.f 
+   zlahef.f zlahef_rook.f zlahqr.f 
    zlahrd.f zlahr2.f zlaic1.f zlals0.f zlalsa.f zlalsd.f zlangb.f zlange.f 
    zlangt.f zlanhb.f 
    zlanhe.f 
@@ -344,7 +357,7 @@ set(ZLASRC
    zlarfg.f zlarfgp.f zlarft.f
    zlarfx.f zlargv.f zlarnv.f zlarrv.f zlartg.f zlartv.f 
    zlarz.f  zlarzb.f zlarzt.f zlascl.f zlaset.f zlasr.f  
-   zlassq.f zlaswp.f zlasyf.f 
+   zlassq.f zlaswp.f zlasyf.f zlasyf_rook.f 
    zlatbs.f zlatdf.f zlatps.f zlatrd.f zlatrs.f zlatrz.f zlatzm.f zlauu2.f 
    zlauum.f zpbcon.f zpbequ.f zpbrfs.f zpbstf.f zpbsv.f  
    zpbsvx.f zpbtf2.f zpbtrf.f zpbtrs.f zpocon.f zpoequ.f zporfs.f 
@@ -357,6 +370,8 @@ set(ZLASRC
    zsyr.f   zsyrfs.f zsysv.f  zsysvx.f zsytf2.f zsytrf.f zsytri.f 
    zsytri2.f zsytri2x.f zsyswapr.f
    zsytrs.f zsytrs2.f zsyconv.f
+   zsytf2_rook.f zsytrf_rook.f zsytrs_rook.f
+   zsytri_rook.f zsycon_rook.f zsysv_rook.f
    ztbcon.f ztbrfs.f ztbtrs.f ztgevc.f ztgex2.f 
    ztgexc.f ztgsen.f ztgsja.f ztgsna.f ztgsy2.f ztgsyl.f ztpcon.f 
    ztprfs.f ztptri.f 
@@ -371,7 +386,8 @@ set(ZLASRC
    zhfrk.f ztfttp.f zlanhf.f zpftrf.f zpftri.f zpftrs.f ztfsm.f ztftri.f 
    ztfttr.f ztpttf.f ztpttr.f ztrttf.f ztrttp.f 
    zgeequb.f zgbequb.f zsyequb.f zpoequb.f zheequb.f
-   zbbcsd.f zlapmr.f zunbdb.f zuncsd.f  
+   zbbcsd.f zlapmr.f zunbdb.f zunbdb1.f zunbdb2.f zunbdb3.f zunbdb4.f
+   zunbdb5.f zunbdb6.f zuncsd.f zuncsd2by1.f
    zgeqrt.f zgeqrt2.f zgeqrt3.f zgemqrt.f
    ztpqrt.f ztpqrt2.f ztpmqrt.f ztprfb.f)
 

lapack-netlib/SRC/Makefile

@@ -118,7 +118,7 @@ SLASRC = \
    slaqtr.o slar1v.o slar2v.o ilaslr.o ilaslc.o \
    slarf.o  slarfb.o slarfg.o slarfgp.o slarft.o slarfx.o slargv.o \
    slarrv.o slartv.o  \
-   slarz.o  slarzb.o slarzt.o slasy2.o slasyf.o \
+   slarz.o  slarzb.o slarzt.o slasy2.o slasyf.o slasyf_rook.o \
    slatbs.o slatdf.o slatps.o slatrd.o slatrs.o slatrz.o slatzm.o \
    sopgtr.o sopmtr.o sorg2l.o sorg2r.o \
    sorgbr.o sorghr.o sorgl2.o sorglq.o sorgql.o sorgqr.o sorgr2.o \
@@ -140,6 +140,8 @@ SLASRC = \
    ssygst.o ssygv.o  ssygvd.o ssygvx.o ssyrfs.o ssysv.o  ssysvx.o \
    ssytd2.o ssytf2.o ssytrd.o ssytrf.o ssytri.o ssytri2.o ssytri2x.o \
    ssyswapr.o ssytrs.o ssytrs2.o ssyconv.o \
+   ssytf2_rook.o ssytrf_rook.o ssytrs_rook.o \
+   ssytri_rook.o ssycon_rook.o ssysv_rook.o \
    stbcon.o \
    stbrfs.o stbtrs.o stgevc.o stgex2.o stgexc.o stgsen.o \
    stgsja.o stgsna.o stgsy2.o stgsyl.o stpcon.o stprfs.o stptri.o \
@@ -150,7 +152,8 @@ SLASRC = \
    stfttr.o stpttf.o stpttr.o strttf.o strttp.o \
    sgejsv.o  sgesvj.o  sgsvj0.o  sgsvj1.o \
    sgeequb.o ssyequb.o spoequb.o sgbequb.o \
-   sbbcsd.o slapmr.o sorbdb.o sorcsd.o \
+   sbbcsd.o slapmr.o sorbdb.o sorbdb1.o sorbdb2.o sorbdb3.o sorbdb4.o \
+   sorbdb5.o sorbdb6.o sorcsd.o sorcsd2by1.o \
    sgeqrt.o sgeqrt2.o sgeqrt3.o sgemqrt.o \
    stpqrt.o stpqrt2.o stpmqrt.o stprfb.o
 
@@ -184,14 +187,16 @@ CLASRC = \
    chegv.o  chegvd.o chegvx.o cherfs.o chesv.o  chesvx.o chetd2.o \
    chetf2.o chetrd.o \
    chetrf.o chetri.o chetri2.o chetri2x.o cheswapr.o \
-   chetrs.o chetrs2.o chgeqz.o chpcon.o chpev.o  chpevd.o \
+   chetrs.o chetrs2.o \
+   chetf2_rook.o chetrf_rook.o chetri_rook.o chetrs_rook.o checon_rook.o chesv_rook.o \
+   chgeqz.o chpcon.o chpev.o  chpevd.o \
    chpevx.o chpgst.o chpgv.o  chpgvd.o chpgvx.o chprfs.o chpsv.o  \
    chpsvx.o \
    chptrd.o chptrf.o chptri.o chptrs.o chsein.o chseqr.o clabrd.o \
    clacgv.o clacon.o clacn2.o clacp2.o clacpy.o clacrm.o clacrt.o cladiv.o \
    claed0.o claed7.o claed8.o \
    claein.o claesy.o claev2.o clags2.o clagtm.o \
-   clahef.o clahqr.o \
+   clahef.o clahef_rook.o clahqr.o \
    clahrd.o clahr2.o claic1.o clals0.o clalsa.o clalsd.o clangb.o clange.o clangt.o \
    clanhb.o clanhe.o \
    clanhp.o clanhs.o clanht.o clansb.o clansp.o clansy.o clantb.o \
@@ -202,7 +207,7 @@ CLASRC = \
    clarf.o  clarfb.o clarfg.o clarft.o clarfgp.o \
    clarfx.o clargv.o clarnv.o clarrv.o clartg.o clartv.o \
    clarz.o  clarzb.o clarzt.o clascl.o claset.o clasr.o  classq.o \
-   clasyf.o clatbs.o clatdf.o clatps.o clatrd.o clatrs.o clatrz.o \
+   clasyf.o clasyf_rook.o clatbs.o clatdf.o clatps.o clatrd.o clatrs.o clatrz.o \
    clatzm.o cpbcon.o cpbequ.o cpbrfs.o cpbstf.o cpbsv.o  \
    cpbsvx.o cpbtf2.o cpbtrf.o cpbtrs.o cpocon.o cpoequ.o cporfs.o \
    cposv.o  cposvx.o cpotri.o cpstrf.o cpstf2.o \
@@ -214,6 +219,8 @@ CLASRC = \
    csycon.o csymv.o \
    csyr.o csyrfs.o csysv.o  csysvx.o csytf2.o csytrf.o csytri.o csytri2.o csytri2x.o \
    csyswapr.o csytrs.o csytrs2.o csyconv.o \
+   csytf2_rook.o csytrf_rook.o csytrs_rook.o \
+   csytri_rook.o csycon_rook.o csysv_rook.o \
    ctbcon.o ctbrfs.o ctbtrs.o ctgevc.o ctgex2.o \
    ctgexc.o ctgsen.o ctgsja.o ctgsna.o ctgsy2.o ctgsyl.o ctpcon.o \
    ctprfs.o ctptri.o \
@@ -226,7 +233,8 @@ CLASRC = \
    chfrk.o ctfttp.o clanhf.o cpftrf.o cpftri.o cpftrs.o ctfsm.o ctftri.o \
    ctfttr.o ctpttf.o ctpttr.o ctrttf.o ctrttp.o \
    cgeequb.o cgbequb.o csyequb.o cpoequb.o cheequb.o \
-   cbbcsd.o clapmr.o cunbdb.o cuncsd.o \
+   cbbcsd.o clapmr.o cunbdb.o cunbdb1.o cunbdb2.o cunbdb3.o cunbdb4.o \
+   cunbdb5.o cunbdb6.o cuncsd.o cuncsd2by1.o \
    cgeqrt.o cgeqrt2.o cgeqrt3.o cgemqrt.o \
    ctpqrt.o ctpqrt2.o ctpmqrt.o ctprfb.o
 
@@ -270,7 +278,7 @@ DLASRC = \
    dlaqtr.o dlar1v.o dlar2v.o iladlr.o iladlc.o \
    dlarf.o  dlarfb.o dlarfg.o dlarfgp.o dlarft.o dlarfx.o \
    dlargv.o dlarrv.o dlartv.o  \
-   dlarz.o  dlarzb.o dlarzt.o dlasy2.o dlasyf.o \
+   dlarz.o  dlarzb.o dlarzt.o dlasy2.o dlasyf.o dlasyf_rook.o \
    dlatbs.o dlatdf.o dlatps.o dlatrd.o dlatrs.o dlatrz.o dlatzm.o \
    dopgtr.o dopmtr.o dorg2l.o dorg2r.o \
    dorgbr.o dorghr.o dorgl2.o dorglq.o dorgql.o dorgqr.o dorgr2.o \
@@ -293,6 +301,8 @@ DLASRC = \
    dsysv.o  dsysvx.o \
    dsytd2.o dsytf2.o dsytrd.o dsytrf.o dsytri.o dsytri2.o dsytri2x.o \
    dsyswapr.o dsytrs.o dsytrs2.o dsyconv.o \
+   dsytf2_rook.o dsytrf_rook.o dsytrs_rook.o \
+   dsytri_rook.o dsycon_rook.o dsysv_rook.o \
    dtbcon.o dtbrfs.o dtbtrs.o dtgevc.o dtgex2.o dtgexc.o dtgsen.o \
    dtgsja.o dtgsna.o dtgsy2.o dtgsyl.o dtpcon.o dtprfs.o dtptri.o \
    dtptrs.o \
@@ -303,7 +313,8 @@ DLASRC = \
    dtfttr.o dtpttf.o dtpttr.o dtrttf.o dtrttp.o \
    dgejsv.o  dgesvj.o  dgsvj0.o  dgsvj1.o \
    dgeequb.o dsyequb.o dpoequb.o dgbequb.o \
-   dbbcsd.o dlapmr.o dorbdb.o dorcsd.o \
+   dbbcsd.o dlapmr.o dorbdb.o dorbdb1.o dorbdb2.o dorbdb3.o dorbdb4.o \
+   dorbdb5.o dorbdb6.o dorcsd.o dorcsd2by1.o \
    dgeqrt.o dgeqrt2.o dgeqrt3.o dgemqrt.o \
    dtpqrt.o dtpqrt2.o dtpmqrt.o dtprfb.o
 
@@ -335,14 +346,16 @@ ZLASRC = \
    zhegv.o  zhegvd.o zhegvx.o zherfs.o zhesv.o  zhesvx.o zhetd2.o \
    zhetf2.o zhetrd.o \
    zhetrf.o zhetri.o zhetri2.o zhetri2x.o zheswapr.o \
-   zhetrs.o zhetrs2.o zhgeqz.o zhpcon.o zhpev.o  zhpevd.o \
+   zhetrs.o zhetrs2.o \
+   zhetf2_rook.o zhetrf_rook.o zhetri_rook.o zhetrs_rook.o zhecon_rook.o zhesv_rook.o \
+   zhgeqz.o zhpcon.o zhpev.o  zhpevd.o \
    zhpevx.o zhpgst.o zhpgv.o  zhpgvd.o zhpgvx.o zhprfs.o zhpsv.o  \
    zhpsvx.o \
    zhptrd.o zhptrf.o zhptri.o zhptrs.o zhsein.o zhseqr.o zlabrd.o \
    zlacgv.o zlacon.o zlacn2.o zlacp2.o zlacpy.o zlacrm.o zlacrt.o zladiv.o \
    zlaed0.o zlaed7.o zlaed8.o \
    zlaein.o zlaesy.o zlaev2.o zlags2.o zlagtm.o \
-   zlahef.o zlahqr.o \
+   zlahef.o zlahef_rook.o zlahqr.o \
    zlahrd.o zlahr2.o zlaic1.o zlals0.o zlalsa.o zlalsd.o zlangb.o zlange.o \
    zlangt.o zlanhb.o \
    zlanhe.o \
@@ -355,7 +368,7 @@ ZLASRC = \
    zlarfg.o zlarft.o zlarfgp.o \
    zlarfx.o zlargv.o zlarnv.o zlarrv.o zlartg.o zlartv.o \
    zlarz.o  zlarzb.o zlarzt.o zlascl.o zlaset.o zlasr.o  \
-   zlassq.o zlasyf.o \
+   zlassq.o zlasyf.o zlasyf_rook.o \
    zlatbs.o zlatdf.o zlatps.o zlatrd.o zlatrs.o zlatrz.o zlatzm.o zlauu2.o \
    zpbcon.o zpbequ.o zpbrfs.o zpbstf.o zpbsv.o  \
    zpbsvx.o zpbtf2.o zpbtrf.o zpbtrs.o zpocon.o zpoequ.o zporfs.o \
@@ -368,6 +381,8 @@ ZLASRC = \
    zsycon.o zsymv.o \
    zsyr.o zsyrfs.o zsysv.o  zsysvx.o zsytf2.o zsytrf.o zsytri.o zsytri2.o zsytri2x.o \
    zsyswapr.o zsytrs.o zsytrs2.o zsyconv.o \
+   zsytf2_rook.o zsytrf_rook.o zsytrs_rook.o \
+   zsytri_rook.o zsycon_rook.o zsysv_rook.o \
    ztbcon.o ztbrfs.o ztbtrs.o ztgevc.o ztgex2.o \
    ztgexc.o ztgsen.o ztgsja.o ztgsna.o ztgsy2.o ztgsyl.o ztpcon.o \
    ztprfs.o ztptri.o \
@@ -382,7 +397,8 @@ ZLASRC = \
    zhfrk.o ztfttp.o zlanhf.o zpftrf.o zpftri.o zpftrs.o ztfsm.o ztftri.o \
    ztfttr.o ztpttf.o ztpttr.o ztrttf.o ztrttp.o \
    zgeequb.o zgbequb.o zsyequb.o zpoequb.o zheequb.o \
-   zbbcsd.o zlapmr.o zunbdb.o zuncsd.o \
+   zbbcsd.o zlapmr.o zunbdb.o zunbdb1.o zunbdb2.o zunbdb3.o zunbdb4.o \
+   zunbdb5.o zunbdb6.o zuncsd.o zuncsd2by1.o \
    zgeqrt.o zgeqrt2.o zgeqrt3.o zgemqrt.o \
    ztpqrt.o ztpqrt2.o ztpmqrt.o ztprfb.o
 

lapack-netlib/SRC/cbbcsd.f

@@ -322,7 +322,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date November 2011
+*> \date November 2013
 *
 *> \ingroup complexOTHERcomputational
 *
@@ -332,10 +332,10 @@
      $                   V2T, LDV2T, B11D, B11E, B12D, B12E, B21D, B21E,
      $                   B22D, B22E, RWORK, LRWORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2011
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS
@@ -477,7 +477,10 @@
 *     Initial deflation
 *
       IMAX = Q
-      DO WHILE( ( IMAX .GT. 1 ) .AND. ( PHI(IMAX-1) .EQ. ZERO ) )
+      DO WHILE( IMAX .GT. 1 )
+         IF( PHI(IMAX-1) .NE. ZERO ) THEN
+            EXIT
+         END IF
          IMAX = IMAX - 1
       END DO
       IMIN = IMAX - 1

lapack-netlib/SRC/cgebal.f

@@ -122,7 +122,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date November 2011
+*> \date November 2013
 *
 *> \ingroup complexGEcomputational
 *
@@ -161,10 +161,10 @@
 *  =====================================================================
       SUBROUTINE CGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2011
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOB
@@ -195,8 +195,8 @@
 *     .. External Functions ..
       LOGICAL            SISNAN, LSAME
       INTEGER            ICAMAX
-      REAL               SLAMCH
-      EXTERNAL           SISNAN, LSAME, ICAMAX, SLAMCH
+      REAL               SLAMCH, SCNRM2
+      EXTERNAL           SISNAN, LSAME, ICAMAX, SLAMCH, SCNRM2
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           CSSCAL, CSWAP, XERBLA
@@ -325,15 +325,9 @@
       NOCONV = .FALSE.
 *
       DO 200 I = K, L
-         C = ZERO
-         R = ZERO
-*
-         DO 150 J = K, L
-            IF( J.EQ.I )
-     $         GO TO 150
-            C = C + CABS1( A( J, I ) )
-            R = R + CABS1( A( I, J ) )
-  150    CONTINUE
+*
+         C = SCNRM2( L-K+1, A( K, I ), 1 )
+         R = SCNRM2( L-K+1, A( I , K ), LDA )
          ICA = ICAMAX( L, A( 1, I ), 1 )
          CA = ABS( A( ICA, I ) )
          IRA = ICAMAX( N-K+1, A( I, K ), LDA )

lapack-netlib/SRC/cgemqrt.f

@@ -160,7 +160,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date November 2011
+*> \date November 2013
 *
 *> \ingroup complexGEcomputational
 *
@@ -168,10 +168,10 @@
       SUBROUTINE CGEMQRT( SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT, 
      $                   C, LDC, WORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2011
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER SIDE, TRANS
@@ -225,7 +225,7 @@
          INFO = -4
       ELSE IF( K.LT.0 .OR. K.GT.Q ) THEN
          INFO = -5
-      ELSE IF( NB.LT.1 .OR. NB.GT.K ) THEN
+      ELSE IF( NB.LT.1 .OR. (NB.GT.K .AND. K.GT.0)) THEN
          INFO = -6
       ELSE IF( LDV.LT.MAX( 1, Q ) ) THEN
          INFO = -8

lapack-netlib/SRC/cgeqrt.f

@@ -108,7 +108,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date November 2011
+*> \date November 2013
 *
 *> \ingroup complexGEcomputational
 *
@@ -141,10 +141,10 @@
 *  =====================================================================
       SUBROUTINE CGEQRT( M, N, NB, A, LDA, T, LDT, WORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2011
+*     November 2013
 *
 *     .. Scalar Arguments ..
       INTEGER INFO, LDA, LDT, M, N, NB
@@ -173,7 +173,7 @@
          INFO = -1
       ELSE IF( N.LT.0 ) THEN
          INFO = -2
-      ELSE IF( NB.LT.1 .OR. NB.GT.MIN(M,N) ) THEN
+      ELSE IF( NB.LT.1 .OR. ( NB.GT.MIN(M,N) .AND. MIN(M,N).GT.0 ) )THEN
          INFO = -3
       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
          INFO = -5

lapack-netlib/SRC/cgetc2.f

@@ -98,7 +98,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date September 2012
+*> \date November 2013
 *
 *> \ingroup complexGEauxiliary
 *
@@ -111,10 +111,10 @@
 *  =====================================================================
       SUBROUTINE CGETC2( N, A, LDA, IPIV, JPIV, INFO )
 *
-*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK auxiliary routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     September 2012
+*     November 2013
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, N
@@ -203,6 +203,12 @@
          INFO = N
          A( N, N ) = CMPLX( SMIN, ZERO )
       END IF
+*
+*     Set last pivots to N
+*
+      IPIV( N ) = N
+      JPIV( N ) = N
+*
       RETURN
 *
 *     End of CGETC2

lapack-netlib/SRC/checon_rook.f

@@ -0,0 +1,253 @@
+*> \brief \b CHECON_ROOK estimates the reciprocal of the condition number fort HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges)
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download CHECON_ROOK + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/checon_rook.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/checon_rook.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/checon_rook.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CHECON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
+*                               INFO )
+*
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, N
+*       REAL               ANORM, RCOND
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       COMPLEX            A( LDA, * ), WORK( * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> CHECON_ROOK estimates the reciprocal of the condition number of a complex
+*> Hermitian matrix A using the factorization A = U*D*U**H or
+*> A = L*D*L**H computed by CHETRF_ROOK.
+*>
+*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
+*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          Specifies whether the details of the factorization are stored
+*>          as an upper or lower triangular matrix.
+*>          = 'U':  Upper triangular, form is A = U*D*U**H;
+*>          = 'L':  Lower triangular, form is A = L*D*L**H.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*>          A is COMPLEX array, dimension (LDA,N)
+*>          The block diagonal matrix D and the multipliers used to
+*>          obtain the factor U or L as computed by CHETRF_ROOK.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          Details of the interchanges and the block structure of D
+*>          as determined by CHETRF_ROOK.
+*> \endverbatim
+*>
+*> \param[in] ANORM
+*> \verbatim
+*>          ANORM is REAL
+*>          The 1-norm of the original matrix A.
+*> \endverbatim
+*>
+*> \param[out] RCOND
+*> \verbatim
+*>          RCOND is REAL
+*>          The reciprocal of the condition number of the matrix A,
+*>          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
+*>          estimate of the 1-norm of inv(A) computed in this routine.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX array, dimension (2*N)
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0:  successful exit
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2013
+*
+*> \ingroup complexHEcomputational
+*
+*> \par Contributors:
+*  ==================
+*> \verbatim
+*>
+*>  November 2013,  Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*>
+*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*>                  School of Mathematics,
+*>                  University of Manchester
+*>
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE CHECON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
+     $                        INFO )
+*
+*  -- LAPACK computational routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2013
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, N
+      REAL               ANORM, RCOND
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      COMPLEX            A( LDA, * ), WORK( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      REAL               ONE, ZERO
+      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            UPPER
+      INTEGER            I, KASE
+      REAL               AINVNM
+*     ..
+*     .. Local Arrays ..
+      INTEGER            ISAVE( 3 )
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      EXTERNAL           LSAME
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           CHETRS_ROOK, CLACN2, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      UPPER = LSAME( UPLO, 'U' )
+      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -4
+      ELSE IF( ANORM.LT.ZERO ) THEN
+         INFO = -6
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'CHECON_ROOK', -INFO )
+         RETURN
+      END IF
+*
+*     Quick return if possible
+*
+      RCOND = ZERO
+      IF( N.EQ.0 ) THEN
+         RCOND = ONE
+         RETURN
+      ELSE IF( ANORM.LE.ZERO ) THEN
+         RETURN
+      END IF
+*
+*     Check that the diagonal matrix D is nonsingular.
+*
+      IF( UPPER ) THEN
+*
+*        Upper triangular storage: examine D from bottom to top
+*
+         DO 10 I = N, 1, -1
+            IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
+     $         RETURN
+   10    CONTINUE
+      ELSE
+*
+*        Lower triangular storage: examine D from top to bottom.
+*
+         DO 20 I = 1, N
+            IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
+     $         RETURN
+   20    CONTINUE
+      END IF
+*
+*     Estimate the 1-norm of the inverse.
+*
+      KASE = 0
+   30 CONTINUE
+      CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
+      IF( KASE.NE.0 ) THEN
+*
+*        Multiply by inv(L*D*L**H) or inv(U*D*U**H).
+*
+         CALL CHETRS_ROOK( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
+         GO TO 30
+      END IF
+*
+*     Compute the estimate of the reciprocal condition number.
+*
+      IF( AINVNM.NE.ZERO )
+     $   RCOND = ( ONE / AINVNM ) / ANORM
+*
+      RETURN
+*
+*     End of CHECON_ROOK
+*
+      END

lapack-netlib/SRC/chesv_rook.f

@@ -0,0 +1,295 @@
+*> \brief \b CHESV_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using the bounded Bunch-Kaufman ("rook") diagonal pivoting method
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download CHESV_ROOK + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chesv_rook.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chesv_rook.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chesv_rook.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CHESV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+*                              LWORK, INFO )
+*
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       COMPLEX            A( LDA, * ), B( LDB, * ), WORK( * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> CHESV_ROOK computes the solution to a complex system of linear equations
+*>    A * X = B,
+*> where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
+*> matrices.
+*>
+*> The bounded Bunch-Kaufman ("rook") diagonal pivoting method is used
+*> to factor A as
+*>    A = U * D * U**T,  if UPLO = 'U', or
+*>    A = L * D * L**T,  if UPLO = 'L',
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, and D is Hermitian and block diagonal with
+*> 1-by-1 and 2-by-2 diagonal blocks.
+*>
+*> CHETRF_ROOK is called to compute the factorization of a complex
+*> Hermition matrix A using the bounded Bunch-Kaufman ("rook") diagonal
+*> pivoting method.
+*>
+*> The factored form of A is then used to solve the system
+*> of equations A * X = B by calling CHETRS_ROOK (uses BLAS 2).
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          = 'U':  Upper triangle of A is stored;
+*>          = 'L':  Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The number of linear equations, i.e., the order of the
+*>          matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*>          NRHS is INTEGER
+*>          The number of right hand sides, i.e., the number of columns
+*>          of the matrix B.  NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is COMPLEX array, dimension (LDA,N)
+*>          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
+*>          N-by-N upper triangular part of A contains the upper
+*>          triangular part of the matrix A, and the strictly lower
+*>          triangular part of A is not referenced.  If UPLO = 'L', the
+*>          leading N-by-N lower triangular part of A contains the lower
+*>          triangular part of the matrix A, and the strictly upper
+*>          triangular part of A is not referenced.
+*>
+*>          On exit, if INFO = 0, the block diagonal matrix D and the
+*>          multipliers used to obtain the factor U or L from the
+*>          factorization A = U*D*U**H or A = L*D*L**H as computed by
+*>          CHETRF_ROOK.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          Details of the interchanges and the block structure of D.
+*>
+*>          If UPLO = 'U':
+*>             Only the last KB elements of IPIV are set.
+*>
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
+*>             columns k and -IPIV(k) were interchanged and rows and
+*>             columns k-1 and -IPIV(k-1) were inerchaged,
+*>             D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>             Only the first KB elements of IPIV are set.
+*>
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k)
+*>             were interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
+*>             columns k and -IPIV(k) were interchanged and rows and
+*>             columns k+1 and -IPIV(k+1) were inerchaged,
+*>             D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*>          B is COMPLEX array, dimension (LDB,NRHS)
+*>          On entry, the N-by-NRHS right hand side matrix B.
+*>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*>          LDB is INTEGER
+*>          The leading dimension of the array B.  LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
+*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>          The length of WORK.  LWORK >= 1, and for best performance
+*>          LWORK >= max(1,N*NB), where NB is the optimal blocksize for
+*>          CHETRF_ROOK.
+*>          for LWORK < N, TRS will be done with Level BLAS 2
+*>          for LWORK >= N, TRS will be done with Level BLAS 3
+*>
+*>          If LWORK = -1, then a workspace query is assumed; the routine
+*>          only calculates the optimal size of the WORK array, returns
+*>          this value as the first entry of the WORK array, and no error
+*>          message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0: successful exit
+*>          < 0: if INFO = -i, the i-th argument had an illegal value
+*>          > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
+*>               has been completed, but the block diagonal matrix D is
+*>               exactly singular, so the solution could not be computed.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2013
+*
+*> \ingroup complexHEsolve
+*>
+*> \verbatim
+*>
+*>  November 2013,  Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*>
+*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*>                  School of Mathematics,
+*>                  University of Manchester
+*>
+*> \endverbatim
+*
+*
+*  =====================================================================
+      SUBROUTINE CHESV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+     $                       LWORK, INFO )
+*
+*  -- LAPACK driver routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2013
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      COMPLEX            A( LDA, * ), B( LDB, * ), WORK( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Local Scalars ..
+      LOGICAL            LQUERY
+      INTEGER            LWKOPT, NB
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      INTEGER            ILAENV
+      EXTERNAL           LSAME, ILAENV
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           XERBLA, CHETRF_ROOK, CHETRS_ROOK
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      LQUERY = ( LWORK.EQ.-1 )
+      IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( NRHS.LT.0 ) THEN
+         INFO = -3
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -5
+      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+         INFO = -8
+      ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
+         INFO = -10
+      END IF
+*
+      IF( INFO.EQ.0 ) THEN
+         IF( N.EQ.0 ) THEN
+            LWKOPT = 1
+         ELSE
+            NB = ILAENV( 1, 'CHETRF_ROOK', UPLO, N, -1, -1, -1 )
+            LWKOPT = N*NB
+         END IF
+         WORK( 1 ) = LWKOPT
+      END IF
+*
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'CHESV_ROOK ', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+*
+*     Compute the factorization A = U*D*U**H or A = L*D*L**H.
+*
+      CALL CHETRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+      IF( INFO.EQ.0 ) THEN
+*
+*        Solve the system A*X = B, overwriting B with X.
+*
+*        Solve with TRS ( Use Level BLAS 2)
+*
+         CALL CHETRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
+*
+      END IF
+*
+      WORK( 1 ) = LWKOPT
+*
+      RETURN
+*
+*     End of CHESV_ROOK
+*
+      END

lapack-netlib/SRC/chetf2.f

@@ -1,4 +1,4 @@
-*> \brief \b CHETF2 computes the factorization of a complex Hermitian matrix, using the diagonal pivoting method (unblocked algorithm).
+*> \brief \b CHETF2 computes the factorization of a complex Hermitian matrix, using the diagonal pivoting method (unblocked algorithm calling Level 2 BLAS).
 *
 *  =========== DOCUMENTATION ===========
 *
@@ -90,13 +90,22 @@
 *> \verbatim
 *>          IPIV is INTEGER array, dimension (N)
 *>          Details of the interchanges and the block structure of D.
-*>          If IPIV(k) > 0, then rows and columns k and IPIV(k) were
-*>          interchanged and D(k,k) is a 1-by-1 diagonal block.
-*>          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
-*>          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
-*>          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
-*>          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
-*>          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'U':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k-1) < 0, then rows and columns
+*>             k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
+*>             is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k+1) < 0, then rows and columns
+*>             k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1)
+*>             is a 2-by-2 diagonal block.
 *> \endverbatim
 *>
 *> \param[out] INFO
@@ -118,7 +127,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date September 2012
+*> \date November 2013
 *
 *> \ingroup complexHEcomputational
 *
@@ -177,10 +186,10 @@
 *  =====================================================================
       SUBROUTINE CHETF2( UPLO, N, A, LDA, IPIV, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.2) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     September 2012
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          UPLO
@@ -268,7 +277,8 @@
          ABSAKK = ABS( REAL( A( K, K ) ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.GT.1 ) THEN
             IMAX = ICAMAX( K-1, A( 1, K ), 1 )
@@ -279,7 +289,8 @@
 *
          IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. SISNAN(ABSAKK) ) THEN
 *
-*           Column K is zero or contains a NaN: set INFO and continue
+*           Column K is or underflow, or contains a NaN:
+*           set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
@@ -450,7 +461,8 @@
          ABSAKK = ABS( REAL( A( K, K ) ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.LT.N ) THEN
             IMAX = K + ICAMAX( N-K, A( K+1, K ), 1 )
@@ -461,7 +473,8 @@
 *
          IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. SISNAN(ABSAKK) ) THEN
 *
-*           Column K is zero or contains a NaN: set INFO and continue
+*           Column K is zero or underflow, contains a NaN:
+*           set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K

lapack-netlib/SRC/chetf2_rook.f

@@ -0,0 +1,910 @@
+*> \brief \b CHETF2_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (unblocked algorithm).
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download CHETF2_ROOK + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chetf2_rook.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chetf2_rook.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chetf2_rook.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CHETF2_ROOK( UPLO, N, A, LDA, IPIV, INFO )
+*
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, N
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       COMPLEX            A( LDA, * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> CHETF2_ROOK computes the factorization of a complex Hermitian matrix A
+*> using the bounded Bunch-Kaufman ("rook") diagonal pivoting method:
+*>
+*>    A = U*D*U**H  or  A = L*D*L**H
+*>
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, U**H is the conjugate transpose of U, and D is
+*> Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
+*>
+*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          Specifies whether the upper or lower triangular part of the
+*>          Hermitian matrix A is stored:
+*>          = 'U':  Upper triangular
+*>          = 'L':  Lower triangular
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is COMPLEX array, dimension (LDA,N)
+*>          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
+*>          n-by-n upper triangular part of A contains the upper
+*>          triangular part of the matrix A, and the strictly lower
+*>          triangular part of A is not referenced.  If UPLO = 'L', the
+*>          leading n-by-n lower triangular part of A contains the lower
+*>          triangular part of the matrix A, and the strictly upper
+*>          triangular part of A is not referenced.
+*>
+*>          On exit, the block diagonal matrix D and the multipliers used
+*>          to obtain the factor U or L (see below for further details).
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          Details of the interchanges and the block structure of D.
+*>
+*>          If UPLO = 'U':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
+*>             columns k and -IPIV(k) were interchanged and rows and
+*>             columns k-1 and -IPIV(k-1) were inerchaged,
+*>             D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k)
+*>             were interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
+*>             columns k and -IPIV(k) were interchanged and rows and
+*>             columns k+1 and -IPIV(k+1) were inerchaged,
+*>             D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0: successful exit
+*>          < 0: if INFO = -k, the k-th argument had an illegal value
+*>          > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
+*>               has been completed, but the block diagonal matrix D is
+*>               exactly singular, and division by zero will occur if it
+*>               is used to solve a system of equations.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2013
+*
+*> \ingroup complexHEcomputational
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  If UPLO = 'U', then A = U*D*U**H, where
+*>     U = P(n)*U(n)* ... *P(k)U(k)* ...,
+*>  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
+*>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
+*>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
+*>  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
+*>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
+*>
+*>             (   I    v    0   )   k-s
+*>     U(k) =  (   0    I    0   )   s
+*>             (   0    0    I   )   n-k
+*>                k-s   s   n-k
+*>
+*>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
+*>  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
+*>  and A(k,k), and v overwrites A(1:k-2,k-1:k).
+*>
+*>  If UPLO = 'L', then A = L*D*L**H, where
+*>     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
+*>  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
+*>  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
+*>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
+*>  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
+*>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
+*>
+*>             (   I    0     0   )  k-1
+*>     L(k) =  (   0    I     0   )  s
+*>             (   0    v     I   )  n-k-s+1
+*>                k-1   s  n-k-s+1
+*>
+*>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
+*>  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
+*>  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
+*> \endverbatim
+*
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>  November 2013,  Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*>
+*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*>                  School of Mathematics,
+*>                  University of Manchester
+*>
+*>  01-01-96 - Based on modifications by
+*>    J. Lewis, Boeing Computer Services Company
+*>    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE CHETF2_ROOK( UPLO, N, A, LDA, IPIV, INFO )
+*
+*  -- LAPACK computational routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2013
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, N
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      COMPLEX            A( LDA, * )
+*     ..
+*
+*  ======================================================================
+*
+*     .. Parameters ..
+      REAL               ZERO, ONE
+      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
+      REAL               EIGHT, SEVTEN
+      PARAMETER          ( EIGHT = 8.0E+0, SEVTEN = 17.0E+0 )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            DONE, UPPER
+      INTEGER            I, II, IMAX, ITEMP, J, JMAX, K, KK, KP, KSTEP,
+     $                   P
+      REAL               ABSAKK, ALPHA, COLMAX, D, D11, D22, R1, STEMP,
+     $                   ROWMAX, TT, SFMIN
+      COMPLEX            D12, D21, T, WK, WKM1, WKP1, Z
+*     ..
+*     .. External Functions ..
+*
+      LOGICAL            LSAME
+      INTEGER            ICAMAX
+      REAL               SLAMCH, SLAPY2
+      EXTERNAL           LSAME, ICAMAX, SLAMCH, SLAPY2
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           XERBLA, CSSCAL, CHER, CSWAP
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, AIMAG, CMPLX, CONJG, MAX, REAL, SQRT
+*     ..
+*     .. Statement Functions ..
+      REAL   CABS1
+*     ..
+*     .. Statement Function definitions ..
+      CABS1( Z ) = ABS( REAL( Z ) ) + ABS( AIMAG( Z ) )
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      UPPER = LSAME( UPLO, 'U' )
+      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -4
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'CHETF2_ROOK', -INFO )
+         RETURN
+      END IF
+*
+*     Initialize ALPHA for use in choosing pivot block size.
+*
+      ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT
+*
+*     Compute machine safe minimum
+*
+      SFMIN = SLAMCH( 'S' )
+*
+      IF( UPPER ) THEN
+*
+*        Factorize A as U*D*U**H using the upper triangle of A
+*
+*        K is the main loop index, decreasing from N to 1 in steps of
+*        1 or 2
+*
+         K = N
+   10    CONTINUE
+*
+*        If K < 1, exit from loop
+*
+         IF( K.LT.1 )
+     $      GO TO 70
+         KSTEP = 1
+         P = K
+*
+*        Determine rows and columns to be interchanged and whether
+*        a 1-by-1 or 2-by-2 pivot block will be used
+*
+         ABSAKK = ABS( REAL( A( K, K ) ) )
+*
+*        IMAX is the row-index of the largest off-diagonal element in
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
+*
+         IF( K.GT.1 ) THEN
+            IMAX = ICAMAX( K-1, A( 1, K ), 1 )
+            COLMAX = CABS1( A( IMAX, K ) )
+         ELSE
+            COLMAX = ZERO
+         END IF
+*
+         IF( ( MAX( ABSAKK, COLMAX ).EQ.ZERO ) ) THEN
+*
+*           Column K is zero or underflow: set INFO and continue
+*
+            IF( INFO.EQ.0 )
+     $         INFO = K
+            KP = K
+            A( K, K ) = REAL( A( K, K ) )
+         ELSE
+*
+*           ============================================================
+*
+*           BEGIN pivot search
+*
+*           Case(1)
+*           Equivalent to testing for ABSAKK.GE.ALPHA*COLMAX
+*           (used to handle NaN and Inf)
+*
+            IF( .NOT.( ABSAKK.LT.ALPHA*COLMAX ) ) THEN
+*
+*              no interchange, use 1-by-1 pivot block
+*
+               KP = K
+*
+            ELSE
+*
+               DONE = .FALSE.
+*
+*              Loop until pivot found
+*
+   12          CONTINUE
+*
+*                 BEGIN pivot search loop body
+*
+*
+*                 JMAX is the column-index of the largest off-diagonal
+*                 element in row IMAX, and ROWMAX is its absolute value.
+*                 Determine both ROWMAX and JMAX.
+*
+                  IF( IMAX.NE.K ) THEN
+                     JMAX = IMAX + ICAMAX( K-IMAX, A( IMAX, IMAX+1 ),
+     $                                     LDA )
+                     ROWMAX = CABS1( A( IMAX, JMAX ) )
+                  ELSE
+                     ROWMAX = ZERO
+                  END IF
+*
+                  IF( IMAX.GT.1 ) THEN
+                     ITEMP = ICAMAX( IMAX-1, A( 1, IMAX ), 1 )
+                     STEMP = CABS1( A( ITEMP, IMAX ) )
+                     IF( STEMP.GT.ROWMAX ) THEN
+                        ROWMAX = STEMP
+                        JMAX = ITEMP
+                     END IF
+                  END IF
+*
+*                 Case(2)
+*                 Equivalent to testing for
+*                 ABS( REAL( W( IMAX,KW-1 ) ) ).GE.ALPHA*ROWMAX
+*                 (used to handle NaN and Inf)
+*
+                  IF( .NOT.( ABS( REAL( A( IMAX, IMAX ) ) )
+     $                       .LT.ALPHA*ROWMAX ) ) THEN
+*
+*                    interchange rows and columns K and IMAX,
+*                    use 1-by-1 pivot block
+*
+                     KP = IMAX
+                     DONE = .TRUE.
+*
+*                 Case(3)
+*                 Equivalent to testing for ROWMAX.EQ.COLMAX,
+*                 (used to handle NaN and Inf)
+*
+                  ELSE IF( ( P.EQ.JMAX ) .OR. ( ROWMAX.LE.COLMAX ) )
+     $            THEN
+*
+*                    interchange rows and columns K-1 and IMAX,
+*                    use 2-by-2 pivot block
+*
+                     KP = IMAX
+                     KSTEP = 2
+                     DONE = .TRUE.
+*
+*                 Case(4)
+                  ELSE
+*
+*                    Pivot not found: set params and repeat
+*
+                     P = IMAX
+                     COLMAX = ROWMAX
+                     IMAX = JMAX
+                  END IF
+*
+*                 END pivot search loop body
+*
+               IF( .NOT.DONE ) GOTO 12
+*
+            END IF
+*
+*           END pivot search
+*
+*           ============================================================
+*
+*           KK is the column of A where pivoting step stopped
+*
+            KK = K - KSTEP + 1
+*
+*           For only a 2x2 pivot, interchange rows and columns K and P
+*           in the leading submatrix A(1:k,1:k)
+*
+            IF( ( KSTEP.EQ.2 ) .AND. ( P.NE.K ) ) THEN
+*              (1) Swap columnar parts
+               IF( P.GT.1 )
+     $            CALL CSWAP( P-1, A( 1, K ), 1, A( 1, P ), 1 )
+*              (2) Swap and conjugate middle parts
+               DO 14 J = P + 1, K - 1
+                  T = CONJG( A( J, K ) )
+                  A( J, K ) = CONJG( A( P, J ) )
+                  A( P, J ) = T
+   14          CONTINUE
+*              (3) Swap and conjugate corner elements at row-col interserction
+               A( P, K ) = CONJG( A( P, K ) )
+*              (4) Swap diagonal elements at row-col intersection
+               R1 = REAL( A( K, K ) )
+               A( K, K ) = REAL( A( P, P ) )
+               A( P, P ) = R1
+            END IF
+*
+*           For both 1x1 and 2x2 pivots, interchange rows and
+*           columns KK and KP in the leading submatrix A(1:k,1:k)
+*
+            IF( KP.NE.KK ) THEN
+*              (1) Swap columnar parts
+               IF( KP.GT.1 )
+     $            CALL CSWAP( KP-1, A( 1, KK ), 1, A( 1, KP ), 1 )
+*              (2) Swap and conjugate middle parts
+               DO 15 J = KP + 1, KK - 1
+                  T = CONJG( A( J, KK ) )
+                  A( J, KK ) = CONJG( A( KP, J ) )
+                  A( KP, J ) = T
+   15          CONTINUE
+*              (3) Swap and conjugate corner elements at row-col interserction
+               A( KP, KK ) = CONJG( A( KP, KK ) )
+*              (4) Swap diagonal elements at row-col intersection
+               R1 = REAL( A( KK, KK ) )
+               A( KK, KK ) = REAL( A( KP, KP ) )
+               A( KP, KP ) = R1
+*
+               IF( KSTEP.EQ.2 ) THEN
+*                 (*) Make sure that diagonal element of pivot is real
+                  A( K, K ) = REAL( A( K, K ) )
+*                 (5) Swap row elements
+                  T = A( K-1, K )
+                  A( K-1, K ) = A( KP, K )
+                  A( KP, K ) = T
+               END IF
+            ELSE
+*              (*) Make sure that diagonal element of pivot is real
+               A( K, K ) = REAL( A( K, K ) )
+               IF( KSTEP.EQ.2 )
+     $            A( K-1, K-1 ) = REAL( A( K-1, K-1 ) )
+            END IF
+*
+*           Update the leading submatrix
+*
+            IF( KSTEP.EQ.1 ) THEN
+*
+*              1-by-1 pivot block D(k): column k now holds
+*
+*              W(k) = U(k)*D(k)
+*
+*              where U(k) is the k-th column of U
+*
+               IF( K.GT.1 ) THEN
+*
+*                 Perform a rank-1 update of A(1:k-1,1:k-1) and
+*                 store U(k) in column k
+*
+                  IF( ABS( REAL( A( K, K ) ) ).GE.SFMIN ) THEN
+*
+*                    Perform a rank-1 update of A(1:k-1,1:k-1) as
+*                    A := A - U(k)*D(k)*U(k)**T
+*                       = A - W(k)*1/D(k)*W(k)**T
+*
+                     D11 = ONE / REAL( A( K, K ) )
+                     CALL CHER( UPLO, K-1, -D11, A( 1, K ), 1, A, LDA )
+*
+*                    Store U(k) in column k
+*
+                     CALL CSSCAL( K-1, D11, A( 1, K ), 1 )
+                  ELSE
+*
+*                    Store L(k) in column K
+*
+                     D11 = REAL( A( K, K ) )
+                     DO 16 II = 1, K - 1
+                        A( II, K ) = A( II, K ) / D11
+   16                CONTINUE
+*
+*                    Perform a rank-1 update of A(k+1:n,k+1:n) as
+*                    A := A - U(k)*D(k)*U(k)**T
+*                       = A - W(k)*(1/D(k))*W(k)**T
+*                       = A - (W(k)/D(k))*(D(k))*(W(k)/D(K))**T
+*
+                     CALL CHER( UPLO, K-1, -D11, A( 1, K ), 1, A, LDA )
+                  END IF
+               END IF
+*
+            ELSE
+*
+*              2-by-2 pivot block D(k): columns k and k-1 now hold
+*
+*              ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
+*
+*              where U(k) and U(k-1) are the k-th and (k-1)-th columns
+*              of U
+*
+*              Perform a rank-2 update of A(1:k-2,1:k-2) as
+*
+*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T
+*                 = A - ( ( A(k-1)A(k) )*inv(D(k)) ) * ( A(k-1)A(k) )**T
+*
+*              and store L(k) and L(k+1) in columns k and k+1
+*
+               IF( K.GT.2 ) THEN
+*                 D = |A12|
+                  D = SLAPY2( REAL( A( K-1, K ) ),
+     $                AIMAG( A( K-1, K ) ) )
+                  D11 = A( K, K ) / D
+                  D22 = A( K-1, K-1 ) / D
+                  D12 = A( K-1, K ) / D
+                  TT = ONE / ( D11*D22-ONE )
+*
+                  DO 30 J = K - 2, 1, -1
+*
+*                    Compute  D21 * ( W(k)W(k+1) ) * inv(D(k)) for row J
+*
+                     WKM1 = TT*( D11*A( J, K-1 )-CONJG( D12 )*
+     $                      A( J, K ) )
+                     WK = TT*( D22*A( J, K )-D12*A( J, K-1 ) )
+*
+*                    Perform a rank-2 update of A(1:k-2,1:k-2)
+*
+                     DO 20 I = J, 1, -1
+                        A( I, J ) = A( I, J ) -
+     $                              ( A( I, K ) / D )*CONJG( WK ) -
+     $                              ( A( I, K-1 ) / D )*CONJG( WKM1 )
+   20                CONTINUE
+*
+*                    Store U(k) and U(k-1) in cols k and k-1 for row J
+*
+                     A( J, K ) = WK / D
+                     A( J, K-1 ) = WKM1 / D
+*                    (*) Make sure that diagonal element of pivot is real
+                     A( J, J ) = CMPLX( REAL( A( J, J ) ), ZERO )
+*
+   30             CONTINUE
+*
+               END IF
+*
+            END IF
+*
+         END IF
+*
+*        Store details of the interchanges in IPIV
+*
+         IF( KSTEP.EQ.1 ) THEN
+            IPIV( K ) = KP
+         ELSE
+            IPIV( K ) = -P
+            IPIV( K-1 ) = -KP
+         END IF
+*
+*        Decrease K and return to the start of the main loop
+*
+         K = K - KSTEP
+         GO TO 10
+*
+      ELSE
+*
+*        Factorize A as L*D*L**H using the lower triangle of A
+*
+*        K is the main loop index, increasing from 1 to N in steps of
+*        1 or 2
+*
+         K = 1
+   40    CONTINUE
+*
+*        If K > N, exit from loop
+*
+         IF( K.GT.N )
+     $      GO TO 70
+         KSTEP = 1
+         P = K
+*
+*        Determine rows and columns to be interchanged and whether
+*        a 1-by-1 or 2-by-2 pivot block will be used
+*
+         ABSAKK = ABS( REAL( A( K, K ) ) )
+*
+*        IMAX is the row-index of the largest off-diagonal element in
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
+*
+         IF( K.LT.N ) THEN
+            IMAX = K + ICAMAX( N-K, A( K+1, K ), 1 )
+            COLMAX = CABS1( A( IMAX, K ) )
+         ELSE
+            COLMAX = ZERO
+         END IF
+*
+         IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
+*
+*           Column K is zero or underflow: set INFO and continue
+*
+            IF( INFO.EQ.0 )
+     $         INFO = K
+            KP = K
+            A( K, K ) = REAL( A( K, K ) )
+         ELSE
+*
+*           ============================================================
+*
+*           BEGIN pivot search
+*
+*           Case(1)
+*           Equivalent to testing for ABSAKK.GE.ALPHA*COLMAX
+*           (used to handle NaN and Inf)
+*
+            IF( .NOT.( ABSAKK.LT.ALPHA*COLMAX ) ) THEN
+*
+*              no interchange, use 1-by-1 pivot block
+*
+               KP = K
+*
+            ELSE
+*
+               DONE = .FALSE.
+*
+*              Loop until pivot found
+*
+   42          CONTINUE
+*
+*                 BEGIN pivot search loop body
+*
+*
+*                 JMAX is the column-index of the largest off-diagonal
+*                 element in row IMAX, and ROWMAX is its absolute value.
+*                 Determine both ROWMAX and JMAX.
+*
+                  IF( IMAX.NE.K ) THEN
+                     JMAX = K - 1 + ICAMAX( IMAX-K, A( IMAX, K ), LDA )
+                     ROWMAX = CABS1( A( IMAX, JMAX ) )
+                  ELSE
+                     ROWMAX = ZERO
+                  END IF
+*
+                  IF( IMAX.LT.N ) THEN
+                     ITEMP = IMAX + ICAMAX( N-IMAX, A( IMAX+1, IMAX ),
+     $                                     1 )
+                     STEMP = CABS1( A( ITEMP, IMAX ) )
+                     IF( STEMP.GT.ROWMAX ) THEN
+                        ROWMAX = STEMP
+                        JMAX = ITEMP
+                     END IF
+                  END IF
+*
+*                 Case(2)
+*                 Equivalent to testing for
+*                 ABS( REAL( W( IMAX,KW-1 ) ) ).GE.ALPHA*ROWMAX
+*                 (used to handle NaN and Inf)
+*
+                  IF( .NOT.( ABS( REAL( A( IMAX, IMAX ) ) )
+     $                       .LT.ALPHA*ROWMAX ) ) THEN
+*
+*                    interchange rows and columns K and IMAX,
+*                    use 1-by-1 pivot block
+*
+                     KP = IMAX
+                     DONE = .TRUE.
+*
+*                 Case(3)
+*                 Equivalent to testing for ROWMAX.EQ.COLMAX,
+*                 (used to handle NaN and Inf)
+*
+                  ELSE IF( ( P.EQ.JMAX ) .OR. ( ROWMAX.LE.COLMAX ) )
+     $            THEN
+*
+*                    interchange rows and columns K+1 and IMAX,
+*                    use 2-by-2 pivot block
+*
+                     KP = IMAX
+                     KSTEP = 2
+                     DONE = .TRUE.
+*
+*                 Case(4)
+                  ELSE
+*
+*                    Pivot not found: set params and repeat
+*
+                     P = IMAX
+                     COLMAX = ROWMAX
+                     IMAX = JMAX
+                  END IF
+*
+*
+*                 END pivot search loop body
+*
+               IF( .NOT.DONE ) GOTO 42
+*
+            END IF
+*
+*           END pivot search
+*
+*           ============================================================
+*
+*           KK is the column of A where pivoting step stopped
+*
+            KK = K + KSTEP - 1
+*
+*           For only a 2x2 pivot, interchange rows and columns K and P
+*           in the trailing submatrix A(k:n,k:n)
+*
+            IF( ( KSTEP.EQ.2 ) .AND. ( P.NE.K ) ) THEN
+*              (1) Swap columnar parts
+               IF( P.LT.N )
+     $            CALL CSWAP( N-P, A( P+1, K ), 1, A( P+1, P ), 1 )
+*              (2) Swap and conjugate middle parts
+               DO 44 J = K + 1, P - 1
+                  T = CONJG( A( J, K ) )
+                  A( J, K ) = CONJG( A( P, J ) )
+                  A( P, J ) = T
+   44          CONTINUE
+*              (3) Swap and conjugate corner elements at row-col interserction
+               A( P, K ) = CONJG( A( P, K ) )
+*              (4) Swap diagonal elements at row-col intersection
+               R1 = REAL( A( K, K ) )
+               A( K, K ) = REAL( A( P, P ) )
+               A( P, P ) = R1
+            END IF
+*
+*           For both 1x1 and 2x2 pivots, interchange rows and
+*           columns KK and KP in the trailing submatrix A(k:n,k:n)
+*
+            IF( KP.NE.KK ) THEN
+*              (1) Swap columnar parts
+               IF( KP.LT.N )
+     $            CALL CSWAP( N-KP, A( KP+1, KK ), 1, A( KP+1, KP ), 1 )
+*              (2) Swap and conjugate middle parts
+               DO 45 J = KK + 1, KP - 1
+                  T = CONJG( A( J, KK ) )
+                  A( J, KK ) = CONJG( A( KP, J ) )
+                  A( KP, J ) = T
+   45          CONTINUE
+*              (3) Swap and conjugate corner elements at row-col interserction
+               A( KP, KK ) = CONJG( A( KP, KK ) )
+*              (4) Swap diagonal elements at row-col intersection
+               R1 = REAL( A( KK, KK ) )
+               A( KK, KK ) = REAL( A( KP, KP ) )
+               A( KP, KP ) = R1
+*
+               IF( KSTEP.EQ.2 ) THEN
+*                 (*) Make sure that diagonal element of pivot is real
+                  A( K, K ) = REAL( A( K, K ) )
+*                 (5) Swap row elements
+                  T = A( K+1, K )
+                  A( K+1, K ) = A( KP, K )
+                  A( KP, K ) = T
+               END IF
+            ELSE
+*              (*) Make sure that diagonal element of pivot is real
+               A( K, K ) = REAL( A( K, K ) )
+               IF( KSTEP.EQ.2 )
+     $            A( K+1, K+1 ) = REAL( A( K+1, K+1 ) )
+            END IF
+*
+*           Update the trailing submatrix
+*
+            IF( KSTEP.EQ.1 ) THEN
+*
+*              1-by-1 pivot block D(k): column k of A now holds
+*
+*              W(k) = L(k)*D(k),
+*
+*              where L(k) is the k-th column of L
+*
+               IF( K.LT.N ) THEN
+*
+*                 Perform a rank-1 update of A(k+1:n,k+1:n) and
+*                 store L(k) in column k
+*
+*                 Handle division by a small number
+*
+                  IF( ABS( REAL( A( K, K ) ) ).GE.SFMIN ) THEN
+*
+*                    Perform a rank-1 update of A(k+1:n,k+1:n) as
+*                    A := A - L(k)*D(k)*L(k)**T
+*                       = A - W(k)*(1/D(k))*W(k)**T
+*
+                     D11 = ONE / REAL( A( K, K ) )
+                     CALL CHER( UPLO, N-K, -D11, A( K+1, K ), 1,
+     $                          A( K+1, K+1 ), LDA )
+*
+*                    Store L(k) in column k
+*
+                     CALL CSSCAL( N-K, D11, A( K+1, K ), 1 )
+                  ELSE
+*
+*                    Store L(k) in column k
+*
+                     D11 = REAL( A( K, K ) )
+                     DO 46 II = K + 1, N
+                        A( II, K ) = A( II, K ) / D11
+   46                CONTINUE
+*
+*                    Perform a rank-1 update of A(k+1:n,k+1:n) as
+*                    A := A - L(k)*D(k)*L(k)**T
+*                       = A - W(k)*(1/D(k))*W(k)**T
+*                       = A - (W(k)/D(k))*(D(k))*(W(k)/D(K))**T
+*
+                     CALL CHER( UPLO, N-K, -D11, A( K+1, K ), 1,
+     $                          A( K+1, K+1 ), LDA )
+                  END IF
+               END IF
+*
+            ELSE
+*
+*              2-by-2 pivot block D(k): columns k and k+1 now hold
+*
+*              ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k)
+*
+*              where L(k) and L(k+1) are the k-th and (k+1)-th columns
+*              of L
+*
+*
+*              Perform a rank-2 update of A(k+2:n,k+2:n) as
+*
+*              A := A - ( L(k) L(k+1) ) * D(k) * ( L(k) L(k+1) )**T
+*                 = A - ( ( A(k)A(k+1) )*inv(D(k) ) * ( A(k)A(k+1) )**T
+*
+*              and store L(k) and L(k+1) in columns k and k+1
+*
+               IF( K.LT.N-1 ) THEN
+*                 D = |A21|
+                  D = SLAPY2( REAL( A( K+1, K ) ),
+     $                AIMAG( A( K+1, K ) ) )
+                  D11 = REAL( A( K+1, K+1 ) ) / D
+                  D22 = REAL( A( K, K ) ) / D
+                  D21 = A( K+1, K ) / D
+                  TT = ONE / ( D11*D22-ONE )
+*
+                  DO 60 J = K + 2, N
+*
+*                    Compute  D21 * ( W(k)W(k+1) ) * inv(D(k)) for row J
+*
+                     WK = TT*( D11*A( J, K )-D21*A( J, K+1 ) )
+                     WKP1 = TT*( D22*A( J, K+1 )-CONJG( D21 )*
+     $                      A( J, K ) )
+*
+*                    Perform a rank-2 update of A(k+2:n,k+2:n)
+*
+                     DO 50 I = J, N
+                        A( I, J ) = A( I, J ) -
+     $                              ( A( I, K ) / D )*CONJG( WK ) -
+     $                              ( A( I, K+1 ) / D )*CONJG( WKP1 )
+   50                CONTINUE
+*
+*                    Store L(k) and L(k+1) in cols k and k+1 for row J
+*
+                     A( J, K ) = WK / D
+                     A( J, K+1 ) = WKP1 / D
+*                    (*) Make sure that diagonal element of pivot is real
+                     A( J, J ) = CMPLX( REAL( A( J, J ) ), ZERO )
+*
+   60             CONTINUE
+*
+               END IF
+*
+            END IF
+*
+         END IF
+*
+*        Store details of the interchanges in IPIV
+*
+         IF( KSTEP.EQ.1 ) THEN
+            IPIV( K ) = KP
+         ELSE
+            IPIV( K ) = -P
+            IPIV( K+1 ) = -KP
+         END IF
+*
+*        Increase K and return to the start of the main loop
+*
+         K = K + KSTEP
+         GO TO 40
+*
+      END IF
+*
+   70 CONTINUE
+*
+      RETURN
+*
+*     End of CHETF2_ROOK
+*
+      END

lapack-netlib/SRC/chetrf_rook.f

@@ -0,0 +1,397 @@
+*> \brief \b CHETRF_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download CHETRF_ROOK + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chetrf_rook.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chetrf_rook.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chetrf_rook.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CHETRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+*
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, LWORK, N
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       COMPLEX            A( LDA, * ), WORK( * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> CHETRF_ROOK computes the factorization of a comlex Hermitian matrix A
+*> using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
+*> The form of the factorization is
+*>
+*>    A = U*D*U**T  or  A = L*D*L**T
+*>
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, and D is Hermitian and block diagonal with
+*> 1-by-1 and 2-by-2 diagonal blocks.
+*>
+*> This is the blocked version of the algorithm, calling Level 3 BLAS.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          = 'U':  Upper triangle of A is stored;
+*>          = 'L':  Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is COMPLEX array, dimension (LDA,N)
+*>          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
+*>          N-by-N upper triangular part of A contains the upper
+*>          triangular part of the matrix A, and the strictly lower
+*>          triangular part of A is not referenced.  If UPLO = 'L', the
+*>          leading N-by-N lower triangular part of A contains the lower
+*>          triangular part of the matrix A, and the strictly upper
+*>          triangular part of A is not referenced.
+*>
+*>          On exit, the block diagonal matrix D and the multipliers used
+*>          to obtain the factor U or L (see below for further details).
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          Details of the interchanges and the block structure of D.
+*>
+*>          If UPLO = 'U':
+*>             Only the last KB elements of IPIV are set.
+*>
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
+*>             columns k and -IPIV(k) were interchanged and rows and
+*>             columns k-1 and -IPIV(k-1) were inerchaged,
+*>             D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>             Only the first KB elements of IPIV are set.
+*>
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k)
+*>             were interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
+*>             columns k and -IPIV(k) were interchanged and rows and
+*>             columns k+1 and -IPIV(k+1) were inerchaged,
+*>             D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX array, dimension (MAX(1,LWORK)).
+*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>          The length of WORK.  LWORK >=1.  For best performance
+*>          LWORK >= N*NB, where NB is the block size returned by ILAENV.
+*>
+*>          If LWORK = -1, then a workspace query is assumed; the routine
+*>          only calculates the optimal size of the WORK array, returns
+*>          this value as the first entry of the WORK array, and no error
+*>          message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0:  successful exit
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value
+*>          > 0:  if INFO = i, D(i,i) is exactly zero.  The factorization
+*>                has been completed, but the block diagonal matrix D is
+*>                exactly singular, and division by zero will occur if it
+*>                is used to solve a system of equations.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2013
+*
+*> \ingroup complexHEcomputational
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  If UPLO = 'U', then A = U*D*U**T, where
+*>     U = P(n)*U(n)* ... *P(k)U(k)* ...,
+*>  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
+*>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
+*>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
+*>  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
+*>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
+*>
+*>             (   I    v    0   )   k-s
+*>     U(k) =  (   0    I    0   )   s
+*>             (   0    0    I   )   n-k
+*>                k-s   s   n-k
+*>
+*>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
+*>  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
+*>  and A(k,k), and v overwrites A(1:k-2,k-1:k).
+*>
+*>  If UPLO = 'L', then A = L*D*L**T, where
+*>     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
+*>  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
+*>  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
+*>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
+*>  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
+*>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
+*>
+*>             (   I    0     0   )  k-1
+*>     L(k) =  (   0    I     0   )  s
+*>             (   0    v     I   )  n-k-s+1
+*>                k-1   s  n-k-s+1
+*>
+*>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
+*>  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
+*>  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
+*> \endverbatim
+*
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>  November 2013,  Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*>
+*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*>                  School of Mathematics,
+*>                  University of Manchester
+*>
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE CHETRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+*
+*  -- LAPACK computational routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2013
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, LWORK, N
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      COMPLEX            A( LDA, * ), WORK( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Local Scalars ..
+      LOGICAL            LQUERY, UPPER
+      INTEGER            IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      INTEGER            ILAENV
+      EXTERNAL           LSAME, ILAENV
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           CLAHEF_ROOK, CHETF2_ROOK, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      UPPER = LSAME( UPLO, 'U' )
+      LQUERY = ( LWORK.EQ.-1 )
+      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -4
+      ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
+         INFO = -7
+      END IF
+*
+      IF( INFO.EQ.0 ) THEN
+*
+*        Determine the block size
+*
+         NB = ILAENV( 1, 'CHETRF_ROOK', UPLO, N, -1, -1, -1 )
+         LWKOPT = N*NB
+         WORK( 1 ) = LWKOPT
+      END IF
+*
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'CHETRF_ROOK', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+*
+      NBMIN = 2
+      LDWORK = N
+      IF( NB.GT.1 .AND. NB.LT.N ) THEN
+         IWS = LDWORK*NB
+         IF( LWORK.LT.IWS ) THEN
+            NB = MAX( LWORK / LDWORK, 1 )
+            NBMIN = MAX( 2, ILAENV( 2, 'CHETRF_ROOK',
+     $                              UPLO, N, -1, -1, -1 ) )
+         END IF
+      ELSE
+         IWS = 1
+      END IF
+      IF( NB.LT.NBMIN )
+     $   NB = N
+*
+      IF( UPPER ) THEN
+*
+*        Factorize A as U*D*U**T using the upper triangle of A
+*
+*        K is the main loop index, decreasing from N to 1 in steps of
+*        KB, where KB is the number of columns factorized by CLAHEF_ROOK;
+*        KB is either NB or NB-1, or K for the last block
+*
+         K = N
+   10    CONTINUE
+*
+*        If K < 1, exit from loop
+*
+         IF( K.LT.1 )
+     $      GO TO 40
+*
+         IF( K.GT.NB ) THEN
+*
+*           Factorize columns k-kb+1:k of A and use blocked code to
+*           update columns 1:k-kb
+*
+            CALL CLAHEF_ROOK( UPLO, K, NB, KB, A, LDA,
+     $                        IPIV, WORK, LDWORK, IINFO )
+         ELSE
+*
+*           Use unblocked code to factorize columns 1:k of A
+*
+            CALL CHETF2_ROOK( UPLO, K, A, LDA, IPIV, IINFO )
+            KB = K
+         END IF
+*
+*        Set INFO on the first occurrence of a zero pivot
+*
+         IF( INFO.EQ.0 .AND. IINFO.GT.0 )
+     $      INFO = IINFO
+*
+*        No need to adjust IPIV
+*
+*        Decrease K and return to the start of the main loop
+*
+         K = K - KB
+         GO TO 10
+*
+      ELSE
+*
+*        Factorize A as L*D*L**T using the lower triangle of A
+*
+*        K is the main loop index, increasing from 1 to N in steps of
+*        KB, where KB is the number of columns factorized by CLAHEF_ROOK;
+*        KB is either NB or NB-1, or N-K+1 for the last block
+*
+         K = 1
+   20    CONTINUE
+*
+*        If K > N, exit from loop
+*
+         IF( K.GT.N )
+     $      GO TO 40
+*
+         IF( K.LE.N-NB ) THEN
+*
+*           Factorize columns k:k+kb-1 of A and use blocked code to
+*           update columns k+kb:n
+*
+            CALL CLAHEF_ROOK( UPLO, N-K+1, NB, KB, A( K, K ), LDA,
+     $                        IPIV( K ), WORK, LDWORK, IINFO )
+         ELSE
+*
+*           Use unblocked code to factorize columns k:n of A
+*
+            CALL CHETF2_ROOK( UPLO, N-K+1, A( K, K ), LDA, IPIV( K ),
+     $                        IINFO )
+            KB = N - K + 1
+         END IF
+*
+*        Set INFO on the first occurrence of a zero pivot
+*
+         IF( INFO.EQ.0 .AND. IINFO.GT.0 )
+     $      INFO = IINFO + K - 1
+*
+*        Adjust IPIV
+*
+         DO 30 J = K, K + KB - 1
+            IF( IPIV( J ).GT.0 ) THEN
+               IPIV( J ) = IPIV( J ) + K - 1
+            ELSE
+               IPIV( J ) = IPIV( J ) - K + 1
+            END IF
+   30    CONTINUE
+*
+*        Increase K and return to the start of the main loop
+*
+         K = K + KB
+         GO TO 20
+*
+      END IF
+*
+   40 CONTINUE
+      WORK( 1 ) = LWKOPT
+      RETURN
+*
+*     End of CHETRF_ROOK
+*
+      END

lapack-netlib/SRC/chetri_rook.f

@@ -0,0 +1,516 @@
+*> \brief \b CHETRI_ROOK computes the inverse of HE matrix using the factorization obtained with the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download CHETRI_ROOK + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chetri_rook.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chetri_rook.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chetri_rook.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CHETRI_ROOK( UPLO, N, A, LDA, IPIV, WORK, INFO )
+*
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, N
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       COMPLEX            A( LDA, * ), WORK( * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> CHETRI_ROOK computes the inverse of a complex Hermitian indefinite matrix
+*> A using the factorization A = U*D*U**H or A = L*D*L**H computed by
+*> CHETRF_ROOK.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          Specifies whether the details of the factorization are stored
+*>          as an upper or lower triangular matrix.
+*>          = 'U':  Upper triangular, form is A = U*D*U**H;
+*>          = 'L':  Lower triangular, form is A = L*D*L**H.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is COMPLEX array, dimension (LDA,N)
+*>          On entry, the block diagonal matrix D and the multipliers
+*>          used to obtain the factor U or L as computed by CHETRF_ROOK.
+*>
+*>          On exit, if INFO = 0, the (Hermitian) inverse of the original
+*>          matrix.  If UPLO = 'U', the upper triangular part of the
+*>          inverse is formed and the part of A below the diagonal is not
+*>          referenced; if UPLO = 'L' the lower triangular part of the
+*>          inverse is formed and the part of A above the diagonal is
+*>          not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          Details of the interchanges and the block structure of D
+*>          as determined by CHETRF_ROOK.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0: successful exit
+*>          < 0: if INFO = -i, the i-th argument had an illegal value
+*>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
+*>               inverse could not be computed.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2013
+*
+*> \ingroup complexHEcomputational
+*
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>  November 2013,  Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*>
+*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*>                  School of Mathematics,
+*>                  University of Manchester
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE CHETRI_ROOK( UPLO, N, A, LDA, IPIV, WORK, INFO )
+*
+*  -- LAPACK computational routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2013
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, N
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      COMPLEX            A( LDA, * ), WORK( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      REAL               ONE
+      COMPLEX            CONE, CZERO
+      PARAMETER          ( ONE = 1.0E+0, CONE = ( 1.0E+0, 0.0E+0 ),
+     $                   CZERO = ( 0.0E+0, 0.0E+0 ) )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            UPPER
+      INTEGER            J, K, KP, KSTEP
+      REAL               AK, AKP1, D, T
+      COMPLEX            AKKP1, TEMP
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      COMPLEX            CDOTC
+      EXTERNAL           LSAME, CDOTC
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           CCOPY, CHEMV, CSWAP, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, CONJG, MAX, REAL
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      UPPER = LSAME( UPLO, 'U' )
+      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -4
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'CHETRI_ROOK', -INFO )
+         RETURN
+      END IF
+*
+*     Quick return if possible
+*
+      IF( N.EQ.0 )
+     $   RETURN
+*
+*     Check that the diagonal matrix D is nonsingular.
+*
+      IF( UPPER ) THEN
+*
+*        Upper triangular storage: examine D from bottom to top
+*
+         DO 10 INFO = N, 1, -1
+            IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.CZERO )
+     $         RETURN
+   10    CONTINUE
+      ELSE
+*
+*        Lower triangular storage: examine D from top to bottom.
+*
+         DO 20 INFO = 1, N
+            IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.CZERO )
+     $         RETURN
+   20    CONTINUE
+      END IF
+      INFO = 0
+*
+      IF( UPPER ) THEN
+*
+*        Compute inv(A) from the factorization A = U*D*U**H.
+*
+*        K is the main loop index, increasing from 1 to N in steps of
+*        1 or 2, depending on the size of the diagonal blocks.
+*
+         K = 1
+   30    CONTINUE
+*
+*        If K > N, exit from loop.
+*
+         IF( K.GT.N )
+     $      GO TO 70
+*
+         IF( IPIV( K ).GT.0 ) THEN
+*
+*           1 x 1 diagonal block
+*
+*           Invert the diagonal block.
+*
+            A( K, K ) = ONE / REAL( A( K, K ) )
+*
+*           Compute column K of the inverse.
+*
+            IF( K.GT.1 ) THEN
+               CALL CCOPY( K-1, A( 1, K ), 1, WORK, 1 )
+               CALL CHEMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, CZERO,
+     $                     A( 1, K ), 1 )
+               A( K, K ) = A( K, K ) - REAL( CDOTC( K-1, WORK, 1, A( 1,
+     $                     K ), 1 ) )
+            END IF
+            KSTEP = 1
+         ELSE
+*
+*           2 x 2 diagonal block
+*
+*           Invert the diagonal block.
+*
+            T = ABS( A( K, K+1 ) )
+            AK = REAL( A( K, K ) ) / T
+            AKP1 = REAL( A( K+1, K+1 ) ) / T
+            AKKP1 = A( K, K+1 ) / T
+            D = T*( AK*AKP1-ONE )
+            A( K, K ) = AKP1 / D
+            A( K+1, K+1 ) = AK / D
+            A( K, K+1 ) = -AKKP1 / D
+*
+*           Compute columns K and K+1 of the inverse.
+*
+            IF( K.GT.1 ) THEN
+               CALL CCOPY( K-1, A( 1, K ), 1, WORK, 1 )
+               CALL CHEMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, CZERO,
+     $                     A( 1, K ), 1 )
+               A( K, K ) = A( K, K ) - REAL( CDOTC( K-1, WORK, 1, A( 1,
+     $                     K ), 1 ) )
+               A( K, K+1 ) = A( K, K+1 ) -
+     $                       CDOTC( K-1, A( 1, K ), 1, A( 1, K+1 ), 1 )
+               CALL CCOPY( K-1, A( 1, K+1 ), 1, WORK, 1 )
+               CALL CHEMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, CZERO,
+     $                     A( 1, K+1 ), 1 )
+               A( K+1, K+1 ) = A( K+1, K+1 ) -
+     $                         REAL( CDOTC( K-1, WORK, 1, A( 1, K+1 ),
+     $                         1 ) )
+            END IF
+            KSTEP = 2
+         END IF
+*
+         IF( KSTEP.EQ.1 ) THEN
+*
+*           Interchange rows and columns K and IPIV(K) in the leading
+*           submatrix A(1:k,1:k)
+*
+            KP = IPIV( K )
+            IF( KP.NE.K ) THEN
+*
+               IF( KP.GT.1 )
+     $            CALL CSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
+*
+               DO 40 J = KP + 1, K - 1
+                  TEMP = CONJG( A( J, K ) )
+                  A( J, K ) = CONJG( A( KP, J ) )
+                  A( KP, J ) = TEMP
+   40          CONTINUE
+*
+               A( KP, K ) = CONJG( A( KP, K ) )
+*
+               TEMP = A( K, K )
+               A( K, K ) = A( KP, KP )
+               A( KP, KP ) = TEMP
+            END IF
+         ELSE
+*
+*           Interchange rows and columns K and K+1 with -IPIV(K) and
+*           -IPIV(K+1) in the leading submatrix A(k+1:n,k+1:n)
+*
+*           (1) Interchange rows and columns K and -IPIV(K)
+*
+            KP = -IPIV( K )
+            IF( KP.NE.K ) THEN
+*
+               IF( KP.GT.1 )
+     $            CALL CSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
+*
+               DO 50 J = KP + 1, K - 1
+                  TEMP = CONJG( A( J, K ) )
+                  A( J, K ) = CONJG( A( KP, J ) )
+                  A( KP, J ) = TEMP
+   50          CONTINUE
+*
+               A( KP, K ) = CONJG( A( KP, K ) )
+*
+               TEMP = A( K, K )
+               A( K, K ) = A( KP, KP )
+               A( KP, KP ) = TEMP
+*
+               TEMP = A( K, K+1 )
+               A( K, K+1 ) = A( KP, K+1 )
+               A( KP, K+1 ) = TEMP
+            END IF
+*
+*           (2) Interchange rows and columns K+1 and -IPIV(K+1)
+*
+            K = K + 1
+            KP = -IPIV( K )
+            IF( KP.NE.K ) THEN
+*
+               IF( KP.GT.1 )
+     $            CALL CSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
+*
+               DO 60 J = KP + 1, K - 1
+                  TEMP = CONJG( A( J, K ) )
+                  A( J, K ) = CONJG( A( KP, J ) )
+                  A( KP, J ) = TEMP
+   60          CONTINUE
+*
+               A( KP, K ) = CONJG( A( KP, K ) )
+*
+               TEMP = A( K, K )
+               A( K, K ) = A( KP, KP )
+               A( KP, KP ) = TEMP
+            END IF
+         END IF
+*
+         K = K + 1
+         GO TO 30
+   70    CONTINUE
+*
+      ELSE
+*
+*        Compute inv(A) from the factorization A = L*D*L**H.
+*
+*        K is the main loop index, decreasing from N to 1 in steps of
+*        1 or 2, depending on the size of the diagonal blocks.
+*
+         K = N
+   80    CONTINUE
+*
+*        If K < 1, exit from loop.
+*
+         IF( K.LT.1 )
+     $      GO TO 120
+*
+         IF( IPIV( K ).GT.0 ) THEN
+*
+*           1 x 1 diagonal block
+*
+*           Invert the diagonal block.
+*
+            A( K, K ) = ONE / REAL( A( K, K ) )
+*
+*           Compute column K of the inverse.
+*
+            IF( K.LT.N ) THEN
+               CALL CCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
+               CALL CHEMV( UPLO, N-K, -CONE, A( K+1, K+1 ), LDA, WORK,
+     $                     1, CZERO, A( K+1, K ), 1 )
+               A( K, K ) = A( K, K ) - REAL( CDOTC( N-K, WORK, 1,
+     $                     A( K+1, K ), 1 ) )
+            END IF
+            KSTEP = 1
+         ELSE
+*
+*           2 x 2 diagonal block
+*
+*           Invert the diagonal block.
+*
+            T = ABS( A( K, K-1 ) )
+            AK = REAL( A( K-1, K-1 ) ) / T
+            AKP1 = REAL( A( K, K ) ) / T
+            AKKP1 = A( K, K-1 ) / T
+            D = T*( AK*AKP1-ONE )
+            A( K-1, K-1 ) = AKP1 / D
+            A( K, K ) = AK / D
+            A( K, K-1 ) = -AKKP1 / D
+*
+*           Compute columns K-1 and K of the inverse.
+*
+            IF( K.LT.N ) THEN
+               CALL CCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
+               CALL CHEMV( UPLO, N-K, -CONE, A( K+1, K+1 ), LDA, WORK,
+     $                     1, CZERO, A( K+1, K ), 1 )
+               A( K, K ) = A( K, K ) - REAL( CDOTC( N-K, WORK, 1,
+     $                     A( K+1, K ), 1 ) )
+               A( K, K-1 ) = A( K, K-1 ) -
+     $                       CDOTC( N-K, A( K+1, K ), 1, A( K+1, K-1 ),
+     $                       1 )
+               CALL CCOPY( N-K, A( K+1, K-1 ), 1, WORK, 1 )
+               CALL CHEMV( UPLO, N-K, -CONE, A( K+1, K+1 ), LDA, WORK,
+     $                     1, CZERO, A( K+1, K-1 ), 1 )
+               A( K-1, K-1 ) = A( K-1, K-1 ) -
+     $                         REAL( CDOTC( N-K, WORK, 1, A( K+1, K-1 ),
+     $                         1 ) )
+            END IF
+            KSTEP = 2
+         END IF
+*
+         IF( KSTEP.EQ.1 ) THEN
+*
+*           Interchange rows and columns K and IPIV(K) in the trailing
+*           submatrix A(k:n,k:n)
+*
+            KP = IPIV( K )
+            IF( KP.NE.K ) THEN
+*
+               IF( KP.LT.N )
+     $            CALL CSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
+*
+               DO 90 J = K + 1, KP - 1
+                  TEMP = CONJG( A( J, K ) )
+                  A( J, K ) = CONJG( A( KP, J ) )
+                  A( KP, J ) = TEMP
+   90          CONTINUE
+*
+               A( KP, K ) = CONJG( A( KP, K ) )
+*
+               TEMP = A( K, K )
+               A( K, K ) = A( KP, KP )
+               A( KP, KP ) = TEMP
+            END IF
+         ELSE
+*
+*           Interchange rows and columns K and K-1 with -IPIV(K) and
+*           -IPIV(K-1) in the trailing submatrix A(k-1:n,k-1:n)
+*
+*           (1) Interchange rows and columns K and -IPIV(K)
+*
+            KP = -IPIV( K )
+            IF( KP.NE.K ) THEN
+*
+               IF( KP.LT.N )
+     $            CALL CSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
+*
+               DO 100 J = K + 1, KP - 1
+                  TEMP = CONJG( A( J, K ) )
+                  A( J, K ) = CONJG( A( KP, J ) )
+                  A( KP, J ) = TEMP
+  100         CONTINUE
+*
+               A( KP, K ) = CONJG( A( KP, K ) )
+*
+               TEMP = A( K, K )
+               A( K, K ) = A( KP, KP )
+               A( KP, KP ) = TEMP
+*
+               TEMP = A( K, K-1 )
+               A( K, K-1 ) = A( KP, K-1 )
+               A( KP, K-1 ) = TEMP
+            END IF
+*
+*           (2) Interchange rows and columns K-1 and -IPIV(K-1)
+*
+            K = K - 1
+            KP = -IPIV( K )
+            IF( KP.NE.K ) THEN
+*
+               IF( KP.LT.N )
+     $            CALL CSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
+*
+               DO 110 J = K + 1, KP - 1
+                  TEMP = CONJG( A( J, K ) )
+                  A( J, K ) = CONJG( A( KP, J ) )
+                  A( KP, J ) = TEMP
+  110         CONTINUE
+*
+               A( KP, K ) = CONJG( A( KP, K ) )
+*
+               TEMP = A( K, K )
+               A( K, K ) = A( KP, KP )
+               A( KP, KP ) = TEMP
+            END IF
+         END IF
+*
+         K = K - 1
+         GO TO 80
+  120    CONTINUE
+      END IF
+*
+      RETURN
+*
+*     End of CHETRI_ROOK
+*
+      END

lapack-netlib/SRC/chetrs_rook.f

@@ -0,0 +1,503 @@
+*> \brief \b  CHETRS_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges)
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download CHETRS_ROOK + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chetrs_rook.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chetrs_rook.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chetrs_rook.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CHETRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
+*
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, LDB, N, NRHS
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       COMPLEX            A( LDA, * ), B( LDB, * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> CHETRS_ROOK solves a system of linear equations A*X = B with a complex
+*> Hermitian matrix A using the factorization A = U*D*U**H or
+*> A = L*D*L**H computed by CHETRF_ROOK.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          Specifies whether the details of the factorization are stored
+*>          as an upper or lower triangular matrix.
+*>          = 'U':  Upper triangular, form is A = U*D*U**H;
+*>          = 'L':  Lower triangular, form is A = L*D*L**H.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*>          NRHS is INTEGER
+*>          The number of right hand sides, i.e., the number of columns
+*>          of the matrix B.  NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*>          A is COMPLEX array, dimension (LDA,N)
+*>          The block diagonal matrix D and the multipliers used to
+*>          obtain the factor U or L as computed by CHETRF_ROOK.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          Details of the interchanges and the block structure of D
+*>          as determined by CHETRF_ROOK.
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*>          B is COMPLEX array, dimension (LDB,NRHS)
+*>          On entry, the right hand side matrix B.
+*>          On exit, the solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*>          LDB is INTEGER
+*>          The leading dimension of the array B.  LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0:  successful exit
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2013
+*
+*> \ingroup complexHEcomputational
+*
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>  November 2013,  Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*>
+*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*>                  School of Mathematics,
+*>                  University of Manchester
+*>
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE CHETRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
+     $                        INFO )
+*
+*  -- LAPACK computational routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2013
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, LDB, N, NRHS
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      COMPLEX            A( LDA, * ), B( LDB, * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      COMPLEX            ONE
+      PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ) )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            UPPER
+      INTEGER            J, K, KP
+      REAL               S
+      COMPLEX            AK, AKM1, AKM1K, BK, BKM1, DENOM
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      EXTERNAL           LSAME
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           CGEMV, CGERU, CLACGV, CSSCAL, CSWAP, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          CONJG, MAX, REAL
+*     ..
+*     .. Executable Statements ..
+*
+      INFO = 0
+      UPPER = LSAME( UPLO, 'U' )
+      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( NRHS.LT.0 ) THEN
+         INFO = -3
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -5
+      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+         INFO = -8
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'CHETRS_ROOK', -INFO )
+         RETURN
+      END IF
+*
+*     Quick return if possible
+*
+      IF( N.EQ.0 .OR. NRHS.EQ.0 )
+     $   RETURN
+*
+      IF( UPPER ) THEN
+*
+*        Solve A*X = B, where A = U*D*U**H.
+*
+*        First solve U*D*X = B, overwriting B with X.
+*
+*        K is the main loop index, decreasing from N to 1 in steps of
+*        1 or 2, depending on the size of the diagonal blocks.
+*
+         K = N
+   10    CONTINUE
+*
+*        If K < 1, exit from loop.
+*
+         IF( K.LT.1 )
+     $      GO TO 30
+*
+         IF( IPIV( K ).GT.0 ) THEN
+*
+*           1 x 1 diagonal block
+*
+*           Interchange rows K and IPIV(K).
+*
+            KP = IPIV( K )
+            IF( KP.NE.K )
+     $         CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+*
+*           Multiply by inv(U(K)), where U(K) is the transformation
+*           stored in column K of A.
+*
+            CALL CGERU( K-1, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
+     $                  B( 1, 1 ), LDB )
+*
+*           Multiply by the inverse of the diagonal block.
+*
+            S = REAL( ONE ) / REAL( A( K, K ) )
+            CALL CSSCAL( NRHS, S, B( K, 1 ), LDB )
+            K = K - 1
+         ELSE
+*
+*           2 x 2 diagonal block
+*
+*           Interchange rows K and -IPIV(K), then K-1 and -IPIV(K-1)
+*
+            KP = -IPIV( K )
+            IF( KP.NE.K )
+     $         CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+*
+            KP = -IPIV( K-1)
+            IF( KP.NE.K-1 )
+     $         CALL CSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
+*
+*           Multiply by inv(U(K)), where U(K) is the transformation
+*           stored in columns K-1 and K of A.
+*
+            CALL CGERU( K-2, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
+     $                  B( 1, 1 ), LDB )
+            CALL CGERU( K-2, NRHS, -ONE, A( 1, K-1 ), 1, B( K-1, 1 ),
+     $                  LDB, B( 1, 1 ), LDB )
+*
+*           Multiply by the inverse of the diagonal block.
+*
+            AKM1K = A( K-1, K )
+            AKM1 = A( K-1, K-1 ) / AKM1K
+            AK = A( K, K ) / CONJG( AKM1K )
+            DENOM = AKM1*AK - ONE
+            DO 20 J = 1, NRHS
+               BKM1 = B( K-1, J ) / AKM1K
+               BK = B( K, J ) / CONJG( AKM1K )
+               B( K-1, J ) = ( AK*BKM1-BK ) / DENOM
+               B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM
+   20       CONTINUE
+            K = K - 2
+         END IF
+*
+         GO TO 10
+   30    CONTINUE
+*
+*        Next solve U**H *X = B, overwriting B with X.
+*
+*        K is the main loop index, increasing from 1 to N in steps of
+*        1 or 2, depending on the size of the diagonal blocks.
+*
+         K = 1
+   40    CONTINUE
+*
+*        If K > N, exit from loop.
+*
+         IF( K.GT.N )
+     $      GO TO 50
+*
+         IF( IPIV( K ).GT.0 ) THEN
+*
+*           1 x 1 diagonal block
+*
+*           Multiply by inv(U**H(K)), where U(K) is the transformation
+*           stored in column K of A.
+*
+            IF( K.GT.1 ) THEN
+               CALL CLACGV( NRHS, B( K, 1 ), LDB )
+               CALL CGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B,
+     $                     LDB, A( 1, K ), 1, ONE, B( K, 1 ), LDB )
+               CALL CLACGV( NRHS, B( K, 1 ), LDB )
+            END IF
+*
+*           Interchange rows K and IPIV(K).
+*
+            KP = IPIV( K )
+            IF( KP.NE.K )
+     $         CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+            K = K + 1
+         ELSE
+*
+*           2 x 2 diagonal block
+*
+*           Multiply by inv(U**H(K+1)), where U(K+1) is the transformation
+*           stored in columns K and K+1 of A.
+*
+            IF( K.GT.1 ) THEN
+               CALL CLACGV( NRHS, B( K, 1 ), LDB )
+               CALL CGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B,
+     $                     LDB, A( 1, K ), 1, ONE, B( K, 1 ), LDB )
+               CALL CLACGV( NRHS, B( K, 1 ), LDB )
+*
+               CALL CLACGV( NRHS, B( K+1, 1 ), LDB )
+               CALL CGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B,
+     $                     LDB, A( 1, K+1 ), 1, ONE, B( K+1, 1 ), LDB )
+               CALL CLACGV( NRHS, B( K+1, 1 ), LDB )
+            END IF
+*
+*           Interchange rows K and -IPIV(K), then K+1 and -IPIV(K+1)
+*
+            KP = -IPIV( K )
+            IF( KP.NE.K )
+     $         CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+*
+            KP = -IPIV( K+1 )
+            IF( KP.NE.K+1 )
+     $         CALL CSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
+*
+            K = K + 2
+         END IF
+*
+         GO TO 40
+   50    CONTINUE
+*
+      ELSE
+*
+*        Solve A*X = B, where A = L*D*L**H.
+*
+*        First solve L*D*X = B, overwriting B with X.
+*
+*        K is the main loop index, increasing from 1 to N in steps of
+*        1 or 2, depending on the size of the diagonal blocks.
+*
+         K = 1
+   60    CONTINUE
+*
+*        If K > N, exit from loop.
+*
+         IF( K.GT.N )
+     $      GO TO 80
+*
+         IF( IPIV( K ).GT.0 ) THEN
+*
+*           1 x 1 diagonal block
+*
+*           Interchange rows K and IPIV(K).
+*
+            KP = IPIV( K )
+            IF( KP.NE.K )
+     $         CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+*
+*           Multiply by inv(L(K)), where L(K) is the transformation
+*           stored in column K of A.
+*
+            IF( K.LT.N )
+     $         CALL CGERU( N-K, NRHS, -ONE, A( K+1, K ), 1, B( K, 1 ),
+     $                     LDB, B( K+1, 1 ), LDB )
+*
+*           Multiply by the inverse of the diagonal block.
+*
+            S = REAL( ONE ) / REAL( A( K, K ) )
+            CALL CSSCAL( NRHS, S, B( K, 1 ), LDB )
+            K = K + 1
+         ELSE
+*
+*           2 x 2 diagonal block
+*
+*           Interchange rows K and -IPIV(K), then K+1 and -IPIV(K+1)
+*
+            KP = -IPIV( K )
+            IF( KP.NE.K )
+     $         CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+*
+            KP = -IPIV( K+1 )
+            IF( KP.NE.K+1 )
+     $         CALL CSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
+*
+*           Multiply by inv(L(K)), where L(K) is the transformation
+*           stored in columns K and K+1 of A.
+*
+            IF( K.LT.N-1 ) THEN
+               CALL CGERU( N-K-1, NRHS, -ONE, A( K+2, K ), 1, B( K, 1 ),
+     $                     LDB, B( K+2, 1 ), LDB )
+               CALL CGERU( N-K-1, NRHS, -ONE, A( K+2, K+1 ), 1,
+     $                     B( K+1, 1 ), LDB, B( K+2, 1 ), LDB )
+            END IF
+*
+*           Multiply by the inverse of the diagonal block.
+*
+            AKM1K = A( K+1, K )
+            AKM1 = A( K, K ) / CONJG( AKM1K )
+            AK = A( K+1, K+1 ) / AKM1K
+            DENOM = AKM1*AK - ONE
+            DO 70 J = 1, NRHS
+               BKM1 = B( K, J ) / CONJG( AKM1K )
+               BK = B( K+1, J ) / AKM1K
+               B( K, J ) = ( AK*BKM1-BK ) / DENOM
+               B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
+   70       CONTINUE
+            K = K + 2
+         END IF
+*
+         GO TO 60
+   80    CONTINUE
+*
+*        Next solve L**H *X = B, overwriting B with X.
+*
+*        K is the main loop index, decreasing from N to 1 in steps of
+*        1 or 2, depending on the size of the diagonal blocks.
+*
+         K = N
+   90    CONTINUE
+*
+*        If K < 1, exit from loop.
+*
+         IF( K.LT.1 )
+     $      GO TO 100
+*
+         IF( IPIV( K ).GT.0 ) THEN
+*
+*           1 x 1 diagonal block
+*
+*           Multiply by inv(L**H(K)), where L(K) is the transformation
+*           stored in column K of A.
+*
+            IF( K.LT.N ) THEN
+               CALL CLACGV( NRHS, B( K, 1 ), LDB )
+               CALL CGEMV( 'Conjugate transpose', N-K, NRHS, -ONE,
+     $                     B( K+1, 1 ), LDB, A( K+1, K ), 1, ONE,
+     $                     B( K, 1 ), LDB )
+               CALL CLACGV( NRHS, B( K, 1 ), LDB )
+            END IF
+*
+*           Interchange rows K and IPIV(K).
+*
+            KP = IPIV( K )
+            IF( KP.NE.K )
+     $         CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+            K = K - 1
+         ELSE
+*
+*           2 x 2 diagonal block
+*
+*           Multiply by inv(L**H(K-1)), where L(K-1) is the transformation
+*           stored in columns K-1 and K of A.
+*
+            IF( K.LT.N ) THEN
+               CALL CLACGV( NRHS, B( K, 1 ), LDB )
+               CALL CGEMV( 'Conjugate transpose', N-K, NRHS, -ONE,
+     $                     B( K+1, 1 ), LDB, A( K+1, K ), 1, ONE,
+     $                     B( K, 1 ), LDB )
+               CALL CLACGV( NRHS, B( K, 1 ), LDB )
+*
+               CALL CLACGV( NRHS, B( K-1, 1 ), LDB )
+               CALL CGEMV( 'Conjugate transpose', N-K, NRHS, -ONE,
+     $                     B( K+1, 1 ), LDB, A( K+1, K-1 ), 1, ONE,
+     $                     B( K-1, 1 ), LDB )
+               CALL CLACGV( NRHS, B( K-1, 1 ), LDB )
+            END IF
+*
+*           Interchange rows K and -IPIV(K), then K-1 and -IPIV(K-1)
+*
+            KP = -IPIV( K )
+            IF( KP.NE.K )
+     $         CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+*
+            KP = -IPIV( K-1 )
+            IF( KP.NE.K-1 )
+     $         CALL CSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
+*
+            K = K - 2
+         END IF
+*
+         GO TO 90
+  100    CONTINUE
+      END IF
+*
+      RETURN
+*
+*     End of CHETRS_ROOK
+*
+      END

lapack-netlib/SRC/chsein.f

@@ -104,6 +104,7 @@
 *> \verbatim
 *>          H is COMPLEX array, dimension (LDH,N)
 *>          The upper Hessenberg matrix H.
+*>          If a NaN is detected in H, the routine will return with INFO=-6.
 *> \endverbatim
 *>
 *> \param[in] LDH
@@ -225,7 +226,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date November 2011
+*> \date November 2013
 *
 *> \ingroup complexOTHERcomputational
 *
@@ -244,10 +245,10 @@
      $                   LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL,
      $                   IFAILR, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2011
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          EIGSRC, INITV, SIDE
@@ -276,9 +277,9 @@
       COMPLEX            CDUM, WK
 *     ..
 *     .. External Functions ..
-      LOGICAL            LSAME
+      LOGICAL            LSAME, SISNAN
       REAL               CLANHS, SLAMCH
-      EXTERNAL           LSAME, CLANHS, SLAMCH
+      EXTERNAL           LSAME, CLANHS, SLAMCH, SISNAN
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           CLAEIN, XERBLA
@@ -399,7 +400,10 @@
 *              has not ben computed before.
 *
                HNORM = CLANHS( 'I', KR-KL+1, H( KL, KL ), LDH, RWORK )
-               IF( HNORM.GT.RZERO ) THEN
+               IF( SISNAN( HNORM ) ) THEN
+                  INFO = -6
+                  RETURN
+               ELSE IF( (HNORM.GT.RZERO) ) THEN
                   EPS3 = HNORM*ULP
                ELSE
                   EPS3 = SMLNUM

lapack-netlib/SRC/chseqr.f

@@ -43,7 +43,7 @@
 *>    Optionally Z may be postmultiplied into an input unitary
 *>    matrix Q so that this routine can give the Schur factorization
 *>    of a matrix A which has been reduced to the Hessenberg form H
-*>    by the unitary matrix Q:  A = Q*H*Q**H = (QZ)*H*(QZ)**H.
+*>    by the unitary matrix Q:  A = Q*H*Q**H = (QZ)*T*(QZ)**H.
 *> \endverbatim
 *
 *  Arguments:
@@ -216,7 +216,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date November 2011
+*> \date November 2013
 *
 *> \ingroup complexOTHERcomputational
 *
@@ -299,10 +299,10 @@
       SUBROUTINE CHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, W, Z, LDZ,
      $                   WORK, LWORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2011
+*     November 2013
 *
 *     .. Scalar Arguments ..
       INTEGER            IHI, ILO, INFO, LDH, LDZ, LWORK, N

lapack-netlib/SRC/cla_lin_berr.f

@@ -67,14 +67,14 @@
 *>
 *> \param[in] RES
 *> \verbatim
-*>          RES is DOUBLE PRECISION array, dimension (N,NRHS)
+*>          RES is REAL array, dimension (N,NRHS)
 *>     The residual matrix, i.e., the matrix R in the relative backward
 *>     error formula above.
 *> \endverbatim
 *>
 *> \param[in] AYB
 *> \verbatim
-*>          AYB is DOUBLE PRECISION array, dimension (N, NRHS)
+*>          AYB is REAL array, dimension (N, NRHS)
 *>     The denominator in the relative backward error formula above, i.e.,
 *>     the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B
 *>     are from iterative refinement (see cla_gerfsx_extended.f).
@@ -94,17 +94,17 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date September 2012
+*> \date November 2013
 *
 *> \ingroup complexOTHERcomputational
 *
 *  =====================================================================
       SUBROUTINE CLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
 *
-*  -- LAPACK computational routine (version 3.4.2) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     September 2012
+*     November 2013
 *
 *     .. Scalar Arguments ..
       INTEGER            N, NZ, NRHS

lapack-netlib/SRC/clahef.f

@@ -1,25 +1,25 @@
-*> \brief \b CLAHEF computes a partial factorization of a complex Hermitian indefinite matrix, using the diagonal pivoting method.
+*> \brief \b CLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).
 *
 *  =========== DOCUMENTATION ===========
 *
-* Online html documentation available at 
-*            http://www.netlib.org/lapack/explore-html/ 
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
 *
 *> \htmlonly
-*> Download CLAHEF + dependencies 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clahef.f"> 
-*> [TGZ]</a> 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clahef.f"> 
-*> [ZIP]</a> 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clahef.f"> 
+*> Download CLAHEF + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clahef.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clahef.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clahef.f">
 *> [TXT]</a>
-*> \endhtmlonly 
+*> \endhtmlonly
 *
 *  Definition:
 *  ===========
 *
 *       SUBROUTINE CLAHEF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
-* 
+*
 *       .. Scalar Arguments ..
 *       CHARACTER          UPLO
 *       INTEGER            INFO, KB, LDA, LDW, N, NB
@@ -28,7 +28,7 @@
 *       INTEGER            IPIV( * )
 *       COMPLEX            A( LDA, * ), W( LDW, * )
 *       ..
-*  
+*
 *
 *> \par Purpose:
 *  =============
@@ -110,16 +110,26 @@
 *> \verbatim
 *>          IPIV is INTEGER array, dimension (N)
 *>          Details of the interchanges and the block structure of D.
-*>          If UPLO = 'U', only the last KB elements of IPIV are set;
-*>          if UPLO = 'L', only the first KB elements are set.
 *>
-*>          If IPIV(k) > 0, then rows and columns k and IPIV(k) were
-*>          interchanged and D(k,k) is a 1-by-1 diagonal block.
-*>          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
-*>          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
-*>          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
-*>          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
-*>          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*>          If UPLO = 'U':
+*>             Only the last KB elements of IPIV are set.
+*>
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k-1) < 0, then rows and columns
+*>             k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
+*>             is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>             Only the first KB elements of IPIV are set.
+*>
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k+1) < 0, then rows and columns
+*>             k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1)
+*>             is a 2-by-2 diagonal block.
 *> \endverbatim
 *>
 *> \param[out] W
@@ -145,22 +155,32 @@
 *  Authors:
 *  ========
 *
-*> \author Univ. of Tennessee 
-*> \author Univ. of California Berkeley 
-*> \author Univ. of Colorado Denver 
-*> \author NAG Ltd. 
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
 *
-*> \date September 2012
+*> \date November 2013
 *
 *> \ingroup complexHEcomputational
 *
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>  November 2013,  Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*> \endverbatim
+*
 *  =====================================================================
       SUBROUTINE CLAHEF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.2) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     September 2012
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          UPLO
@@ -219,17 +239,20 @@
 *        for use in updating A11 (note that conjg(W) is actually stored)
 *
 *        K is the main loop index, decreasing from N in steps of 1 or 2
-*
-*        KW is the column of W which corresponds to column K of A
 *
          K = N
    10    CONTINUE
+*
+*        KW is the column of W which corresponds to column K of A
+*
          KW = NB + K - N
 *
 *        Exit from loop
 *
          IF( ( K.LE.N-NB+1 .AND. NB.LT.N ) .OR. K.LT.1 )
      $      GO TO 30
+*
+         KSTEP = 1
 *
 *        Copy column K of A to column KW of W and update it
 *
@@ -240,8 +263,6 @@
      $                  W( K, KW+1 ), LDW, CONE, W( 1, KW ), 1 )
             W( K, KW ) = REAL( W( K, KW ) )
          END IF
-*
-         KSTEP = 1
 *
 *        Determine rows and columns to be interchanged and whether
 *        a 1-by-1 or 2-by-2 pivot block will be used
@@ -249,7 +270,8 @@
          ABSAKK = ABS( REAL( W( K, KW ) ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.GT.1 ) THEN
             IMAX = ICAMAX( K-1, W( 1, KW ), 1 )
@@ -260,13 +282,19 @@
 *
          IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
 *
-*           Column K is zero: set INFO and continue
+*           Column K is zero or underflow: set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
             KP = K
             A( K, K ) = REAL( A( K, K ) )
          ELSE
+*
+*           ============================================================
+*
+*           BEGIN pivot search
+*
+*           Case(1)
             IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
 *
 *              no interchange, use 1-by-1 pivot block
@@ -274,6 +302,9 @@
                KP = K
             ELSE
 *
+*              BEGIN pivot search along IMAX row
+*
+*
 *              Copy column IMAX to column KW-1 of W and update it
 *
                CALL CCOPY( IMAX-1, A( 1, IMAX ), 1, W( 1, KW-1 ), 1 )
@@ -289,7 +320,8 @@
                END IF
 *
 *              JMAX is the column-index of the largest off-diagonal
-*              element in row IMAX, and ROWMAX is its absolute value
+*              element in row IMAX, and ROWMAX is its absolute value.
+*              Determine only ROWMAX.
 *
                JMAX = IMAX + ICAMAX( K-IMAX, W( IMAX+1, KW-1 ), 1 )
                ROWMAX = CABS1( W( JMAX, KW-1 ) )
@@ -298,11 +330,14 @@
                   ROWMAX = MAX( ROWMAX, CABS1( W( JMAX, KW-1 ) ) )
                END IF
 *
+*              Case(2)
                IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN
 *
 *                 no interchange, use 1-by-1 pivot block
 *
                   KP = K
+*
+*              Case(3)
                ELSE IF( ABS( REAL( W( IMAX, KW-1 ) ) ).GE.ALPHA*ROWMAX )
      $                   THEN
 *
@@ -311,9 +346,11 @@
 *
                   KP = IMAX
 *
-*                 copy column KW-1 of W to column KW
+*                 copy column KW-1 of W to column KW of W
 *
                   CALL CCOPY( K, W( 1, KW-1 ), 1, W( 1, KW ), 1 )
+*
+*              Case(4)
                ELSE
 *
 *                 interchange rows and columns K-1 and IMAX, use 2-by-2
@@ -322,27 +359,48 @@
                   KP = IMAX
                   KSTEP = 2
                END IF
+*
+*
+*              END pivot search along IMAX row
+*
             END IF
+*
+*           END pivot search
+*
+*           ============================================================
+*
+*           KK is the column of A where pivoting step stopped
 *
             KK = K - KSTEP + 1
+*
+*           KKW is the column of W which corresponds to column KK of A
+*
             KKW = NB + KK - N
 *
-*           Updated column KP is already stored in column KKW of W
+*           Interchange rows and columns KP and KK.
+*           Updated column KP is already stored in column KKW of W.
 *
             IF( KP.NE.KK ) THEN
 *
-*              Copy non-updated column KK to column KP
+*              Copy non-updated column KK to column KP of submatrix A
+*              at step K. No need to copy element into column K
+*              (or K and K-1 for 2-by-2 pivot) of A, since these columns
+*              will be later overwritten.
 *
                A( KP, KP ) = REAL( A( KK, KK ) )
                CALL CCOPY( KK-1-KP, A( KP+1, KK ), 1, A( KP, KP+1 ),
      $                     LDA )
                CALL CLACGV( KK-1-KP, A( KP, KP+1 ), LDA )
-               CALL CCOPY( KP-1, A( 1, KK ), 1, A( 1, KP ), 1 )
+               IF( KP.GT.1 )
+     $            CALL CCOPY( KP-1, A( 1, KK ), 1, A( 1, KP ), 1 )
 *
-*              Interchange rows KK and KP in last KK columns of A and W
+*              Interchange rows KK and KP in last K+1 to N columns of A
+*              (columns K (or K and K-1 for 2-by-2 pivot) of A will be
+*              later overwritten). Interchange rows KK and KP
+*              in last KKW to NB columns of W.
 *
-               IF( KK.LT.N )
-     $            CALL CSWAP( N-KK, A( KK, KK+1 ), LDA, A( KP, KK+1 ),
+               IF( K.LT.N )
+     $            CALL CSWAP( N-K, A( KK, K+1 ), LDA, A( KP, K+1 ),
      $                        LDA )
                CALL CSWAP( N-KK+1, W( KK, KKW ), LDW, W( KP, KKW ),
      $                     LDW )
@@ -350,40 +408,108 @@
 *
             IF( KSTEP.EQ.1 ) THEN
 *
-*              1-by-1 pivot block D(k): column KW of W now holds
+*              1-by-1 pivot block D(k): column kw of W now holds
 *
-*              W(k) = U(k)*D(k)
+*              W(kw) = U(k)*D(k),
 *
 *              where U(k) is the k-th column of U
 *
-*              Store U(k) in column k of A
+*              (1) Store subdiag. elements of column U(k)
+*              and 1-by-1 block D(k) in column k of A.
+*              (NOTE: Diagonal element U(k,k) is a UNIT element
+*              and not stored)
+*                 A(k,k) := D(k,k) = W(k,kw)
+*                 A(1:k-1,k) := U(1:k-1,k) = W(1:k-1,kw)/D(k,k)
 *
+*              (NOTE: No need to use for Hermitian matrix
+*              A( K, K ) = DBLE( W( K, K) ) to separately copy diagonal
+*              element D(k,k) from W (potentially saves only one load))
                CALL CCOPY( K, W( 1, KW ), 1, A( 1, K ), 1 )
-               R1 = ONE / REAL( A( K, K ) )
-               CALL CSSCAL( K-1, R1, A( 1, K ), 1 )
+               IF( K.GT.1 ) THEN
 *
-*              Conjugate W(k)
+*                 (NOTE: No need to check if A(k,k) is NOT ZERO,
+*                  since that was ensured earlier in pivot search:
+*                  case A(k,k) = 0 falls into 2x2 pivot case(4))
+*
+                  R1 = ONE / REAL( A( K, K ) )
+                  CALL CSSCAL( K-1, R1, A( 1, K ), 1 )
+*
+*                 (2) Conjugate column W(kw)
+*
+                  CALL CLACGV( K-1, W( 1, KW ), 1 )
+               END IF
 *
-               CALL CLACGV( K-1, W( 1, KW ), 1 )
             ELSE
 *
-*              2-by-2 pivot block D(k): columns KW and KW-1 of W now
-*              hold
+*              2-by-2 pivot block D(k): columns kw and kw-1 of W now hold
 *
-*              ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
+*              ( W(kw-1) W(kw) ) = ( U(k-1) U(k) )*D(k)
 *
 *              where U(k) and U(k-1) are the k-th and (k-1)-th columns
 *              of U
+*
+*              (1) Store U(1:k-2,k-1) and U(1:k-2,k) and 2-by-2
+*              block D(k-1:k,k-1:k) in columns k-1 and k of A.
+*              (NOTE: 2-by-2 diagonal block U(k-1:k,k-1:k) is a UNIT
+*              block and not stored)
+*                 A(k-1:k,k-1:k) := D(k-1:k,k-1:k) = W(k-1:k,kw-1:kw)
+*                 A(1:k-2,k-1:k) := U(1:k-2,k:k-1:k) =
+*                 = W(1:k-2,kw-1:kw) * ( D(k-1:k,k-1:k)**(-1) )
 *
                IF( K.GT.2 ) THEN
 *
-*                 Store U(k) and U(k-1) in columns k and k-1 of A
+*                 Factor out the columns of the inverse of 2-by-2 pivot
+*                 block D, so that each column contains 1, to reduce the
+*                 number of FLOPS when we multiply panel
+*                 ( W(kw-1) W(kw) ) by this inverse, i.e. by D**(-1).
+*
+*                 D**(-1) = ( d11 cj(d21) )**(-1) =
+*                           ( d21    d22 )
+*
+*                 = 1/(d11*d22-|d21|**2) * ( ( d22) (-cj(d21) ) ) =
+*                                          ( (-d21) (     d11 ) )
+*
+*                 = 1/(|d21|**2) * 1/((d11/cj(d21))*(d22/d21)-1) *
+*
+*                   * ( d21*( d22/d21 ) conj(d21)*(           - 1 ) ) =
+*                     (     (      -1 )           ( d11/conj(d21) ) )
+*
+*                 = 1/(|d21|**2) * 1/(D22*D11-1) *
+*
+*                   * ( d21*( D11 ) conj(d21)*(  -1 ) ) =
+*                     (     (  -1 )           ( D22 ) )
+*
+*                 = (1/|d21|**2) * T * ( d21*( D11 ) conj(d21)*(  -1 ) ) =
+*                                      (     (  -1 )           ( D22 ) )
+*
+*                 = ( (T/conj(d21))*( D11 ) (T/d21)*(  -1 ) ) =
+*                   (               (  -1 )         ( D22 ) )
+*
+*                 = ( conj(D21)*( D11 ) D21*(  -1 ) )
+*                   (           (  -1 )     ( D22 ) ),
+*
+*                 where D11 = d22/d21,
+*                       D22 = d11/conj(d21),
+*                       D21 = T/d21,
+*                       T = 1/(D22*D11-1).
+*
+*                 (NOTE: No need to check for division by ZERO,
+*                  since that was ensured earlier in pivot search:
+*                  (a) d21 != 0, since in 2x2 pivot case(4)
+*                      |d21| should be larger than |d11| and |d22|;
+*                  (b) (D22*D11 - 1) != 0, since from (a),
+*                      both |D11| < 1, |D22| < 1, hence |D22*D11| << 1.)
 *
                   D21 = W( K-1, KW )
                   D11 = W( K, KW ) / CONJG( D21 )
                   D22 = W( K-1, KW-1 ) / D21
                   T = ONE / ( REAL( D11*D22 )-ONE )
                   D21 = T / D21
+*
+*                 Update elements in columns A(k-1) and A(k) as
+*                 dot products of rows of ( W(kw-1) W(kw) ) and columns
+*                 of D**(-1)
+*
                   DO 20 J = 1, K - 2
                      A( J, K-1 ) = D21*( D11*W( J, KW-1 )-W( J, KW ) )
                      A( J, K ) = CONJG( D21 )*
@@ -397,11 +523,13 @@
                A( K-1, K ) = W( K-1, KW )
                A( K, K ) = W( K, KW )
 *
-*              Conjugate W(k) and W(k-1)
+*              (2) Conjugate columns W(kw) and W(kw-1)
 *
                CALL CLACGV( K-1, W( 1, KW ), 1 )
                CALL CLACGV( K-2, W( 1, KW-1 ), 1 )
+*
             END IF
+*
          END IF
 *
 *        Store details of the interchanges in IPIV
@@ -448,19 +576,27 @@
    50    CONTINUE
 *
 *        Put U12 in standard form by partially undoing the interchanges
-*        in columns k+1:n
+*        in of rows in columns k+1:n looping backwards from k+1 to n
 *
          J = K + 1
    60    CONTINUE
-         JJ = J
-         JP = IPIV( J )
-         IF( JP.LT.0 ) THEN
-            JP = -JP
+*
+*           Undo the interchanges (if any) of rows J and JP
+*           at each step J
+*
+*           (Here, J is a diagonal index)
+            JJ = J
+            JP = IPIV( J )
+            IF( JP.LT.0 ) THEN
+               JP = -JP
+*              (Here, J is a diagonal index)
+               J = J + 1
+            END IF
+*           (NOTE: Here, J is used to determine row length. Length N-J+1
+*           of the rows to swap back doesn't include diagonal element)
             J = J + 1
-         END IF
-         J = J + 1
-         IF( JP.NE.JJ .AND. J.LE.N )
-     $      CALL CSWAP( N-J+1, A( JP, J ), LDA, A( JJ, J ), LDA )
+            IF( JP.NE.JJ .AND. J.LE.N )
+     $         CALL CSWAP( N-J+1, A( JP, J ), LDA, A( JJ, J ), LDA )
          IF( J.LE.N )
      $      GO TO 60
 *
@@ -483,6 +619,8 @@
 *
          IF( ( K.GE.NB .AND. NB.LT.N ) .OR. K.GT.N )
      $      GO TO 90
+*
+         KSTEP = 1
 *
 *        Copy column K of A to column K of W and update it
 *
@@ -492,8 +630,6 @@
          CALL CGEMV( 'No transpose', N-K+1, K-1, -CONE, A( K, 1 ), LDA,
      $               W( K, 1 ), LDW, CONE, W( K, K ), 1 )
          W( K, K ) = REAL( W( K, K ) )
-*
-         KSTEP = 1
 *
 *        Determine rows and columns to be interchanged and whether
 *        a 1-by-1 or 2-by-2 pivot block will be used
@@ -501,7 +637,8 @@
          ABSAKK = ABS( REAL( W( K, K ) ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.LT.N ) THEN
             IMAX = K + ICAMAX( N-K, W( K+1, K ), 1 )
@@ -512,13 +649,19 @@
 *
          IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
 *
-*           Column K is zero: set INFO and continue
+*           Column K is zero or underflow: set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
             KP = K
             A( K, K ) = REAL( A( K, K ) )
          ELSE
+*
+*           ============================================================
+*
+*           BEGIN pivot search
+*
+*           Case(1)
             IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
 *
 *              no interchange, use 1-by-1 pivot block
@@ -526,6 +669,9 @@
                KP = K
             ELSE
 *
+*              BEGIN pivot search along IMAX row
+*
+*
 *              Copy column IMAX to column K+1 of W and update it
 *
                CALL CCOPY( IMAX-K, A( IMAX, K ), LDA, W( K, K+1 ), 1 )
@@ -540,7 +686,8 @@
                W( IMAX, K+1 ) = REAL( W( IMAX, K+1 ) )
 *
 *              JMAX is the column-index of the largest off-diagonal
-*              element in row IMAX, and ROWMAX is its absolute value
+*              element in row IMAX, and ROWMAX is its absolute value.
+*              Determine only ROWMAX.
 *
                JMAX = K - 1 + ICAMAX( IMAX-K, W( K, K+1 ), 1 )
                ROWMAX = CABS1( W( JMAX, K+1 ) )
@@ -549,11 +696,14 @@
                   ROWMAX = MAX( ROWMAX, CABS1( W( JMAX, K+1 ) ) )
                END IF
 *
+*              Case(2)
                IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN
 *
 *                 no interchange, use 1-by-1 pivot block
 *
                   KP = K
+*
+*              Case(3)
                ELSE IF( ABS( REAL( W( IMAX, K+1 ) ) ).GE.ALPHA*ROWMAX )
      $                   THEN
 *
@@ -562,9 +712,11 @@
 *
                   KP = IMAX
 *
-*                 copy column K+1 of W to column K
+*                 copy column K+1 of W to column K of W
 *
                   CALL CCOPY( N-K+1, W( K, K+1 ), 1, W( K, K ), 1 )
+*
+*              Case(4)
                ELSE
 *
 *                 interchange rows and columns K+1 and IMAX, use 2-by-2
@@ -573,15 +725,29 @@
                   KP = IMAX
                   KSTEP = 2
                END IF
+*
+*
+*              END pivot search along IMAX row
+*
             END IF
+*
+*           END pivot search
+*
+*           ============================================================
+*
+*           KK is the column of A where pivoting step stopped
 *
             KK = K + KSTEP - 1
 *
-*           Updated column KP is already stored in column KK of W
+*           Interchange rows and columns KP and KK.
+*           Updated column KP is already stored in column KK of W.
 *
             IF( KP.NE.KK ) THEN
 *
-*              Copy non-updated column KK to column KP
+*              Copy non-updated column KK to column KP of submatrix A
+*              at step K. No need to copy element into column K
+*              (or K and K+1 for 2-by-2 pivot) of A, since these columns
+*              will be later overwritten.
 *
                A( KP, KP ) = REAL( A( KK, KK ) )
                CALL CCOPY( KP-KK-1, A( KK+1, KK ), 1, A( KP, KK+1 ),
@@ -590,9 +756,13 @@
                IF( KP.LT.N )
      $            CALL CCOPY( N-KP, A( KP+1, KK ), 1, A( KP+1, KP ), 1 )
 *
-*              Interchange rows KK and KP in first KK columns of A and W
+*              Interchange rows KK and KP in first K-1 columns of A
+*              (columns K (or K and K+1 for 2-by-2 pivot) of A will be
+*              later overwritten). Interchange rows KK and KP
+*              in first KK columns of W.
 *
-               CALL CSWAP( KK-1, A( KK, 1 ), LDA, A( KP, 1 ), LDA )
+               IF( K.GT.1 )
+     $            CALL CSWAP( K-1, A( KK, 1 ), LDA, A( KP, 1 ), LDA )
                CALL CSWAP( KK, W( KK, 1 ), LDW, W( KP, 1 ), LDW )
             END IF
 *
@@ -600,21 +770,35 @@
 *
 *              1-by-1 pivot block D(k): column k of W now holds
 *
-*              W(k) = L(k)*D(k)
+*              W(k) = L(k)*D(k),
 *
 *              where L(k) is the k-th column of L
 *
-*              Store L(k) in column k of A
+*              (1) Store subdiag. elements of column L(k)
+*              and 1-by-1 block D(k) in column k of A.
+*              (NOTE: Diagonal element L(k,k) is a UNIT element
+*              and not stored)
+*                 A(k,k) := D(k,k) = W(k,k)
+*                 A(k+1:N,k) := L(k+1:N,k) = W(k+1:N,k)/D(k,k)
 *
+*              (NOTE: No need to use for Hermitian matrix
+*              A( K, K ) = DBLE( W( K, K) ) to separately copy diagonal
+*              element D(k,k) from W (potentially saves only one load))
                CALL CCOPY( N-K+1, W( K, K ), 1, A( K, K ), 1 )
                IF( K.LT.N ) THEN
+*
+*                 (NOTE: No need to check if A(k,k) is NOT ZERO,
+*                  since that was ensured earlier in pivot search:
+*                  case A(k,k) = 0 falls into 2x2 pivot case(4))
+*
                   R1 = ONE / REAL( A( K, K ) )
                   CALL CSSCAL( N-K, R1, A( K+1, K ), 1 )
 *
-*                 Conjugate W(k)
+*                 (2) Conjugate column W(k)
 *
                   CALL CLACGV( N-K, W( K+1, K ), 1 )
                END IF
+*
             ELSE
 *
 *              2-by-2 pivot block D(k): columns k and k+1 of W now hold
@@ -623,16 +807,69 @@
 *
 *              where L(k) and L(k+1) are the k-th and (k+1)-th columns
 *              of L
+*
+*              (1) Store L(k+2:N,k) and L(k+2:N,k+1) and 2-by-2
+*              block D(k:k+1,k:k+1) in columns k and k+1 of A.
+*              (NOTE: 2-by-2 diagonal block L(k:k+1,k:k+1) is a UNIT
+*              block and not stored)
+*                 A(k:k+1,k:k+1) := D(k:k+1,k:k+1) = W(k:k+1,k:k+1)
+*                 A(k+2:N,k:k+1) := L(k+2:N,k:k+1) =
+*                 = W(k+2:N,k:k+1) * ( D(k:k+1,k:k+1)**(-1) )
 *
                IF( K.LT.N-1 ) THEN
 *
-*                 Store L(k) and L(k+1) in columns k and k+1 of A
+*                 Factor out the columns of the inverse of 2-by-2 pivot
+*                 block D, so that each column contains 1, to reduce the
+*                 number of FLOPS when we multiply panel
+*                 ( W(kw-1) W(kw) ) by this inverse, i.e. by D**(-1).
+*
+*                 D**(-1) = ( d11 cj(d21) )**(-1) =
+*                           ( d21    d22 )
+*
+*                 = 1/(d11*d22-|d21|**2) * ( ( d22) (-cj(d21) ) ) =
+*                                          ( (-d21) (     d11 ) )
+*
+*                 = 1/(|d21|**2) * 1/((d11/cj(d21))*(d22/d21)-1) *
+*
+*                   * ( d21*( d22/d21 ) conj(d21)*(           - 1 ) ) =
+*                     (     (      -1 )           ( d11/conj(d21) ) )
+*
+*                 = 1/(|d21|**2) * 1/(D22*D11-1) *
+*
+*                   * ( d21*( D11 ) conj(d21)*(  -1 ) ) =
+*                     (     (  -1 )           ( D22 ) )
+*
+*                 = (1/|d21|**2) * T * ( d21*( D11 ) conj(d21)*(  -1 ) ) =
+*                                      (     (  -1 )           ( D22 ) )
+*
+*                 = ( (T/conj(d21))*( D11 ) (T/d21)*(  -1 ) ) =
+*                   (               (  -1 )         ( D22 ) )
+*
+*                 = ( conj(D21)*( D11 ) D21*(  -1 ) )
+*                   (           (  -1 )     ( D22 ) )
+*
+*                 where D11 = d22/d21,
+*                       D22 = d11/conj(d21),
+*                       D21 = T/d21,
+*                       T = 1/(D22*D11-1).
+*
+*                 (NOTE: No need to check for division by ZERO,
+*                  since that was ensured earlier in pivot search:
+*                  (a) d21 != 0, since in 2x2 pivot case(4)
+*                      |d21| should be larger than |d11| and |d22|;
+*                  (b) (D22*D11 - 1) != 0, since from (a),
+*                      both |D11| < 1, |D22| < 1, hence |D22*D11| << 1.)
 *
                   D21 = W( K+1, K )
                   D11 = W( K+1, K+1 ) / D21
                   D22 = W( K, K ) / CONJG( D21 )
                   T = ONE / ( REAL( D11*D22 )-ONE )
                   D21 = T / D21
+*
+*                 Update elements in columns A(k) and A(k+1) as
+*                 dot products of rows of ( W(k) W(k+1) ) and columns
+*                 of D**(-1)
+*
                   DO 80 J = K + 2, N
                      A( J, K ) = CONJG( D21 )*
      $                           ( D11*W( J, K )-W( J, K+1 ) )
@@ -646,11 +883,13 @@
                A( K+1, K ) = W( K+1, K )
                A( K+1, K+1 ) = W( K+1, K+1 )
 *
-*              Conjugate W(k) and W(k+1)
+*              (2) Conjugate columns W(k) and W(k+1)
 *
                CALL CLACGV( N-K, W( K+1, K ), 1 )
                CALL CLACGV( N-K-1, W( K+2, K+1 ), 1 )
+*
             END IF
+*
          END IF
 *
 *        Store details of the interchanges in IPIV
@@ -698,19 +937,27 @@
   110    CONTINUE
 *
 *        Put L21 in standard form by partially undoing the interchanges
-*        in columns 1:k-1
+*        of rows in columns 1:k-1 looping backwards from k-1 to 1
 *
          J = K - 1
   120    CONTINUE
-         JJ = J
-         JP = IPIV( J )
-         IF( JP.LT.0 ) THEN
-            JP = -JP
+*
+*           Undo the interchanges (if any) of rows J and JP
+*           at each step J
+*
+*           (Here, J is a diagonal index)
+            JJ = J
+            JP = IPIV( J )
+            IF( JP.LT.0 ) THEN
+               JP = -JP
+*              (Here, J is a diagonal index)
+               J = J - 1
+            END IF
+*           (NOTE: Here, J is used to determine row length. Length J
+*           of the rows to swap back doesn't include diagonal element)
             J = J - 1
-         END IF
-         J = J - 1
-         IF( JP.NE.JJ .AND. J.GE.1 )
-     $      CALL CSWAP( J, A( JP, 1 ), LDA, A( JJ, 1 ), LDA )
+            IF( JP.NE.JJ .AND. J.GE.1 )
+     $         CALL CSWAP( J, A( JP, 1 ), LDA, A( JJ, 1 ), LDA )
          IF( J.GE.1 )
      $      GO TO 120
 *

lapack-netlib/SRC/clarfb.f

@@ -159,7 +159,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date September 2012
+*> \date June 2013
 *
 *> \ingroup complexOTHERauxiliary
 *
@@ -195,10 +195,10 @@
       SUBROUTINE CLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,
      $                   T, LDT, C, LDC, WORK, LDWORK )
 *
-*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK auxiliary routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     September 2012
+*     June 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          DIRECT, SIDE, STOREV, TRANS
@@ -217,12 +217,11 @@
 *     ..
 *     .. Local Scalars ..
       CHARACTER          TRANST
-      INTEGER            I, J, LASTV, LASTC
+      INTEGER            I, J
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
-      INTEGER            ILACLR, ILACLC
-      EXTERNAL           LSAME, ILACLR, ILACLC
+      EXTERNAL           LSAME
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           CCOPY, CGEMM, CLACGV, CTRMM
@@ -255,36 +254,33 @@
 *
 *              Form  H * C  or  H**H * C  where  C = ( C1 )
 *                                                    ( C2 )
-*
-               LASTV = MAX( K, ILACLR( M, K, V, LDV ) )
-               LASTC = ILACLC( LASTV, N, C, LDC )
 *
 *              W := C**H * V  =  (C1**H * V1 + C2**H * V2)  (stored in WORK)
 *
 *              W := C1**H
 *
                DO 10 J = 1, K
-                  CALL CCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
-                  CALL CLACGV( LASTC, WORK( 1, J ), 1 )
+                  CALL CCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
+                  CALL CLACGV( N, WORK( 1, J ), 1 )
    10          CONTINUE
 *
 *              W := W * V1
 *
-               CALL CTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
-     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
-               IF( LASTV.GT.K ) THEN
+               CALL CTRMM( 'Right', 'Lower', 'No transpose', 'Unit', N,
+     $                     K, ONE, V, LDV, WORK, LDWORK )
+               IF( M.GT.K ) THEN
 *
 *                 W := W + C2**H *V2
 *
-                  CALL CGEMM( 'Conjugate transpose', 'No transpose',
-     $                 LASTC, K, LASTV-K, ONE, C( K+1, 1 ), LDC,
-     $                 V( K+1, 1 ), LDV, ONE, WORK, LDWORK )
+                  CALL CGEMM( 'Conjugate transpose', 'No transpose', N,
+     $                        K, M-K, ONE, C( K+1, 1 ), LDC,
+     $                        V( K+1, 1 ), LDV, ONE, WORK, LDWORK )
                END IF
 *
 *              W := W * T**H  or  W * T
 *
-               CALL CTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
-     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
+               CALL CTRMM( 'Right', 'Upper', TRANST, 'Non-unit', N, K,
+     $                     ONE, T, LDT, WORK, LDWORK )
 *
 *              C := C - V * W**H
 *
@@ -293,19 +289,19 @@
 *                 C2 := C2 - V2 * W**H
 *
                   CALL CGEMM( 'No transpose', 'Conjugate transpose',
-     $                 LASTV-K, LASTC, K, -ONE, V( K+1, 1 ), LDV,
-     $                 WORK, LDWORK, ONE, C( K+1, 1 ), LDC )
+     $                        M-K, N, K, -ONE, V( K+1, 1 ), LDV, WORK,
+     $                        LDWORK, ONE, C( K+1, 1 ), LDC )
                END IF
 *
 *              W := W * V1**H
 *
                CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose',
-     $              'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
+     $                     'Unit', N, K, ONE, V, LDV, WORK, LDWORK )
 *
 *              C1 := C1 - W**H
 *
                DO 30 J = 1, K
-                  DO 20 I = 1, LASTC
+                  DO 20 I = 1, N
                      C( J, I ) = C( J, I ) - CONJG( WORK( I, J ) )
    20             CONTINUE
    30          CONTINUE
@@ -313,58 +309,53 @@
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
 *              Form  C * H  or  C * H**H  where  C = ( C1  C2 )
-*
-               LASTV = MAX( K, ILACLR( N, K, V, LDV ) )
-               LASTC = ILACLR( M, LASTV, C, LDC )
 *
 *              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)
 *
 *              W := C1
 *
                DO 40 J = 1, K
-                  CALL CCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )
+                  CALL CCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 )
    40          CONTINUE
 *
 *              W := W * V1
 *
-               CALL CTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
-     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
-               IF( LASTV.GT.K ) THEN
+               CALL CTRMM( 'Right', 'Lower', 'No transpose', 'Unit', M,
+     $                     K, ONE, V, LDV, WORK, LDWORK )
+               IF( N.GT.K ) THEN
 *
 *                 W := W + C2 * V2
 *
-                  CALL CGEMM( 'No transpose', 'No transpose',
-     $                 LASTC, K, LASTV-K,
-     $                 ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV,
-     $                 ONE, WORK, LDWORK )
+                  CALL CGEMM( 'No transpose', 'No transpose', M, K, N-K,
+     $                        ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV,
+     $                        ONE, WORK, LDWORK )
                END IF
 *
 *              W := W * T  or  W * T**H
 *
-               CALL CTRMM( 'Right', 'Upper', TRANS, 'Non-unit',
-     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
+               CALL CTRMM( 'Right', 'Upper', TRANS, 'Non-unit', M, K,
+     $                     ONE, T, LDT, WORK, LDWORK )
 *
 *              C := C - W * V**H
 *
-               IF( LASTV.GT.K ) THEN
+               IF( N.GT.K ) THEN
 *
 *                 C2 := C2 - W * V2**H
 *
-                  CALL CGEMM( 'No transpose', 'Conjugate transpose',
-     $                 LASTC, LASTV-K, K,
-     $                 -ONE, WORK, LDWORK, V( K+1, 1 ), LDV,
-     $                 ONE, C( 1, K+1 ), LDC )
+                  CALL CGEMM( 'No transpose', 'Conjugate transpose', M,
+     $                        N-K, K, -ONE, WORK, LDWORK, V( K+1, 1 ),
+     $                        LDV, ONE, C( 1, K+1 ), LDC )
                END IF
 *
 *              W := W * V1**H
 *
                CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose',
-     $              'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
+     $                     'Unit', M, K, ONE, V, LDV, WORK, LDWORK )
 *
 *              C1 := C1 - W
 *
                DO 60 J = 1, K
-                  DO 50 I = 1, LASTC
+                  DO 50 I = 1, M
                      C( I, J ) = C( I, J ) - WORK( I, J )
    50             CONTINUE
    60          CONTINUE
@@ -379,38 +370,34 @@
             IF( LSAME( SIDE, 'L' ) ) THEN
 *
 *              Form  H * C  or  H**H * C  where  C = ( C1 )
-*                                                    ( C2 )
-*
-               LASTC = ILACLC( M, N, C, LDC )
+*                                                  ( C2 )
 *
 *              W := C**H * V  =  (C1**H * V1 + C2**H * V2)  (stored in WORK)
 *
 *              W := C2**H
 *
                DO 70 J = 1, K
-                  CALL CCOPY( LASTC, C( M-K+J, 1 ), LDC,
-     $                 WORK( 1, J ), 1 )
-                  CALL CLACGV( LASTC, WORK( 1, J ), 1 )
+                  CALL CCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 )
+                  CALL CLACGV( N, WORK( 1, J ), 1 )
    70          CONTINUE
 *
 *              W := W * V2
 *
-               CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
-     $              LASTC, K, ONE, V( M-K+1, 1 ), LDV,
-     $              WORK, LDWORK )
+               CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit', N,
+     $                     K, ONE, V( M-K+1, 1 ), LDV, WORK, LDWORK )
                IF( M.GT.K ) THEN
 *
-*                 W := W + C1**H*V1
+*                 W := W + C1**H * V1
 *
-                  CALL CGEMM( 'Conjugate transpose', 'No transpose',
-     $                 LASTC, K, M-K, ONE, C, LDC, V, LDV,
-     $                 ONE, WORK, LDWORK )
+                  CALL CGEMM( 'Conjugate transpose', 'No transpose', N,
+     $                        K, M-K, ONE, C, LDC, V, LDV, ONE, WORK,
+     $                        LDWORK )
                END IF
 *
 *              W := W * T**H  or  W * T
 *
-               CALL CTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
-     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
+               CALL CTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K,
+     $                     ONE, T, LDT, WORK, LDWORK )
 *
 *              C := C - V * W**H
 *
@@ -419,20 +406,20 @@
 *                 C1 := C1 - V1 * W**H
 *
                   CALL CGEMM( 'No transpose', 'Conjugate transpose',
-     $                 M-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,
-     $                 ONE, C, LDC )
+     $                        M-K, N, K, -ONE, V, LDV, WORK, LDWORK,
+     $                        ONE, C, LDC )
                END IF
 *
 *              W := W * V2**H
 *
                CALL CTRMM( 'Right', 'Upper', 'Conjugate transpose',
-     $              'Unit', LASTC, K, ONE, V( M-K+1, 1 ), LDV,
-     $              WORK, LDWORK )
+     $                     'Unit', N, K, ONE, V( M-K+1, 1 ), LDV, WORK,
+     $                     LDWORK )
 *
 *              C2 := C2 - W**H
 *
                DO 90 J = 1, K
-                  DO 80 I = 1, LASTC
+                  DO 80 I = 1, N
                      C( M-K+J, I ) = C( M-K+J, I ) -
      $                               CONJG( WORK( I, J ) )
    80             CONTINUE
@@ -441,36 +428,31 @@
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
 *              Form  C * H  or  C * H**H  where  C = ( C1  C2 )
-*
-               LASTC = ILACLR( M, N, C, LDC )
 *
 *              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)
 *
 *              W := C2
 *
                DO 100 J = 1, K
-                  CALL CCOPY( LASTC, C( 1, N-K+J ), 1,
-     $                 WORK( 1, J ), 1 )
+                  CALL CCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 )
   100          CONTINUE
 *
 *              W := W * V2
 *
-               CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
-     $              LASTC, K, ONE, V( N-K+1, 1 ), LDV,
-     $              WORK, LDWORK )
+               CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit', M,
+     $                     K, ONE, V( N-K+1, 1 ), LDV, WORK, LDWORK )
                IF( N.GT.K ) THEN
 *
 *                 W := W + C1 * V1
 *
-                  CALL CGEMM( 'No transpose', 'No transpose',
-     $                 LASTC, K, N-K,
-     $                 ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
+                  CALL CGEMM( 'No transpose', 'No transpose', M, K, N-K,
+     $                        ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
                END IF
 *
 *              W := W * T  or  W * T**H
 *
-               CALL CTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
-     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
+               CALL CTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K,
+     $                     ONE, T, LDT, WORK, LDWORK )
 *
 *              C := C - W * V**H
 *
@@ -478,23 +460,22 @@
 *
 *                 C1 := C1 - W * V1**H
 *
-                  CALL CGEMM( 'No transpose', 'Conjugate transpose',
-     $                 LASTC, N-K, K, -ONE, WORK, LDWORK, V, LDV,
-     $                 ONE, C, LDC )
+                  CALL CGEMM( 'No transpose', 'Conjugate transpose', M,
+     $                        N-K, K, -ONE, WORK, LDWORK, V, LDV, ONE,
+     $                        C, LDC )
                END IF
 *
 *              W := W * V2**H
 *
                CALL CTRMM( 'Right', 'Upper', 'Conjugate transpose',
-     $              'Unit', LASTC, K, ONE, V( N-K+1, 1 ), LDV,
-     $              WORK, LDWORK )
+     $                     'Unit', M, K, ONE, V( N-K+1, 1 ), LDV, WORK,
+     $                     LDWORK )
 *
 *              C2 := C2 - W
 *
                DO 120 J = 1, K
-                  DO 110 I = 1, LASTC
-                     C( I, N-K+J ) = C( I, N-K+J )
-     $                    - WORK( I, J )
+                  DO 110 I = 1, M
+                     C( I, N-K+J ) = C( I, N-K+J ) - WORK( I, J )
   110             CONTINUE
   120          CONTINUE
             END IF
@@ -511,59 +492,56 @@
 *
 *              Form  H * C  or  H**H * C  where  C = ( C1 )
 *                                                    ( C2 )
-*
-               LASTV = MAX( K, ILACLC( K, M, V, LDV ) )
-               LASTC = ILACLC( LASTV, N, C, LDC )
 *
 *              W := C**H * V**H  =  (C1**H * V1**H + C2**H * V2**H) (stored in WORK)
 *
 *              W := C1**H
 *
                DO 130 J = 1, K
-                  CALL CCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
-                  CALL CLACGV( LASTC, WORK( 1, J ), 1 )
+                  CALL CCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
+                  CALL CLACGV( N, WORK( 1, J ), 1 )
   130          CONTINUE
 *
 *              W := W * V1**H
 *
                CALL CTRMM( 'Right', 'Upper', 'Conjugate transpose',
-     $                     'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
-               IF( LASTV.GT.K ) THEN
+     $                     'Unit', N, K, ONE, V, LDV, WORK, LDWORK )
+               IF( M.GT.K ) THEN
 *
-*                 W := W + C2**H*V2**H
+*                 W := W + C2**H * V2**H
 *
                   CALL CGEMM( 'Conjugate transpose',
-     $                 'Conjugate transpose', LASTC, K, LASTV-K,
-     $                 ONE, C( K+1, 1 ), LDC, V( 1, K+1 ), LDV,
-     $                 ONE, WORK, LDWORK )
+     $                        'Conjugate transpose', N, K, M-K, ONE,
+     $                        C( K+1, 1 ), LDC, V( 1, K+1 ), LDV, ONE,
+     $                        WORK, LDWORK )
                END IF
 *
 *              W := W * T**H  or  W * T
 *
-               CALL CTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
-     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
+               CALL CTRMM( 'Right', 'Upper', TRANST, 'Non-unit', N, K,
+     $                     ONE, T, LDT, WORK, LDWORK )
 *
 *              C := C - V**H * W**H
 *
-               IF( LASTV.GT.K ) THEN
+               IF( M.GT.K ) THEN
 *
 *                 C2 := C2 - V2**H * W**H
 *
                   CALL CGEMM( 'Conjugate transpose',
-     $                 'Conjugate transpose', LASTV-K, LASTC, K,
-     $                 -ONE, V( 1, K+1 ), LDV, WORK, LDWORK,
-     $                 ONE, C( K+1, 1 ), LDC )
+     $                        'Conjugate transpose', M-K, N, K, -ONE,
+     $                        V( 1, K+1 ), LDV, WORK, LDWORK, ONE,
+     $                        C( K+1, 1 ), LDC )
                END IF
 *
 *              W := W * V1
 *
-               CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
-     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
+               CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit', N,
+     $                     K, ONE, V, LDV, WORK, LDWORK )
 *
 *              C1 := C1 - W**H
 *
                DO 150 J = 1, K
-                  DO 140 I = 1, LASTC
+                  DO 140 I = 1, N
                      C( J, I ) = C( J, I ) - CONJG( WORK( I, J ) )
   140             CONTINUE
   150          CONTINUE
@@ -571,57 +549,53 @@
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
 *              Form  C * H  or  C * H**H  where  C = ( C1  C2 )
-*
-               LASTV = MAX( K, ILACLC( K, N, V, LDV ) )
-               LASTC = ILACLR( M, LASTV, C, LDC )
 *
 *              W := C * V**H  =  (C1*V1**H + C2*V2**H)  (stored in WORK)
 *
 *              W := C1
 *
                DO 160 J = 1, K
-                  CALL CCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )
+                  CALL CCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 )
   160          CONTINUE
 *
 *              W := W * V1**H
 *
                CALL CTRMM( 'Right', 'Upper', 'Conjugate transpose',
-     $                     'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
-               IF( LASTV.GT.K ) THEN
+     $                     'Unit', M, K, ONE, V, LDV, WORK, LDWORK )
+               IF( N.GT.K ) THEN
 *
 *                 W := W + C2 * V2**H
 *
-                  CALL CGEMM( 'No transpose', 'Conjugate transpose',
-     $                 LASTC, K, LASTV-K, ONE, C( 1, K+1 ), LDC,
-     $                 V( 1, K+1 ), LDV, ONE, WORK, LDWORK )
+                  CALL CGEMM( 'No transpose', 'Conjugate transpose', M,
+     $                        K, N-K, ONE, C( 1, K+1 ), LDC,
+     $                        V( 1, K+1 ), LDV, ONE, WORK, LDWORK )
                END IF
 *
 *              W := W * T  or  W * T**H
 *
-               CALL CTRMM( 'Right', 'Upper', TRANS, 'Non-unit',
-     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
+               CALL CTRMM( 'Right', 'Upper', TRANS, 'Non-unit', M, K,
+     $                     ONE, T, LDT, WORK, LDWORK )
 *
 *              C := C - W * V
 *
-               IF( LASTV.GT.K ) THEN
+               IF( N.GT.K ) THEN
 *
 *                 C2 := C2 - W * V2
 *
-                  CALL CGEMM( 'No transpose', 'No transpose',
-     $                 LASTC, LASTV-K, K,
-     $                 -ONE, WORK, LDWORK, V( 1, K+1 ), LDV,
-     $                 ONE, C( 1, K+1 ), LDC )
+                  CALL CGEMM( 'No transpose', 'No transpose', M, N-K, K,
+     $                        -ONE, WORK, LDWORK, V( 1, K+1 ), LDV, ONE,
+     $                        C( 1, K+1 ), LDC )
                END IF
 *
 *              W := W * V1
 *
-               CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
-     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
+               CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit', M,
+     $                     K, ONE, V, LDV, WORK, LDWORK )
 *
 *              C1 := C1 - W
 *
                DO 180 J = 1, K
-                  DO 170 I = 1, LASTC
+                  DO 170 I = 1, M
                      C( I, J ) = C( I, J ) - WORK( I, J )
   170             CONTINUE
   180          CONTINUE
@@ -637,37 +611,34 @@
 *
 *              Form  H * C  or  H**H * C  where  C = ( C1 )
 *                                                    ( C2 )
-*
-               LASTC = ILACLC( M, N, C, LDC )
 *
 *              W := C**H * V**H  =  (C1**H * V1**H + C2**H * V2**H) (stored in WORK)
 *
 *              W := C2**H
 *
                DO 190 J = 1, K
-                  CALL CCOPY( LASTC, C( M-K+J, 1 ), LDC,
-     $                 WORK( 1, J ), 1 )
-                  CALL CLACGV( LASTC, WORK( 1, J ), 1 )
+                  CALL CCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 )
+                  CALL CLACGV( N, WORK( 1, J ), 1 )
   190          CONTINUE
 *
 *              W := W * V2**H
 *
                CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose',
-     $              'Unit', LASTC, K, ONE, V( 1, M-K+1 ), LDV,
-     $              WORK, LDWORK )
+     $                     'Unit', N, K, ONE, V( 1, M-K+1 ), LDV, WORK,
+     $                     LDWORK )
                IF( M.GT.K ) THEN
 *
 *                 W := W + C1**H * V1**H
 *
                   CALL CGEMM( 'Conjugate transpose',
-     $                 'Conjugate transpose', LASTC, K, M-K,
-     $                 ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
+     $                        'Conjugate transpose', N, K, M-K, ONE, C,
+     $                        LDC, V, LDV, ONE, WORK, LDWORK )
                END IF
 *
 *              W := W * T**H  or  W * T
 *
-               CALL CTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
-     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
+               CALL CTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K,
+     $                     ONE, T, LDT, WORK, LDWORK )
 *
 *              C := C - V**H * W**H
 *
@@ -676,20 +647,19 @@
 *                 C1 := C1 - V1**H * W**H
 *
                   CALL CGEMM( 'Conjugate transpose',
-     $                 'Conjugate transpose', M-K, LASTC, K,
-     $                 -ONE, V, LDV, WORK, LDWORK, ONE, C, LDC )
+     $                        'Conjugate transpose', M-K, N, K, -ONE, V,
+     $                        LDV, WORK, LDWORK, ONE, C, LDC )
                END IF
 *
 *              W := W * V2
 *
-               CALL CTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
-     $              LASTC, K, ONE, V( 1, M-K+1 ), LDV,
-     $              WORK, LDWORK )
+               CALL CTRMM( 'Right', 'Lower', 'No transpose', 'Unit', N,
+     $                     K, ONE, V( 1, M-K+1 ), LDV, WORK, LDWORK )
 *
 *              C2 := C2 - W**H
 *
                DO 210 J = 1, K
-                  DO 200 I = 1, LASTC
+                  DO 200 I = 1, N
                      C( M-K+J, I ) = C( M-K+J, I ) -
      $                               CONJG( WORK( I, J ) )
   200             CONTINUE
@@ -698,36 +668,33 @@
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
 *              Form  C * H  or  C * H**H  where  C = ( C1  C2 )
-*
-               LASTC = ILACLR( M, N, C, LDC )
 *
 *              W := C * V**H  =  (C1*V1**H + C2*V2**H)  (stored in WORK)
 *
 *              W := C2
 *
                DO 220 J = 1, K
-                  CALL CCOPY( LASTC, C( 1, N-K+J ), 1,
-     $                 WORK( 1, J ), 1 )
+                  CALL CCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 )
   220          CONTINUE
 *
 *              W := W * V2**H
 *
                CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose',
-     $              'Unit', LASTC, K, ONE, V( 1, N-K+1 ), LDV,
-     $              WORK, LDWORK )
+     $                     'Unit', M, K, ONE, V( 1, N-K+1 ), LDV, WORK,
+     $                     LDWORK )
                IF( N.GT.K ) THEN
 *
 *                 W := W + C1 * V1**H
 *
-                  CALL CGEMM( 'No transpose', 'Conjugate transpose',
-     $                 LASTC, K, N-K, ONE, C, LDC, V, LDV, ONE,
-     $                 WORK, LDWORK )
+                  CALL CGEMM( 'No transpose', 'Conjugate transpose', M,
+     $                        K, N-K, ONE, C, LDC, V, LDV, ONE, WORK,
+     $                        LDWORK )
                END IF
 *
 *              W := W * T  or  W * T**H
 *
-               CALL CTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
-     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
+               CALL CTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K,
+     $                     ONE, T, LDT, WORK, LDWORK )
 *
 *              C := C - W * V
 *
@@ -735,21 +702,19 @@
 *
 *                 C1 := C1 - W * V1
 *
-                  CALL CGEMM( 'No transpose', 'No transpose',
-     $                 LASTC, N-K, K, -ONE, WORK, LDWORK, V, LDV,
-     $                 ONE, C, LDC )
+                  CALL CGEMM( 'No transpose', 'No transpose', M, N-K, K,
+     $                        -ONE, WORK, LDWORK, V, LDV, ONE, C, LDC )
                END IF
 *
 *              W := W * V2
 *
-               CALL CTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
-     $              LASTC, K, ONE, V( 1, N-K+1 ), LDV,
-     $              WORK, LDWORK )
+               CALL CTRMM( 'Right', 'Lower', 'No transpose', 'Unit', M,
+     $                     K, ONE, V( 1, N-K+1 ), LDV, WORK, LDWORK )
 *
 *              C1 := C1 - W
 *
                DO 240 J = 1, K
-                  DO 230 I = 1, LASTC
+                  DO 230 I = 1, M
                      C( I, N-K+J ) = C( I, N-K+J ) - WORK( I, J )
   230             CONTINUE
   240          CONTINUE

lapack-netlib/SRC/clartg.f

@@ -85,7 +85,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date September 2012
+*> \date November 2013
 *
 *> \ingroup complexOTHERauxiliary
 *
@@ -103,10 +103,10 @@
 *  =====================================================================
       SUBROUTINE CLARTG( F, G, CS, SN, R )
 *
-*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK auxiliary routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     September 2012
+*     November 2013
 *
 *     .. Scalar Arguments ..
       REAL               CS
@@ -130,7 +130,8 @@
 *     ..
 *     .. External Functions ..
       REAL               SLAMCH, SLAPY2
-      EXTERNAL           SLAMCH, SLAPY2
+      LOGICAL            SISNAN
+      EXTERNAL           SLAMCH, SLAPY2, SISNAN
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          ABS, AIMAG, CMPLX, CONJG, INT, LOG, MAX, REAL,
@@ -139,26 +140,17 @@
 *     .. Statement Functions ..
       REAL               ABS1, ABSSQ
 *     ..
-*     .. Save statement ..
-*     SAVE               FIRST, SAFMX2, SAFMIN, SAFMN2
-*     ..
-*     .. Data statements ..
-*     DATA               FIRST / .TRUE. /
-*     ..
 *     .. Statement Function definitions ..
       ABS1( FF ) = MAX( ABS( REAL( FF ) ), ABS( AIMAG( FF ) ) )
       ABSSQ( FF ) = REAL( FF )**2 + AIMAG( FF )**2
 *     ..
 *     .. Executable Statements ..
 *
-*     IF( FIRST ) THEN
-         SAFMIN = SLAMCH( 'S' )
-         EPS = SLAMCH( 'E' )
-         SAFMN2 = SLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) /
-     $            LOG( SLAMCH( 'B' ) ) / TWO )
-         SAFMX2 = ONE / SAFMN2
-*        FIRST = .FALSE.
-*     END IF
+      SAFMIN = SLAMCH( 'S' )
+      EPS = SLAMCH( 'E' )
+      SAFMN2 = SLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) /
+     $         LOG( SLAMCH( 'B' ) ) / TWO )
+      SAFMX2 = ONE / SAFMN2
       SCALE = MAX( ABS1( F ), ABS1( G ) )
       FS = F
       GS = G
@@ -172,7 +164,7 @@
          IF( SCALE.GE.SAFMX2 )
      $      GO TO 10
       ELSE IF( SCALE.LE.SAFMN2 ) THEN
-         IF( G.EQ.CZERO ) THEN
+         IF( G.EQ.CZERO.OR.SISNAN( ABS( G ) ) ) THEN
             CS = ONE
             SN = CZERO
             R = F

lapack-netlib/SRC/clasyf.f

@@ -1,25 +1,25 @@
-*> \brief \b CLASYF computes a partial factorization of a complex symmetric matrix, using the diagonal pivoting method.
+*> \brief \b CLASYF computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method.
 *
 *  =========== DOCUMENTATION ===========
 *
-* Online html documentation available at 
-*            http://www.netlib.org/lapack/explore-html/ 
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
 *
 *> \htmlonly
-*> Download CLASYF + dependencies 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clasyf.f"> 
-*> [TGZ]</a> 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clasyf.f"> 
-*> [ZIP]</a> 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clasyf.f"> 
+*> Download CLASYF + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clasyf.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clasyf.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clasyf.f">
 *> [TXT]</a>
-*> \endhtmlonly 
+*> \endhtmlonly
 *
 *  Definition:
 *  ===========
 *
 *       SUBROUTINE CLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
-* 
+*
 *       .. Scalar Arguments ..
 *       CHARACTER          UPLO
 *       INTEGER            INFO, KB, LDA, LDW, N, NB
@@ -28,7 +28,7 @@
 *       INTEGER            IPIV( * )
 *       COMPLEX            A( LDA, * ), W( LDW, * )
 *       ..
-*  
+*
 *
 *> \par Purpose:
 *  =============
@@ -110,16 +110,26 @@
 *> \verbatim
 *>          IPIV is INTEGER array, dimension (N)
 *>          Details of the interchanges and the block structure of D.
-*>          If UPLO = 'U', only the last KB elements of IPIV are set;
-*>          if UPLO = 'L', only the first KB elements are set.
 *>
-*>          If IPIV(k) > 0, then rows and columns k and IPIV(k) were
-*>          interchanged and D(k,k) is a 1-by-1 diagonal block.
-*>          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
-*>          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
-*>          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
-*>          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
-*>          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*>          If UPLO = 'U':
+*>             Only the last KB elements of IPIV are set.
+*>
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k-1) < 0, then rows and columns
+*>             k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
+*>             is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>             Only the first KB elements of IPIV are set.
+*>
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k+1) < 0, then rows and columns
+*>             k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1)
+*>             is a 2-by-2 diagonal block.
 *> \endverbatim
 *>
 *> \param[out] W
@@ -145,22 +155,32 @@
 *  Authors:
 *  ========
 *
-*> \author Univ. of Tennessee 
-*> \author Univ. of California Berkeley 
-*> \author Univ. of Colorado Denver 
-*> \author NAG Ltd. 
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
 *
-*> \date September 2012
+*> \date November 2013
 *
 *> \ingroup complexSYcomputational
 *
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>  November 2013,  Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*> \endverbatim
+*
 *  =====================================================================
       SUBROUTINE CLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.2) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     September 2012
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          UPLO
@@ -246,7 +266,8 @@
          ABSAKK = CABS1( W( K, KW ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.GT.1 ) THEN
             IMAX = ICAMAX( K-1, W( 1, KW ), 1 )
@@ -257,7 +278,7 @@
 *
          IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
 *
-*           Column K is zero: set INFO and continue
+*           Column K is zero or underflow: set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
@@ -302,7 +323,7 @@
 *
                   KP = IMAX
 *
-*                 copy column KW-1 of W to column KW
+*                 copy column KW-1 of W to column KW of W
 *
                   CALL CCOPY( K, W( 1, KW-1 ), 1, W( 1, KW ), 1 )
                ELSE
@@ -314,59 +335,117 @@
                   KSTEP = 2
                END IF
             END IF
+*
+*           ============================================================
+*
+*           KK is the column of A where pivoting step stopped
 *
             KK = K - KSTEP + 1
+*
+*           KKW is the column of W which corresponds to column KK of A
+*
             KKW = NB + KK - N
 *
-*           Updated column KP is already stored in column KKW of W
+*           Interchange rows and columns KP and KK.
+*           Updated column KP is already stored in column KKW of W.
 *
             IF( KP.NE.KK ) THEN
 *
-*              Copy non-updated column KK to column KP
+*              Copy non-updated column KK to column KP of submatrix A
+*              at step K. No need to copy element into column K
+*              (or K and K-1 for 2-by-2 pivot) of A, since these columns
+*              will be later overwritten.
 *
-               A( KP, K ) = A( KK, K )
-               CALL CCOPY( K-1-KP, A( KP+1, KK ), 1, A( KP, KP+1 ),
+               A( KP, KP ) = A( KK, KK )
+               CALL CCOPY( KK-1-KP, A( KP+1, KK ), 1, A( KP, KP+1 ),
      $                     LDA )
-               CALL CCOPY( KP, A( 1, KK ), 1, A( 1, KP ), 1 )
+               IF( KP.GT.1 )
+     $            CALL CCOPY( KP-1, A( 1, KK ), 1, A( 1, KP ), 1 )
 *
-*              Interchange rows KK and KP in last KK columns of A and W
+*              Interchange rows KK and KP in last K+1 to N columns of A
+*              (columns K (or K and K-1 for 2-by-2 pivot) of A will be
+*              later overwritten). Interchange rows KK and KP
+*              in last KKW to NB columns of W.
 *
-               CALL CSWAP( N-KK+1, A( KK, KK ), LDA, A( KP, KK ), LDA )
+               IF( K.LT.N )
+     $            CALL CSWAP( N-K, A( KK, K+1 ), LDA, A( KP, K+1 ),
+     $                        LDA )
                CALL CSWAP( N-KK+1, W( KK, KKW ), LDW, W( KP, KKW ),
      $                     LDW )
             END IF
 *
             IF( KSTEP.EQ.1 ) THEN
 *
-*              1-by-1 pivot block D(k): column KW of W now holds
+*              1-by-1 pivot block D(k): column kw of W now holds
 *
-*              W(k) = U(k)*D(k)
+*              W(kw) = U(k)*D(k),
 *
 *              where U(k) is the k-th column of U
 *
-*              Store U(k) in column k of A
+*              Store subdiag. elements of column U(k)
+*              and 1-by-1 block D(k) in column k of A.
+*              NOTE: Diagonal element U(k,k) is a UNIT element
+*              and not stored.
+*                 A(k,k) := D(k,k) = W(k,kw)
+*                 A(1:k-1,k) := U(1:k-1,k) = W(1:k-1,kw)/D(k,k)
 *
                CALL CCOPY( K, W( 1, KW ), 1, A( 1, K ), 1 )
                R1 = CONE / A( K, K )
                CALL CSCAL( K-1, R1, A( 1, K ), 1 )
+*
             ELSE
 *
-*              2-by-2 pivot block D(k): columns KW and KW-1 of W now
-*              hold
+*              2-by-2 pivot block D(k): columns kw and kw-1 of W now hold
 *
-*              ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
+*              ( W(kw-1) W(kw) ) = ( U(k-1) U(k) )*D(k)
 *
 *              where U(k) and U(k-1) are the k-th and (k-1)-th columns
 *              of U
+*
+*              Store U(1:k-2,k-1) and U(1:k-2,k) and 2-by-2
+*              block D(k-1:k,k-1:k) in columns k-1 and k of A.
+*              NOTE: 2-by-2 diagonal block U(k-1:k,k-1:k) is a UNIT
+*              block and not stored.
+*                 A(k-1:k,k-1:k) := D(k-1:k,k-1:k) = W(k-1:k,kw-1:kw)
+*                 A(1:k-2,k-1:k) := U(1:k-2,k:k-1:k) =
+*                 = W(1:k-2,kw-1:kw) * ( D(k-1:k,k-1:k)**(-1) )
 *
                IF( K.GT.2 ) THEN
 *
-*                 Store U(k) and U(k-1) in columns k and k-1 of A
+*                 Compose the columns of the inverse of 2-by-2 pivot
+*                 block D in the following way to reduce the number
+*                 of FLOPS when we myltiply panel ( W(kw-1) W(kw) ) by
+*                 this inverse
+*
+*                 D**(-1) = ( d11 d21 )**(-1) =
+*                           ( d21 d22 )
+*
+*                 = 1/(d11*d22-d21**2) * ( ( d22 ) (-d21 ) ) =
+*                                        ( (-d21 ) ( d11 ) )
+*
+*                 = 1/d21 * 1/((d11/d21)*(d22/d21)-1) *
+*
+*                   * ( ( d22/d21 ) (      -1 ) ) =
+*                     ( (      -1 ) ( d11/d21 ) )
+*
+*                 = 1/d21 * 1/(D22*D11-1) * ( ( D11 ) (  -1 ) ) =
+*                                           ( ( -1  ) ( D22 ) )
+*
+*                 = 1/d21 * T * ( ( D11 ) (  -1 ) )
+*                               ( (  -1 ) ( D22 ) )
+*
+*                 = D21 * ( ( D11 ) (  -1 ) )
+*                         ( (  -1 ) ( D22 ) )
 *
                   D21 = W( K-1, KW )
                   D11 = W( K, KW ) / D21
                   D22 = W( K-1, KW-1 ) / D21
                   T = CONE / ( D11*D22-CONE )
+*
+*                 Update elements in columns A(k-1) and A(k) as
+*                 dot products of rows of ( W(kw-1) W(kw) ) and columns
+*                 of D**(-1)
+*
                   D21 = T / D21
                   DO 20 J = 1, K - 2
                      A( J, K-1 ) = D21*( D11*W( J, KW-1 )-W( J, KW ) )
@@ -379,7 +458,9 @@
                A( K-1, K-1 ) = W( K-1, KW-1 )
                A( K-1, K ) = W( K-1, KW )
                A( K, K ) = W( K, KW )
+*
             END IF
+*
          END IF
 *
 *        Store details of the interchanges in IPIV
@@ -423,20 +504,28 @@
    50    CONTINUE
 *
 *        Put U12 in standard form by partially undoing the interchanges
-*        in columns k+1:n
+*        in columns k+1:n looping backwards from k+1 to n
 *
          J = K + 1
    60    CONTINUE
-         JJ = J
-         JP = IPIV( J )
-         IF( JP.LT.0 ) THEN
-            JP = -JP
+*
+*           Undo the interchanges (if any) of rows JJ and JP at each
+*           step J
+*
+*           (Here, J is a diagonal index)
+            JJ = J
+            JP = IPIV( J )
+            IF( JP.LT.0 ) THEN
+               JP = -JP
+*              (Here, J is a diagonal index)
+               J = J + 1
+            END IF
+*           (NOTE: Here, J is used to determine row length. Length N-J+1
+*           of the rows to swap back doesn't include diagonal element)
             J = J + 1
-         END IF
-         J = J + 1
-         IF( JP.NE.JJ .AND. J.LE.N )
-     $      CALL CSWAP( N-J+1, A( JP, J ), LDA, A( JJ, J ), LDA )
-         IF( J.LE.N )
+            IF( JP.NE.JJ .AND. J.LE.N )
+     $         CALL CSWAP( N-J+1, A( JP, J ), LDA, A( JJ, J ), LDA )
+         IF( J.LT.N )
      $      GO TO 60
 *
 *        Set KB to the number of columns factorized
@@ -473,7 +562,8 @@
          ABSAKK = CABS1( W( K, K ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.LT.N ) THEN
             IMAX = K + ICAMAX( N-K, W( K+1, K ), 1 )
@@ -484,7 +574,7 @@
 *
          IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
 *
-*           Column K is zero: set INFO and continue
+*           Column K is zero or underflow: set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
@@ -528,7 +618,7 @@
 *
                   KP = IMAX
 *
-*                 copy column K+1 of W to column K
+*                 copy column K+1 of W to column K of W
 *
                   CALL CCOPY( N-K+1, W( K, K+1 ), 1, W( K, K ), 1 )
                ELSE
@@ -540,22 +630,36 @@
                   KSTEP = 2
                END IF
             END IF
+*
+*           ============================================================
+*
+*           KK is the column of A where pivoting step stopped
 *
             KK = K + KSTEP - 1
 *
-*           Updated column KP is already stored in column KK of W
+*           Interchange rows and columns KP and KK.
+*           Updated column KP is already stored in column KK of W.
 *
             IF( KP.NE.KK ) THEN
 *
-*              Copy non-updated column KK to column KP
+*              Copy non-updated column KK to column KP of submatrix A
+*              at step K. No need to copy element into column K
+*              (or K and K+1 for 2-by-2 pivot) of A, since these columns
+*              will be later overwritten.
 *
-               A( KP, K ) = A( KK, K )
-               CALL CCOPY( KP-K-1, A( K+1, KK ), 1, A( KP, K+1 ), LDA )
-               CALL CCOPY( N-KP+1, A( KP, KK ), 1, A( KP, KP ), 1 )
+               A( KP, KP ) = A( KK, KK )
+               CALL CCOPY( KP-KK-1, A( KK+1, KK ), 1, A( KP, KK+1 ),
+     $                     LDA )
+               IF( KP.LT.N )
+     $            CALL CCOPY( N-KP, A( KP+1, KK ), 1, A( KP+1, KP ), 1 )
 *
-*              Interchange rows KK and KP in first KK columns of A and W
+*              Interchange rows KK and KP in first K-1 columns of A
+*              (columns K (or K and K+1 for 2-by-2 pivot) of A will be
+*              later overwritten). Interchange rows KK and KP
+*              in first KK columns of W.
 *
-               CALL CSWAP( KK, A( KK, 1 ), LDA, A( KP, 1 ), LDA )
+               IF( K.GT.1 )
+     $            CALL CSWAP( K-1, A( KK, 1 ), LDA, A( KP, 1 ), LDA )
                CALL CSWAP( KK, W( KK, 1 ), LDW, W( KP, 1 ), LDW )
             END IF
 *
@@ -563,17 +667,23 @@
 *
 *              1-by-1 pivot block D(k): column k of W now holds
 *
-*              W(k) = L(k)*D(k)
+*              W(k) = L(k)*D(k),
 *
 *              where L(k) is the k-th column of L
 *
-*              Store L(k) in column k of A
+*              Store subdiag. elements of column L(k)
+*              and 1-by-1 block D(k) in column k of A.
+*              (NOTE: Diagonal element L(k,k) is a UNIT element
+*              and not stored)
+*                 A(k,k) := D(k,k) = W(k,k)
+*                 A(k+1:N,k) := L(k+1:N,k) = W(k+1:N,k)/D(k,k)
 *
                CALL CCOPY( N-K+1, W( K, K ), 1, A( K, K ), 1 )
                IF( K.LT.N ) THEN
                   R1 = CONE / A( K, K )
                   CALL CSCAL( N-K, R1, A( K+1, K ), 1 )
                END IF
+*
             ELSE
 *
 *              2-by-2 pivot block D(k): columns k and k+1 of W now hold
@@ -582,16 +692,52 @@
 *
 *              where L(k) and L(k+1) are the k-th and (k+1)-th columns
 *              of L
+*
+*              Store L(k+2:N,k) and L(k+2:N,k+1) and 2-by-2
+*              block D(k:k+1,k:k+1) in columns k and k+1 of A.
+*              (NOTE: 2-by-2 diagonal block L(k:k+1,k:k+1) is a UNIT
+*              block and not stored)
+*                 A(k:k+1,k:k+1) := D(k:k+1,k:k+1) = W(k:k+1,k:k+1)
+*                 A(k+2:N,k:k+1) := L(k+2:N,k:k+1) =
+*                 = W(k+2:N,k:k+1) * ( D(k:k+1,k:k+1)**(-1) )
 *
                IF( K.LT.N-1 ) THEN
 *
-*                 Store L(k) and L(k+1) in columns k and k+1 of A
+*                 Compose the columns of the inverse of 2-by-2 pivot
+*                 block D in the following way to reduce the number
+*                 of FLOPS when we myltiply panel ( W(k) W(k+1) ) by
+*                 this inverse
+*
+*                 D**(-1) = ( d11 d21 )**(-1) =
+*                           ( d21 d22 )
+*
+*                 = 1/(d11*d22-d21**2) * ( ( d22 ) (-d21 ) ) =
+*                                        ( (-d21 ) ( d11 ) )
+*
+*                 = 1/d21 * 1/((d11/d21)*(d22/d21)-1) *
+*
+*                   * ( ( d22/d21 ) (      -1 ) ) =
+*                     ( (      -1 ) ( d11/d21 ) )
+*
+*                 = 1/d21 * 1/(D22*D11-1) * ( ( D11 ) (  -1 ) ) =
+*                                           ( ( -1  ) ( D22 ) )
+*
+*                 = 1/d21 * T * ( ( D11 ) (  -1 ) )
+*                               ( (  -1 ) ( D22 ) )
+*
+*                 = D21 * ( ( D11 ) (  -1 ) )
+*                         ( (  -1 ) ( D22 ) )
 *
                   D21 = W( K+1, K )
                   D11 = W( K+1, K+1 ) / D21
                   D22 = W( K, K ) / D21
                   T = CONE / ( D11*D22-CONE )
                   D21 = T / D21
+*
+*                 Update elements in columns A(k) and A(k+1) as
+*                 dot products of rows of ( W(k) W(k+1) ) and columns
+*                 of D**(-1)
+*
                   DO 80 J = K + 2, N
                      A( J, K ) = D21*( D11*W( J, K )-W( J, K+1 ) )
                      A( J, K+1 ) = D21*( D22*W( J, K+1 )-W( J, K ) )
@@ -603,7 +749,9 @@
                A( K, K ) = W( K, K )
                A( K+1, K ) = W( K+1, K )
                A( K+1, K+1 ) = W( K+1, K+1 )
+*
             END IF
+*
          END IF
 *
 *        Store details of the interchanges in IPIV
@@ -648,20 +796,28 @@
   110    CONTINUE
 *
 *        Put L21 in standard form by partially undoing the interchanges
-*        in columns 1:k-1
+*        of rows in columns 1:k-1 looping backwards from k-1 to 1
 *
          J = K - 1
   120    CONTINUE
-         JJ = J
-         JP = IPIV( J )
-         IF( JP.LT.0 ) THEN
-            JP = -JP
+*
+*           Undo the interchanges (if any) of rows JJ and JP at each
+*           step J
+*
+*           (Here, J is a diagonal index)
+            JJ = J
+            JP = IPIV( J )
+            IF( JP.LT.0 ) THEN
+               JP = -JP
+*              (Here, J is a diagonal index)
+               J = J - 1
+            END IF
+*           (NOTE: Here, J is used to determine row length. Length J
+*           of the rows to swap back doesn't include diagonal element)
             J = J - 1
-         END IF
-         J = J - 1
-         IF( JP.NE.JJ .AND. J.GE.1 )
-     $      CALL CSWAP( J, A( JP, 1 ), LDA, A( JJ, 1 ), LDA )
-         IF( J.GE.1 )
+            IF( JP.NE.JJ .AND. J.GE.1 )
+     $         CALL CSWAP( J, A( JP, 1 ), LDA, A( JJ, 1 ), LDA )
+         IF( J.GT.1 )
      $      GO TO 120
 *
 *        Set KB to the number of columns factorized

lapack-netlib/SRC/clasyf_rook.f

@@ -0,0 +1,900 @@
+*> \brief \b CLASYF_ROOK computes a partial factorization of a complex symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download CLASYF_ROOK + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clasyf_rook.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clasyf_rook.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clasyf_rook.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CLASYF_ROOK( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
+*
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, KB, LDA, LDW, N, NB
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       COMPLEX            A( LDA, * ), W( LDW, * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> CLASYF_ROOK computes a partial factorization of a complex symmetric
+*> matrix A using the bounded Bunch-Kaufman ("rook") diagonal
+*> pivoting method. The partial factorization has the form:
+*>
+*> A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
+*>       ( 0  U22 ) (  0   D  ) ( U12**T U22**T )
+*>
+*> A  =  ( L11  0 ) (  D   0  ) ( L11**T L21**T )  if UPLO = 'L'
+*>       ( L21  I ) (  0  A22 ) (  0       I    )
+*>
+*> where the order of D is at most NB. The actual order is returned in
+*> the argument KB, and is either NB or NB-1, or N if N <= NB.
+*>
+*> CLASYF_ROOK is an auxiliary routine called by CSYTRF_ROOK. It uses
+*> blocked code (calling Level 3 BLAS) to update the submatrix
+*> A11 (if UPLO = 'U') or A22 (if UPLO = 'L').
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          Specifies whether the upper or lower triangular part of the
+*>          symmetric matrix A is stored:
+*>          = 'U':  Upper triangular
+*>          = 'L':  Lower triangular
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NB
+*> \verbatim
+*>          NB is INTEGER
+*>          The maximum number of columns of the matrix A that should be
+*>          factored.  NB should be at least 2 to allow for 2-by-2 pivot
+*>          blocks.
+*> \endverbatim
+*>
+*> \param[out] KB
+*> \verbatim
+*>          KB is INTEGER
+*>          The number of columns of A that were actually factored.
+*>          KB is either NB-1 or NB, or N if N <= NB.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is COMPLEX array, dimension (LDA,N)
+*>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
+*>          n-by-n upper triangular part of A contains the upper
+*>          triangular part of the matrix A, and the strictly lower
+*>          triangular part of A is not referenced.  If UPLO = 'L', the
+*>          leading n-by-n lower triangular part of A contains the lower
+*>          triangular part of the matrix A, and the strictly upper
+*>          triangular part of A is not referenced.
+*>          On exit, A contains details of the partial factorization.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          Details of the interchanges and the block structure of D.
+*>
+*>          If UPLO = 'U':
+*>             Only the last KB elements of IPIV are set.
+*>
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
+*>             columns k and -IPIV(k) were interchanged and rows and
+*>             columns k-1 and -IPIV(k-1) were inerchaged,
+*>             D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>             Only the first KB elements of IPIV are set.
+*>
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k)
+*>             were interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
+*>             columns k and -IPIV(k) were interchanged and rows and
+*>             columns k+1 and -IPIV(k+1) were inerchaged,
+*>             D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*> \endverbatim
+*>
+*> \param[out] W
+*> \verbatim
+*>          W is COMPLEX array, dimension (LDW,NB)
+*> \endverbatim
+*>
+*> \param[in] LDW
+*> \verbatim
+*>          LDW is INTEGER
+*>          The leading dimension of the array W.  LDW >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0: successful exit
+*>          > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
+*>               has been completed, but the block diagonal matrix D is
+*>               exactly singular.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2013
+*
+*> \ingroup complexSYcomputational
+*
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>  November 2013,     Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*>
+*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*>                  School of Mathematics,
+*>                  University of Manchester
+*>
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE CLASYF_ROOK( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW,
+     $                        INFO )
+*
+*  -- LAPACK computational routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2013
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, KB, LDA, LDW, N, NB
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      COMPLEX            A( LDA, * ), W( LDW, * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      REAL               ZERO, ONE
+      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
+      REAL               EIGHT, SEVTEN
+      PARAMETER          ( EIGHT = 8.0E+0, SEVTEN = 17.0E+0 )
+      COMPLEX            CONE, CZERO
+      PARAMETER          ( CONE = ( 1.0E+0, 0.0E+0 ),
+     $                   CZERO = ( 0.0E+0, 0.0E+0 ) )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            DONE
+      INTEGER            IMAX, ITEMP, J, JB, JJ, JMAX, JP1, JP2, K, KK,
+     $                   KW, KKW, KP, KSTEP, P, II
+      REAL               ABSAKK, ALPHA, COLMAX, ROWMAX, STEMP, SFMIN
+      COMPLEX            D11, D12, D21, D22, R1, T, Z
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      INTEGER            ICAMAX
+      REAL               SLAMCH
+      EXTERNAL           LSAME, ICAMAX, SLAMCH
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           CCOPY, CGEMM, CGEMV, CSCAL, CSWAP
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, MAX, MIN, SQRT, AIMAG, REAL
+*     ..
+*     .. Statement Functions ..
+      REAL               CABS1
+*     ..
+*     .. Statement Function definitions ..
+      CABS1( Z ) = ABS( REAL( Z ) ) + ABS( AIMAG( Z ) )
+*     ..
+*     .. Executable Statements ..
+*
+      INFO = 0
+*
+*     Initialize ALPHA for use in choosing pivot block size.
+*
+      ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT
+*
+*     Compute machine safe minimum
+*
+      SFMIN = SLAMCH( 'S' )
+*
+      IF( LSAME( UPLO, 'U' ) ) THEN
+*
+*        Factorize the trailing columns of A using the upper triangle
+*        of A and working backwards, and compute the matrix W = U12*D
+*        for use in updating A11
+*
+*        K is the main loop index, decreasing from N in steps of 1 or 2
+*
+         K = N
+   10    CONTINUE
+*
+*        KW is the column of W which corresponds to column K of A
+*
+         KW = NB + K - N
+*
+*        Exit from loop
+*
+         IF( ( K.LE.N-NB+1 .AND. NB.LT.N ) .OR. K.LT.1 )
+     $      GO TO 30
+*
+         KSTEP = 1
+         P = K
+*
+*        Copy column K of A to column KW of W and update it
+*
+         CALL CCOPY( K, A( 1, K ), 1, W( 1, KW ), 1 )
+         IF( K.LT.N )
+     $      CALL CGEMV( 'No transpose', K, N-K, -CONE, A( 1, K+1 ),
+     $                  LDA, W( K, KW+1 ), LDW, CONE, W( 1, KW ), 1 )
+*
+*        Determine rows and columns to be interchanged and whether
+*        a 1-by-1 or 2-by-2 pivot block will be used
+*
+         ABSAKK = CABS1( W( K, KW ) )
+*
+*        IMAX is the row-index of the largest off-diagonal element in
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
+*
+         IF( K.GT.1 ) THEN
+            IMAX = ICAMAX( K-1, W( 1, KW ), 1 )
+            COLMAX = CABS1( W( IMAX, KW ) )
+         ELSE
+            COLMAX = ZERO
+         END IF
+*
+         IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
+*
+*           Column K is zero or underflow: set INFO and continue
+*
+            IF( INFO.EQ.0 )
+     $         INFO = K
+            KP = K
+            CALL CCOPY( K, W( 1, KW ), 1, A( 1, K ), 1 )
+         ELSE
+*
+*           ============================================================
+*
+*           Test for interchange
+*
+*           Equivalent to testing for ABSAKK.GE.ALPHA*COLMAX
+*           (used to handle NaN and Inf)
+*
+            IF( .NOT.( ABSAKK.LT.ALPHA*COLMAX ) ) THEN
+*
+*              no interchange, use 1-by-1 pivot block
+*
+               KP = K
+*
+            ELSE
+*
+               DONE = .FALSE.
+*
+*              Loop until pivot found
+*
+   12          CONTINUE
+*
+*                 Begin pivot search loop body
+*
+*
+*                 Copy column IMAX to column KW-1 of W and update it
+*
+                  CALL CCOPY( IMAX, A( 1, IMAX ), 1, W( 1, KW-1 ), 1 )
+                  CALL CCOPY( K-IMAX, A( IMAX, IMAX+1 ), LDA,
+     $                        W( IMAX+1, KW-1 ), 1 )
+*
+                  IF( K.LT.N )
+     $               CALL CGEMV( 'No transpose', K, N-K, -CONE,
+     $                           A( 1, K+1 ), LDA, W( IMAX, KW+1 ), LDW,
+     $                           CONE, W( 1, KW-1 ), 1 )
+*
+*                 JMAX is the column-index of the largest off-diagonal
+*                 element in row IMAX, and ROWMAX is its absolute value.
+*                 Determine both ROWMAX and JMAX.
+*
+                  IF( IMAX.NE.K ) THEN
+                     JMAX = IMAX + ICAMAX( K-IMAX, W( IMAX+1, KW-1 ),
+     $                                     1 )
+                     ROWMAX = CABS1( W( JMAX, KW-1 ) )
+                  ELSE
+                     ROWMAX = ZERO
+                  END IF
+*
+                  IF( IMAX.GT.1 ) THEN
+                     ITEMP = ICAMAX( IMAX-1, W( 1, KW-1 ), 1 )
+                     STEMP = CABS1( W( ITEMP, KW-1 ) )
+                     IF( STEMP.GT.ROWMAX ) THEN
+                        ROWMAX = STEMP
+                        JMAX = ITEMP
+                     END IF
+                  END IF
+*
+*                 Equivalent to testing for
+*                 CABS1( W( IMAX, KW-1 ) ).GE.ALPHA*ROWMAX
+*                 (used to handle NaN and Inf)
+*
+                  IF( .NOT.(CABS1( W( IMAX, KW-1 ) ).LT.ALPHA*ROWMAX ) )
+     $            THEN
+*
+*                    interchange rows and columns K and IMAX,
+*                    use 1-by-1 pivot block
+*
+                     KP = IMAX
+*
+*                    copy column KW-1 of W to column KW of W
+*
+                     CALL CCOPY( K, W( 1, KW-1 ), 1, W( 1, KW ), 1 )
+*
+                     DONE = .TRUE.
+*
+*                 Equivalent to testing for ROWMAX.EQ.COLMAX,
+*                 (used to handle NaN and Inf)
+*
+                  ELSE IF( ( P.EQ.JMAX ) .OR. ( ROWMAX.LE.COLMAX ) )
+     $            THEN
+*
+*                    interchange rows and columns K-1 and IMAX,
+*                    use 2-by-2 pivot block
+*
+                     KP = IMAX
+                     KSTEP = 2
+                     DONE = .TRUE.
+                  ELSE
+*
+*                    Pivot not found: set params and repeat
+*
+                     P = IMAX
+                     COLMAX = ROWMAX
+                     IMAX = JMAX
+*
+*                    Copy updated JMAXth (next IMAXth) column to Kth of W
+*
+                     CALL CCOPY( K, W( 1, KW-1 ), 1, W( 1, KW ), 1 )
+*
+                  END IF
+*
+*                 End pivot search loop body
+*
+               IF( .NOT. DONE ) GOTO 12
+*
+            END IF
+*
+*           ============================================================
+*
+            KK = K - KSTEP + 1
+*
+*           KKW is the column of W which corresponds to column KK of A
+*
+            KKW = NB + KK - N
+*
+            IF( ( KSTEP.EQ.2 ) .AND. ( P.NE.K ) ) THEN
+*
+*              Copy non-updated column K to column P
+*
+               CALL CCOPY( K-P, A( P+1, K ), 1, A( P, P+1 ), LDA )
+               CALL CCOPY( P, A( 1, K ), 1, A( 1, P ), 1 )
+*
+*              Interchange rows K and P in last N-K+1 columns of A
+*              and last N-K+2 columns of W
+*
+               CALL CSWAP( N-K+1, A( K, K ), LDA, A( P, K ), LDA )
+               CALL CSWAP( N-KK+1, W( K, KKW ), LDW, W( P, KKW ), LDW )
+            END IF
+*
+*           Updated column KP is already stored in column KKW of W
+*
+            IF( KP.NE.KK ) THEN
+*
+*              Copy non-updated column KK to column KP
+*
+               A( KP, K ) = A( KK, K )
+               CALL CCOPY( K-1-KP, A( KP+1, KK ), 1, A( KP, KP+1 ),
+     $                     LDA )
+               CALL CCOPY( KP, A( 1, KK ), 1, A( 1, KP ), 1 )
+*
+*              Interchange rows KK and KP in last N-KK+1 columns
+*              of A and W
+*
+               CALL CSWAP( N-KK+1, A( KK, KK ), LDA, A( KP, KK ), LDA )
+               CALL CSWAP( N-KK+1, W( KK, KKW ), LDW, W( KP, KKW ),
+     $                     LDW )
+            END IF
+*
+            IF( KSTEP.EQ.1 ) THEN
+*
+*              1-by-1 pivot block D(k): column KW of W now holds
+*
+*              W(k) = U(k)*D(k)
+*
+*              where U(k) is the k-th column of U
+*
+*              Store U(k) in column k of A
+*
+               CALL CCOPY( K, W( 1, KW ), 1, A( 1, K ), 1 )
+               IF( K.GT.1 ) THEN
+                  IF( CABS1( A( K, K ) ).GE.SFMIN ) THEN
+                     R1 = CONE / A( K, K )
+                     CALL CSCAL( K-1, R1, A( 1, K ), 1 )
+                  ELSE IF( A( K, K ).NE.CZERO ) THEN
+                     DO 14 II = 1, K - 1
+                        A( II, K ) = A( II, K ) / A( K, K )
+   14                CONTINUE
+                  END IF
+               END IF
+*
+            ELSE
+*
+*              2-by-2 pivot block D(k): columns KW and KW-1 of W now
+*              hold
+*
+*              ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
+*
+*              where U(k) and U(k-1) are the k-th and (k-1)-th columns
+*              of U
+*
+               IF( K.GT.2 ) THEN
+*
+*                 Store U(k) and U(k-1) in columns k and k-1 of A
+*
+                  D12 = W( K-1, KW )
+                  D11 = W( K, KW ) / D12
+                  D22 = W( K-1, KW-1 ) / D12
+                  T = CONE / ( D11*D22-CONE )
+                  DO 20 J = 1, K - 2
+                     A( J, K-1 ) = T*( (D11*W( J, KW-1 )-W( J, KW ) ) /
+     $                             D12 )
+                     A( J, K ) = T*( ( D22*W( J, KW )-W( J, KW-1 ) ) /
+     $                           D12 )
+   20             CONTINUE
+               END IF
+*
+*              Copy D(k) to A
+*
+               A( K-1, K-1 ) = W( K-1, KW-1 )
+               A( K-1, K ) = W( K-1, KW )
+               A( K, K ) = W( K, KW )
+            END IF
+         END IF
+*
+*        Store details of the interchanges in IPIV
+*
+         IF( KSTEP.EQ.1 ) THEN
+            IPIV( K ) = KP
+         ELSE
+            IPIV( K ) = -P
+            IPIV( K-1 ) = -KP
+         END IF
+*
+*        Decrease K and return to the start of the main loop
+*
+         K = K - KSTEP
+         GO TO 10
+*
+   30    CONTINUE
+*
+*        Update the upper triangle of A11 (= A(1:k,1:k)) as
+*
+*        A11 := A11 - U12*D*U12**T = A11 - U12*W**T
+*
+*        computing blocks of NB columns at a time
+*
+         DO 50 J = ( ( K-1 ) / NB )*NB + 1, 1, -NB
+            JB = MIN( NB, K-J+1 )
+*
+*           Update the upper triangle of the diagonal block
+*
+            DO 40 JJ = J, J + JB - 1
+               CALL CGEMV( 'No transpose', JJ-J+1, N-K, -CONE,
+     $                     A( J, K+1 ), LDA, W( JJ, KW+1 ), LDW, CONE,
+     $                     A( J, JJ ), 1 )
+   40       CONTINUE
+*
+*           Update the rectangular superdiagonal block
+*
+            IF( J.GE.2 )
+     $         CALL CGEMM( 'No transpose', 'Transpose', J-1, JB,
+     $                  N-K, -CONE, A( 1, K+1 ), LDA, W( J, KW+1 ), LDW,
+     $                  CONE, A( 1, J ), LDA )
+   50    CONTINUE
+*
+*        Put U12 in standard form by partially undoing the interchanges
+*        in columns k+1:n
+*
+         J = K + 1
+   60    CONTINUE
+*
+            KSTEP = 1
+            JP1 = 1
+            JJ = J
+            JP2 = IPIV( J )
+            IF( JP2.LT.0 ) THEN
+               JP2 = -JP2
+               J = J + 1
+               JP1 = -IPIV( J )
+               KSTEP = 2
+            END IF
+*
+            J = J + 1
+            IF( JP2.NE.JJ .AND. J.LE.N )
+     $         CALL CSWAP( N-J+1, A( JP2, J ), LDA, A( JJ, J ), LDA )
+            JJ = J - 1
+            IF( JP1.NE.JJ .AND. KSTEP.EQ.2 )
+     $         CALL CSWAP( N-J+1, A( JP1, J ), LDA, A( JJ, J ), LDA )
+         IF( J.LE.N )
+     $      GO TO 60
+*
+*        Set KB to the number of columns factorized
+*
+         KB = N - K
+*
+      ELSE
+*
+*        Factorize the leading columns of A using the lower triangle
+*        of A and working forwards, and compute the matrix W = L21*D
+*        for use in updating A22
+*
+*        K is the main loop index, increasing from 1 in steps of 1 or 2
+*
+         K = 1
+   70   CONTINUE
+*
+*        Exit from loop
+*
+         IF( ( K.GE.NB .AND. NB.LT.N ) .OR. K.GT.N )
+     $      GO TO 90
+*
+         KSTEP = 1
+         P = K
+*
+*        Copy column K of A to column K of W and update it
+*
+         CALL CCOPY( N-K+1, A( K, K ), 1, W( K, K ), 1 )
+         IF( K.GT.1 )
+     $      CALL CGEMV( 'No transpose', N-K+1, K-1, -CONE, A( K, 1 ),
+     $                  LDA, W( K, 1 ), LDW, CONE, W( K, K ), 1 )
+*
+*        Determine rows and columns to be interchanged and whether
+*        a 1-by-1 or 2-by-2 pivot block will be used
+*
+         ABSAKK = CABS1( W( K, K ) )
+*
+*        IMAX is the row-index of the largest off-diagonal element in
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
+*
+         IF( K.LT.N ) THEN
+            IMAX = K + ICAMAX( N-K, W( K+1, K ), 1 )
+            COLMAX = CABS1( W( IMAX, K ) )
+         ELSE
+            COLMAX = ZERO
+         END IF
+*
+         IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
+*
+*           Column K is zero or underflow: set INFO and continue
+*
+            IF( INFO.EQ.0 )
+     $         INFO = K
+            KP = K
+            CALL CCOPY( N-K+1, W( K, K ), 1, A( K, K ), 1 )
+         ELSE
+*
+*           ============================================================
+*
+*           Test for interchange
+*
+*           Equivalent to testing for ABSAKK.GE.ALPHA*COLMAX
+*           (used to handle NaN and Inf)
+*
+            IF( .NOT.( ABSAKK.LT.ALPHA*COLMAX ) ) THEN
+*
+*              no interchange, use 1-by-1 pivot block
+*
+               KP = K
+*
+            ELSE
+*
+               DONE = .FALSE.
+*
+*              Loop until pivot found
+*
+   72          CONTINUE
+*
+*                 Begin pivot search loop body
+*
+*
+*                 Copy column IMAX to column K+1 of W and update it
+*
+                  CALL CCOPY( IMAX-K, A( IMAX, K ), LDA, W( K, K+1 ), 1)
+                  CALL CCOPY( N-IMAX+1, A( IMAX, IMAX ), 1,
+     $                        W( IMAX, K+1 ), 1 )
+                  IF( K.GT.1 )
+     $               CALL CGEMV( 'No transpose', N-K+1, K-1, -CONE,
+     $                           A( K, 1 ), LDA, W( IMAX, 1 ), LDW,
+     $                           CONE, W( K, K+1 ), 1 )
+*
+*                 JMAX is the column-index of the largest off-diagonal
+*                 element in row IMAX, and ROWMAX is its absolute value.
+*                 Determine both ROWMAX and JMAX.
+*
+                  IF( IMAX.NE.K ) THEN
+                     JMAX = K - 1 + ICAMAX( IMAX-K, W( K, K+1 ), 1 )
+                     ROWMAX = CABS1( W( JMAX, K+1 ) )
+                  ELSE
+                     ROWMAX = ZERO
+                  END IF
+*
+                  IF( IMAX.LT.N ) THEN
+                     ITEMP = IMAX + ICAMAX( N-IMAX, W( IMAX+1, K+1 ), 1)
+                     STEMP = CABS1( W( ITEMP, K+1 ) )
+                     IF( STEMP.GT.ROWMAX ) THEN
+                        ROWMAX = STEMP
+                        JMAX = ITEMP
+                     END IF
+                  END IF
+*
+*                 Equivalent to testing for
+*                 CABS1( W( IMAX, K+1 ) ).GE.ALPHA*ROWMAX
+*                 (used to handle NaN and Inf)
+*
+                  IF( .NOT.( CABS1( W( IMAX, K+1 ) ).LT.ALPHA*ROWMAX ) )
+     $            THEN
+*
+*                    interchange rows and columns K and IMAX,
+*                    use 1-by-1 pivot block
+*
+                     KP = IMAX
+*
+*                    copy column K+1 of W to column K of W
+*
+                     CALL CCOPY( N-K+1, W( K, K+1 ), 1, W( K, K ), 1 )
+*
+                     DONE = .TRUE.
+*
+*                 Equivalent to testing for ROWMAX.EQ.COLMAX,
+*                 (used to handle NaN and Inf)
+*
+                  ELSE IF( ( P.EQ.JMAX ) .OR. ( ROWMAX.LE.COLMAX ) )
+     $            THEN
+*
+*                    interchange rows and columns K+1 and IMAX,
+*                    use 2-by-2 pivot block
+*
+                     KP = IMAX
+                     KSTEP = 2
+                     DONE = .TRUE.
+                  ELSE
+*
+*                    Pivot not found: set params and repeat
+*
+                     P = IMAX
+                     COLMAX = ROWMAX
+                     IMAX = JMAX
+*
+*                    Copy updated JMAXth (next IMAXth) column to Kth of W
+*
+                     CALL CCOPY( N-K+1, W( K, K+1 ), 1, W( K, K ), 1 )
+*
+                  END IF
+*
+*                 End pivot search loop body
+*
+               IF( .NOT. DONE ) GOTO 72
+*
+            END IF
+*
+*           ============================================================
+*
+            KK = K + KSTEP - 1
+*
+            IF( ( KSTEP.EQ.2 ) .AND. ( P.NE.K ) ) THEN
+*
+*              Copy non-updated column K to column P
+*
+               CALL CCOPY( P-K, A( K, K ), 1, A( P, K ), LDA )
+               CALL CCOPY( N-P+1, A( P, K ), 1, A( P, P ), 1 )
+*
+*              Interchange rows K and P in first K columns of A
+*              and first K+1 columns of W
+*
+               CALL CSWAP( K, A( K, 1 ), LDA, A( P, 1 ), LDA )
+               CALL CSWAP( KK, W( K, 1 ), LDW, W( P, 1 ), LDW )
+            END IF
+*
+*           Updated column KP is already stored in column KK of W
+*
+            IF( KP.NE.KK ) THEN
+*
+*              Copy non-updated column KK to column KP
+*
+               A( KP, K ) = A( KK, K )
+               CALL CCOPY( KP-K-1, A( K+1, KK ), 1, A( KP, K+1 ), LDA )
+               CALL CCOPY( N-KP+1, A( KP, KK ), 1, A( KP, KP ), 1 )
+*
+*              Interchange rows KK and KP in first KK columns of A and W
+*
+               CALL CSWAP( KK, A( KK, 1 ), LDA, A( KP, 1 ), LDA )
+               CALL CSWAP( KK, W( KK, 1 ), LDW, W( KP, 1 ), LDW )
+            END IF
+*
+            IF( KSTEP.EQ.1 ) THEN
+*
+*              1-by-1 pivot block D(k): column k of W now holds
+*
+*              W(k) = L(k)*D(k)
+*
+*              where L(k) is the k-th column of L
+*
+*              Store L(k) in column k of A
+*
+               CALL CCOPY( N-K+1, W( K, K ), 1, A( K, K ), 1 )
+               IF( K.LT.N ) THEN
+                  IF( CABS1( A( K, K ) ).GE.SFMIN ) THEN
+                     R1 = CONE / A( K, K )
+                     CALL CSCAL( N-K, R1, A( K+1, K ), 1 )
+                  ELSE IF( A( K, K ).NE.CZERO ) THEN
+                     DO 74 II = K + 1, N
+                        A( II, K ) = A( II, K ) / A( K, K )
+   74                CONTINUE
+                  END IF
+               END IF
+*
+            ELSE
+*
+*              2-by-2 pivot block D(k): columns k and k+1 of W now hold
+*
+*              ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k)
+*
+*              where L(k) and L(k+1) are the k-th and (k+1)-th columns
+*              of L
+*
+               IF( K.LT.N-1 ) THEN
+*
+*                 Store L(k) and L(k+1) in columns k and k+1 of A
+*
+                  D21 = W( K+1, K )
+                  D11 = W( K+1, K+1 ) / D21
+                  D22 = W( K, K ) / D21
+                  T = CONE / ( D11*D22-CONE )
+                  DO 80 J = K + 2, N
+                     A( J, K ) = T*( ( D11*W( J, K )-W( J, K+1 ) ) /
+     $                           D21 )
+                     A( J, K+1 ) = T*( ( D22*W( J, K+1 )-W( J, K ) ) /
+     $                             D21 )
+   80             CONTINUE
+               END IF
+*
+*              Copy D(k) to A
+*
+               A( K, K ) = W( K, K )
+               A( K+1, K ) = W( K+1, K )
+               A( K+1, K+1 ) = W( K+1, K+1 )
+            END IF
+         END IF
+*
+*        Store details of the interchanges in IPIV
+*
+         IF( KSTEP.EQ.1 ) THEN
+            IPIV( K ) = KP
+         ELSE
+            IPIV( K ) = -P
+            IPIV( K+1 ) = -KP
+         END IF
+*
+*        Increase K and return to the start of the main loop
+*
+         K = K + KSTEP
+         GO TO 70
+*
+   90    CONTINUE
+*
+*        Update the lower triangle of A22 (= A(k:n,k:n)) as
+*
+*        A22 := A22 - L21*D*L21**T = A22 - L21*W**T
+*
+*        computing blocks of NB columns at a time
+*
+         DO 110 J = K, N, NB
+            JB = MIN( NB, N-J+1 )
+*
+*           Update the lower triangle of the diagonal block
+*
+            DO 100 JJ = J, J + JB - 1
+               CALL CGEMV( 'No transpose', J+JB-JJ, K-1, -CONE,
+     $                     A( JJ, 1 ), LDA, W( JJ, 1 ), LDW, CONE,
+     $                     A( JJ, JJ ), 1 )
+  100       CONTINUE
+*
+*           Update the rectangular subdiagonal block
+*
+            IF( J+JB.LE.N )
+     $         CALL CGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB,
+     $                    K-1, -CONE, A( J+JB, 1 ), LDA, W( J, 1 ), LDW,
+     $                    CONE, A( J+JB, J ), LDA )
+  110    CONTINUE
+*
+*        Put L21 in standard form by partially undoing the interchanges
+*        in columns 1:k-1
+*
+         J = K - 1
+  120    CONTINUE
+*
+            KSTEP = 1
+            JP1 = 1
+            JJ = J
+            JP2 = IPIV( J )
+            IF( JP2.LT.0 ) THEN
+               JP2 = -JP2
+               J = J - 1
+               JP1 = -IPIV( J )
+               KSTEP = 2
+            END IF
+*
+            J = J - 1
+            IF( JP2.NE.JJ .AND. J.GE.1 )
+     $         CALL CSWAP( J, A( JP2, 1 ), LDA, A( JJ, 1 ), LDA )
+            JJ = J + 1
+            IF( JP1.NE.JJ .AND. KSTEP.EQ.2 )
+     $         CALL CSWAP( J, A( JP1, 1 ), LDA, A( JJ, 1 ), LDA )
+         IF( J.GE.1 )
+     $      GO TO 120
+*
+*        Set KB to the number of columns factorized
+*
+         KB = K - 1
+*
+      END IF
+      RETURN
+*
+*     End of CLASYF_ROOK
+*
+      END

lapack-netlib/SRC/cstemr.f

@@ -311,7 +311,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date September 2012
+*> \date November 2013
 *
 *> \ingroup complexOTHERcomputational
 *
@@ -329,10 +329,10 @@
      $                   M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK,
      $                   IWORK, LIWORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.2) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     September 2012
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBZ, RANGE
@@ -408,6 +408,7 @@
       WU = ZERO
       IIL = 0
       IIU = 0
+      NSPLIT = 0
 
       IF( VALEIG ) THEN
 *        We do not reference VL, VU in the cases RANGE = 'I','A'

lapack-netlib/SRC/csycon_rook.f

@@ -0,0 +1,255 @@
+*> \brief \b CSYCON_ROOK
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download CSYCON_ROOK + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/csycon_rook.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/csycon_rook.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/csycon_rook.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CSYCON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND,
+*                               WORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, N
+*       REAL               ANORM, RCOND
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       COMPLEX            A( LDA, * ), WORK( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> CSYCON_ROOK estimates the reciprocal of the condition number (in the
+*> 1-norm) of a complex symmetric matrix A using the factorization
+*> A = U*D*U**T or A = L*D*L**T computed by CSYTRF_ROOK.
+*>
+*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
+*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          Specifies whether the details of the factorization are stored
+*>          as an upper or lower triangular matrix.
+*>          = 'U':  Upper triangular, form is A = U*D*U**T;
+*>          = 'L':  Lower triangular, form is A = L*D*L**T.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*>          A is COMPLEX array, dimension (LDA,N)
+*>          The block diagonal matrix D and the multipliers used to
+*>          obtain the factor U or L as computed by CSYTRF_ROOK.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          Details of the interchanges and the block structure of D
+*>          as determined by CSYTRF_ROOK.
+*> \endverbatim
+*>
+*> \param[in] ANORM
+*> \verbatim
+*>          ANORM is REAL
+*>          The 1-norm of the original matrix A.
+*> \endverbatim
+*>
+*> \param[out] RCOND
+*> \verbatim
+*>          RCOND is REAL
+*>          The reciprocal of the condition number of the matrix A,
+*>          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
+*>          estimate of the 1-norm of inv(A) computed in this routine.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX array, dimension (2*N)
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0:  successful exit
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date April 2012
+*
+*> \ingroup complexSYcomputational
+*
+*> \par Contributors:
+*  ==================
+*> \verbatim
+*>
+*>   April 2012, Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*>
+*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*>                  School of Mathematics,
+*>                  University of Manchester
+*>
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE CSYCON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
+     $                        INFO )
+*
+*  -- LAPACK computational routine (version 3.4.1) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     April 2012
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, N
+      REAL               ANORM, RCOND
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      COMPLEX            A( LDA, * ), WORK( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      REAL               ONE, ZERO
+      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
+      COMPLEX            CZERO
+      PARAMETER          ( CZERO = ( 0.0E+0, 0.0E+0 ) )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            UPPER
+      INTEGER            I, KASE
+      REAL               AINVNM
+*     ..
+*     .. Local Arrays ..
+      INTEGER            ISAVE( 3 )
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      EXTERNAL           LSAME
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           CLACN2, CSYTRS_ROOK, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      UPPER = LSAME( UPLO, 'U' )
+      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -4
+      ELSE IF( ANORM.LT.ZERO ) THEN
+         INFO = -6
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'CSYCON_ROOK', -INFO )
+         RETURN
+      END IF
+*
+*     Quick return if possible
+*
+      RCOND = ZERO
+      IF( N.EQ.0 ) THEN
+         RCOND = ONE
+         RETURN
+      ELSE IF( ANORM.LE.ZERO ) THEN
+         RETURN
+      END IF
+*
+*     Check that the diagonal matrix D is nonsingular.
+*
+      IF( UPPER ) THEN
+*
+*        Upper triangular storage: examine D from bottom to top
+*
+         DO 10 I = N, 1, -1
+            IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.CZERO )
+     $         RETURN
+   10    CONTINUE
+      ELSE
+*
+*        Lower triangular storage: examine D from top to bottom.
+*
+         DO 20 I = 1, N
+            IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.CZERO )
+     $         RETURN
+   20    CONTINUE
+      END IF
+*
+*     Estimate the 1-norm of the inverse.
+*
+      KASE = 0
+   30 CONTINUE
+      CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
+      IF( KASE.NE.0 ) THEN
+*
+*        Multiply by inv(L*D*L**T) or inv(U*D*U**T).
+*
+         CALL CSYTRS_ROOK( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
+         GO TO 30
+      END IF
+*
+*     Compute the estimate of the reciprocal condition number.
+*
+      IF( AINVNM.NE.ZERO )
+     $   RCOND = ( ONE / AINVNM ) / ANORM
+*
+      RETURN
+*
+*     End of CSYCON_ROOK
+*
+      END

lapack-netlib/SRC/csysv_rook.f

@@ -0,0 +1,293 @@
+*> \brief <b> CSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices</b>
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download CSYSV_ROOK + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/csysv_rook.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/csysv_rook.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/csysv_rook.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CSYSV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+*                         LWORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       COMPLEX            A( LDA, * ), B( LDB, * ), WORK( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> CSYSV_ROOK computes the solution to a complex system of linear
+*> equations
+*>    A * X = B,
+*> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
+*> matrices.
+*>
+*> The diagonal pivoting method is used to factor A as
+*>    A = U * D * U**T,  if UPLO = 'U', or
+*>    A = L * D * L**T,  if UPLO = 'L',
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, and D is symmetric and block diagonal with
+*> 1-by-1 and 2-by-2 diagonal blocks.  
+*>
+*> CSYTRF_ROOK is called to compute the factorization of a complex
+*> symmetric matrix A using the bounded Bunch-Kaufman ("rook") diagonal
+*> pivoting method.
+*>
+*> The factored form of A is then used to solve the system 
+*> of equations A * X = B by calling CSYTRS_ROOK.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          = 'U':  Upper triangle of A is stored;
+*>          = 'L':  Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The number of linear equations, i.e., the order of the
+*>          matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*>          NRHS is INTEGER
+*>          The number of right hand sides, i.e., the number of columns
+*>          of the matrix B.  NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is COMPLEX array, dimension (LDA,N)
+*>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
+*>          N-by-N upper triangular part of A contains the upper
+*>          triangular part of the matrix A, and the strictly lower
+*>          triangular part of A is not referenced.  If UPLO = 'L', the
+*>          leading N-by-N lower triangular part of A contains the lower
+*>          triangular part of the matrix A, and the strictly upper
+*>          triangular part of A is not referenced.
+*>
+*>          On exit, if INFO = 0, the block diagonal matrix D and the
+*>          multipliers used to obtain the factor U or L from the
+*>          factorization A = U*D*U**T or A = L*D*L**T as computed by
+*>          CSYTRF_ROOK.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          Details of the interchanges and the block structure of D,
+*>          as determined by CSYTRF_ROOK.
+*>
+*>          If UPLO = 'U':
+*>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
+*>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>               If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
+*>               columns k and -IPIV(k) were interchanged and rows and
+*>               columns k-1 and -IPIV(k-1) were inerchaged,
+*>               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
+*>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>               If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
+*>               columns k and -IPIV(k) were interchanged and rows and
+*>               columns k+1 and -IPIV(k+1) were inerchaged,
+*>               D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*>          B is COMPLEX array, dimension (LDB,NRHS)
+*>          On entry, the N-by-NRHS right hand side matrix B.
+*>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*>          LDB is INTEGER
+*>          The leading dimension of the array B.  LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
+*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>          The length of WORK.  LWORK >= 1, and for best performance
+*>          LWORK >= max(1,N*NB), where NB is the optimal blocksize for
+*>          CSYTRF_ROOK.
+*>          
+*>          TRS will be done with Level 2 BLAS
+*>
+*>          If LWORK = -1, then a workspace query is assumed; the routine
+*>          only calculates the optimal size of the WORK array, returns
+*>          this value as the first entry of the WORK array, and no error
+*>          message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0: successful exit
+*>          < 0: if INFO = -i, the i-th argument had an illegal value
+*>          > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
+*>               has been completed, but the block diagonal matrix D is
+*>               exactly singular, so the solution could not be computed.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date April 2012
+*
+*> \ingroup complexSYsolve
+*
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>   April 2012, Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*>
+*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*>                  School of Mathematics,
+*>                  University of Manchester
+*>
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE CSYSV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+     $                  LWORK, INFO )
+*
+*  -- LAPACK driver routine (version 3.4.1) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     April 2012
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      COMPLEX            A( LDA, * ), B( LDB, * ), WORK( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Local Scalars ..
+      LOGICAL            LQUERY
+      INTEGER            LWKOPT
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      EXTERNAL           LSAME
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           XERBLA, CSYTRF_ROOK, CSYTRS_ROOK
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      LQUERY = ( LWORK.EQ.-1 )
+      IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( NRHS.LT.0 ) THEN
+         INFO = -3
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -5
+      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+         INFO = -8
+      ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
+         INFO = -10
+      END IF
+*
+      IF( INFO.EQ.0 ) THEN
+         IF( N.EQ.0 ) THEN
+            LWKOPT = 1
+         ELSE
+            CALL CSYTRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, -1, INFO )
+            LWKOPT = WORK(1)
+         END IF
+         WORK( 1 ) = LWKOPT
+      END IF
+*
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'CSYSV_ROOK ', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+*
+*     Compute the factorization A = U*D*U**T or A = L*D*L**T.
+*
+      CALL CSYTRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+      IF( INFO.EQ.0 ) THEN
+*
+*        Solve the system A*X = B, overwriting B with X.
+*
+*        Solve with TRS_ROOK ( Use Level 2 BLAS)
+*
+         CALL CSYTRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
+*
+      END IF
+*
+      WORK( 1 ) = LWKOPT
+*
+      RETURN
+*
+*     End of CSYSV_ROOK
+*
+      END

lapack-netlib/SRC/csytf2.f

@@ -90,13 +90,22 @@
 *> \verbatim
 *>          IPIV is INTEGER array, dimension (N)
 *>          Details of the interchanges and the block structure of D.
-*>          If IPIV(k) > 0, then rows and columns k and IPIV(k) were
-*>          interchanged and D(k,k) is a 1-by-1 diagonal block.
-*>          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
-*>          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
-*>          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
-*>          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
-*>          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'U':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k-1) < 0, then rows and columns
+*>             k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
+*>             is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k+1) < 0, then rows and columns
+*>             k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1)
+*>             is a 2-by-2 diagonal block.
 *> \endverbatim
 *>
 *> \param[out] INFO
@@ -118,7 +127,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date September 2012
+*> \date November 2013
 *
 *> \ingroup complexSYcomputational
 *
@@ -182,10 +191,10 @@
 *  =====================================================================
       SUBROUTINE CSYTF2( UPLO, N, A, LDA, IPIV, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.2) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     September 2012
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          UPLO
@@ -273,7 +282,8 @@
          ABSAKK = CABS1( A( K, K ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.GT.1 ) THEN
             IMAX = ICAMAX( K-1, A( 1, K ), 1 )
@@ -284,7 +294,8 @@
 *
          IF( MAX( ABSAKK, COLMAX ).EQ.ZERO .OR. SISNAN(ABSAKK) ) THEN
 *
-*           Column K is zero or NaN: set INFO and continue
+*           Column K is zero or underflow, or contains a NaN:
+*           set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
@@ -441,7 +452,8 @@
          ABSAKK = CABS1( A( K, K ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.LT.N ) THEN
             IMAX = K + ICAMAX( N-K, A( K+1, K ), 1 )
@@ -452,7 +464,8 @@
 *
          IF( MAX( ABSAKK, COLMAX ).EQ.ZERO .OR. SISNAN(ABSAKK) ) THEN
 *
-*           Column K is zero or NaN: set INFO and continue
+*           Column K is zero or underflow, or contains a NaN:
+*           set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K

lapack-netlib/SRC/csytf2_rook.f

@@ -0,0 +1,821 @@
+*> \brief \b CSYTF2_ROOK computes the factorization of a complex symmetric indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (unblocked algorithm).
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download CSYTF2_ROOK + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/csytf2_rook.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/csytf2_rook.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/csytf2_rook.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CSYTF2_ROOK( UPLO, N, A, LDA, IPIV, INFO )
+*
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, N
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       COMPLEX            A( LDA, * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> CSYTF2_ROOK computes the factorization of a complex symmetric matrix A
+*> using the bounded Bunch-Kaufman ("rook") diagonal pivoting method:
+*>
+*>    A = U*D*U**T  or  A = L*D*L**T
+*>
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, U**T is the transpose of U, and D is symmetric and
+*> block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
+*>
+*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          Specifies whether the upper or lower triangular part of the
+*>          symmetric matrix A is stored:
+*>          = 'U':  Upper triangular
+*>          = 'L':  Lower triangular
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is COMPLEX array, dimension (LDA,N)
+*>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
+*>          n-by-n upper triangular part of A contains the upper
+*>          triangular part of the matrix A, and the strictly lower
+*>          triangular part of A is not referenced.  If UPLO = 'L', the
+*>          leading n-by-n lower triangular part of A contains the lower
+*>          triangular part of the matrix A, and the strictly upper
+*>          triangular part of A is not referenced.
+*>
+*>          On exit, the block diagonal matrix D and the multipliers used
+*>          to obtain the factor U or L (see below for further details).
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          Details of the interchanges and the block structure of D.
+*>
+*>          If UPLO = 'U':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k)
+*>             were interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
+*>             columns k and -IPIV(k) were interchanged and rows and
+*>             columns k-1 and -IPIV(k-1) were inerchaged,
+*>             D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k)
+*>             were interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
+*>             columns k and -IPIV(k) were interchanged and rows and
+*>             columns k+1 and -IPIV(k+1) were inerchaged,
+*>             D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0: successful exit
+*>          < 0: if INFO = -k, the k-th argument had an illegal value
+*>          > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
+*>               has been completed, but the block diagonal matrix D is
+*>               exactly singular, and division by zero will occur if it
+*>               is used to solve a system of equations.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2013
+*
+*> \ingroup complexSYcomputational
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  If UPLO = 'U', then A = U*D*U**T, where
+*>     U = P(n)*U(n)* ... *P(k)U(k)* ...,
+*>  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
+*>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
+*>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
+*>  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
+*>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
+*>
+*>             (   I    v    0   )   k-s
+*>     U(k) =  (   0    I    0   )   s
+*>             (   0    0    I   )   n-k
+*>                k-s   s   n-k
+*>
+*>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
+*>  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
+*>  and A(k,k), and v overwrites A(1:k-2,k-1:k).
+*>
+*>  If UPLO = 'L', then A = L*D*L**T, where
+*>     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
+*>  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
+*>  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
+*>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
+*>  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
+*>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
+*>
+*>             (   I    0     0   )  k-1
+*>     L(k) =  (   0    I     0   )  s
+*>             (   0    v     I   )  n-k-s+1
+*>                k-1   s  n-k-s+1
+*>
+*>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
+*>  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
+*>  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
+*> \endverbatim
+*
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>  November 2013,     Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*>
+*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*>                  School of Mathematics,
+*>                  University of Manchester
+*>
+*>  01-01-96 - Based on modifications by
+*>    J. Lewis, Boeing Computer Services Company
+*>    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville abd , USA
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE CSYTF2_ROOK( UPLO, N, A, LDA, IPIV, INFO )
+*
+*  -- LAPACK computational routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2013
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, N
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      COMPLEX            A( LDA, * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      REAL               ZERO, ONE
+      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
+      REAL               EIGHT, SEVTEN
+      PARAMETER          ( EIGHT = 8.0E+0, SEVTEN = 17.0E+0 )
+      COMPLEX            CONE
+      PARAMETER          ( CONE = ( 1.0E+0, 0.0E+0 ) )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            UPPER, DONE
+      INTEGER            I, IMAX, J, JMAX, ITEMP, K, KK, KP, KSTEP,
+     $                   P, II
+      REAL               ABSAKK, ALPHA, COLMAX, ROWMAX, STEMP, SFMIN
+      COMPLEX            D11, D12, D21, D22, T, WK, WKM1, WKP1, Z
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      INTEGER            ICAMAX
+      REAL               SLAMCH
+      EXTERNAL           LSAME, ICAMAX, SLAMCH
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           CSCAL, CSWAP, CSYR, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, MAX, SQRT, AIMAG, REAL
+*     ..
+*     .. Statement Functions ..
+      REAL               CABS1
+*     ..
+*     .. Statement Function definitions ..
+      CABS1( Z ) = ABS( REAL( Z ) ) + ABS( AIMAG( Z ) )
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      UPPER = LSAME( UPLO, 'U' )
+      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -4
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'CSYTF2_ROOK', -INFO )
+         RETURN
+      END IF
+*
+*     Initialize ALPHA for use in choosing pivot block size.
+*
+      ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT
+*
+*     Compute machine safe minimum
+*
+      SFMIN = SLAMCH( 'S' )
+*
+      IF( UPPER ) THEN
+*
+*        Factorize A as U*D*U**T using the upper triangle of A
+*
+*        K is the main loop index, decreasing from N to 1 in steps of
+*        1 or 2
+*
+         K = N
+   10    CONTINUE
+*
+*        If K < 1, exit from loop
+*
+         IF( K.LT.1 )
+     $      GO TO 70
+         KSTEP = 1
+         P = K
+*
+*        Determine rows and columns to be interchanged and whether
+*        a 1-by-1 or 2-by-2 pivot block will be used
+*
+         ABSAKK = CABS1( A( K, K ) )
+*
+*        IMAX is the row-index of the largest off-diagonal element in
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
+*
+         IF( K.GT.1 ) THEN
+            IMAX = ICAMAX( K-1, A( 1, K ), 1 )
+            COLMAX = CABS1( A( IMAX, K ) )
+         ELSE
+            COLMAX = ZERO
+         END IF
+*
+         IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) ) THEN
+*
+*           Column K is zero or underflow: set INFO and continue
+*
+            IF( INFO.EQ.0 )
+     $         INFO = K
+            KP = K
+         ELSE
+*
+*           Test for interchange
+*
+*           Equivalent to testing for (used to handle NaN and Inf)
+*           ABSAKK.GE.ALPHA*COLMAX
+*
+            IF( .NOT.( ABSAKK.LT.ALPHA*COLMAX ) ) THEN
+*
+*              no interchange,
+*              use 1-by-1 pivot block
+*
+               KP = K
+            ELSE
+*
+               DONE = .FALSE.
+*
+*              Loop until pivot found
+*
+   12          CONTINUE
+*
+*                 Begin pivot search loop body
+*
+*                 JMAX is the column-index of the largest off-diagonal
+*                 element in row IMAX, and ROWMAX is its absolute value.
+*                 Determine both ROWMAX and JMAX.
+*
+                  IF( IMAX.NE.K ) THEN
+                     JMAX = IMAX + ICAMAX( K-IMAX, A( IMAX, IMAX+1 ),
+     $                                    LDA )
+                     ROWMAX = CABS1( A( IMAX, JMAX ) )
+                  ELSE
+                     ROWMAX = ZERO
+                  END IF
+*
+                  IF( IMAX.GT.1 ) THEN
+                     ITEMP = ICAMAX( IMAX-1, A( 1, IMAX ), 1 )
+                     STEMP = CABS1( A( ITEMP, IMAX ) )
+                     IF( STEMP.GT.ROWMAX ) THEN
+                        ROWMAX = STEMP
+                        JMAX = ITEMP
+                     END IF
+                  END IF
+*
+*                 Equivalent to testing for (used to handle NaN and Inf)
+*                 CABS1( A( IMAX, IMAX ) ).GE.ALPHA*ROWMAX
+*
+                  IF( .NOT.( CABS1(A( IMAX, IMAX )).LT.ALPHA*ROWMAX ) )
+     $            THEN
+*
+*                    interchange rows and columns K and IMAX,
+*                    use 1-by-1 pivot block
+*
+                     KP = IMAX
+                     DONE = .TRUE.
+*
+*                 Equivalent to testing for ROWMAX .EQ. COLMAX,
+*                 used to handle NaN and Inf
+*
+                  ELSE IF( ( P.EQ.JMAX ).OR.( ROWMAX.LE.COLMAX ) ) THEN
+*
+*                    interchange rows and columns K+1 and IMAX,
+*                    use 2-by-2 pivot block
+*
+                     KP = IMAX
+                     KSTEP = 2
+                     DONE = .TRUE.
+                  ELSE
+*
+*                    Pivot NOT found, set variables and repeat
+*
+                     P = IMAX
+                     COLMAX = ROWMAX
+                     IMAX = JMAX
+                  END IF
+*
+*                 End pivot search loop body
+*
+               IF( .NOT. DONE ) GOTO 12
+*
+            END IF
+*
+*           Swap TWO rows and TWO columns
+*
+*           First swap
+*
+            IF( ( KSTEP.EQ.2 ) .AND. ( P.NE.K ) ) THEN
+*
+*              Interchange rows and column K and P in the leading
+*              submatrix A(1:k,1:k) if we have a 2-by-2 pivot
+*
+               IF( P.GT.1 )
+     $            CALL CSWAP( P-1, A( 1, K ), 1, A( 1, P ), 1 )
+               IF( P.LT.(K-1) )
+     $            CALL CSWAP( K-P-1, A( P+1, K ), 1, A( P, P+1 ),
+     $                     LDA )
+               T = A( K, K )
+               A( K, K ) = A( P, P )
+               A( P, P ) = T
+            END IF
+*
+*           Second swap
+*
+            KK = K - KSTEP + 1
+            IF( KP.NE.KK ) THEN
+*
+*              Interchange rows and columns KK and KP in the leading
+*              submatrix A(1:k,1:k)
+*
+               IF( KP.GT.1 )
+     $            CALL CSWAP( KP-1, A( 1, KK ), 1, A( 1, KP ), 1 )
+               IF( ( KK.GT.1 ) .AND. ( KP.LT.(KK-1) ) )
+     $            CALL CSWAP( KK-KP-1, A( KP+1, KK ), 1, A( KP, KP+1 ),
+     $                     LDA )
+               T = A( KK, KK )
+               A( KK, KK ) = A( KP, KP )
+               A( KP, KP ) = T
+               IF( KSTEP.EQ.2 ) THEN
+                  T = A( K-1, K )
+                  A( K-1, K ) = A( KP, K )
+                  A( KP, K ) = T
+               END IF
+            END IF
+*
+*           Update the leading submatrix
+*
+            IF( KSTEP.EQ.1 ) THEN
+*
+*              1-by-1 pivot block D(k): column k now holds
+*
+*              W(k) = U(k)*D(k)
+*
+*              where U(k) is the k-th column of U
+*
+               IF( K.GT.1 ) THEN
+*
+*                 Perform a rank-1 update of A(1:k-1,1:k-1) and
+*                 store U(k) in column k
+*
+                  IF( CABS1( A( K, K ) ).GE.SFMIN ) THEN
+*
+*                    Perform a rank-1 update of A(1:k-1,1:k-1) as
+*                    A := A - U(k)*D(k)*U(k)**T
+*                       = A - W(k)*1/D(k)*W(k)**T
+*
+                     D11 = CONE / A( K, K )
+                     CALL CSYR( UPLO, K-1, -D11, A( 1, K ), 1, A, LDA )
+*
+*                    Store U(k) in column k
+*
+                     CALL CSCAL( K-1, D11, A( 1, K ), 1 )
+                  ELSE
+*
+*                    Store L(k) in column K
+*
+                     D11 = A( K, K )
+                     DO 16 II = 1, K - 1
+                        A( II, K ) = A( II, K ) / D11
+   16                CONTINUE
+*
+*                    Perform a rank-1 update of A(k+1:n,k+1:n) as
+*                    A := A - U(k)*D(k)*U(k)**T
+*                       = A - W(k)*(1/D(k))*W(k)**T
+*                       = A - (W(k)/D(k))*(D(k))*(W(k)/D(K))**T
+*
+                     CALL CSYR( UPLO, K-1, -D11, A( 1, K ), 1, A, LDA )
+                  END IF
+               END IF
+*
+            ELSE
+*
+*              2-by-2 pivot block D(k): columns k and k-1 now hold
+*
+*              ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
+*
+*              where U(k) and U(k-1) are the k-th and (k-1)-th columns
+*              of U
+*
+*              Perform a rank-2 update of A(1:k-2,1:k-2) as
+*
+*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T
+*                 = A - ( ( A(k-1)A(k) )*inv(D(k)) ) * ( A(k-1)A(k) )**T
+*
+*              and store L(k) and L(k+1) in columns k and k+1
+*
+               IF( K.GT.2 ) THEN
+*
+                  D12 = A( K-1, K )
+                  D22 = A( K-1, K-1 ) / D12
+                  D11 = A( K, K ) / D12
+                  T = CONE / ( D11*D22-CONE )
+*
+                  DO 30 J = K - 2, 1, -1
+*
+                     WKM1 = T*( D11*A( J, K-1 )-A( J, K ) )
+                     WK = T*( D22*A( J, K )-A( J, K-1 ) )
+*
+                     DO 20 I = J, 1, -1
+                        A( I, J ) = A( I, J ) - (A( I, K ) / D12 )*WK -
+     $                              ( A( I, K-1 ) / D12 )*WKM1
+   20                CONTINUE
+*
+*                    Store U(k) and U(k-1) in cols k and k-1 for row J
+*
+                     A( J, K ) = WK / D12
+                     A( J, K-1 ) = WKM1 / D12
+*
+   30             CONTINUE
+*
+               END IF
+*
+            END IF
+         END IF
+*
+*        Store details of the interchanges in IPIV
+*
+         IF( KSTEP.EQ.1 ) THEN
+            IPIV( K ) = KP
+         ELSE
+            IPIV( K ) = -P
+            IPIV( K-1 ) = -KP
+         END IF
+*
+*        Decrease K and return to the start of the main loop
+*
+         K = K - KSTEP
+         GO TO 10
+*
+      ELSE
+*
+*        Factorize A as L*D*L**T using the lower triangle of A
+*
+*        K is the main loop index, increasing from 1 to N in steps of
+*        1 or 2
+*
+         K = 1
+   40    CONTINUE
+*
+*        If K > N, exit from loop
+*
+         IF( K.GT.N )
+     $      GO TO 70
+         KSTEP = 1
+         P = K
+*
+*        Determine rows and columns to be interchanged and whether
+*        a 1-by-1 or 2-by-2 pivot block will be used
+*
+         ABSAKK = CABS1( A( K, K ) )
+*
+*        IMAX is the row-index of the largest off-diagonal element in
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
+*
+         IF( K.LT.N ) THEN
+            IMAX = K + ICAMAX( N-K, A( K+1, K ), 1 )
+            COLMAX = CABS1( A( IMAX, K ) )
+         ELSE
+            COLMAX = ZERO
+         END IF
+*
+         IF( ( MAX( ABSAKK, COLMAX ).EQ.ZERO ) ) THEN
+*
+*           Column K is zero or underflow: set INFO and continue
+*
+            IF( INFO.EQ.0 )
+     $         INFO = K
+            KP = K
+         ELSE
+*
+*           Test for interchange
+*
+*           Equivalent to testing for (used to handle NaN and Inf)
+*           ABSAKK.GE.ALPHA*COLMAX
+*
+            IF( .NOT.( ABSAKK.LT.ALPHA*COLMAX ) ) THEN
+*
+*              no interchange, use 1-by-1 pivot block
+*
+               KP = K
+            ELSE
+*
+               DONE = .FALSE.
+*
+*              Loop until pivot found
+*
+   42          CONTINUE
+*
+*                 Begin pivot search loop body
+*
+*                 JMAX is the column-index of the largest off-diagonal
+*                 element in row IMAX, and ROWMAX is its absolute value.
+*                 Determine both ROWMAX and JMAX.
+*
+                  IF( IMAX.NE.K ) THEN
+                     JMAX = K - 1 + ICAMAX( IMAX-K, A( IMAX, K ), LDA )
+                     ROWMAX = CABS1( A( IMAX, JMAX ) )
+                  ELSE
+                     ROWMAX = ZERO
+                  END IF
+*
+                  IF( IMAX.LT.N ) THEN
+                     ITEMP = IMAX + ICAMAX( N-IMAX, A( IMAX+1, IMAX ),
+     $                                     1 )
+                     STEMP = CABS1( A( ITEMP, IMAX ) )
+                     IF( STEMP.GT.ROWMAX ) THEN
+                        ROWMAX = STEMP
+                        JMAX = ITEMP
+                     END IF
+                  END IF
+*
+*                 Equivalent to testing for (used to handle NaN and Inf)
+*                 CABS1( A( IMAX, IMAX ) ).GE.ALPHA*ROWMAX
+*
+                  IF( .NOT.( CABS1(A( IMAX, IMAX )).LT.ALPHA*ROWMAX ) )
+     $            THEN
+*
+*                    interchange rows and columns K and IMAX,
+*                    use 1-by-1 pivot block
+*
+                     KP = IMAX
+                     DONE = .TRUE.
+*
+*                 Equivalent to testing for ROWMAX .EQ. COLMAX,
+*                 used to handle NaN and Inf
+*
+                  ELSE IF( ( P.EQ.JMAX ).OR.( ROWMAX.LE.COLMAX ) ) THEN
+*
+*                    interchange rows and columns K+1 and IMAX,
+*                    use 2-by-2 pivot block
+*
+                     KP = IMAX
+                     KSTEP = 2
+                     DONE = .TRUE.
+                  ELSE
+*
+*                    Pivot NOT found, set variables and repeat
+*
+                     P = IMAX
+                     COLMAX = ROWMAX
+                     IMAX = JMAX
+                  END IF
+*
+*                 End pivot search loop body
+*
+               IF( .NOT. DONE ) GOTO 42
+*
+            END IF
+*
+*           Swap TWO rows and TWO columns
+*
+*           First swap
+*
+            IF( ( KSTEP.EQ.2 ) .AND. ( P.NE.K ) ) THEN
+*
+*              Interchange rows and column K and P in the trailing
+*              submatrix A(k:n,k:n) if we have a 2-by-2 pivot
+*
+               IF( P.LT.N )
+     $            CALL CSWAP( N-P, A( P+1, K ), 1, A( P+1, P ), 1 )
+               IF( P.GT.(K+1) )
+     $            CALL CSWAP( P-K-1, A( K+1, K ), 1, A( P, K+1 ), LDA )
+               T = A( K, K )
+               A( K, K ) = A( P, P )
+               A( P, P ) = T
+            END IF
+*
+*           Second swap
+*
+            KK = K + KSTEP - 1
+            IF( KP.NE.KK ) THEN
+*
+*              Interchange rows and columns KK and KP in the trailing
+*              submatrix A(k:n,k:n)
+*
+               IF( KP.LT.N )
+     $            CALL CSWAP( N-KP, A( KP+1, KK ), 1, A( KP+1, KP ), 1 )
+               IF( ( KK.LT.N ) .AND. ( KP.GT.(KK+1) ) )
+     $            CALL CSWAP( KP-KK-1, A( KK+1, KK ), 1, A( KP, KK+1 ),
+     $                     LDA )
+               T = A( KK, KK )
+               A( KK, KK ) = A( KP, KP )
+               A( KP, KP ) = T
+               IF( KSTEP.EQ.2 ) THEN
+                  T = A( K+1, K )
+                  A( K+1, K ) = A( KP, K )
+                  A( KP, K ) = T
+               END IF
+            END IF
+*
+*           Update the trailing submatrix
+*
+            IF( KSTEP.EQ.1 ) THEN
+*
+*              1-by-1 pivot block D(k): column k now holds
+*
+*              W(k) = L(k)*D(k)
+*
+*              where L(k) is the k-th column of L
+*
+               IF( K.LT.N ) THEN
+*
+*              Perform a rank-1 update of A(k+1:n,k+1:n) and
+*              store L(k) in column k
+*
+                  IF( CABS1( A( K, K ) ).GE.SFMIN ) THEN
+*
+*                    Perform a rank-1 update of A(k+1:n,k+1:n) as
+*                    A := A - L(k)*D(k)*L(k)**T
+*                       = A - W(k)*(1/D(k))*W(k)**T
+*
+                     D11 = CONE / A( K, K )
+                     CALL CSYR( UPLO, N-K, -D11, A( K+1, K ), 1,
+     $                          A( K+1, K+1 ), LDA )
+*
+*                    Store L(k) in column k
+*
+                     CALL CSCAL( N-K, D11, A( K+1, K ), 1 )
+                  ELSE
+*
+*                    Store L(k) in column k
+*
+                     D11 = A( K, K )
+                     DO 46 II = K + 1, N
+                        A( II, K ) = A( II, K ) / D11
+   46                CONTINUE
+*
+*                    Perform a rank-1 update of A(k+1:n,k+1:n) as
+*                    A := A - L(k)*D(k)*L(k)**T
+*                       = A - W(k)*(1/D(k))*W(k)**T
+*                       = A - (W(k)/D(k))*(D(k))*(W(k)/D(K))**T
+*
+                     CALL CSYR( UPLO, N-K, -D11, A( K+1, K ), 1,
+     $                          A( K+1, K+1 ), LDA )
+                  END IF
+               END IF
+*
+            ELSE
+*
+*              2-by-2 pivot block D(k): columns k and k+1 now hold
+*
+*              ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k)
+*
+*              where L(k) and L(k+1) are the k-th and (k+1)-th columns
+*              of L
+*
+*
+*              Perform a rank-2 update of A(k+2:n,k+2:n) as
+*
+*              A := A - ( L(k) L(k+1) ) * D(k) * ( L(k) L(k+1) )**T
+*                 = A - ( ( A(k)A(k+1) )*inv(D(k) ) * ( A(k)A(k+1) )**T
+*
+*              and store L(k) and L(k+1) in columns k and k+1
+*
+               IF( K.LT.N-1 ) THEN
+*
+                  D21 = A( K+1, K )
+                  D11 = A( K+1, K+1 ) / D21
+                  D22 = A( K, K ) / D21
+                  T = CONE / ( D11*D22-CONE )
+*
+                  DO 60 J = K + 2, N
+*
+*                    Compute  D21 * ( W(k)W(k+1) ) * inv(D(k)) for row J
+*
+                     WK = T*( D11*A( J, K )-A( J, K+1 ) )
+                     WKP1 = T*( D22*A( J, K+1 )-A( J, K ) )
+*
+*                    Perform a rank-2 update of A(k+2:n,k+2:n)
+*
+                     DO 50 I = J, N
+                        A( I, J ) = A( I, J ) - ( A( I, K ) / D21 )*WK -
+     $                              ( A( I, K+1 ) / D21 )*WKP1
+   50                CONTINUE
+*
+*                    Store L(k) and L(k+1) in cols k and k+1 for row J
+*
+                     A( J, K ) = WK / D21
+                     A( J, K+1 ) = WKP1 / D21
+*
+   60             CONTINUE
+*
+               END IF
+*
+            END IF
+         END IF
+*
+*        Store details of the interchanges in IPIV
+*
+         IF( KSTEP.EQ.1 ) THEN
+            IPIV( K ) = KP
+         ELSE
+            IPIV( K ) = -P
+            IPIV( K+1 ) = -KP
+         END IF
+*
+*        Increase K and return to the start of the main loop
+*
+         K = K + KSTEP
+         GO TO 40
+*
+      END IF
+*
+   70 CONTINUE
+*
+      RETURN
+*
+*     End of CSYTF2_ROOK
+*
+      END

lapack-netlib/SRC/csytrf_rook.f

@@ -0,0 +1,393 @@
+*> \brief \b CSYTRF_ROOK
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download CSYTRF_ROOK + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/csytrf_rook.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/csytrf_rook.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/csytrf_rook.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CSYTRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, LWORK, N
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       COMPLEX            A( LDA, * ), WORK( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> CSYTRF_ROOK computes the factorization of a complex symmetric matrix A
+*> using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
+*> The form of the factorization is
+*>
+*>    A = U*D*U**T  or  A = L*D*L**T
+*>
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, and D is symmetric and block diagonal with
+*> 1-by-1 and 2-by-2 diagonal blocks.
+*>
+*> This is the blocked version of the algorithm, calling Level 3 BLAS.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          = 'U':  Upper triangle of A is stored;
+*>          = 'L':  Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is COMPLEX array, dimension (LDA,N)
+*>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
+*>          N-by-N upper triangular part of A contains the upper
+*>          triangular part of the matrix A, and the strictly lower
+*>          triangular part of A is not referenced.  If UPLO = 'L', the
+*>          leading N-by-N lower triangular part of A contains the lower
+*>          triangular part of the matrix A, and the strictly upper
+*>          triangular part of A is not referenced.
+*>
+*>          On exit, the block diagonal matrix D and the multipliers used
+*>          to obtain the factor U or L (see below for further details).
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          Details of the interchanges and the block structure of D.
+*>
+*>          If UPLO = 'U':
+*>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
+*>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>               If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
+*>               columns k and -IPIV(k) were interchanged and rows and
+*>               columns k-1 and -IPIV(k-1) were inerchaged,
+*>               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
+*>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>               If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
+*>               columns k and -IPIV(k) were interchanged and rows and
+*>               columns k+1 and -IPIV(k+1) were inerchaged,
+*>               D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX array, dimension (MAX(1,LWORK)).
+*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>          The length of WORK.  LWORK >=1.  For best performance
+*>          LWORK >= N*NB, where NB is the block size returned by ILAENV.
+*>
+*>          If LWORK = -1, then a workspace query is assumed; the routine
+*>          only calculates the optimal size of the WORK array, returns
+*>          this value as the first entry of the WORK array, and no error
+*>          message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0:  successful exit
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value
+*>          > 0:  if INFO = i, D(i,i) is exactly zero.  The factorization
+*>                has been completed, but the block diagonal matrix D is
+*>                exactly singular, and division by zero will occur if it
+*>                is used to solve a system of equations.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup complexSYcomputational
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  If UPLO = 'U', then A = U*D*U**T, where
+*>     U = P(n)*U(n)* ... *P(k)U(k)* ...,
+*>  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
+*>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
+*>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
+*>  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
+*>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
+*>
+*>             (   I    v    0   )   k-s
+*>     U(k) =  (   0    I    0   )   s
+*>             (   0    0    I   )   n-k
+*>                k-s   s   n-k
+*>
+*>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
+*>  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
+*>  and A(k,k), and v overwrites A(1:k-2,k-1:k).
+*>
+*>  If UPLO = 'L', then A = L*D*L**T, where
+*>     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
+*>  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
+*>  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
+*>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
+*>  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
+*>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
+*>
+*>             (   I    0     0   )  k-1
+*>     L(k) =  (   0    I     0   )  s
+*>             (   0    v     I   )  n-k-s+1
+*>                k-1   s  n-k-s+1
+*>
+*>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
+*>  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
+*>  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
+*> \endverbatim
+*
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>   November 2011, Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*>
+*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*>                  School of Mathematics,
+*>                  University of Manchester
+*>
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE CSYTRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+*
+*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, LWORK, N
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      COMPLEX            A( LDA, * ), WORK( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Local Scalars ..
+      LOGICAL            LQUERY, UPPER
+      INTEGER            IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      INTEGER            ILAENV
+      EXTERNAL           LSAME, ILAENV
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           CLASYF_ROOK, CSYTF2_ROOK, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      UPPER = LSAME( UPLO, 'U' )
+      LQUERY = ( LWORK.EQ.-1 )
+      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -4
+      ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
+         INFO = -7
+      END IF
+*
+      IF( INFO.EQ.0 ) THEN
+*
+*        Determine the block size
+*
+         NB = ILAENV( 1, 'CSYTRF_ROOK', UPLO, N, -1, -1, -1 )
+         LWKOPT = N*NB
+         WORK( 1 ) = LWKOPT
+      END IF
+*
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'CSYTRF_ROOK', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+*
+      NBMIN = 2
+      LDWORK = N
+      IF( NB.GT.1 .AND. NB.LT.N ) THEN
+         IWS = LDWORK*NB
+         IF( LWORK.LT.IWS ) THEN
+            NB = MAX( LWORK / LDWORK, 1 )
+            NBMIN = MAX( 2, ILAENV( 2, 'CSYTRF_ROOK',
+     $                              UPLO, N, -1, -1, -1 ) )
+         END IF
+      ELSE
+         IWS = 1
+      END IF
+      IF( NB.LT.NBMIN )
+     $   NB = N
+*
+      IF( UPPER ) THEN
+*
+*        Factorize A as U*D*U**T using the upper triangle of A
+*
+*        K is the main loop index, decreasing from N to 1 in steps of
+*        KB, where KB is the number of columns factorized by CLASYF_ROOK;
+*        KB is either NB or NB-1, or K for the last block
+*
+         K = N
+   10    CONTINUE
+*
+*        If K < 1, exit from loop
+*
+         IF( K.LT.1 )
+     $      GO TO 40
+*
+         IF( K.GT.NB ) THEN
+*
+*           Factorize columns k-kb+1:k of A and use blocked code to
+*           update columns 1:k-kb
+*
+            CALL CLASYF_ROOK( UPLO, K, NB, KB, A, LDA,
+     $                        IPIV, WORK, LDWORK, IINFO )
+         ELSE
+*
+*           Use unblocked code to factorize columns 1:k of A
+*
+            CALL CSYTF2_ROOK( UPLO, K, A, LDA, IPIV, IINFO )
+            KB = K
+         END IF
+*
+*        Set INFO on the first occurrence of a zero pivot
+*
+         IF( INFO.EQ.0 .AND. IINFO.GT.0 )
+     $      INFO = IINFO     
+*
+*        No need to adjust IPIV
+*
+*        Decrease K and return to the start of the main loop
+*
+         K = K - KB
+         GO TO 10
+*
+      ELSE
+*
+*        Factorize A as L*D*L**T using the lower triangle of A
+*
+*        K is the main loop index, increasing from 1 to N in steps of
+*        KB, where KB is the number of columns factorized by CLASYF_ROOK;
+*        KB is either NB or NB-1, or N-K+1 for the last block
+*
+         K = 1
+   20    CONTINUE
+*
+*        If K > N, exit from loop
+*
+         IF( K.GT.N )
+     $      GO TO 40
+*
+         IF( K.LE.N-NB ) THEN
+*
+*           Factorize columns k:k+kb-1 of A and use blocked code to
+*           update columns k+kb:n
+*
+            CALL CLASYF_ROOK( UPLO, N-K+1, NB, KB, A( K, K ), LDA,
+     $                        IPIV( K ), WORK, LDWORK, IINFO )
+         ELSE
+*
+*           Use unblocked code to factorize columns k:n of A
+*
+            CALL CSYTF2_ROOK( UPLO, N-K+1, A( K, K ), LDA, IPIV( K ),
+     $                   IINFO )
+            KB = N - K + 1
+         END IF
+*
+*        Set INFO on the first occurrence of a zero pivot
+*
+         IF( INFO.EQ.0 .AND. IINFO.GT.0 )
+     $      INFO = IINFO + K - 1
+*
+*        Adjust IPIV
+*
+         DO 30 J = K, K + KB - 1
+            IF( IPIV( J ).GT.0 ) THEN
+               IPIV( J ) = IPIV( J ) + K - 1
+            ELSE
+               IPIV( J ) = IPIV( J ) - K + 1
+            END IF
+   30    CONTINUE
+*
+*        Increase K and return to the start of the main loop
+*
+         K = K + KB
+         GO TO 20
+*
+      END IF
+*
+   40 CONTINUE
+      WORK( 1 ) = LWKOPT
+      RETURN
+*
+*     End of CSYTRF_ROOK
+*
+      END

lapack-netlib/SRC/csytri_rook.f

@@ -0,0 +1,451 @@
+*> \brief \b CSYTRI_ROOK
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download CSYTRI_ROOK + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/csytri_rook.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/csytri_rook.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/csytri_rook.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CSYTRI_ROOK( UPLO, N, A, LDA, IPIV, WORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, N
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       COMPLEX            A( LDA, * ), WORK( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> CSYTRI_ROOK computes the inverse of a complex symmetric
+*> matrix A using the factorization A = U*D*U**T or A = L*D*L**T
+*> computed by CSYTRF_ROOK.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          Specifies whether the details of the factorization are stored
+*>          as an upper or lower triangular matrix.
+*>          = 'U':  Upper triangular, form is A = U*D*U**T;
+*>          = 'L':  Lower triangular, form is A = L*D*L**T.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is COMPLEX array, dimension (LDA,N)
+*>          On entry, the block diagonal matrix D and the multipliers
+*>          used to obtain the factor U or L as computed by CSYTRF_ROOK.
+*>
+*>          On exit, if INFO = 0, the (symmetric) inverse of the original
+*>          matrix.  If UPLO = 'U', the upper triangular part of the
+*>          inverse is formed and the part of A below the diagonal is not
+*>          referenced; if UPLO = 'L' the lower triangular part of the
+*>          inverse is formed and the part of A above the diagonal is
+*>          not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          Details of the interchanges and the block structure of D
+*>          as determined by CSYTRF_ROOK.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0: successful exit
+*>          < 0: if INFO = -i, the i-th argument had an illegal value
+*>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
+*>               inverse could not be computed.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup complexSYcomputational
+*
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>   November 2011, Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*>
+*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*>                  School of Mathematics,
+*>                  University of Manchester
+*>
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE CSYTRI_ROOK( UPLO, N, A, LDA, IPIV, WORK, INFO )
+*
+*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, N
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      COMPLEX            A( LDA, * ), WORK( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      COMPLEX            CONE, CZERO
+      PARAMETER          ( CONE = ( 1.0E+0, 0.0E+0 ),
+     $                   CZERO = ( 0.0E+0, 0.0E+0 ) )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            UPPER
+      INTEGER            K, KP, KSTEP
+      COMPLEX            AK, AKKP1, AKP1, D, T, TEMP
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      COMPLEX            CDOTU
+      EXTERNAL           LSAME, CDOTU
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           CCOPY, CSWAP, CSYMV, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      UPPER = LSAME( UPLO, 'U' )
+      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -4
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'CSYTRI_ROOK', -INFO )
+         RETURN
+      END IF
+*
+*     Quick return if possible
+*
+      IF( N.EQ.0 )
+     $   RETURN
+*
+*     Check that the diagonal matrix D is nonsingular.
+*
+      IF( UPPER ) THEN
+*
+*        Upper triangular storage: examine D from bottom to top
+*
+         DO 10 INFO = N, 1, -1
+            IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.CZERO )
+     $         RETURN
+   10    CONTINUE
+      ELSE
+*
+*        Lower triangular storage: examine D from top to bottom.
+*
+         DO 20 INFO = 1, N
+            IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.CZERO )
+     $         RETURN
+   20    CONTINUE
+      END IF
+      INFO = 0
+*
+      IF( UPPER ) THEN
+*
+*        Compute inv(A) from the factorization A = U*D*U**T.
+*
+*        K is the main loop index, increasing from 1 to N in steps of
+*        1 or 2, depending on the size of the diagonal blocks.
+*
+         K = 1
+   30    CONTINUE
+*
+*        If K > N, exit from loop.
+*
+         IF( K.GT.N )
+     $      GO TO 40
+*
+         IF( IPIV( K ).GT.0 ) THEN
+*
+*           1 x 1 diagonal block
+*
+*           Invert the diagonal block.
+*
+            A( K, K ) = CONE / A( K, K )
+*
+*           Compute column K of the inverse.
+*
+            IF( K.GT.1 ) THEN
+               CALL CCOPY( K-1, A( 1, K ), 1, WORK, 1 )
+               CALL CSYMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, CZERO,
+     $                     A( 1, K ), 1 )
+               A( K, K ) = A( K, K ) - CDOTU( K-1, WORK, 1, A( 1, K ),
+     $                     1 )
+            END IF
+            KSTEP = 1
+         ELSE
+*
+*           2 x 2 diagonal block
+*
+*           Invert the diagonal block.
+*
+            T = A( K, K+1 )
+            AK = A( K, K ) / T
+            AKP1 = A( K+1, K+1 ) / T
+            AKKP1 = A( K, K+1 ) / T
+            D = T*( AK*AKP1-CONE )
+            A( K, K ) = AKP1 / D
+            A( K+1, K+1 ) = AK / D
+            A( K, K+1 ) = -AKKP1 / D
+*
+*           Compute columns K and K+1 of the inverse.
+*
+            IF( K.GT.1 ) THEN
+               CALL CCOPY( K-1, A( 1, K ), 1, WORK, 1 )
+               CALL CSYMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, CZERO,
+     $                     A( 1, K ), 1 )
+               A( K, K ) = A( K, K ) - CDOTU( K-1, WORK, 1, A( 1, K ),
+     $                     1 )
+               A( K, K+1 ) = A( K, K+1 ) -
+     $                       CDOTU( K-1, A( 1, K ), 1, A( 1, K+1 ), 1 )
+               CALL CCOPY( K-1, A( 1, K+1 ), 1, WORK, 1 )
+               CALL CSYMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, CZERO,
+     $                     A( 1, K+1 ), 1 )
+               A( K+1, K+1 ) = A( K+1, K+1 ) -
+     $                         CDOTU( K-1, WORK, 1, A( 1, K+1 ), 1 )
+            END IF
+            KSTEP = 2
+         END IF
+*
+         IF( KSTEP.EQ.1 ) THEN
+*
+*           Interchange rows and columns K and IPIV(K) in the leading
+*           submatrix A(1:k+1,1:k+1)
+*
+            KP = IPIV( K )
+            IF( KP.NE.K ) THEN
+               IF( KP.GT.1 )
+     $             CALL CSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
+               CALL CSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA )
+               TEMP = A( K, K )
+               A( K, K ) = A( KP, KP )
+               A( KP, KP ) = TEMP
+            END IF
+         ELSE
+*
+*           Interchange rows and columns K and K+1 with -IPIV(K) and
+*           -IPIV(K+1)in the leading submatrix A(1:k+1,1:k+1)
+*
+            KP = -IPIV( K )
+            IF( KP.NE.K ) THEN
+               IF( KP.GT.1 )
+     $            CALL CSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
+               CALL CSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA )
+*               
+               TEMP = A( K, K )
+               A( K, K ) = A( KP, KP )
+               A( KP, KP ) = TEMP
+               TEMP = A( K, K+1 )
+               A( K, K+1 ) = A( KP, K+1 )
+               A( KP, K+1 ) = TEMP
+            END IF
+*
+            K = K + 1
+            KP = -IPIV( K )
+            IF( KP.NE.K ) THEN
+               IF( KP.GT.1 )
+     $            CALL CSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
+               CALL CSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA )
+               TEMP = A( K, K )
+               A( K, K ) = A( KP, KP )
+               A( KP, KP ) = TEMP
+            END IF
+         END IF
+*
+         K = K + 1
+         GO TO 30
+   40    CONTINUE
+*
+      ELSE
+*
+*        Compute inv(A) from the factorization A = L*D*L**T.
+*
+*        K is the main loop index, increasing from 1 to N in steps of
+*        1 or 2, depending on the size of the diagonal blocks.
+*
+         K = N
+   50    CONTINUE
+*
+*        If K < 1, exit from loop.
+*
+         IF( K.LT.1 )
+     $      GO TO 60
+*
+         IF( IPIV( K ).GT.0 ) THEN
+*
+*           1 x 1 diagonal block
+*
+*           Invert the diagonal block.
+*
+            A( K, K ) = CONE / A( K, K )
+*
+*           Compute column K of the inverse.
+*
+            IF( K.LT.N ) THEN
+               CALL CCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
+               CALL CSYMV( UPLO, N-K,-CONE, A( K+1, K+1 ), LDA, WORK, 1,
+     $                     CZERO, A( K+1, K ), 1 )
+               A( K, K ) = A( K, K ) - CDOTU( N-K, WORK, 1, A( K+1, K ),
+     $                     1 )
+            END IF
+            KSTEP = 1
+         ELSE
+*
+*           2 x 2 diagonal block
+*
+*           Invert the diagonal block.
+*
+            T = A( K, K-1 )
+            AK = A( K-1, K-1 ) / T
+            AKP1 = A( K, K ) / T
+            AKKP1 = A( K, K-1 ) / T
+            D = T*( AK*AKP1-CONE )
+            A( K-1, K-1 ) = AKP1 / D
+            A( K, K ) = AK / D
+            A( K, K-1 ) = -AKKP1 / D
+*
+*           Compute columns K-1 and K of the inverse.
+*
+            IF( K.LT.N ) THEN
+               CALL CCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
+               CALL CSYMV( UPLO, N-K,-CONE, A( K+1, K+1 ), LDA, WORK, 1,
+     $                     CZERO, A( K+1, K ), 1 )
+               A( K, K ) = A( K, K ) - CDOTU( N-K, WORK, 1, A( K+1, K ),
+     $                     1 )
+               A( K, K-1 ) = A( K, K-1 ) -
+     $                       CDOTU( N-K, A( K+1, K ), 1, A( K+1, K-1 ),
+     $                       1 )
+               CALL CCOPY( N-K, A( K+1, K-1 ), 1, WORK, 1 )
+               CALL CSYMV( UPLO, N-K,-CONE, A( K+1, K+1 ), LDA, WORK, 1,
+     $                     CZERO, A( K+1, K-1 ), 1 )
+               A( K-1, K-1 ) = A( K-1, K-1 ) -
+     $                         CDOTU( N-K, WORK, 1, A( K+1, K-1 ), 1 )
+            END IF
+            KSTEP = 2
+         END IF  
+*
+         IF( KSTEP.EQ.1 ) THEN
+*
+*           Interchange rows and columns K and IPIV(K) in the trailing
+*           submatrix A(k-1:n,k-1:n)
+*
+            KP = IPIV( K )
+            IF( KP.NE.K ) THEN
+               IF( KP.LT.N )
+     $            CALL CSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
+               CALL CSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA )
+               TEMP = A( K, K )
+               A( K, K ) = A( KP, KP )
+               A( KP, KP ) = TEMP
+            END IF
+         ELSE
+*
+*           Interchange rows and columns K and K-1 with -IPIV(K) and
+*           -IPIV(K-1) in the trailing submatrix A(k-1:n,k-1:n)
+*
+            KP = -IPIV( K )
+            IF( KP.NE.K ) THEN
+               IF( KP.LT.N )
+     $            CALL CSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
+               CALL CSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA )
+*
+               TEMP = A( K, K )
+               A( K, K ) = A( KP, KP )
+               A( KP, KP ) = TEMP
+               TEMP = A( K, K-1 )
+               A( K, K-1 ) = A( KP, K-1 )
+               A( KP, K-1 ) = TEMP
+            END IF
+*
+            K = K - 1
+            KP = -IPIV( K )
+            IF( KP.NE.K ) THEN
+               IF( KP.LT.N )
+     $            CALL CSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
+               CALL CSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA )
+               TEMP = A( K, K )
+               A( K, K ) = A( KP, KP )
+               A( KP, KP ) = TEMP
+            END IF
+         END IF
+*
+         K = K - 1
+         GO TO 50
+   60    CONTINUE
+      END IF
+*
+      RETURN
+*
+*     End of CSYTRI_ROOK
+*
+      END

lapack-netlib/SRC/csytrs_rook.f

@@ -0,0 +1,484 @@
+*> \brief \b CSYTRS_ROOK
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download CSYTRS_ROOK + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/csytrs_rook.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/csytrs_rook.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/csytrs_rook.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CSYTRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, LDB, N, NRHS
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       COMPLEX            A( LDA, * ), B( LDB, * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> CSYTRS_ROOK solves a system of linear equations A*X = B with
+*> a complex symmetric matrix A using the factorization A = U*D*U**T or
+*> A = L*D*L**T computed by CSYTRF_ROOK.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          Specifies whether the details of the factorization are stored
+*>          as an upper or lower triangular matrix.
+*>          = 'U':  Upper triangular, form is A = U*D*U**T;
+*>          = 'L':  Lower triangular, form is A = L*D*L**T.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*>          NRHS is INTEGER
+*>          The number of right hand sides, i.e., the number of columns
+*>          of the matrix B.  NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*>          A is COMPLEX array, dimension (LDA,N)
+*>          The block diagonal matrix D and the multipliers used to
+*>          obtain the factor U or L as computed by CSYTRF_ROOK.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          Details of the interchanges and the block structure of D
+*>          as determined by CSYTRF_ROOK.
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*>          B is COMPLEX array, dimension (LDB,NRHS)
+*>          On entry, the right hand side matrix B.
+*>          On exit, the solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*>          LDB is INTEGER
+*>          The leading dimension of the array B.  LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0:  successful exit
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup complexSYcomputational
+*
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>   November 2011, Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*>
+*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*>                  School of Mathematics,
+*>                  University of Manchester
+*>
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE CSYTRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
+     $                        INFO )
+*
+*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, LDB, N, NRHS
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      COMPLEX            A( LDA, * ), B( LDB, * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      COMPLEX            CONE
+      PARAMETER          ( CONE = ( 1.0E+0, 0.0E+0 ) )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            UPPER
+      INTEGER            J, K, KP
+      COMPLEX            AK, AKM1, AKM1K, BK, BKM1, DENOM
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      EXTERNAL           LSAME
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           CGEMV, CGERU, CSCAL, CSWAP, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+      INFO = 0
+      UPPER = LSAME( UPLO, 'U' )
+      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( NRHS.LT.0 ) THEN
+         INFO = -3
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -5
+      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+         INFO = -8
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'CSYTRS_ROOK', -INFO )
+         RETURN
+      END IF
+*
+*     Quick return if possible
+*
+      IF( N.EQ.0 .OR. NRHS.EQ.0 )
+     $   RETURN
+*
+      IF( UPPER ) THEN
+*
+*        Solve A*X = B, where A = U*D*U**T.
+*
+*        First solve U*D*X = B, overwriting B with X.
+*
+*        K is the main loop index, decreasing from N to 1 in steps of
+*        1 or 2, depending on the size of the diagonal blocks.
+*
+         K = N
+   10    CONTINUE
+*
+*        If K < 1, exit from loop.
+*
+         IF( K.LT.1 )
+     $      GO TO 30
+*
+         IF( IPIV( K ).GT.0 ) THEN
+*
+*           1 x 1 diagonal block
+*
+*           Interchange rows K and IPIV(K).
+*
+            KP = IPIV( K )
+            IF( KP.NE.K )
+     $         CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+*
+*           Multiply by inv(U(K)), where U(K) is the transformation
+*           stored in column K of A.
+*
+            CALL CGERU( K-1, NRHS, -CONE, A( 1, K ), 1, B( K, 1 ), LDB,
+     $                 B( 1, 1 ), LDB )
+*
+*           Multiply by the inverse of the diagonal block.
+*
+            CALL CSCAL( NRHS, CONE / A( K, K ), B( K, 1 ), LDB )
+            K = K - 1
+         ELSE
+*
+*           2 x 2 diagonal block
+*
+*           Interchange rows K and -IPIV(K) THEN K-1 and -IPIV(K-1)
+*
+            KP = -IPIV( K )
+            IF( KP.NE.K )
+     $         CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+*
+            KP = -IPIV( K-1 )
+            IF( KP.NE.K-1 )
+     $         CALL CSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
+*
+*           Multiply by inv(U(K)), where U(K) is the transformation
+*           stored in columns K-1 and K of A.
+*
+            IF( K.GT.2 ) THEN
+               CALL CGERU( K-2, NRHS,-CONE, A( 1, K ), 1, B( K, 1 ),
+     $                    LDB, B( 1, 1 ), LDB )
+               CALL CGERU( K-2, NRHS,-CONE, A( 1, K-1 ), 1, B( K-1, 1 ),
+     $                    LDB, B( 1, 1 ), LDB )
+            END IF
+*
+*           Multiply by the inverse of the diagonal block.
+*
+            AKM1K = A( K-1, K )
+            AKM1 = A( K-1, K-1 ) / AKM1K
+            AK = A( K, K ) / AKM1K
+            DENOM = AKM1*AK - CONE
+            DO 20 J = 1, NRHS
+               BKM1 = B( K-1, J ) / AKM1K
+               BK = B( K, J ) / AKM1K
+               B( K-1, J ) = ( AK*BKM1-BK ) / DENOM
+               B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM
+   20       CONTINUE
+            K = K - 2
+         END IF
+*
+         GO TO 10
+   30    CONTINUE
+*
+*        Next solve U**T *X = B, overwriting B with X.
+*
+*        K is the main loop index, increasing from 1 to N in steps of
+*        1 or 2, depending on the size of the diagonal blocks.
+*
+         K = 1
+   40    CONTINUE
+*
+*        If K > N, exit from loop.
+*
+         IF( K.GT.N )
+     $      GO TO 50
+*
+         IF( IPIV( K ).GT.0 ) THEN
+*
+*           1 x 1 diagonal block
+*
+*           Multiply by inv(U**T(K)), where U(K) is the transformation
+*           stored in column K of A.
+*
+            IF( K.GT.1 )
+     $         CALL CGEMV( 'Transpose', K-1, NRHS, -CONE, B,
+     $                     LDB, A( 1, K ), 1, CONE, B( K, 1 ), LDB )
+*
+*           Interchange rows K and IPIV(K).
+*
+            KP = IPIV( K )
+            IF( KP.NE.K )
+     $         CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+            K = K + 1
+         ELSE
+*
+*           2 x 2 diagonal block
+*
+*           Multiply by inv(U**T(K+1)), where U(K+1) is the transformation
+*           stored in columns K and K+1 of A.
+*
+            IF( K.GT.1 ) THEN
+               CALL CGEMV( 'Transpose', K-1, NRHS, -CONE, B,
+     $                     LDB, A( 1, K ), 1, CONE, B( K, 1 ), LDB )
+               CALL CGEMV( 'Transpose', K-1, NRHS, -CONE, B,
+     $                     LDB, A( 1, K+1 ), 1, CONE, B( K+1, 1 ), LDB )
+            END IF
+*
+*           Interchange rows K and -IPIV(K) THEN K+1 and -IPIV(K+1).
+*
+            KP = -IPIV( K )
+            IF( KP.NE.K )
+     $         CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+*
+            KP = -IPIV( K+1 )
+            IF( KP.NE.K+1 )
+     $         CALL CSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
+*
+            K = K + 2
+         END IF
+*
+         GO TO 40
+   50    CONTINUE
+*
+      ELSE
+*
+*        Solve A*X = B, where A = L*D*L**T.
+*
+*        First solve L*D*X = B, overwriting B with X.
+*
+*        K is the main loop index, increasing from 1 to N in steps of
+*        1 or 2, depending on the size of the diagonal blocks.
+*
+         K = 1
+   60    CONTINUE
+*
+*        If K > N, exit from loop.
+*
+         IF( K.GT.N )
+     $      GO TO 80
+*
+         IF( IPIV( K ).GT.0 ) THEN
+*
+*           1 x 1 diagonal block
+*
+*           Interchange rows K and IPIV(K).
+*
+            KP = IPIV( K )
+            IF( KP.NE.K )
+     $         CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+*
+*           Multiply by inv(L(K)), where L(K) is the transformation
+*           stored in column K of A.
+*
+            IF( K.LT.N )
+     $         CALL CGERU( N-K, NRHS, -CONE, A( K+1, K ), 1, B( K, 1 ),
+     $                    LDB, B( K+1, 1 ), LDB )
+*
+*           Multiply by the inverse of the diagonal block.
+*
+            CALL CSCAL( NRHS, CONE / A( K, K ), B( K, 1 ), LDB )
+            K = K + 1
+         ELSE
+*
+*           2 x 2 diagonal block
+*
+*           Interchange rows K and -IPIV(K) THEN K+1 and -IPIV(K+1)
+*
+            KP = -IPIV( K )
+            IF( KP.NE.K )
+     $         CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+*
+            KP = -IPIV( K+1 )
+            IF( KP.NE.K+1 )
+     $         CALL CSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
+*
+*           Multiply by inv(L(K)), where L(K) is the transformation
+*           stored in columns K and K+1 of A.
+*
+            IF( K.LT.N-1 ) THEN
+               CALL CGERU( N-K-1, NRHS,-CONE, A( K+2, K ), 1, B( K, 1 ),
+     $                    LDB, B( K+2, 1 ), LDB )
+               CALL CGERU( N-K-1, NRHS,-CONE, A( K+2, K+1 ), 1,
+     $                    B( K+1, 1 ), LDB, B( K+2, 1 ), LDB )
+            END IF
+*
+*           Multiply by the inverse of the diagonal block.
+*
+            AKM1K = A( K+1, K )
+            AKM1 = A( K, K ) / AKM1K
+            AK = A( K+1, K+1 ) / AKM1K
+            DENOM = AKM1*AK - CONE
+            DO 70 J = 1, NRHS
+               BKM1 = B( K, J ) / AKM1K
+               BK = B( K+1, J ) / AKM1K
+               B( K, J ) = ( AK*BKM1-BK ) / DENOM
+               B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
+   70       CONTINUE
+            K = K + 2
+         END IF
+*
+         GO TO 60
+   80    CONTINUE
+*
+*        Next solve L**T *X = B, overwriting B with X.
+*
+*        K is the main loop index, decreasing from N to 1 in steps of
+*        1 or 2, depending on the size of the diagonal blocks.
+*
+         K = N
+   90    CONTINUE
+*
+*        If K < 1, exit from loop.
+*
+         IF( K.LT.1 )
+     $      GO TO 100
+*
+         IF( IPIV( K ).GT.0 ) THEN
+*
+*           1 x 1 diagonal block
+*
+*           Multiply by inv(L**T(K)), where L(K) is the transformation
+*           stored in column K of A.
+*
+            IF( K.LT.N )
+     $         CALL CGEMV( 'Transpose', N-K, NRHS, -CONE, B( K+1, 1 ),
+     $                     LDB, A( K+1, K ), 1, CONE, B( K, 1 ), LDB )
+*
+*           Interchange rows K and IPIV(K).
+*
+            KP = IPIV( K )
+            IF( KP.NE.K )
+     $         CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+            K = K - 1
+         ELSE
+*
+*           2 x 2 diagonal block
+*
+*           Multiply by inv(L**T(K-1)), where L(K-1) is the transformation
+*           stored in columns K-1 and K of A.
+*
+            IF( K.LT.N ) THEN
+               CALL CGEMV( 'Transpose', N-K, NRHS, -CONE, B( K+1, 1 ),
+     $                     LDB, A( K+1, K ), 1, CONE, B( K, 1 ), LDB )
+               CALL CGEMV( 'Transpose', N-K, NRHS, -CONE, B( K+1, 1 ),
+     $                     LDB, A( K+1, K-1 ), 1, CONE, B( K-1, 1 ),
+     $                     LDB )
+            END IF
+*
+*           Interchange rows K and -IPIV(K) THEN K-1 and -IPIV(K-1)
+*
+            KP = -IPIV( K )
+            IF( KP.NE.K )
+     $         CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+*
+            KP = -IPIV( K-1 )
+            IF( KP.NE.K-1 )
+     $         CALL CSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
+*
+            K = K - 2
+         END IF
+*
+         GO TO 90
+  100    CONTINUE
+      END IF
+*
+      RETURN
+*
+*     End of CSYTRS_ROOK
+*
+      END

lapack-netlib/SRC/ctpmqrt.f

@@ -175,7 +175,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date April 2012
+*> \date November 2013
 *
 *> \ingroup complexOTHERcomputational
 *
@@ -216,10 +216,10 @@
       SUBROUTINE CTPMQRT( SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT,
      $                    A, LDA, B, LDB, WORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.1) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     April 2012
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER SIDE, TRANS
@@ -235,7 +235,7 @@
 *     ..
 *     .. Local Scalars ..
       LOGICAL            LEFT, RIGHT, TRAN, NOTRAN
-      INTEGER            I, IB, MB, LB, KF, Q
+      INTEGER            I, IB, MB, LB, KF, LDAQ, LDVQ
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -257,10 +257,12 @@
       TRAN   = LSAME( TRANS, 'C' )
       NOTRAN = LSAME( TRANS, 'N' )
 *      
-      IF( LEFT ) THEN
-         Q = M
+      IF ( LEFT ) THEN
+         LDVQ = MAX( 1, M )
+         LDAQ = MAX( 1, K )
       ELSE IF ( RIGHT ) THEN
-         Q = N
+         LDVQ = MAX( 1, N )
+         LDAQ = MAX( 1, M )
       END IF
       IF( .NOT.LEFT .AND. .NOT.RIGHT ) THEN
          INFO = -1
@@ -274,13 +276,13 @@
          INFO = -5
       ELSE IF( L.LT.0 .OR. L.GT.K ) THEN
          INFO = -6         
-      ELSE IF( NB.LT.1 .OR. NB.GT.K ) THEN
+      ELSE IF( NB.LT.1 .OR. (NB.GT.K .AND. K.GT.0) ) THEN
          INFO = -7
-      ELSE IF( LDV.LT.MAX( 1, Q ) ) THEN
+      ELSE IF( LDV.LT.LDVQ ) THEN
          INFO = -9
       ELSE IF( LDT.LT.NB ) THEN
          INFO = -11
-      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
+      ELSE IF( LDA.LT.LDAQ ) THEN
          INFO = -13
       ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
          INFO = -15

lapack-netlib/SRC/ctpqrt.f

@@ -132,7 +132,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date April 2012
+*> \date November 2013
 *
 *> \ingroup complexOTHERcomputational
 *
@@ -189,10 +189,10 @@
       SUBROUTINE CTPQRT( M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK,
      $                   INFO )
 *
-*  -- LAPACK computational routine (version 3.4.1) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     April 2012
+*     November 2013
 *
 *     .. Scalar Arguments ..
       INTEGER INFO, LDA, LDB, LDT, N, M, L, NB
@@ -219,9 +219,9 @@
          INFO = -1
       ELSE IF( N.LT.0 ) THEN
          INFO = -2
-      ELSE IF( L.LT.0 .OR. L.GT.MIN(M,N) ) THEN
+      ELSE IF( L.LT.0 .OR. (L.GT.MIN(M,N) .AND. MIN(M,N).GE.0)) THEN
          INFO = -3
-      ELSE IF( NB.LT.1 .OR. NB.GT.N ) THEN
+      ELSE IF( NB.LT.1 .OR. (NB.GT.N .AND. N.GT.0)) THEN
          INFO = -4
       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
          INFO = -6

lapack-netlib/SRC/cunbdb.f

@@ -255,7 +255,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date November 2011
+*> \date November 2013
 *
 *> \ingroup complexOTHERcomputational
 *
@@ -287,10 +287,10 @@
      $                   X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
      $                   TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2011
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          SIGNS, TRANS
@@ -420,19 +420,33 @@
             THETA(I) = ATAN2( SCNRM2( M-P-I+1, X21(I,I), 1 ),
      $                 SCNRM2( P-I+1, X11(I,I), 1 ) )
 *
-            CALL CLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) )
+            IF( P .GT. I ) THEN
+               CALL CLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) )
+            ELSE IF ( P .EQ. I ) THEN
+               CALL CLARFGP( P-I+1, X11(I,I), X11(I,I), 1, TAUP1(I) )
+            END IF
             X11(I,I) = ONE
-            CALL CLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1, TAUP2(I) )
+            IF ( M-P .GT. I ) THEN
+               CALL CLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1, 
+     $                       TAUP2(I) )
+            ELSE IF ( M-P .EQ. I ) THEN
+               CALL CLARFGP( M-P-I+1, X21(I,I), X21(I,I), 1,
+     $                       TAUP2(I) )
+            END IF
             X21(I,I) = ONE
 *
-            CALL CLARF( 'L', P-I+1, Q-I, X11(I,I), 1, CONJG(TAUP1(I)),
-     $                  X11(I,I+1), LDX11, WORK )
-            CALL CLARF( 'L', P-I+1, M-Q-I+1, X11(I,I), 1,
-     $                  CONJG(TAUP1(I)), X12(I,I), LDX12, WORK )
-            CALL CLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1, CONJG(TAUP2(I)),
-     $                  X21(I,I+1), LDX21, WORK )
-            CALL CLARF( 'L', M-P-I+1, M-Q-I+1, X21(I,I), 1,
-     $                  CONJG(TAUP2(I)), X22(I,I), LDX22, WORK )
+            IF ( Q .GT. I ) THEN
+               CALL CLARF( 'L', P-I+1, Q-I, X11(I,I), 1, 
+     $                     CONJG(TAUP1(I)), X11(I,I+1), LDX11, WORK )
+               CALL CLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1,
+     $                     CONJG(TAUP2(I)), X21(I,I+1), LDX21, WORK )
+            END IF
+            IF ( M-Q+1 .GT. I ) THEN
+               CALL CLARF( 'L', P-I+1, M-Q-I+1, X11(I,I), 1,
+     $                     CONJG(TAUP1(I)), X12(I,I), LDX12, WORK )
+               CALL CLARF( 'L', M-P-I+1, M-Q-I+1, X21(I,I), 1,
+     $                     CONJG(TAUP2(I)), X22(I,I), LDX22, WORK )
+            END IF
 *
             IF( I .LT. Q ) THEN
                CALL CSCAL( Q-I, CMPLX( -Z1*Z3*SIN(THETA(I)), 0.0E0 ),
@@ -451,13 +465,25 @@
 *
             IF( I .LT. Q ) THEN
                CALL CLACGV( Q-I, X11(I,I+1), LDX11 )
-               CALL CLARFGP( Q-I, X11(I,I+1), X11(I,I+2), LDX11,
-     $                       TAUQ1(I) )
+               IF ( I .EQ. Q-1 ) THEN
+                  CALL CLARFGP( Q-I, X11(I,I+1), X11(I,I+1), LDX11,
+     $                          TAUQ1(I) )
+               ELSE
+                  CALL CLARFGP( Q-I, X11(I,I+1), X11(I,I+2), LDX11,
+     $                          TAUQ1(I) )
+               END IF
                X11(I,I+1) = ONE
             END IF
-            CALL CLACGV( M-Q-I+1, X12(I,I), LDX12 )
-            CALL CLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12,
-     $                    TAUQ2(I) )
+            IF ( M-Q+1 .GT. I ) THEN
+               CALL CLACGV( M-Q-I+1, X12(I,I), LDX12 )
+               IF ( M-Q .EQ. I ) THEN
+                  CALL CLARFGP( M-Q-I+1, X12(I,I), X12(I,I), LDX12,
+     $                          TAUQ2(I) )
+               ELSE
+                  CALL CLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12,
+     $                          TAUQ2(I) )
+               END IF
+            END IF
             X12(I,I) = ONE
 *
             IF( I .LT. Q ) THEN
@@ -466,10 +492,14 @@
                CALL CLARF( 'R', M-P-I, Q-I, X11(I,I+1), LDX11, TAUQ1(I),
      $                     X21(I+1,I+1), LDX21, WORK )
             END IF
-            CALL CLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
-     $                  X12(I+1,I), LDX12, WORK )
-            CALL CLARF( 'R', M-P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
-     $                  X22(I+1,I), LDX22, WORK )
+            IF ( P .GT. I ) THEN
+               CALL CLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
+     $                     X12(I+1,I), LDX12, WORK )
+            END IF
+            IF ( M-P .GT. I ) THEN
+               CALL CLARF( 'R', M-P-I, M-Q-I+1, X12(I,I), LDX12,
+     $                     TAUQ2(I), X22(I+1,I), LDX22, WORK )
+            END IF
 *
             IF( I .LT. Q )
      $         CALL CLACGV( Q-I, X11(I,I+1), LDX11 )
@@ -484,12 +514,19 @@
             CALL CSCAL( M-Q-I+1, CMPLX( -Z1*Z4, 0.0E0 ), X12(I,I),
      $                  LDX12 )
             CALL CLACGV( M-Q-I+1, X12(I,I), LDX12 )
-            CALL CLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12,
-     $                    TAUQ2(I) )
+            IF ( I .GE. M-Q ) THEN
+               CALL CLARFGP( M-Q-I+1, X12(I,I), X12(I,I), LDX12,
+     $                       TAUQ2(I) )
+            ELSE
+               CALL CLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12,
+     $                       TAUQ2(I) )
+            END IF
             X12(I,I) = ONE
 *
-            CALL CLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
-     $                  X12(I+1,I), LDX12, WORK )
+            IF ( P .GT. I ) THEN
+               CALL CLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
+     $                     X12(I+1,I), LDX12, WORK )
+            END IF
             IF( M-P-Q .GE. 1 )
      $         CALL CLARF( 'R', M-P-Q, M-Q-I+1, X12(I,I), LDX12,
      $                     TAUQ2(I), X22(Q+1,I), LDX22, WORK )
@@ -548,8 +585,13 @@
 *
             CALL CLARFGP( P-I+1, X11(I,I), X11(I,I+1), LDX11, TAUP1(I) )
             X11(I,I) = ONE
-            CALL CLARFGP( M-P-I+1, X21(I,I), X21(I,I+1), LDX21,
-     $                    TAUP2(I) )
+            IF ( I .EQ. M-P ) THEN
+               CALL CLARFGP( M-P-I+1, X21(I,I), X21(I,I), LDX21,
+     $                       TAUP2(I) )
+            ELSE
+               CALL CLARFGP( M-P-I+1, X21(I,I), X21(I,I+1), LDX21,
+     $                       TAUP2(I) )
+            END IF
             X21(I,I) = ONE
 *
             CALL CLARF( 'R', Q-I, P-I+1, X11(I,I), LDX11, TAUP1(I),
@@ -594,9 +636,11 @@
             END IF
             CALL CLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1, CONJG(TAUQ2(I)),
      $                  X12(I,I+1), LDX12, WORK )
-            CALL CLARF( 'L', M-Q-I+1, M-P-I, X12(I,I), 1,
-     $                  CONJG(TAUQ2(I)), X22(I,I+1), LDX22, WORK )
-*
+
+            IF ( M-P .GT. I ) THEN
+               CALL CLARF( 'L', M-Q-I+1, M-P-I, X12(I,I), 1,
+     $                     CONJG(TAUQ2(I)), X22(I,I+1), LDX22, WORK )
+            END IF
          END DO
 *
 *        Reduce columns Q + 1, ..., P of X12, X22
@@ -607,8 +651,10 @@
             CALL CLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, TAUQ2(I) )
             X12(I,I) = ONE
 *
-            CALL CLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1, CONJG(TAUQ2(I)),
-     $                  X12(I,I+1), LDX12, WORK )
+            IF ( P .GT. I ) THEN
+               CALL CLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1,
+     $                     CONJG(TAUQ2(I)), X12(I,I+1), LDX12, WORK )
+            END IF
             IF( M-P-Q .GE. 1 )
      $         CALL CLARF( 'L', M-Q-I+1, M-P-Q, X12(I,I), 1,
      $                     CONJG(TAUQ2(I)), X22(I,Q+1), LDX22, WORK )
@@ -624,10 +670,11 @@
             CALL CLARFGP( M-P-Q-I+1, X22(P+I,Q+I), X22(P+I+1,Q+I), 1,
      $                    TAUQ2(P+I) )
             X22(P+I,Q+I) = ONE
-*
-            CALL CLARF( 'L', M-P-Q-I+1, M-P-Q-I, X22(P+I,Q+I), 1,
-     $                  CONJG(TAUQ2(P+I)), X22(P+I,Q+I+1), LDX22, WORK )
-*
+            IF ( M-P-Q .NE. I ) THEN
+               CALL CLARF( 'L', M-P-Q-I+1, M-P-Q-I, X22(P+I,Q+I), 1,
+     $                     CONJG(TAUQ2(P+I)), X22(P+I,Q+I+1), LDX22,
+     $                     WORK )
+            END IF
          END DO
 *
       END IF

lapack-netlib/SRC/cunbdb1.f

@@ -0,0 +1,327 @@
+*> \brief \b CUNBDB1
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download CUNBDB1 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cunbdb1.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cunbdb1.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cunbdb1.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CUNBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
+*                           TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            INFO, LWORK, M, P, Q, LDX11, LDX21
+*       ..
+*       .. Array Arguments ..
+*       REAL               PHI(*), THETA(*)
+*       COMPLEX            TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*),
+*      $                   X11(LDX11,*), X21(LDX21,*)
+*       ..
+*  
+* 
+*> \par Purpose:
+*> =============
+*>
+*>\verbatim
+*>
+*> CUNBDB1 simultaneously bidiagonalizes the blocks of a tall and skinny
+*> matrix X with orthonomal columns:
+*>
+*>                            [ B11 ]
+*>      [ X11 ]   [ P1 |    ] [  0  ]
+*>      [-----] = [---------] [-----] Q1**T .
+*>      [ X21 ]   [    | P2 ] [ B21 ]
+*>                            [  0  ]
+*>
+*> X11 is P-by-Q, and X21 is (M-P)-by-Q. Q must be no larger than P,
+*> M-P, or M-Q. Routines CUNBDB2, CUNBDB3, and CUNBDB4 handle cases in
+*> which Q is not the minimum dimension.
+*>
+*> The unitary matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P),
+*> and (M-Q)-by-(M-Q), respectively. They are represented implicitly by
+*> Householder vectors.
+*>
+*> B11 and B12 are Q-by-Q bidiagonal matrices represented implicitly by
+*> angles THETA, PHI.
+*>
+*>\endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>           The number of rows X11 plus the number of rows in X21.
+*> \endverbatim
+*>
+*> \param[in] P
+*> \verbatim
+*>          P is INTEGER
+*>           The number of rows in X11. 0 <= P <= M.
+*> \endverbatim
+*>
+*> \param[in] Q
+*> \verbatim
+*>          Q is INTEGER
+*>           The number of columns in X11 and X21. 0 <= Q <=
+*>           MIN(P,M-P,M-Q).
+*> \endverbatim
+*>
+*> \param[in,out] X11
+*> \verbatim
+*>          X11 is COMPLEX array, dimension (LDX11,Q)
+*>           On entry, the top block of the matrix X to be reduced. On
+*>           exit, the columns of tril(X11) specify reflectors for P1 and
+*>           the rows of triu(X11,1) specify reflectors for Q1.
+*> \endverbatim
+*>
+*> \param[in] LDX11
+*> \verbatim
+*>          LDX11 is INTEGER
+*>           The leading dimension of X11. LDX11 >= P.
+*> \endverbatim
+*>
+*> \param[in,out] X21
+*> \verbatim
+*>          X21 is COMPLEX array, dimension (LDX21,Q)
+*>           On entry, the bottom block of the matrix X to be reduced. On
+*>           exit, the columns of tril(X21) specify reflectors for P2.
+*> \endverbatim
+*>
+*> \param[in] LDX21
+*> \verbatim
+*>          LDX21 is INTEGER
+*>           The leading dimension of X21. LDX21 >= M-P.
+*> \endverbatim
+*>
+*> \param[out] THETA
+*> \verbatim
+*>          THETA is REAL array, dimension (Q)
+*>           The entries of the bidiagonal blocks B11, B21 are defined by
+*>           THETA and PHI. See Further Details.
+*> \endverbatim
+*>
+*> \param[out] PHI
+*> \verbatim
+*>          PHI is REAL array, dimension (Q-1)
+*>           The entries of the bidiagonal blocks B11, B21 are defined by
+*>           THETA and PHI. See Further Details.
+*> \endverbatim
+*>
+*> \param[out] TAUP1
+*> \verbatim
+*>          TAUP1 is COMPLEX array, dimension (P)
+*>           The scalar factors of the elementary reflectors that define
+*>           P1.
+*> \endverbatim
+*>
+*> \param[out] TAUP2
+*> \verbatim
+*>          TAUP2 is COMPLEX array, dimension (M-P)
+*>           The scalar factors of the elementary reflectors that define
+*>           P2.
+*> \endverbatim
+*>
+*> \param[out] TAUQ1
+*> \verbatim
+*>          TAUQ1 is COMPLEX array, dimension (Q)
+*>           The scalar factors of the elementary reflectors that define
+*>           Q1.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX array, dimension (LWORK)
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>           The dimension of the array WORK. LWORK >= M-Q.
+*> 
+*>           If LWORK = -1, then a workspace query is assumed; the routine
+*>           only calculates the optimal size of the WORK array, returns
+*>           this value as the first entry of the WORK array, and no error
+*>           message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>           = 0:  successful exit.
+*>           < 0:  if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date July 2012
+*
+*> \ingroup complexOTHERcomputational
+*
+*> \par Further Details:
+*  =====================
+
+*> \verbatim
+*>
+*>  The upper-bidiagonal blocks B11, B21 are represented implicitly by
+*>  angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry
+*>  in each bidiagonal band is a product of a sine or cosine of a THETA
+*>  with a sine or cosine of a PHI. See [1] or CUNCSD for details.
+*>
+*>  P1, P2, and Q1 are represented as products of elementary reflectors.
+*>  See CUNCSD2BY1 for details on generating P1, P2, and Q1 using CUNGQR
+*>  and CUNGLQ.
+*> \endverbatim
+*
+*> \par References:
+*  ================
+*>
+*>  [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
+*>      Algorithms, 50(1):33-65, 2009.
+*>
+*  =====================================================================
+      SUBROUTINE CUNBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
+     $                    TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO )
+*
+*  -- LAPACK computational routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     July 2012
+*
+*     .. Scalar Arguments ..
+      INTEGER            INFO, LWORK, M, P, Q, LDX11, LDX21
+*     ..
+*     .. Array Arguments ..
+      REAL               PHI(*), THETA(*)
+      COMPLEX            TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*),
+     $                   X11(LDX11,*), X21(LDX21,*)
+*     ..
+*
+*  ====================================================================
+*
+*     .. Parameters ..
+      COMPLEX            ONE
+      PARAMETER          ( ONE = (1.0E0,0.0E0) )
+*     ..
+*     .. Local Scalars ..
+      REAL               C, S
+      INTEGER            CHILDINFO, I, ILARF, IORBDB5, LLARF, LORBDB5,
+     $                   LWORKMIN, LWORKOPT
+      LOGICAL            LQUERY
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           CLARF, CLARFGP, CUNBDB5, CSROT, XERBLA
+      EXTERNAL           CLACGV
+*     ..
+*     .. External Functions ..
+      REAL               SCNRM2
+      EXTERNAL           SCNRM2
+*     ..
+*     .. Intrinsic Function ..
+      INTRINSIC          ATAN2, COS, MAX, SIN, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+*     Test input arguments
+*
+      INFO = 0
+      LQUERY = LWORK .EQ. -1
+*
+      IF( M .LT. 0 ) THEN
+         INFO = -1
+      ELSE IF( P .LT. Q .OR. M-P .LT. Q ) THEN
+         INFO = -2
+      ELSE IF( Q .LT. 0 .OR. M-Q .LT. Q ) THEN
+         INFO = -3
+      ELSE IF( LDX11 .LT. MAX( 1, P ) ) THEN
+         INFO = -5
+      ELSE IF( LDX21 .LT. MAX( 1, M-P ) ) THEN
+         INFO = -7
+      END IF
+*
+*     Compute workspace
+*
+      IF( INFO .EQ. 0 ) THEN
+         ILARF = 2
+         LLARF = MAX( P-1, M-P-1, Q-1 )
+         IORBDB5 = 2
+         LORBDB5 = Q-2
+         LWORKOPT = MAX( ILARF+LLARF-1, IORBDB5+LORBDB5-1 )
+         LWORKMIN = LWORKOPT
+         WORK(1) = LWORKOPT
+         IF( LWORK .LT. LWORKMIN .AND. .NOT.LQUERY ) THEN
+           INFO = -14
+         END IF
+      END IF
+      IF( INFO .NE. 0 ) THEN
+         CALL XERBLA( 'CUNBDB1', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+*
+*     Reduce columns 1, ..., Q of X11 and X21
+*
+      DO I = 1, Q
+*
+         CALL CLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) )
+         CALL CLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1, TAUP2(I) )
+         THETA(I) = ATAN2( REAL( X21(I,I) ), REAL( X11(I,I) ) )
+         C = COS( THETA(I) )
+         S = SIN( THETA(I) )
+         X11(I,I) = ONE
+         X21(I,I) = ONE
+         CALL CLARF( 'L', P-I+1, Q-I, X11(I,I), 1, CONJG(TAUP1(I)),
+     $               X11(I,I+1), LDX11, WORK(ILARF) )
+         CALL CLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1, CONJG(TAUP2(I)),
+     $               X21(I,I+1), LDX21, WORK(ILARF) )
+*
+         IF( I .LT. Q ) THEN
+            CALL CSROT( Q-I, X11(I,I+1), LDX11, X21(I,I+1), LDX21, C,
+     $                  S )
+            CALL CLACGV( Q-I, X21(I,I+1), LDX21 )
+            CALL CLARFGP( Q-I, X21(I,I+1), X21(I,I+2), LDX21, TAUQ1(I) )
+            S = REAL( X21(I,I+1) )
+            X21(I,I+1) = ONE
+            CALL CLARF( 'R', P-I, Q-I, X21(I,I+1), LDX21, TAUQ1(I),
+     $                  X11(I+1,I+1), LDX11, WORK(ILARF) )
+            CALL CLARF( 'R', M-P-I, Q-I, X21(I,I+1), LDX21, TAUQ1(I),
+     $                  X21(I+1,I+1), LDX21, WORK(ILARF) )
+            CALL CLACGV( Q-I, X21(I,I+1), LDX21 )
+            C = SQRT( SCNRM2( P-I, X11(I+1,I+1), 1, X11(I+1,I+1),
+     $          1 )**2 + SCNRM2( M-P-I, X21(I+1,I+1), 1, X21(I+1,I+1),
+     $          1 )**2 )
+            PHI(I) = ATAN2( S, C )
+            CALL CUNBDB5( P-I, M-P-I, Q-I-1, X11(I+1,I+1), 1,
+     $                    X21(I+1,I+1), 1, X11(I+1,I+2), LDX11,
+     $                    X21(I+1,I+2), LDX21, WORK(IORBDB5), LORBDB5,
+     $                    CHILDINFO )
+         END IF
+*
+      END DO
+*
+      RETURN
+*
+*     End of CUNBDB1
+*
+      END
+

lapack-netlib/SRC/cunbdb2.f

@@ -0,0 +1,337 @@
+*> \brief \b CUNBDB2
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download CUNBDB2 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cunbdb2.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cunbdb2.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cunbdb2.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CUNBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
+*                           TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            INFO, LWORK, M, P, Q, LDX11, LDX21
+*       ..
+*       .. Array Arguments ..
+*       REAL               PHI(*), THETA(*)
+*       COMPLEX            TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*),
+*      $                   X11(LDX11,*), X21(LDX21,*)
+*       ..
+*  
+* 
+*> \par Purpose:
+*> =============
+*>
+*>\verbatim
+*>
+*> CUNBDB2 simultaneously bidiagonalizes the blocks of a tall and skinny
+*> matrix X with orthonomal columns:
+*>
+*>                            [ B11 ]
+*>      [ X11 ]   [ P1 |    ] [  0  ]
+*>      [-----] = [---------] [-----] Q1**T .
+*>      [ X21 ]   [    | P2 ] [ B21 ]
+*>                            [  0  ]
+*>
+*> X11 is P-by-Q, and X21 is (M-P)-by-Q. P must be no larger than M-P,
+*> Q, or M-Q. Routines CUNBDB1, CUNBDB3, and CUNBDB4 handle cases in
+*> which P is not the minimum dimension.
+*>
+*> The unitary matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P),
+*> and (M-Q)-by-(M-Q), respectively. They are represented implicitly by
+*> Householder vectors.
+*>
+*> B11 and B12 are P-by-P bidiagonal matrices represented implicitly by
+*> angles THETA, PHI.
+*>
+*>\endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>           The number of rows X11 plus the number of rows in X21.
+*> \endverbatim
+*>
+*> \param[in] P
+*> \verbatim
+*>          P is INTEGER
+*>           The number of rows in X11. 0 <= P <= min(M-P,Q,M-Q).
+*> \endverbatim
+*>
+*> \param[in] Q
+*> \verbatim
+*>          Q is INTEGER
+*>           The number of columns in X11 and X21. 0 <= Q <= M.
+*> \endverbatim
+*>
+*> \param[in,out] X11
+*> \verbatim
+*>          X11 is COMPLEX array, dimension (LDX11,Q)
+*>           On entry, the top block of the matrix X to be reduced. On
+*>           exit, the columns of tril(X11) specify reflectors for P1 and
+*>           the rows of triu(X11,1) specify reflectors for Q1.
+*> \endverbatim
+*>
+*> \param[in] LDX11
+*> \verbatim
+*>          LDX11 is INTEGER
+*>           The leading dimension of X11. LDX11 >= P.
+*> \endverbatim
+*>
+*> \param[in,out] X21
+*> \verbatim
+*>          X21 is COMPLEX array, dimension (LDX21,Q)
+*>           On entry, the bottom block of the matrix X to be reduced. On
+*>           exit, the columns of tril(X21) specify reflectors for P2.
+*> \endverbatim
+*>
+*> \param[in] LDX21
+*> \verbatim
+*>          LDX21 is INTEGER
+*>           The leading dimension of X21. LDX21 >= M-P.
+*> \endverbatim
+*>
+*> \param[out] THETA
+*> \verbatim
+*>          THETA is REAL array, dimension (Q)
+*>           The entries of the bidiagonal blocks B11, B21 are defined by
+*>           THETA and PHI. See Further Details.
+*> \endverbatim
+*>
+*> \param[out] PHI
+*> \verbatim
+*>          PHI is REAL array, dimension (Q-1)
+*>           The entries of the bidiagonal blocks B11, B21 are defined by
+*>           THETA and PHI. See Further Details.
+*> \endverbatim
+*>
+*> \param[out] TAUP1
+*> \verbatim
+*>          TAUP1 is COMPLEX array, dimension (P)
+*>           The scalar factors of the elementary reflectors that define
+*>           P1.
+*> \endverbatim
+*>
+*> \param[out] TAUP2
+*> \verbatim
+*>          TAUP2 is COMPLEX array, dimension (M-P)
+*>           The scalar factors of the elementary reflectors that define
+*>           P2.
+*> \endverbatim
+*>
+*> \param[out] TAUQ1
+*> \verbatim
+*>          TAUQ1 is COMPLEX array, dimension (Q)
+*>           The scalar factors of the elementary reflectors that define
+*>           Q1.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX array, dimension (LWORK)
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>           The dimension of the array WORK. LWORK >= M-Q.
+*> 
+*>           If LWORK = -1, then a workspace query is assumed; the routine
+*>           only calculates the optimal size of the WORK array, returns
+*>           this value as the first entry of the WORK array, and no error
+*>           message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>           = 0:  successful exit.
+*>           < 0:  if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*>
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date July 2012
+*
+*> \ingroup complexOTHERcomputational
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  The upper-bidiagonal blocks B11, B21 are represented implicitly by
+*>  angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry
+*>  in each bidiagonal band is a product of a sine or cosine of a THETA
+*>  with a sine or cosine of a PHI. See [1] or CUNCSD for details.
+*>
+*>  P1, P2, and Q1 are represented as products of elementary reflectors.
+*>  See CUNCSD2BY1 for details on generating P1, P2, and Q1 using CUNGQR
+*>  and CUNGLQ.
+*> \endverbatim
+*
+*> \par References:
+*  ================
+*>
+*>  [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
+*>      Algorithms, 50(1):33-65, 2009.
+*>
+*  =====================================================================
+      SUBROUTINE CUNBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
+     $                    TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO )
+*
+*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     July 2012
+*
+*     .. Scalar Arguments ..
+      INTEGER            INFO, LWORK, M, P, Q, LDX11, LDX21
+*     ..
+*     .. Array Arguments ..
+      REAL               PHI(*), THETA(*)
+      COMPLEX            TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*),
+     $                   X11(LDX11,*), X21(LDX21,*)
+*     ..
+*
+*  ====================================================================
+*
+*     .. Parameters ..
+      COMPLEX            NEGONE, ONE
+      PARAMETER          ( NEGONE = (-1.0E0,0.0E0),
+     $                     ONE = (1.0E0,0.0E0) )
+*     ..
+*     .. Local Scalars ..
+      REAL               C, S
+      INTEGER            CHILDINFO, I, ILARF, IORBDB5, LLARF, LORBDB5,
+     $                   LWORKMIN, LWORKOPT
+      LOGICAL            LQUERY
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           CLARF, CLARFGP, CUNBDB5, CSROT, CSCAL, XERBLA
+*     ..
+*     .. External Functions ..
+      REAL               SCNRM2
+      EXTERNAL           SCNRM2
+*     ..
+*     .. Intrinsic Function ..
+      INTRINSIC          ATAN2, COS, MAX, SIN, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+*     Test input arguments
+*
+      INFO = 0
+      LQUERY = LWORK .EQ. -1
+*
+      IF( M .LT. 0 ) THEN
+         INFO = -1
+      ELSE IF( P .LT. 0 .OR. P .GT. M-P ) THEN
+         INFO = -2
+      ELSE IF( Q .LT. 0 .OR. Q .LT. P .OR. M-Q .LT. P ) THEN
+         INFO = -3
+      ELSE IF( LDX11 .LT. MAX( 1, P ) ) THEN
+         INFO = -5
+      ELSE IF( LDX21 .LT. MAX( 1, M-P ) ) THEN
+         INFO = -7
+      END IF
+*
+*     Compute workspace
+*
+      IF( INFO .EQ. 0 ) THEN
+         ILARF = 2
+         LLARF = MAX( P-1, M-P, Q-1 )
+         IORBDB5 = 2
+         LORBDB5 = Q-1
+         LWORKOPT = MAX( ILARF+LLARF-1, IORBDB5+LORBDB5-1 )
+         LWORKMIN = LWORKOPT
+         WORK(1) = LWORKOPT
+         IF( LWORK .LT. LWORKMIN .AND. .NOT.LQUERY ) THEN
+           INFO = -14
+         END IF
+      END IF
+      IF( INFO .NE. 0 ) THEN
+         CALL XERBLA( 'CUNBDB2', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+*
+*     Reduce rows 1, ..., P of X11 and X21
+*
+      DO I = 1, P
+*      
+         IF( I .GT. 1 ) THEN
+            CALL CSROT( Q-I+1, X11(I,I), LDX11, X21(I-1,I), LDX21, C,
+     $                  S )
+         END IF
+         CALL CLACGV( Q-I+1, X11(I,I), LDX11 )
+         CALL CLARFGP( Q-I+1, X11(I,I), X11(I,I+1), LDX11, TAUQ1(I) )
+         C = REAL( X11(I,I) )
+         X11(I,I) = ONE
+         CALL CLARF( 'R', P-I, Q-I+1, X11(I,I), LDX11, TAUQ1(I),
+     $               X11(I+1,I), LDX11, WORK(ILARF) )
+         CALL CLARF( 'R', M-P-I+1, Q-I+1, X11(I,I), LDX11, TAUQ1(I),
+     $               X21(I,I), LDX21, WORK(ILARF) )
+         CALL CLACGV( Q-I+1, X11(I,I), LDX11 )
+         S = SQRT( SCNRM2( P-I, X11(I+1,I), 1, X11(I+1,I),
+     $       1 )**2 + SCNRM2( M-P-I+1, X21(I,I), 1, X21(I,I), 1 )**2 )
+         THETA(I) = ATAN2( S, C )
+*
+         CALL CUNBDB5( P-I, M-P-I+1, Q-I, X11(I+1,I), 1, X21(I,I), 1,
+     $                 X11(I+1,I+1), LDX11, X21(I,I+1), LDX21,
+     $                 WORK(IORBDB5), LORBDB5, CHILDINFO )
+         CALL CSCAL( P-I, NEGONE, X11(I+1,I), 1 )
+         CALL CLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1, TAUP2(I) )
+         IF( I .LT. P ) THEN
+            CALL CLARFGP( P-I, X11(I+1,I), X11(I+2,I), 1, TAUP1(I) )
+            PHI(I) = ATAN2( REAL( X11(I+1,I) ), REAL( X21(I,I) ) )
+            C = COS( PHI(I) )
+            S = SIN( PHI(I) )
+            X11(I+1,I) = ONE
+            CALL CLARF( 'L', P-I, Q-I, X11(I+1,I), 1, CONJG(TAUP1(I)),
+     $                  X11(I+1,I+1), LDX11, WORK(ILARF) )
+         END IF
+         X21(I,I) = ONE
+         CALL CLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1, CONJG(TAUP2(I)),
+     $               X21(I,I+1), LDX21, WORK(ILARF) )
+*
+      END DO
+*
+*     Reduce the bottom-right portion of X21 to the identity matrix
+*
+      DO I = P + 1, Q
+         CALL CLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1, TAUP2(I) )
+         X21(I,I) = ONE
+         CALL CLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1, CONJG(TAUP2(I)),
+     $               X21(I,I+1), LDX21, WORK(ILARF) )
+      END DO
+*
+      RETURN
+*
+*     End of CUNBDB2
+*
+      END
+

lapack-netlib/SRC/cunbdb3.f

@@ -0,0 +1,336 @@
+*> \brief \b CUNBDB3
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download CUNBDB3 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cunbdb3.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cunbdb3.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cunbdb3.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CUNBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
+*                           TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            INFO, LWORK, M, P, Q, LDX11, LDX21
+*       ..
+*       .. Array Arguments ..
+*       REAL               PHI(*), THETA(*)
+*       COMPLEX            TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*),
+*      $                   X11(LDX11,*), X21(LDX21,*)
+*       ..
+*  
+* 
+*> \par Purpose:
+*> =============
+*>
+*>\verbatim
+*>
+*> CUNBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny
+*> matrix X with orthonomal columns:
+*>
+*>                            [ B11 ]
+*>      [ X11 ]   [ P1 |    ] [  0  ]
+*>      [-----] = [---------] [-----] Q1**T .
+*>      [ X21 ]   [    | P2 ] [ B21 ]
+*>                            [  0  ]
+*>
+*> X11 is P-by-Q, and X21 is (M-P)-by-Q. M-P must be no larger than P,
+*> Q, or M-Q. Routines CUNBDB1, CUNBDB2, and CUNBDB4 handle cases in
+*> which M-P is not the minimum dimension.
+*>
+*> The unitary matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P),
+*> and (M-Q)-by-(M-Q), respectively. They are represented implicitly by
+*> Householder vectors.
+*>
+*> B11 and B12 are (M-P)-by-(M-P) bidiagonal matrices represented
+*> implicitly by angles THETA, PHI.
+*>
+*>\endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>           The number of rows X11 plus the number of rows in X21.
+*> \endverbatim
+*>
+*> \param[in] P
+*> \verbatim
+*>          P is INTEGER
+*>           The number of rows in X11. 0 <= P <= M. M-P <= min(P,Q,M-Q).
+*> \endverbatim
+*>
+*> \param[in] Q
+*> \verbatim
+*>          Q is INTEGER
+*>           The number of columns in X11 and X21. 0 <= Q <= M.
+*> \endverbatim
+*>
+*> \param[in,out] X11
+*> \verbatim
+*>          X11 is COMPLEX array, dimension (LDX11,Q)
+*>           On entry, the top block of the matrix X to be reduced. On
+*>           exit, the columns of tril(X11) specify reflectors for P1 and
+*>           the rows of triu(X11,1) specify reflectors for Q1.
+*> \endverbatim
+*>
+*> \param[in] LDX11
+*> \verbatim
+*>          LDX11 is INTEGER
+*>           The leading dimension of X11. LDX11 >= P.
+*> \endverbatim
+*>
+*> \param[in,out] X21
+*> \verbatim
+*>          X21 is COMPLEX array, dimension (LDX21,Q)
+*>           On entry, the bottom block of the matrix X to be reduced. On
+*>           exit, the columns of tril(X21) specify reflectors for P2.
+*> \endverbatim
+*>
+*> \param[in] LDX21
+*> \verbatim
+*>          LDX21 is INTEGER
+*>           The leading dimension of X21. LDX21 >= M-P.
+*> \endverbatim
+*>
+*> \param[out] THETA
+*> \verbatim
+*>          THETA is REAL array, dimension (Q)
+*>           The entries of the bidiagonal blocks B11, B21 are defined by
+*>           THETA and PHI. See Further Details.
+*> \endverbatim
+*>
+*> \param[out] PHI
+*> \verbatim
+*>          PHI is REAL array, dimension (Q-1)
+*>           The entries of the bidiagonal blocks B11, B21 are defined by
+*>           THETA and PHI. See Further Details.
+*> \endverbatim
+*>
+*> \param[out] TAUP1
+*> \verbatim
+*>          TAUP1 is COMPLEX array, dimension (P)
+*>           The scalar factors of the elementary reflectors that define
+*>           P1.
+*> \endverbatim
+*>
+*> \param[out] TAUP2
+*> \verbatim
+*>          TAUP2 is COMPLEX array, dimension (M-P)
+*>           The scalar factors of the elementary reflectors that define
+*>           P2.
+*> \endverbatim
+*>
+*> \param[out] TAUQ1
+*> \verbatim
+*>          TAUQ1 is COMPLEX array, dimension (Q)
+*>           The scalar factors of the elementary reflectors that define
+*>           Q1.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX array, dimension (LWORK)
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>           The dimension of the array WORK. LWORK >= M-Q.
+*> 
+*>           If LWORK = -1, then a workspace query is assumed; the routine
+*>           only calculates the optimal size of the WORK array, returns
+*>           this value as the first entry of the WORK array, and no error
+*>           message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>           = 0:  successful exit.
+*>           < 0:  if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*>
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date July 2012
+*
+*> \ingroup complexOTHERcomputational
+*
+*> \par Further Details:
+*  =====================
+
+*> \verbatim
+*>
+*>  The upper-bidiagonal blocks B11, B21 are represented implicitly by
+*>  angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry
+*>  in each bidiagonal band is a product of a sine or cosine of a THETA
+*>  with a sine or cosine of a PHI. See [1] or CUNCSD for details.
+*>
+*>  P1, P2, and Q1 are represented as products of elementary reflectors.
+*>  See CUNCSD2BY1 for details on generating P1, P2, and Q1 using CUNGQR
+*>  and CUNGLQ.
+*> \endverbatim
+*
+*> \par References:
+*  ================
+*>
+*>  [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
+*>      Algorithms, 50(1):33-65, 2009.
+*>
+*  =====================================================================
+      SUBROUTINE CUNBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
+     $                    TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO )
+*
+*  -- LAPACK computational routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     July 2012
+*
+*     .. Scalar Arguments ..
+      INTEGER            INFO, LWORK, M, P, Q, LDX11, LDX21
+*     ..
+*     .. Array Arguments ..
+      REAL               PHI(*), THETA(*)
+      COMPLEX            TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*),
+     $                   X11(LDX11,*), X21(LDX21,*)
+*     ..
+*
+*  ====================================================================
+*
+*     .. Parameters ..
+      COMPLEX            ONE
+      PARAMETER          ( ONE = (1.0E0,0.0E0) )
+*     ..
+*     .. Local Scalars ..
+      REAL               C, S
+      INTEGER            CHILDINFO, I, ILARF, IORBDB5, LLARF, LORBDB5,
+     $                   LWORKMIN, LWORKOPT
+      LOGICAL            LQUERY
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           CLARF, CLARFGP, CUNBDB5, CSROT, XERBLA
+*     ..
+*     .. External Functions ..
+      REAL               SCNRM2
+      EXTERNAL           SCNRM2
+*     ..
+*     .. Intrinsic Function ..
+      INTRINSIC          ATAN2, COS, MAX, SIN, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+*     Test input arguments
+*
+      INFO = 0
+      LQUERY = LWORK .EQ. -1
+*
+      IF( M .LT. 0 ) THEN
+         INFO = -1
+      ELSE IF( 2*P .LT. M .OR. P .GT. M ) THEN
+         INFO = -2
+      ELSE IF( Q .LT. M-P .OR. M-Q .LT. M-P ) THEN
+         INFO = -3
+      ELSE IF( LDX11 .LT. MAX( 1, P ) ) THEN
+         INFO = -5
+      ELSE IF( LDX21 .LT. MAX( 1, M-P ) ) THEN
+         INFO = -7
+      END IF
+*
+*     Compute workspace
+*
+      IF( INFO .EQ. 0 ) THEN
+         ILARF = 2
+         LLARF = MAX( P, M-P-1, Q-1 )
+         IORBDB5 = 2
+         LORBDB5 = Q-1
+         LWORKOPT = MAX( ILARF+LLARF-1, IORBDB5+LORBDB5-1 )
+         LWORKMIN = LWORKOPT
+         WORK(1) = LWORKOPT
+         IF( LWORK .LT. LWORKMIN .AND. .NOT.LQUERY ) THEN
+           INFO = -14
+         END IF
+      END IF
+      IF( INFO .NE. 0 ) THEN
+         CALL XERBLA( 'CUNBDB3', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+*
+*     Reduce rows 1, ..., M-P of X11 and X21
+*
+      DO I = 1, M-P
+*      
+         IF( I .GT. 1 ) THEN
+            CALL CSROT( Q-I+1, X11(I-1,I), LDX11, X21(I,I), LDX11, C,
+     $                  S )
+         END IF
+*
+         CALL CLACGV( Q-I+1, X21(I,I), LDX21 )
+         CALL CLARFGP( Q-I+1, X21(I,I), X21(I,I+1), LDX21, TAUQ1(I) )
+         S = REAL( X21(I,I) )
+         X21(I,I) = ONE
+         CALL CLARF( 'R', P-I+1, Q-I+1, X21(I,I), LDX21, TAUQ1(I),
+     $               X11(I,I), LDX11, WORK(ILARF) )
+         CALL CLARF( 'R', M-P-I, Q-I+1, X21(I,I), LDX21, TAUQ1(I),
+     $               X21(I+1,I), LDX21, WORK(ILARF) )
+         CALL CLACGV( Q-I+1, X21(I,I), LDX21 )
+         C = SQRT( SCNRM2( P-I+1, X11(I,I), 1, X11(I,I),
+     $       1 )**2 + SCNRM2( M-P-I, X21(I+1,I), 1, X21(I+1,I), 1 )**2 )
+         THETA(I) = ATAN2( S, C )
+*
+         CALL CUNBDB5( P-I+1, M-P-I, Q-I, X11(I,I), 1, X21(I+1,I), 1,
+     $                 X11(I,I+1), LDX11, X21(I+1,I+1), LDX21,
+     $                 WORK(IORBDB5), LORBDB5, CHILDINFO )
+         CALL CLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) )
+         IF( I .LT. M-P ) THEN
+            CALL CLARFGP( M-P-I, X21(I+1,I), X21(I+2,I), 1, TAUP2(I) )
+            PHI(I) = ATAN2( REAL( X21(I+1,I) ), REAL( X11(I,I) ) )
+            C = COS( PHI(I) )
+            S = SIN( PHI(I) )
+            X21(I+1,I) = ONE
+            CALL CLARF( 'L', M-P-I, Q-I, X21(I+1,I), 1, CONJG(TAUP2(I)),
+     $                  X21(I+1,I+1), LDX21, WORK(ILARF) )
+         END IF
+         X11(I,I) = ONE
+         CALL CLARF( 'L', P-I+1, Q-I, X11(I,I), 1, CONJG(TAUP1(I)),
+     $               X11(I,I+1), LDX11, WORK(ILARF) )
+*
+      END DO
+*
+*     Reduce the bottom-right portion of X11 to the identity matrix
+*
+      DO I = M-P + 1, Q
+         CALL CLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) )
+         X11(I,I) = ONE
+         CALL CLARF( 'L', P-I+1, Q-I, X11(I,I), 1, CONJG(TAUP1(I)),
+     $               X11(I,I+1), LDX11, WORK(ILARF) )
+      END DO
+*
+      RETURN
+*
+*     End of CUNBDB3
+*
+      END
+

lapack-netlib/SRC/cunbdb4.f

@@ -0,0 +1,385 @@
+*> \brief \b CUNBDB4
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download CUNBDB4 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cunbdb4.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cunbdb4.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cunbdb4.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CUNBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
+*                           TAUP1, TAUP2, TAUQ1, PHANTOM, WORK, LWORK,
+*                           INFO )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            INFO, LWORK, M, P, Q, LDX11, LDX21
+*       ..
+*       .. Array Arguments ..
+*       REAL               PHI(*), THETA(*)
+*       COMPLEX            PHANTOM(*), TAUP1(*), TAUP2(*), TAUQ1(*),
+*      $                   WORK(*), X11(LDX11,*), X21(LDX21,*)
+*       ..
+*  
+* 
+*> \par Purpose:
+*> =============
+*>
+*>\verbatim
+*>
+*> CUNBDB4 simultaneously bidiagonalizes the blocks of a tall and skinny
+*> matrix X with orthonomal columns:
+*>
+*>                            [ B11 ]
+*>      [ X11 ]   [ P1 |    ] [  0  ]
+*>      [-----] = [---------] [-----] Q1**T .
+*>      [ X21 ]   [    | P2 ] [ B21 ]
+*>                            [  0  ]
+*>
+*> X11 is P-by-Q, and X21 is (M-P)-by-Q. M-Q must be no larger than P,
+*> M-P, or Q. Routines CUNBDB1, CUNBDB2, and CUNBDB3 handle cases in
+*> which M-Q is not the minimum dimension.
+*>
+*> The unitary matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P),
+*> and (M-Q)-by-(M-Q), respectively. They are represented implicitly by
+*> Householder vectors.
+*>
+*> B11 and B12 are (M-Q)-by-(M-Q) bidiagonal matrices represented
+*> implicitly by angles THETA, PHI.
+*>
+*>\endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>           The number of rows X11 plus the number of rows in X21.
+*> \endverbatim
+*>
+*> \param[in] P
+*> \verbatim
+*>          P is INTEGER
+*>           The number of rows in X11. 0 <= P <= M.
+*> \endverbatim
+*>
+*> \param[in] Q
+*> \verbatim
+*>          Q is INTEGER
+*>           The number of columns in X11 and X21. 0 <= Q <= M and
+*>           M-Q <= min(P,M-P,Q).
+*> \endverbatim
+*>
+*> \param[in,out] X11
+*> \verbatim
+*>          X11 is COMPLEX array, dimension (LDX11,Q)
+*>           On entry, the top block of the matrix X to be reduced. On
+*>           exit, the columns of tril(X11) specify reflectors for P1 and
+*>           the rows of triu(X11,1) specify reflectors for Q1.
+*> \endverbatim
+*>
+*> \param[in] LDX11
+*> \verbatim
+*>          LDX11 is INTEGER
+*>           The leading dimension of X11. LDX11 >= P.
+*> \endverbatim
+*>
+*> \param[in,out] X21
+*> \verbatim
+*>          X21 is COMPLEX array, dimension (LDX21,Q)
+*>           On entry, the bottom block of the matrix X to be reduced. On
+*>           exit, the columns of tril(X21) specify reflectors for P2.
+*> \endverbatim
+*>
+*> \param[in] LDX21
+*> \verbatim
+*>          LDX21 is INTEGER
+*>           The leading dimension of X21. LDX21 >= M-P.
+*> \endverbatim
+*>
+*> \param[out] THETA
+*> \verbatim
+*>          THETA is REAL array, dimension (Q)
+*>           The entries of the bidiagonal blocks B11, B21 are defined by
+*>           THETA and PHI. See Further Details.
+*> \endverbatim
+*>
+*> \param[out] PHI
+*> \verbatim
+*>          PHI is REAL array, dimension (Q-1)
+*>           The entries of the bidiagonal blocks B11, B21 are defined by
+*>           THETA and PHI. See Further Details.
+*> \endverbatim
+*>
+*> \param[out] TAUP1
+*> \verbatim
+*>          TAUP1 is COMPLEX array, dimension (P)
+*>           The scalar factors of the elementary reflectors that define
+*>           P1.
+*> \endverbatim
+*>
+*> \param[out] TAUP2
+*> \verbatim
+*>          TAUP2 is COMPLEX array, dimension (M-P)
+*>           The scalar factors of the elementary reflectors that define
+*>           P2.
+*> \endverbatim
+*>
+*> \param[out] TAUQ1
+*> \verbatim
+*>          TAUQ1 is COMPLEX array, dimension (Q)
+*>           The scalar factors of the elementary reflectors that define
+*>           Q1.
+*> \endverbatim
+*>
+*> \param[out] PHANTOM
+*> \verbatim
+*>          PHANTOM is COMPLEX array, dimension (M)
+*>           The routine computes an M-by-1 column vector Y that is
+*>           orthogonal to the columns of [ X11; X21 ]. PHANTOM(1:P) and
+*>           PHANTOM(P+1:M) contain Householder vectors for Y(1:P) and
+*>           Y(P+1:M), respectively.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX array, dimension (LWORK)
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>           The dimension of the array WORK. LWORK >= M-Q.
+*> 
+*>           If LWORK = -1, then a workspace query is assumed; the routine
+*>           only calculates the optimal size of the WORK array, returns
+*>           this value as the first entry of the WORK array, and no error
+*>           message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>           = 0:  successful exit.
+*>           < 0:  if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date July 2012
+*
+*> \ingroup complexOTHERcomputational
+*
+*> \par Further Details:
+*  =====================
+
+*> \verbatim
+*>
+*>  The upper-bidiagonal blocks B11, B21 are represented implicitly by
+*>  angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry
+*>  in each bidiagonal band is a product of a sine or cosine of a THETA
+*>  with a sine or cosine of a PHI. See [1] or CUNCSD for details.
+*>
+*>  P1, P2, and Q1 are represented as products of elementary reflectors.
+*>  See CUNCSD2BY1 for details on generating P1, P2, and Q1 using CUNGQR
+*>  and CUNGLQ.
+*> \endverbatim
+*
+*> \par References:
+*  ================
+*>
+*>  [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
+*>      Algorithms, 50(1):33-65, 2009.
+*>
+*  =====================================================================
+      SUBROUTINE CUNBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
+     $                    TAUP1, TAUP2, TAUQ1, PHANTOM, WORK, LWORK,
+     $                    INFO )
+*
+*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     July 2012
+*
+*     .. Scalar Arguments ..
+      INTEGER            INFO, LWORK, M, P, Q, LDX11, LDX21
+*     ..
+*     .. Array Arguments ..
+      REAL               PHI(*), THETA(*)
+      COMPLEX            PHANTOM(*), TAUP1(*), TAUP2(*), TAUQ1(*),
+     $                   WORK(*), X11(LDX11,*), X21(LDX21,*)
+*     ..
+*
+*  ====================================================================
+*
+*     .. Parameters ..
+      COMPLEX            NEGONE, ONE, ZERO
+      PARAMETER          ( NEGONE = (-1.0E0,0.0E0), ONE = (1.0E0,0.0E0),
+     $                     ZERO = (0.0E0,0.0E0) )
+*     ..
+*     .. Local Scalars ..
+      REAL               C, S
+      INTEGER            CHILDINFO, I, ILARF, IORBDB5, J, LLARF,
+     $                   LORBDB5, LWORKMIN, LWORKOPT
+      LOGICAL            LQUERY
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           CLARF, CLARFGP, CUNBDB5, CSROT, CSCAL, XERBLA
+*     ..
+*     .. External Functions ..
+      REAL               SCNRM2
+      EXTERNAL           SCNRM2
+*     ..
+*     .. Intrinsic Function ..
+      INTRINSIC          ATAN2, COS, MAX, SIN, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+*     Test input arguments
+*
+      INFO = 0
+      LQUERY = LWORK .EQ. -1
+*
+      IF( M .LT. 0 ) THEN
+         INFO = -1
+      ELSE IF( P .LT. M-Q .OR. M-P .LT. M-Q ) THEN
+         INFO = -2
+      ELSE IF( Q .LT. M-Q .OR. Q .GT. M ) THEN
+         INFO = -3
+      ELSE IF( LDX11 .LT. MAX( 1, P ) ) THEN
+         INFO = -5
+      ELSE IF( LDX21 .LT. MAX( 1, M-P ) ) THEN
+         INFO = -7
+      END IF
+*
+*     Compute workspace
+*
+      IF( INFO .EQ. 0 ) THEN
+         ILARF = 2
+         LLARF = MAX( Q-1, P-1, M-P-1 )
+         IORBDB5 = 2
+         LORBDB5 = Q
+         LWORKOPT = ILARF + LLARF - 1
+         LWORKOPT = MAX( LWORKOPT, IORBDB5 + LORBDB5 - 1 )
+         LWORKMIN = LWORKOPT
+         WORK(1) = LWORKOPT
+         IF( LWORK .LT. LWORKMIN .AND. .NOT.LQUERY ) THEN
+           INFO = -14
+         END IF
+      END IF
+      IF( INFO .NE. 0 ) THEN
+         CALL XERBLA( 'CUNBDB4', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+*
+*     Reduce columns 1, ..., M-Q of X11 and X21
+*
+      DO I = 1, M-Q
+*
+         IF( I .EQ. 1 ) THEN
+            DO J = 1, M
+               PHANTOM(J) = ZERO
+            END DO
+            CALL CUNBDB5( P, M-P, Q, PHANTOM(1), 1, PHANTOM(P+1), 1,
+     $                    X11, LDX11, X21, LDX21, WORK(IORBDB5),
+     $                    LORBDB5, CHILDINFO )
+            CALL CSCAL( P, NEGONE, PHANTOM(1), 1 )
+            CALL CLARFGP( P, PHANTOM(1), PHANTOM(2), 1, TAUP1(1) )
+            CALL CLARFGP( M-P, PHANTOM(P+1), PHANTOM(P+2), 1, TAUP2(1) )
+            THETA(I) = ATAN2( REAL( PHANTOM(1) ), REAL( PHANTOM(P+1) ) )
+            C = COS( THETA(I) )
+            S = SIN( THETA(I) )
+            PHANTOM(1) = ONE
+            PHANTOM(P+1) = ONE
+            CALL CLARF( 'L', P, Q, PHANTOM(1), 1, CONJG(TAUP1(1)), X11,
+     $                  LDX11, WORK(ILARF) )
+            CALL CLARF( 'L', M-P, Q, PHANTOM(P+1), 1, CONJG(TAUP2(1)),
+     $                  X21, LDX21, WORK(ILARF) )
+         ELSE
+            CALL CUNBDB5( P-I+1, M-P-I+1, Q-I+1, X11(I,I-1), 1,
+     $                    X21(I,I-1), 1, X11(I,I), LDX11, X21(I,I),
+     $                    LDX21, WORK(IORBDB5), LORBDB5, CHILDINFO )
+            CALL CSCAL( P-I+1, NEGONE, X11(I,I-1), 1 )
+            CALL CLARFGP( P-I+1, X11(I,I-1), X11(I+1,I-1), 1, TAUP1(I) )
+            CALL CLARFGP( M-P-I+1, X21(I,I-1), X21(I+1,I-1), 1,
+     $                    TAUP2(I) )
+            THETA(I) = ATAN2( REAL( X11(I,I-1) ), REAL( X21(I,I-1) ) )
+            C = COS( THETA(I) )
+            S = SIN( THETA(I) )
+            X11(I,I-1) = ONE
+            X21(I,I-1) = ONE
+            CALL CLARF( 'L', P-I+1, Q-I+1, X11(I,I-1), 1,
+     $                  CONJG(TAUP1(I)), X11(I,I), LDX11, WORK(ILARF) )
+            CALL CLARF( 'L', M-P-I+1, Q-I+1, X21(I,I-1), 1,
+     $                  CONJG(TAUP2(I)), X21(I,I), LDX21, WORK(ILARF) )
+         END IF
+*
+         CALL CSROT( Q-I+1, X11(I,I), LDX11, X21(I,I), LDX21, S, -C )
+         CALL CLACGV( Q-I+1, X21(I,I), LDX21 )
+         CALL CLARFGP( Q-I+1, X21(I,I), X21(I,I+1), LDX21, TAUQ1(I) )
+         C = REAL( X21(I,I) )
+         X21(I,I) = ONE
+         CALL CLARF( 'R', P-I, Q-I+1, X21(I,I), LDX21, TAUQ1(I),
+     $               X11(I+1,I), LDX11, WORK(ILARF) )
+         CALL CLARF( 'R', M-P-I, Q-I+1, X21(I,I), LDX21, TAUQ1(I),
+     $               X21(I+1,I), LDX21, WORK(ILARF) )
+         CALL CLACGV( Q-I+1, X21(I,I), LDX21 )
+         IF( I .LT. M-Q ) THEN
+            S = SQRT( SCNRM2( P-I, X11(I+1,I), 1, X11(I+1,I),
+     $          1 )**2 + SCNRM2( M-P-I, X21(I+1,I), 1, X21(I+1,I),
+     $          1 )**2 )
+            PHI(I) = ATAN2( S, C )
+         END IF
+*
+      END DO
+*
+*     Reduce the bottom-right portion of X11 to [ I 0 ]
+*
+      DO I = M - Q + 1, P
+         CALL CLACGV( Q-I+1, X11(I,I), LDX11 )
+         CALL CLARFGP( Q-I+1, X11(I,I), X11(I,I+1), LDX11, TAUQ1(I) )
+         X11(I,I) = ONE
+         CALL CLARF( 'R', P-I, Q-I+1, X11(I,I), LDX11, TAUQ1(I),
+     $               X11(I+1,I), LDX11, WORK(ILARF) )
+         CALL CLARF( 'R', Q-P, Q-I+1, X11(I,I), LDX11, TAUQ1(I),
+     $               X21(M-Q+1,I), LDX21, WORK(ILARF) )
+         CALL CLACGV( Q-I+1, X11(I,I), LDX11 )
+      END DO
+*
+*     Reduce the bottom-right portion of X21 to [ 0 I ]
+*
+      DO I = P + 1, Q
+         CALL CLACGV( Q-I+1, X21(M-Q+I-P,I), LDX21 )
+         CALL CLARFGP( Q-I+1, X21(M-Q+I-P,I), X21(M-Q+I-P,I+1), LDX21,
+     $                 TAUQ1(I) )
+         X21(M-Q+I-P,I) = ONE
+         CALL CLARF( 'R', Q-I, Q-I+1, X21(M-Q+I-P,I), LDX21, TAUQ1(I),
+     $               X21(M-Q+I-P+1,I), LDX21, WORK(ILARF) )
+         CALL CLACGV( Q-I+1, X21(M-Q+I-P,I), LDX21 )
+      END DO
+*
+      RETURN
+*
+*     End of CUNBDB4
+*
+      END
+

lapack-netlib/SRC/cunbdb5.f

@@ -0,0 +1,274 @@
+*> \brief \b CUNBDB5
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download CUNBDB5 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cunbdb5.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cunbdb5.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cunbdb5.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CUNBDB5( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
+*                           LDQ2, WORK, LWORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            INCX1, INCX2, INFO, LDQ1, LDQ2, LWORK, M1, M2,
+*      $                   N
+*       ..
+*       .. Array Arguments ..
+*       COMPLEX            Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*)
+*       ..
+*  
+* 
+*> \par Purpose:
+*> =============
+*>
+*>\verbatim
+*>
+*> CUNBDB5 orthogonalizes the column vector
+*>      X = [ X1 ]
+*>          [ X2 ]
+*> with respect to the columns of
+*>      Q = [ Q1 ] .
+*>          [ Q2 ]
+*> The columns of Q must be orthonormal.
+*>
+*> If the projection is zero according to Kahan's "twice is enough"
+*> criterion, then some other vector from the orthogonal complement
+*> is returned. This vector is chosen in an arbitrary but deterministic
+*> way.
+*>
+*>\endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] M1
+*> \verbatim
+*>          M1 is INTEGER
+*>           The dimension of X1 and the number of rows in Q1. 0 <= M1.
+*> \endverbatim
+*>
+*> \param[in] M2
+*> \verbatim
+*>          M2 is INTEGER
+*>           The dimension of X2 and the number of rows in Q2. 0 <= M2.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>           The number of columns in Q1 and Q2. 0 <= N.
+*> \endverbatim
+*>
+*> \param[in,out] X1
+*> \verbatim
+*>          X1 is COMPLEX array, dimension (M1)
+*>           On entry, the top part of the vector to be orthogonalized.
+*>           On exit, the top part of the projected vector.
+*> \endverbatim
+*>
+*> \param[in] INCX1
+*> \verbatim
+*>          INCX1 is INTEGER
+*>           Increment for entries of X1.
+*> \endverbatim
+*>
+*> \param[in,out] X2
+*> \verbatim
+*>          X2 is COMPLEX array, dimension (M2)
+*>           On entry, the bottom part of the vector to be
+*>           orthogonalized. On exit, the bottom part of the projected
+*>           vector.
+*> \endverbatim
+*>
+*> \param[in] INCX2
+*> \verbatim
+*>          INCX2 is INTEGER
+*>           Increment for entries of X2.
+*> \endverbatim
+*>
+*> \param[in] Q1
+*> \verbatim
+*>          Q1 is COMPLEX array, dimension (LDQ1, N)
+*>           The top part of the orthonormal basis matrix.
+*> \endverbatim
+*>
+*> \param[in] LDQ1
+*> \verbatim
+*>          LDQ1 is INTEGER
+*>           The leading dimension of Q1. LDQ1 >= M1.
+*> \endverbatim
+*>
+*> \param[in] Q2
+*> \verbatim
+*>          Q2 is COMPLEX array, dimension (LDQ2, N)
+*>           The bottom part of the orthonormal basis matrix.
+*> \endverbatim
+*>
+*> \param[in] LDQ2
+*> \verbatim
+*>          LDQ2 is INTEGER
+*>           The leading dimension of Q2. LDQ2 >= M2.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX array, dimension (LWORK)
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>           The dimension of the array WORK. LWORK >= N.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>           = 0:  successful exit.
+*>           < 0:  if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date July 2012
+*
+*> \ingroup complexOTHERcomputational
+*
+*  =====================================================================
+      SUBROUTINE CUNBDB5( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
+     $                    LDQ2, WORK, LWORK, INFO )
+*
+*  -- LAPACK computational routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     July 2012
+*
+*     .. Scalar Arguments ..
+      INTEGER            INCX1, INCX2, INFO, LDQ1, LDQ2, LWORK, M1, M2,
+     $                   N
+*     ..
+*     .. Array Arguments ..
+      COMPLEX            Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*)
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      COMPLEX            ONE, ZERO
+      PARAMETER          ( ONE = (1.0E0,0.0E0), ZERO = (0.0E0,0.0E0) )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            CHILDINFO, I, J
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           CUNBDB6, XERBLA
+*     ..
+*     .. External Functions ..
+      REAL               SCNRM2
+      EXTERNAL           SCNRM2
+*     ..
+*     .. Intrinsic Function ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+*     Test input arguments
+*
+      INFO = 0
+      IF( M1 .LT. 0 ) THEN
+         INFO = -1
+      ELSE IF( M2 .LT. 0 ) THEN
+         INFO = -2
+      ELSE IF( N .LT. 0 ) THEN
+         INFO = -3
+      ELSE IF( INCX1 .LT. 1 ) THEN
+         INFO = -5
+      ELSE IF( INCX2 .LT. 1 ) THEN
+         INFO = -7
+      ELSE IF( LDQ1 .LT. MAX( 1, M1 ) ) THEN
+         INFO = -9
+      ELSE IF( LDQ2 .LT. MAX( 1, M2 ) ) THEN
+         INFO = -11
+      ELSE IF( LWORK .LT. N ) THEN
+         INFO = -13
+      END IF
+*
+      IF( INFO .NE. 0 ) THEN
+         CALL XERBLA( 'CUNBDB5', -INFO )
+         RETURN
+      END IF
+*
+*     Project X onto the orthogonal complement of Q
+*
+      CALL CUNBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2, LDQ2,
+     $              WORK, LWORK, CHILDINFO )
+*
+*     If the projection is nonzero, then return
+*
+      IF( SCNRM2(M1,X1,INCX1) .NE. ZERO
+     $    .OR. SCNRM2(M2,X2,INCX2) .NE. ZERO ) THEN
+         RETURN
+      END IF
+*
+*     Project each standard basis vector e_1,...,e_M1 in turn, stopping
+*     when a nonzero projection is found
+*
+      DO I = 1, M1
+         DO J = 1, M1
+            X1(J) = ZERO
+         END DO
+         X1(I) = ONE
+         DO J = 1, M2
+            X2(J) = ZERO
+         END DO
+         CALL CUNBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
+     $                 LDQ2, WORK, LWORK, CHILDINFO )
+         IF( SCNRM2(M1,X1,INCX1) .NE. ZERO
+     $       .OR. SCNRM2(M2,X2,INCX2) .NE. ZERO ) THEN
+            RETURN
+         END IF
+      END DO
+*
+*     Project each standard basis vector e_(M1+1),...,e_(M1+M2) in turn,
+*     stopping when a nonzero projection is found
+*
+      DO I = 1, M2
+         DO J = 1, M1
+            X1(J) = ZERO
+         END DO
+         DO J = 1, M2
+            X2(J) = ZERO
+         END DO
+         X2(I) = ONE
+         CALL CUNBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
+     $                 LDQ2, WORK, LWORK, CHILDINFO )
+         IF( SCNRM2(M1,X1,INCX1) .NE. ZERO
+     $       .OR. SCNRM2(M2,X2,INCX2) .NE. ZERO ) THEN
+            RETURN
+         END IF
+      END DO
+*
+      RETURN
+*
+*     End of CUNBDB5
+*      
+      END
+

lapack-netlib/SRC/cunbdb6.f

@@ -0,0 +1,313 @@
+*> \brief \b CUNBDB6
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download CUNBDB6 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cunbdb6.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cunbdb6.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cunbdb6.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CUNBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
+*                           LDQ2, WORK, LWORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            INCX1, INCX2, INFO, LDQ1, LDQ2, LWORK, M1, M2,
+*      $                   N
+*       ..
+*       .. Array Arguments ..
+*       COMPLEX            Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*)
+*       ..
+*  
+* 
+*> \par Purpose:
+*> =============
+*>
+*>\verbatim
+*>
+*> CUNBDB6 orthogonalizes the column vector
+*>      X = [ X1 ]
+*>          [ X2 ]
+*> with respect to the columns of
+*>      Q = [ Q1 ] .
+*>          [ Q2 ]
+*> The columns of Q must be orthonormal.
+*>
+*> If the projection is zero according to Kahan's "twice is enough"
+*> criterion, then the zero vector is returned.
+*>
+*>\endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] M1
+*> \verbatim
+*>          M1 is INTEGER
+*>           The dimension of X1 and the number of rows in Q1. 0 <= M1.
+*> \endverbatim
+*>
+*> \param[in] M2
+*> \verbatim
+*>          M2 is INTEGER
+*>           The dimension of X2 and the number of rows in Q2. 0 <= M2.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>           The number of columns in Q1 and Q2. 0 <= N.
+*> \endverbatim
+*>
+*> \param[in,out] X1
+*> \verbatim
+*>          X1 is COMPLEX array, dimension (M1)
+*>           On entry, the top part of the vector to be orthogonalized.
+*>           On exit, the top part of the projected vector.
+*> \endverbatim
+*>
+*> \param[in] INCX1
+*> \verbatim
+*>          INCX1 is INTEGER
+*>           Increment for entries of X1.
+*> \endverbatim
+*>
+*> \param[in,out] X2
+*> \verbatim
+*>          X2 is COMPLEX array, dimension (M2)
+*>           On entry, the bottom part of the vector to be
+*>           orthogonalized. On exit, the bottom part of the projected
+*>           vector.
+*> \endverbatim
+*>
+*> \param[in] INCX2
+*> \verbatim
+*>          INCX2 is INTEGER
+*>           Increment for entries of X2.
+*> \endverbatim
+*>
+*> \param[in] Q1
+*> \verbatim
+*>          Q1 is COMPLEX array, dimension (LDQ1, N)
+*>           The top part of the orthonormal basis matrix.
+*> \endverbatim
+*>
+*> \param[in] LDQ1
+*> \verbatim
+*>          LDQ1 is INTEGER
+*>           The leading dimension of Q1. LDQ1 >= M1.
+*> \endverbatim
+*>
+*> \param[in] Q2
+*> \verbatim
+*>          Q2 is COMPLEX array, dimension (LDQ2, N)
+*>           The bottom part of the orthonormal basis matrix.
+*> \endverbatim
+*>
+*> \param[in] LDQ2
+*> \verbatim
+*>          LDQ2 is INTEGER
+*>           The leading dimension of Q2. LDQ2 >= M2.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX array, dimension (LWORK)
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>           The dimension of the array WORK. LWORK >= N.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>           = 0:  successful exit.
+*>           < 0:  if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date July 2012
+*
+*> \ingroup complexOTHERcomputational
+*
+*  =====================================================================
+      SUBROUTINE CUNBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
+     $                    LDQ2, WORK, LWORK, INFO )
+*
+*  -- LAPACK computational routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     July 2012
+*
+*     .. Scalar Arguments ..
+      INTEGER            INCX1, INCX2, INFO, LDQ1, LDQ2, LWORK, M1, M2,
+     $                   N
+*     ..
+*     .. Array Arguments ..
+      COMPLEX            Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*)
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      REAL               ALPHASQ, REALONE, REALZERO
+      PARAMETER          ( ALPHASQ = 0.01E0, REALONE = 1.0E0,
+     $                     REALZERO = 0.0E0 )
+      COMPLEX            NEGONE, ONE, ZERO
+      PARAMETER          ( NEGONE = (-1.0E0,0.0E0), ONE = (1.0E0,0.0E0),
+     $                     ZERO = (0.0E0,0.0E0) )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            I
+      REAL               NORMSQ1, NORMSQ2, SCL1, SCL2, SSQ1, SSQ2
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           CGEMV, CLASSQ, XERBLA
+*     ..
+*     .. Intrinsic Function ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+*     Test input arguments
+*
+      INFO = 0
+      IF( M1 .LT. 0 ) THEN
+         INFO = -1
+      ELSE IF( M2 .LT. 0 ) THEN
+         INFO = -2
+      ELSE IF( N .LT. 0 ) THEN
+         INFO = -3
+      ELSE IF( INCX1 .LT. 1 ) THEN
+         INFO = -5
+      ELSE IF( INCX2 .LT. 1 ) THEN
+         INFO = -7
+      ELSE IF( LDQ1 .LT. MAX( 1, M1 ) ) THEN
+         INFO = -9
+      ELSE IF( LDQ2 .LT. MAX( 1, M2 ) ) THEN
+         INFO = -11
+      ELSE IF( LWORK .LT. N ) THEN
+         INFO = -13
+      END IF
+*
+      IF( INFO .NE. 0 ) THEN
+         CALL XERBLA( 'CUNBDB6', -INFO )
+         RETURN
+      END IF
+*
+*     First, project X onto the orthogonal complement of Q's column
+*     space
+*
+      SCL1 = REALZERO
+      SSQ1 = REALONE
+      CALL CLASSQ( M1, X1, INCX1, SCL1, SSQ1 )
+      SCL2 = REALZERO
+      SSQ2 = REALONE
+      CALL CLASSQ( M2, X2, INCX2, SCL2, SSQ2 )
+      NORMSQ1 = SCL1**2*SSQ1 + SCL2**2*SSQ2
+*
+      IF( M1 .EQ. 0 ) THEN
+         DO I = 1, N
+            WORK(I) = ZERO
+         END DO
+      ELSE
+         CALL CGEMV( 'C', M1, N, ONE, Q1, LDQ1, X1, INCX1, ZERO, WORK,
+     $               1 )
+      END IF
+*
+      CALL CGEMV( 'C', M2, N, ONE, Q2, LDQ2, X2, INCX2, ONE, WORK, 1 )
+*
+      CALL CGEMV( 'N', M1, N, NEGONE, Q1, LDQ1, WORK, 1, ONE, X1,
+     $            INCX1 )
+      CALL CGEMV( 'N', M2, N, NEGONE, Q2, LDQ2, WORK, 1, ONE, X2,
+     $            INCX2 )
+*
+      SCL1 = REALZERO
+      SSQ1 = REALONE
+      CALL CLASSQ( M1, X1, INCX1, SCL1, SSQ1 )
+      SCL2 = REALZERO
+      SSQ2 = REALONE
+      CALL CLASSQ( M2, X2, INCX2, SCL2, SSQ2 )
+      NORMSQ2 = SCL1**2*SSQ1 + SCL2**2*SSQ2
+*
+*     If projection is sufficiently large in norm, then stop.
+*     If projection is zero, then stop.
+*     Otherwise, project again.
+*
+      IF( NORMSQ2 .GE. ALPHASQ*NORMSQ1 ) THEN
+         RETURN
+      END IF
+*
+      IF( NORMSQ2 .EQ. ZERO ) THEN
+         RETURN
+      END IF
+*      
+      NORMSQ1 = NORMSQ2
+*
+      DO I = 1, N
+         WORK(I) = ZERO
+      END DO
+*
+      IF( M1 .EQ. 0 ) THEN
+         DO I = 1, N
+            WORK(I) = ZERO
+         END DO
+      ELSE
+         CALL CGEMV( 'C', M1, N, ONE, Q1, LDQ1, X1, INCX1, ZERO, WORK,
+     $               1 )
+      END IF
+*
+      CALL CGEMV( 'C', M2, N, ONE, Q2, LDQ2, X2, INCX2, ONE, WORK, 1 )
+*
+      CALL CGEMV( 'N', M1, N, NEGONE, Q1, LDQ1, WORK, 1, ONE, X1,
+     $            INCX1 )
+      CALL CGEMV( 'N', M2, N, NEGONE, Q2, LDQ2, WORK, 1, ONE, X2,
+     $            INCX2 )
+*
+      SCL1 = REALZERO
+      SSQ1 = REALONE
+      CALL CLASSQ( M1, X1, INCX1, SCL1, SSQ1 )
+      SCL2 = REALZERO
+      SSQ2 = REALONE
+      CALL CLASSQ( M1, X1, INCX1, SCL1, SSQ1 )
+      NORMSQ2 = SCL1**2*SSQ1 + SCL2**2*SSQ2
+*
+*     If second projection is sufficiently large in norm, then do
+*     nothing more. Alternatively, if it shrunk significantly, then
+*     truncate it to zero.
+*
+      IF( NORMSQ2 .LT. ALPHASQ*NORMSQ1 ) THEN
+         DO I = 1, M1
+            X1(I) = ZERO
+         END DO
+         DO I = 1, M2
+            X2(I) = ZERO
+         END DO
+      END IF
+*
+      RETURN
+*      
+*     End of CUNBDB6
+*
+      END
+

lapack-netlib/SRC/cuncsd.f

@@ -308,7 +308,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date November 2011
+*> \date November 2013
 *
 *> \ingroup complexOTHERcomputational
 *
@@ -320,10 +320,10 @@
      $                             LDV2T, WORK, LWORK, RWORK, LRWORK,
      $                             IWORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2011
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS
@@ -356,7 +356,7 @@
      $                   LBBCSDWORKOPT, LORBDBWORK, LORBDBWORKMIN,
      $                   LORBDBWORKOPT, LORGLQWORK, LORGLQWORKMIN,
      $                   LORGLQWORKOPT, LORGQRWORK, LORGQRWORKMIN,
-     $                   LORGQRWORKOPT, LWORKMIN, LWORKOPT
+     $                   LORGQRWORKOPT, LWORKMIN, LWORKOPT, P1, Q1
       LOGICAL            COLMAJOR, DEFAULTSIGNS, LQUERY, WANTU1, WANTU2,
      $                   WANTV1T, WANTV2T
       INTEGER            LRWORKMIN, LRWORKOPT
@@ -392,9 +392,22 @@
          INFO = -8
       ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN
          INFO = -9
-      ELSE IF( ( COLMAJOR .AND. LDX11 .LT. MAX(1,P) ) .OR.
-     $         ( .NOT.COLMAJOR .AND. LDX11 .LT. MAX(1,Q) ) ) THEN
-         INFO = -11
+      ELSE IF ( COLMAJOR .AND.  LDX11 .LT. MAX( 1, P ) ) THEN
+        INFO = -11
+      ELSE IF (.NOT. COLMAJOR .AND. LDX11 .LT. MAX( 1, Q ) ) THEN
+        INFO = -11
+      ELSE IF (COLMAJOR .AND. LDX12 .LT. MAX( 1, P ) ) THEN
+        INFO = -13
+      ELSE IF (.NOT. COLMAJOR .AND. LDX12 .LT. MAX( 1, M-Q ) ) THEN
+        INFO = -13
+      ELSE IF (COLMAJOR .AND. LDX21 .LT. MAX( 1, M-P ) ) THEN
+        INFO = -15
+      ELSE IF (.NOT. COLMAJOR .AND. LDX21 .LT. MAX( 1, Q ) ) THEN
+        INFO = -15
+      ELSE IF (COLMAJOR .AND. LDX22 .LT. MAX( 1, M-P ) ) THEN
+        INFO = -17
+      ELSE IF (.NOT. COLMAJOR .AND. LDX22 .LT. MAX( 1, M-Q ) ) THEN
+        INFO = -17
       ELSE IF( WANTU1 .AND. LDU1 .LT. P ) THEN
          INFO = -20
       ELSE IF( WANTU2 .AND. LDU2 .LT. M-P ) THEN
@@ -458,9 +471,10 @@
          IB22D = IB21E + MAX( 1, Q - 1 )
          IB22E = IB22D + MAX( 1, Q )
          IBBCSD = IB22E + MAX( 1, Q - 1 )
-         CALL CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, 0,
-     $                0, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, 0,
-     $                0, 0, 0, 0, 0, 0, 0, RWORK, -1, CHILDINFO )
+         CALL CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, 
+     $                THETA, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T,
+     $                V2T, LDV2T, THETA, THETA, THETA, THETA, THETA,
+     $                THETA, THETA, THETA, RWORK, -1, CHILDINFO )
          LBBCSDWORKOPT = INT( RWORK(1) )
          LBBCSDWORKMIN = LBBCSDWORKOPT
          LRWORKOPT = IBBCSD + LBBCSDWORKOPT - 1
@@ -474,19 +488,19 @@
          ITAUQ1 = ITAUP2 + MAX( 1, M - P )
          ITAUQ2 = ITAUQ1 + MAX( 1, Q )
          IORGQR = ITAUQ2 + MAX( 1, M - Q )
-         CALL CUNGQR( M-Q, M-Q, M-Q, 0, MAX(1,M-Q), 0, WORK, -1,
+         CALL CUNGQR( M-Q, M-Q, M-Q, 0, MAX(1,M-Q), U1, WORK, -1,
      $                CHILDINFO )
          LORGQRWORKOPT = INT( WORK(1) )
          LORGQRWORKMIN = MAX( 1, M - Q )
          IORGLQ = ITAUQ2 + MAX( 1, M - Q )
-         CALL CUNGLQ( M-Q, M-Q, M-Q, 0, MAX(1,M-Q), 0, WORK, -1,
+         CALL CUNGLQ( M-Q, M-Q, M-Q, 0, MAX(1,M-Q), U1, WORK, -1,
      $                CHILDINFO )
          LORGLQWORKOPT = INT( WORK(1) )
          LORGLQWORKMIN = MAX( 1, M - Q )
          IORBDB = ITAUQ2 + MAX( 1, M - Q )
          CALL CUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
-     $                X21, LDX21, X22, LDX22, 0, 0, 0, 0, 0, 0, WORK,
-     $                -1, CHILDINFO )
+     $                X21, LDX21, X22, LDX22, THETA, THETA, U1, U2,
+     $                V1T, V2T, WORK, -1, CHILDINFO )
          LORBDBWORKOPT = INT( WORK(1) )
          LORBDBWORKMIN = LORBDBWORKOPT
          LWORKOPT = MAX( IORGQR + LORGQRWORKOPT, IORGLQ + LORGLQWORKOPT,
@@ -551,10 +565,14 @@
          END IF
          IF( WANTV2T .AND. M-Q .GT. 0 ) THEN
             CALL CLACPY( 'U', P, M-Q, X12, LDX12, V2T, LDV2T )
-            CALL CLACPY( 'U', M-P-Q, M-P-Q, X22(Q+1,P+1), LDX22,
-     $                   V2T(P+1,P+1), LDV2T )
-            CALL CUNGLQ( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2),
-     $                   WORK(IORGLQ), LORGLQWORK, INFO )
+            IF( M-P .GT. Q ) THEN
+               CALL CLACPY( 'U', M-P-Q, M-P-Q, X22(Q+1,P+1), LDX22,
+     $                      V2T(P+1,P+1), LDV2T )
+            END IF
+            IF( M .GT. Q ) THEN
+               CALL CUNGLQ( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2),
+     $                      WORK(IORGLQ), LORGLQWORK, INFO )
+            END IF
          END IF
       ELSE
          IF( WANTU1 .AND. P .GT. 0 ) THEN
@@ -579,9 +597,13 @@
      $                   WORK(IORGQR), LORGQRWORK, INFO )
          END IF
          IF( WANTV2T .AND. M-Q .GT. 0 ) THEN
+            P1 = MIN( P+1, M )
+            Q1 = MIN( Q+1, M )
             CALL CLACPY( 'L', M-Q, P, X12, LDX12, V2T, LDV2T )
-            CALL CLACPY( 'L', M-P-Q, M-P-Q, X22(P+1,Q+1), LDX22,
-     $                   V2T(P+1,P+1), LDV2T )
+            IF ( M .GT. P+Q ) THEN
+               CALL CLACPY( 'L', M-P-Q, M-P-Q, X22(P1,Q1), LDX22,
+     $                      V2T(P+1,P+1), LDV2T )
+            END IF
             CALL CUNGQR( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2),
      $                   WORK(IORGQR), LORGQRWORK, INFO )
          END IF

lapack-netlib/SRC/cuncsd2by1.f

@@ -0,0 +1,757 @@
+*> \brief \b CUNCSD2BY1
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download CUNCSD2BY1 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cuncsd2by1.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cuncsd2by1.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cuncsd2by1.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CUNCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11,
+*                              X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T,
+*                              LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK,
+*                              INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          JOBU1, JOBU2, JOBV1T
+*       INTEGER            INFO, LDU1, LDU2, LDV1T, LWORK, LDX11, LDX21,
+*      $                   M, P, Q
+*       INTEGER            LRWORK, LRWORKMIN, LRWORKOPT
+*       ..
+*       .. Array Arguments ..
+*       REAL               RWORK(*)
+*       REAL               THETA(*)
+*       COMPLEX            U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), WORK(*),
+*      $                   X11(LDX11,*), X21(LDX21,*)
+*       INTEGER            IWORK(*)
+*       ..
+*    
+* 
+*> \par Purpose:
+*> =============
+*>
+*>\verbatim
+*>
+*> CUNCSD2BY1 computes the CS decomposition of an M-by-Q matrix X with
+*> orthonormal columns that has been partitioned into a 2-by-1 block
+*> structure:
+*>
+*>                                [  I  0  0 ]
+*>                                [  0  C  0 ]
+*>          [ X11 ]   [ U1 |    ] [  0  0  0 ]
+*>      X = [-----] = [---------] [----------] V1**T .
+*>          [ X21 ]   [    | U2 ] [  0  0  0 ]
+*>                                [  0  S  0 ]
+*>                                [  0  0  I ]
+*> 
+*> X11 is P-by-Q. The unitary matrices U1, U2, V1, and V2 are P-by-P,
+*> (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are
+*> R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in
+*> which R = MIN(P,M-P,Q,M-Q).
+*>
+*>\endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] JOBU1
+*> \verbatim
+*>          JOBU1 is CHARACTER
+*>           = 'Y':      U1 is computed;
+*>           otherwise:  U1 is not computed.
+*> \endverbatim
+*>
+*> \param[in] JOBU2
+*> \verbatim
+*>          JOBU2 is CHARACTER
+*>           = 'Y':      U2 is computed;
+*>           otherwise:  U2 is not computed.
+*> \endverbatim
+*>
+*> \param[in] JOBV1T
+*> \verbatim
+*>          JOBV1T is CHARACTER
+*>           = 'Y':      V1T is computed;
+*>           otherwise:  V1T is not computed.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>           The number of rows and columns in X.
+*> \endverbatim
+*>
+*> \param[in] P
+*> \verbatim
+*>          P is INTEGER
+*>           The number of rows in X11 and X12. 0 <= P <= M.
+*> \endverbatim
+*>
+*> \param[in] Q
+*> \verbatim
+*>          Q is INTEGER
+*>           The number of columns in X11 and X21. 0 <= Q <= M.
+*> \endverbatim
+*>
+*> \param[in,out] X11
+*> \verbatim
+*>          X11 is COMPLEX array, dimension (LDX11,Q)
+*>           On entry, part of the unitary matrix whose CSD is
+*>           desired.
+*> \endverbatim
+*>
+*> \param[in] LDX11
+*> \verbatim
+*>          LDX11 is INTEGER
+*>           The leading dimension of X11. LDX11 >= MAX(1,P).
+*> \endverbatim
+*>
+*> \param[in,out] X21
+*> \verbatim
+*>          X21 is COMPLEX array, dimension (LDX21,Q)
+*>           On entry, part of the unitary matrix whose CSD is
+*>           desired.
+*> \endverbatim
+*>
+*> \param[in] LDX21
+*> \verbatim
+*>          LDX21 is INTEGER
+*>           The leading dimension of X21. LDX21 >= MAX(1,M-P).
+*> \endverbatim
+*>
+*> \param[out] THETA
+*> \verbatim
+*>          THETA is COMPLEX array, dimension (R), in which R =
+*>           MIN(P,M-P,Q,M-Q).
+*>           C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and
+*>           S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ).
+*> \endverbatim
+*>
+*> \param[out] U1
+*> \verbatim
+*>          U1 is COMPLEX array, dimension (P)
+*>           If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1.
+*> \endverbatim
+*>
+*> \param[in] LDU1
+*> \verbatim
+*>          LDU1 is INTEGER
+*>           The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
+*>           MAX(1,P).
+*> \endverbatim
+*>
+*> \param[out] U2
+*> \verbatim
+*>          U2 is COMPLEX array, dimension (M-P)
+*>           If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary
+*>           matrix U2.
+*> \endverbatim
+*>
+*> \param[in] LDU2
+*> \verbatim
+*>          LDU2 is INTEGER
+*>           The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=
+*>           MAX(1,M-P).
+*> \endverbatim
+*>
+*> \param[out] V1T
+*> \verbatim
+*>          V1T is COMPLEX array, dimension (Q)
+*>           If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary
+*>           matrix V1**T.
+*> \endverbatim
+*>
+*> \param[in] LDV1T
+*> \verbatim
+*>          LDV1T is INTEGER
+*>           The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
+*>           MAX(1,Q).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
+*>           On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*>           If INFO > 0 on exit, WORK(2:R) contains the values PHI(1),
+*>           ..., PHI(R-1) that, together with THETA(1), ..., THETA(R),
+*>           define the matrix in intermediate bidiagonal-block form
+*>           remaining after nonconvergence. INFO specifies the number
+*>           of nonzero PHI's.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>           The dimension of the array WORK.
+*> \endverbatim
+*> \verbatim
+*>           If LWORK = -1, then a workspace query is assumed; the routine
+*>           only calculates the optimal size of the WORK array, returns
+*>           this value as the first entry of the work array, and no error
+*>           message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*>          RWORK is REAL array, dimension (MAX(1,LRWORK))
+*>           On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
+*>           If INFO > 0 on exit, RWORK(2:R) contains the values PHI(1),
+*>           ..., PHI(R-1) that, together with THETA(1), ..., THETA(R),
+*>           define the matrix in intermediate bidiagonal-block form
+*>           remaining after nonconvergence. INFO specifies the number
+*>           of nonzero PHI's.
+*> \endverbatim
+*>
+*> \param[in] LRWORK
+*> \verbatim
+*>          LRWORK is INTEGER
+*>           The dimension of the array RWORK.
+*> 
+*>           If LRWORK = -1, then a workspace query is assumed; the routine
+*>           only calculates the optimal size of the RWORK array, returns
+*>           this value as the first entry of the work array, and no error
+*>           message related to LRWORK is issued by XERBLA.
+*> \param[out] IWORK
+*> \verbatim
+*>          IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))
+*> \endverbatim
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>           = 0:  successful exit.
+*>           < 0:  if INFO = -i, the i-th argument had an illegal value.
+*>           > 0:  CBBCSD did not converge. See the description of WORK
+*>                above for details.
+*> \endverbatim
+*
+*>  \par References:
+*>  ================
+*>
+*>  [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
+*>      Algorithms, 50(1):33-65, 2009.
+*>
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date July 2012
+*
+*> \ingroup complexOTHERcomputational
+*
+*  =====================================================================
+      SUBROUTINE CUNCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11,
+     $                       X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T,
+     $                       LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK,
+     $                       INFO )
+*
+*  -- LAPACK computational routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     July 2012
+*
+*     .. Scalar Arguments ..
+      CHARACTER          JOBU1, JOBU2, JOBV1T
+      INTEGER            INFO, LDU1, LDU2, LDV1T, LWORK, LDX11, LDX21,
+     $                   M, P, Q
+      INTEGER            LRWORK, LRWORKMIN, LRWORKOPT
+*     ..
+*     .. Array Arguments ..
+      REAL               RWORK(*)
+      REAL               THETA(*)
+      COMPLEX            U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), WORK(*),
+     $                   X11(LDX11,*), X21(LDX21,*)
+      INTEGER            IWORK(*)
+*     ..
+*  
+*  =====================================================================
+*
+*     .. Parameters ..
+      COMPLEX            ONE, ZERO
+      PARAMETER          ( ONE = (1.0E0,0.0E0), ZERO = (0.0E0,0.0E0) )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            CHILDINFO, I, IB11D, IB11E, IB12D, IB12E,
+     $                   IB21D, IB21E, IB22D, IB22E, IBBCSD, IORBDB,
+     $                   IORGLQ, IORGQR, IPHI, ITAUP1, ITAUP2, ITAUQ1,
+     $                   J, LBBCSD, LORBDB, LORGLQ, LORGLQMIN,
+     $                   LORGLQOPT, LORGQR, LORGQRMIN, LORGQROPT,
+     $                   LWORKMIN, LWORKOPT, R
+      LOGICAL            LQUERY, WANTU1, WANTU2, WANTV1T
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           CBBCSD, CCOPY, CLACPY, CLAPMR, CLAPMT, CUNBDB1,
+     $                   CUNBDB2, CUNBDB3, CUNBDB4, CUNGLQ, CUNGQR,
+     $                   XERBLA
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      EXTERNAL           LSAME
+*     ..
+*     .. Intrinsic Function ..
+      INTRINSIC          INT, MAX, MIN
+*     ..
+*     .. Executable Statements ..
+*
+*     Test input arguments
+*
+      INFO = 0
+      WANTU1 = LSAME( JOBU1, 'Y' )
+      WANTU2 = LSAME( JOBU2, 'Y' )
+      WANTV1T = LSAME( JOBV1T, 'Y' )
+      LQUERY = LWORK .EQ. -1
+*
+      IF( M .LT. 0 ) THEN
+         INFO = -4
+      ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN
+         INFO = -5
+      ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN
+         INFO = -6
+      ELSE IF( LDX11 .LT. MAX( 1, P ) ) THEN
+         INFO = -8
+      ELSE IF( LDX21 .LT. MAX( 1, M-P ) ) THEN
+         INFO = -10
+      ELSE IF( WANTU1 .AND. LDU1 .LT. P ) THEN
+         INFO = -13
+      ELSE IF( WANTU2 .AND. LDU2 .LT. M - P ) THEN
+         INFO = -15
+      ELSE IF( WANTV1T .AND. LDV1T .LT. Q ) THEN
+         INFO = -17
+      END IF
+*
+      R = MIN( P, M-P, Q, M-Q )
+*
+*     Compute workspace
+*
+*       WORK layout:
+*     |-----------------------------------------|
+*     | LWORKOPT (1)                            |
+*     |-----------------------------------------|
+*     | TAUP1 (MAX(1,P))                        |
+*     | TAUP2 (MAX(1,M-P))                      |
+*     | TAUQ1 (MAX(1,Q))                        |
+*     |-----------------------------------------|
+*     | CUNBDB WORK | CUNGQR WORK | CUNGLQ WORK |
+*     |             |             |             |
+*     |             |             |             |
+*     |             |             |             |
+*     |             |             |             |
+*     |-----------------------------------------|
+*       RWORK layout:
+*     |------------------|
+*     | LRWORKOPT (1)    |
+*     |------------------|
+*     | PHI (MAX(1,R-1)) |
+*     |------------------|
+*     | B11D (R)         |
+*     | B11E (R-1)       |
+*     | B12D (R)         |
+*     | B12E (R-1)       |
+*     | B21D (R)         |
+*     | B21E (R-1)       |
+*     | B22D (R)         |
+*     | B22E (R-1)       |
+*     | CBBCSD RWORK     |
+*     |------------------|
+*
+      IF( INFO .EQ. 0 ) THEN
+         IPHI = 2
+         IB11D = IPHI + MAX( 1, R-1 )
+         IB11E = IB11D + MAX( 1, R )
+         IB12D = IB11E + MAX( 1, R - 1 )
+         IB12E = IB12D + MAX( 1, R )
+         IB21D = IB12E + MAX( 1, R - 1 )
+         IB21E = IB21D + MAX( 1, R )
+         IB22D = IB21E + MAX( 1, R - 1 )
+         IB22E = IB22D + MAX( 1, R )
+         IBBCSD = IB22E + MAX( 1, R - 1 )
+         ITAUP1 = 2
+         ITAUP2 = ITAUP1 + MAX( 1, P )
+         ITAUQ1 = ITAUP2 + MAX( 1, M-P )
+         IORBDB = ITAUQ1 + MAX( 1, Q )
+         IORGQR = ITAUQ1 + MAX( 1, Q )
+         IORGLQ = ITAUQ1 + MAX( 1, Q )
+         IF( R .EQ. Q ) THEN
+            CALL CUNBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0,
+     $                    0, 0, WORK, -1, CHILDINFO )
+            LORBDB = INT( WORK(1) )
+            IF( P .GE. M-P ) THEN
+               CALL CUNGQR( P, P, Q, U1, LDU1, 0, WORK(1), -1,
+     $                      CHILDINFO )
+               LORGQRMIN = MAX( 1, P )
+               LORGQROPT = INT( WORK(1) )
+            ELSE
+               CALL CUNGQR( M-P, M-P, Q, U2, LDU2, 0, WORK(1), -1,
+     $                      CHILDINFO )
+               LORGQRMIN = MAX( 1, M-P )
+               LORGQROPT = INT( WORK(1) )
+            END IF
+            CALL CUNGLQ( MAX(0,Q-1), MAX(0,Q-1), MAX(0,Q-1), V1T, LDV1T,
+     $                   0, WORK(1), -1, CHILDINFO )
+            LORGLQMIN = MAX( 1, Q-1 )
+            LORGLQOPT = INT( WORK(1) )
+            CALL CBBCSD( JOBU1, JOBU2, JOBV1T, 'N', 'N', M, P, Q, THETA,
+     $                   0, U1, LDU1, U2, LDU2, V1T, LDV1T, 0, 1, 0, 0,
+     $                   0, 0, 0, 0, 0, 0, RWORK(1), -1, CHILDINFO )
+            LBBCSD = INT( RWORK(1) )
+         ELSE IF( R .EQ. P ) THEN
+            CALL CUNBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0,
+     $                    0, 0, WORK(1), -1, CHILDINFO )
+            LORBDB = INT( WORK(1) )
+            IF( P-1 .GE. M-P ) THEN
+               CALL CUNGQR( P-1, P-1, P-1, U1(2,2), LDU1, 0, WORK(1),
+     $                      -1, CHILDINFO )
+               LORGQRMIN = MAX( 1, P-1 )
+               LORGQROPT = INT( WORK(1) )
+            ELSE
+               CALL CUNGQR( M-P, M-P, Q, U2, LDU2, 0, WORK(1), -1,
+     $                      CHILDINFO )
+               LORGQRMIN = MAX( 1, M-P )
+               LORGQROPT = INT( WORK(1) )
+            END IF
+            CALL CUNGLQ( Q, Q, R, V1T, LDV1T, 0, WORK(1), -1,
+     $                   CHILDINFO )
+            LORGLQMIN = MAX( 1, Q )
+            LORGLQOPT = INT( WORK(1) )
+            CALL CBBCSD( JOBV1T, 'N', JOBU1, JOBU2, 'T', M, Q, P, THETA,
+     $                   0, V1T, LDV1T, 0, 1, U1, LDU1, U2, LDU2, 0, 0,
+     $                   0, 0, 0, 0, 0, 0, RWORK(1), -1, CHILDINFO )
+            LBBCSD = INT( RWORK(1) )
+         ELSE IF( R .EQ. M-P ) THEN
+            CALL CUNBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0,
+     $                    0, 0, WORK(1), -1, CHILDINFO )
+            LORBDB = INT( WORK(1) )
+            IF( P .GE. M-P-1 ) THEN
+               CALL CUNGQR( P, P, Q, U1, LDU1, 0, WORK(1), -1,
+     $                      CHILDINFO )
+               LORGQRMIN = MAX( 1, P )
+               LORGQROPT = INT( WORK(1) )
+            ELSE
+               CALL CUNGQR( M-P-1, M-P-1, M-P-1, U2(2,2), LDU2, 0,
+     $                      WORK(1), -1, CHILDINFO )
+               LORGQRMIN = MAX( 1, M-P-1 )
+               LORGQROPT = INT( WORK(1) )
+            END IF
+            CALL CUNGLQ( Q, Q, R, V1T, LDV1T, 0, WORK(1), -1,
+     $                   CHILDINFO )
+            LORGLQMIN = MAX( 1, Q )
+            LORGLQOPT = INT( WORK(1) )
+            CALL CBBCSD( 'N', JOBV1T, JOBU2, JOBU1, 'T', M, M-Q, M-P,
+     $                   THETA, 0, 0, 1, V1T, LDV1T, U2, LDU2, U1, LDU1,
+     $                   0, 0, 0, 0, 0, 0, 0, 0, RWORK(1), -1,
+     $                   CHILDINFO )
+            LBBCSD = INT( RWORK(1) )
+         ELSE
+            CALL CUNBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0,
+     $                    0, 0, 0, WORK(1), -1, CHILDINFO )
+            LORBDB = M + INT( WORK(1) )
+            IF( P .GE. M-P ) THEN
+               CALL CUNGQR( P, P, M-Q, U1, LDU1, 0, WORK(1), -1,
+     $                      CHILDINFO )
+               LORGQRMIN = MAX( 1, P )
+               LORGQROPT = INT( WORK(1) )
+            ELSE
+               CALL CUNGQR( M-P, M-P, M-Q, U2, LDU2, 0, WORK(1), -1,
+     $                      CHILDINFO )
+               LORGQRMIN = MAX( 1, M-P )
+               LORGQROPT = INT( WORK(1) )
+            END IF
+            CALL CUNGLQ( Q, Q, Q, V1T, LDV1T, 0, WORK(1), -1,
+     $                   CHILDINFO )
+            LORGLQMIN = MAX( 1, Q )
+            LORGLQOPT = INT( WORK(1) )
+            CALL CBBCSD( JOBU2, JOBU1, 'N', JOBV1T, 'N', M, M-P, M-Q,
+     $                   THETA, 0, U2, LDU2, U1, LDU1, 0, 1, V1T, LDV1T,
+     $                   0, 0, 0, 0, 0, 0, 0, 0, RWORK(1), -1,
+     $                   CHILDINFO )
+            LBBCSD = INT( RWORK(1) )
+         END IF
+         LRWORKMIN = IBBCSD+LBBCSD-1
+         LRWORKOPT = LRWORKMIN
+         RWORK(1) = LRWORKOPT
+         LWORKMIN = MAX( IORBDB+LORBDB-1,
+     $                   IORGQR+LORGQRMIN-1,
+     $                   IORGLQ+LORGLQMIN-1 )
+         LWORKOPT = MAX( IORBDB+LORBDB-1,
+     $                   IORGQR+LORGQROPT-1,
+     $                   IORGLQ+LORGLQOPT-1 )
+         WORK(1) = LWORKOPT
+         IF( LWORK .LT. LWORKMIN .AND. .NOT.LQUERY ) THEN
+            INFO = -19
+         END IF
+      END IF
+      IF( INFO .NE. 0 ) THEN
+         CALL XERBLA( 'CUNCSD2BY1', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+      LORGQR = LWORK-IORGQR+1
+      LORGLQ = LWORK-IORGLQ+1
+*
+*     Handle four cases separately: R = Q, R = P, R = M-P, and R = M-Q,
+*     in which R = MIN(P,M-P,Q,M-Q)
+*
+      IF( R .EQ. Q ) THEN
+*
+*        Case 1: R = Q
+*
+*        Simultaneously bidiagonalize X11 and X21
+*
+         CALL CUNBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA,
+     $                 RWORK(IPHI), WORK(ITAUP1), WORK(ITAUP2),
+     $                 WORK(ITAUQ1), WORK(IORBDB), LORBDB, CHILDINFO )
+*
+*        Accumulate Householder reflectors
+*
+         IF( WANTU1 .AND. P .GT. 0 ) THEN
+            CALL CLACPY( 'L', P, Q, X11, LDX11, U1, LDU1 )
+            CALL CUNGQR( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGQR),
+     $                   LORGQR, CHILDINFO )
+         END IF
+         IF( WANTU2 .AND. M-P .GT. 0 ) THEN
+            CALL CLACPY( 'L', M-P, Q, X21, LDX21, U2, LDU2 )
+            CALL CUNGQR( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2),
+     $                   WORK(IORGQR), LORGQR, CHILDINFO )
+         END IF
+         IF( WANTV1T .AND. Q .GT. 0 ) THEN
+            V1T(1,1) = ONE
+            DO J = 2, Q
+               V1T(1,J) = ZERO
+               V1T(J,1) = ZERO
+            END DO
+            CALL CLACPY( 'U', Q-1, Q-1, X21(1,2), LDX21, V1T(2,2),
+     $                   LDV1T )
+            CALL CUNGLQ( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1),
+     $                   WORK(IORGLQ), LORGLQ, CHILDINFO )
+         END IF
+*   
+*        Simultaneously diagonalize X11 and X21.
+*   
+         CALL CBBCSD( JOBU1, JOBU2, JOBV1T, 'N', 'N', M, P, Q, THETA,
+     $                RWORK(IPHI), U1, LDU1, U2, LDU2, V1T, LDV1T, 0, 1,
+     $                RWORK(IB11D), RWORK(IB11E), RWORK(IB12D),
+     $                RWORK(IB12E), RWORK(IB21D), RWORK(IB21E),
+     $                RWORK(IB22D), RWORK(IB22E), RWORK(IBBCSD), LBBCSD,
+     $                CHILDINFO )
+*   
+*        Permute rows and columns to place zero submatrices in
+*        preferred positions
+*
+         IF( Q .GT. 0 .AND. WANTU2 ) THEN
+            DO I = 1, Q
+               IWORK(I) = M - P - Q + I
+            END DO
+            DO I = Q + 1, M - P
+               IWORK(I) = I - Q
+            END DO
+            CALL CLAPMT( .FALSE., M-P, M-P, U2, LDU2, IWORK )
+         END IF
+      ELSE IF( R .EQ. P ) THEN
+*
+*        Case 2: R = P
+*
+*        Simultaneously bidiagonalize X11 and X21
+*
+         CALL CUNBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA,
+     $                 RWORK(IPHI), WORK(ITAUP1), WORK(ITAUP2),
+     $                 WORK(ITAUQ1), WORK(IORBDB), LORBDB, CHILDINFO )
+*
+*        Accumulate Householder reflectors
+*
+         IF( WANTU1 .AND. P .GT. 0 ) THEN
+            U1(1,1) = ONE
+            DO J = 2, P
+               U1(1,J) = ZERO
+               U1(J,1) = ZERO
+            END DO
+            CALL CLACPY( 'L', P-1, P-1, X11(2,1), LDX11, U1(2,2), LDU1 )
+            CALL CUNGQR( P-1, P-1, P-1, U1(2,2), LDU1, WORK(ITAUP1),
+     $                   WORK(IORGQR), LORGQR, CHILDINFO )
+         END IF
+         IF( WANTU2 .AND. M-P .GT. 0 ) THEN
+            CALL CLACPY( 'L', M-P, Q, X21, LDX21, U2, LDU2 )
+            CALL CUNGQR( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2),
+     $                   WORK(IORGQR), LORGQR, CHILDINFO )
+         END IF
+         IF( WANTV1T .AND. Q .GT. 0 ) THEN
+            CALL CLACPY( 'U', P, Q, X11, LDX11, V1T, LDV1T )
+            CALL CUNGLQ( Q, Q, R, V1T, LDV1T, WORK(ITAUQ1),
+     $                   WORK(IORGLQ), LORGLQ, CHILDINFO )
+         END IF
+*   
+*        Simultaneously diagonalize X11 and X21.
+*   
+         CALL CBBCSD( JOBV1T, 'N', JOBU1, JOBU2, 'T', M, Q, P, THETA,
+     $                RWORK(IPHI), V1T, LDV1T, 0, 1, U1, LDU1, U2, LDU2,
+     $                RWORK(IB11D), RWORK(IB11E), RWORK(IB12D),
+     $                RWORK(IB12E), RWORK(IB21D), RWORK(IB21E),
+     $                RWORK(IB22D), RWORK(IB22E), RWORK(IBBCSD), LBBCSD,
+     $                CHILDINFO )
+*   
+*        Permute rows and columns to place identity submatrices in
+*        preferred positions
+*
+         IF( Q .GT. 0 .AND. WANTU2 ) THEN
+            DO I = 1, Q
+               IWORK(I) = M - P - Q + I
+            END DO
+            DO I = Q + 1, M - P
+               IWORK(I) = I - Q
+            END DO
+            CALL CLAPMT( .FALSE., M-P, M-P, U2, LDU2, IWORK )
+         END IF
+      ELSE IF( R .EQ. M-P ) THEN
+*
+*        Case 3: R = M-P
+*
+*        Simultaneously bidiagonalize X11 and X21
+*
+         CALL CUNBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA,
+     $                 RWORK(IPHI), WORK(ITAUP1), WORK(ITAUP2),
+     $                 WORK(ITAUQ1), WORK(IORBDB), LORBDB, CHILDINFO )
+*
+*        Accumulate Householder reflectors
+*
+         IF( WANTU1 .AND. P .GT. 0 ) THEN
+            CALL CLACPY( 'L', P, Q, X11, LDX11, U1, LDU1 )
+            CALL CUNGQR( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGQR),
+     $                   LORGQR, CHILDINFO )
+         END IF
+         IF( WANTU2 .AND. M-P .GT. 0 ) THEN
+            U2(1,1) = ONE
+            DO J = 2, M-P
+               U2(1,J) = ZERO
+               U2(J,1) = ZERO
+            END DO
+            CALL CLACPY( 'L', M-P-1, M-P-1, X21(2,1), LDX21, U2(2,2),
+     $                   LDU2 )
+            CALL CUNGQR( M-P-1, M-P-1, M-P-1, U2(2,2), LDU2,
+     $                   WORK(ITAUP2), WORK(IORGQR), LORGQR, CHILDINFO )
+         END IF
+         IF( WANTV1T .AND. Q .GT. 0 ) THEN
+            CALL CLACPY( 'U', M-P, Q, X21, LDX21, V1T, LDV1T )
+            CALL CUNGLQ( Q, Q, R, V1T, LDV1T, WORK(ITAUQ1),
+     $                   WORK(IORGLQ), LORGLQ, CHILDINFO )
+         END IF
+*   
+*        Simultaneously diagonalize X11 and X21.
+*   
+         CALL CBBCSD( 'N', JOBV1T, JOBU2, JOBU1, 'T', M, M-Q, M-P,
+     $                THETA, RWORK(IPHI), 0, 1, V1T, LDV1T, U2, LDU2,
+     $                U1, LDU1, RWORK(IB11D), RWORK(IB11E),
+     $                RWORK(IB12D), RWORK(IB12E), RWORK(IB21D),
+     $                RWORK(IB21E), RWORK(IB22D), RWORK(IB22E),
+     $                RWORK(IBBCSD), LBBCSD, CHILDINFO )
+*   
+*        Permute rows and columns to place identity submatrices in
+*        preferred positions
+*
+         IF( Q .GT. R ) THEN
+            DO I = 1, R
+               IWORK(I) = Q - R + I
+            END DO
+            DO I = R + 1, Q
+               IWORK(I) = I - R
+            END DO
+            IF( WANTU1 ) THEN
+               CALL CLAPMT( .FALSE., P, Q, U1, LDU1, IWORK )
+            END IF
+            IF( WANTV1T ) THEN
+               CALL CLAPMR( .FALSE., Q, Q, V1T, LDV1T, IWORK )
+            END IF
+         END IF
+      ELSE
+*
+*        Case 4: R = M-Q
+*
+*        Simultaneously bidiagonalize X11 and X21
+*
+         CALL CUNBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA,
+     $                 RWORK(IPHI), WORK(ITAUP1), WORK(ITAUP2),
+     $                 WORK(ITAUQ1), WORK(IORBDB), WORK(IORBDB+M),
+     $                 LORBDB-M, CHILDINFO )
+*
+*        Accumulate Householder reflectors
+*
+         IF( WANTU1 .AND. P .GT. 0 ) THEN
+            CALL CCOPY( P, WORK(IORBDB), 1, U1, 1 )
+            DO J = 2, P
+               U1(1,J) = ZERO
+            END DO
+            CALL CLACPY( 'L', P-1, M-Q-1, X11(2,1), LDX11, U1(2,2),
+     $                   LDU1 )
+            CALL CUNGQR( P, P, M-Q, U1, LDU1, WORK(ITAUP1),
+     $                   WORK(IORGQR), LORGQR, CHILDINFO )
+         END IF
+         IF( WANTU2 .AND. M-P .GT. 0 ) THEN
+            CALL CCOPY( M-P, WORK(IORBDB+P), 1, U2, 1 )
+            DO J = 2, M-P
+               U2(1,J) = ZERO
+            END DO
+            CALL CLACPY( 'L', M-P-1, M-Q-1, X21(2,1), LDX21, U2(2,2),
+     $                   LDU2 )
+            CALL CUNGQR( M-P, M-P, M-Q, U2, LDU2, WORK(ITAUP2),
+     $                   WORK(IORGQR), LORGQR, CHILDINFO )
+         END IF
+         IF( WANTV1T .AND. Q .GT. 0 ) THEN
+            CALL CLACPY( 'U', M-Q, Q, X21, LDX21, V1T, LDV1T )
+            CALL CLACPY( 'U', P-(M-Q), Q-(M-Q), X11(M-Q+1,M-Q+1), LDX11,
+     $                   V1T(M-Q+1,M-Q+1), LDV1T )
+            CALL CLACPY( 'U', -P+Q, Q-P, X21(M-Q+1,P+1), LDX21,
+     $                   V1T(P+1,P+1), LDV1T )
+            CALL CUNGLQ( Q, Q, Q, V1T, LDV1T, WORK(ITAUQ1),
+     $                   WORK(IORGLQ), LORGLQ, CHILDINFO )
+         END IF
+*   
+*        Simultaneously diagonalize X11 and X21.
+*   
+         CALL CBBCSD( JOBU2, JOBU1, 'N', JOBV1T, 'N', M, M-P, M-Q,
+     $                THETA, RWORK(IPHI), U2, LDU2, U1, LDU1, 0, 1, V1T,
+     $                LDV1T, RWORK(IB11D), RWORK(IB11E), RWORK(IB12D),
+     $                RWORK(IB12E), RWORK(IB21D), RWORK(IB21E),
+     $                RWORK(IB22D), RWORK(IB22E), RWORK(IBBCSD), LBBCSD,
+     $                CHILDINFO )
+*   
+*        Permute rows and columns to place identity submatrices in
+*        preferred positions
+*
+         IF( P .GT. R ) THEN
+            DO I = 1, R
+               IWORK(I) = P - R + I
+            END DO
+            DO I = R + 1, P
+               IWORK(I) = I - R
+            END DO
+            IF( WANTU1 ) THEN
+               CALL CLAPMT( .FALSE., P, P, U1, LDU1, IWORK )
+            END IF
+            IF( WANTV1T ) THEN
+               CALL CLAPMR( .FALSE., P, Q, V1T, LDV1T, IWORK )
+            END IF
+         END IF
+      END IF
+*
+      RETURN
+*
+*     End of CUNCSD2BY1
+*
+      END
+

lapack-netlib/SRC/dbbcsd.f

@@ -322,7 +322,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date November 2011
+*> \date November 2013
 *
 *> \ingroup doubleOTHERcomputational
 *
@@ -332,10 +332,10 @@
      $                   V2T, LDV2T, B11D, B11E, B12D, B12E, B21D, B21E,
      $                   B22D, B22E, WORK, LWORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2011
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS
@@ -358,8 +358,8 @@
       PARAMETER          ( HUNDRED = 100.0D0, MEIGHTH = -0.125D0,
      $                     ONE = 1.0D0, PIOVER2 = 1.57079632679489662D0,
      $                     TEN = 10.0D0, ZERO = 0.0D0 )
-      DOUBLE PRECISION   NEGONECOMPLEX
-      PARAMETER          ( NEGONECOMPLEX = -1.0D0 )
+      DOUBLE PRECISION   NEGONE
+      PARAMETER          ( NEGONE = -1.0D0 )
 *     ..
 *     .. Local Scalars ..
       LOGICAL            COLMAJOR, LQUERY, RESTART11, RESTART12,
@@ -477,7 +477,10 @@
 *     Initial deflation
 *
       IMAX = Q
-      DO WHILE( ( IMAX .GT. 1 ) .AND. ( PHI(IMAX-1) .EQ. ZERO ) )
+      DO WHILE( IMAX .GT. 1 )
+         IF( PHI(IMAX-1) .NE. ZERO ) THEN
+            EXIT
+         END IF
          IMAX = IMAX - 1
       END DO
       IMIN = IMAX - 1
@@ -939,9 +942,9 @@
             B21D(IMAX) = -B21D(IMAX)
             IF( WANTV1T ) THEN
                IF( COLMAJOR ) THEN
-                  CALL DSCAL( Q, NEGONECOMPLEX, V1T(IMAX,1), LDV1T )
+                  CALL DSCAL( Q, NEGONE, V1T(IMAX,1), LDV1T )
                ELSE
-                  CALL DSCAL( Q, NEGONECOMPLEX, V1T(1,IMAX), 1 )
+                  CALL DSCAL( Q, NEGONE, V1T(1,IMAX), 1 )
                END IF
             END IF
          END IF
@@ -962,9 +965,9 @@
             B12D(IMAX) = -B12D(IMAX)
             IF( WANTU1 ) THEN
                IF( COLMAJOR ) THEN
-                  CALL DSCAL( P, NEGONECOMPLEX, U1(1,IMAX), 1 )
+                  CALL DSCAL( P, NEGONE, U1(1,IMAX), 1 )
                ELSE
-                  CALL DSCAL( P, NEGONECOMPLEX, U1(IMAX,1), LDU1 )
+                  CALL DSCAL( P, NEGONE, U1(IMAX,1), LDU1 )
                END IF
             END IF
          END IF
@@ -972,9 +975,9 @@
             B22D(IMAX) = -B22D(IMAX)
             IF( WANTU2 ) THEN
                IF( COLMAJOR ) THEN
-                  CALL DSCAL( M-P, NEGONECOMPLEX, U2(1,IMAX), 1 )
+                  CALL DSCAL( M-P, NEGONE, U2(1,IMAX), 1 )
                ELSE
-                  CALL DSCAL( M-P, NEGONECOMPLEX, U2(IMAX,1), LDU2 )
+                  CALL DSCAL( M-P, NEGONE, U2(IMAX,1), LDU2 )
                END IF
             END IF
          END IF
@@ -984,9 +987,9 @@
          IF( B12D(IMAX)+B22D(IMAX) .LT. 0 ) THEN
             IF( WANTV2T ) THEN
                IF( COLMAJOR ) THEN
-                  CALL DSCAL( M-Q, NEGONECOMPLEX, V2T(IMAX,1), LDV2T )
+                  CALL DSCAL( M-Q, NEGONE, V2T(IMAX,1), LDV2T )
                ELSE
-                  CALL DSCAL( M-Q, NEGONECOMPLEX, V2T(1,IMAX), 1 )
+                  CALL DSCAL( M-Q, NEGONE, V2T(1,IMAX), 1 )
                END IF
             END IF
          END IF

lapack-netlib/SRC/dgebal.f

@@ -121,7 +121,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date November 2011
+*> \date November 2013
 *
 *> \ingroup doubleGEcomputational
 *
@@ -160,10 +160,10 @@
 *  =====================================================================
       SUBROUTINE DGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2011
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOB
@@ -192,8 +192,8 @@
 *     .. External Functions ..
       LOGICAL            DISNAN, LSAME
       INTEGER            IDAMAX
-      DOUBLE PRECISION   DLAMCH
-      EXTERNAL           DISNAN, LSAME, IDAMAX, DLAMCH
+      DOUBLE PRECISION   DLAMCH, DNRM2
+      EXTERNAL           DISNAN, LSAME, IDAMAX, DLAMCH, DNRM2
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           DSCAL, DSWAP, XERBLA
@@ -312,19 +312,14 @@
       SFMAX1 = ONE / SFMIN1
       SFMIN2 = SFMIN1*SCLFAC
       SFMAX2 = ONE / SFMIN2
+*
   140 CONTINUE
       NOCONV = .FALSE.
 *
       DO 200 I = K, L
-         C = ZERO
-         R = ZERO
-*
-         DO 150 J = K, L
-            IF( J.EQ.I )
-     $         GO TO 150
-            C = C + ABS( A( J, I ) )
-            R = R + ABS( A( I, J ) )
-  150    CONTINUE
+*
+         C = DNRM2( L-K+1, A( K, I ), 1 )
+         R = DNRM2( L-K+1, A( I, K ), LDA )
          ICA = IDAMAX( L, A( 1, I ), 1 )
          CA = ABS( A( ICA, I ) )
          IRA = IDAMAX( N-K+1, A( I, K ), LDA )

lapack-netlib/SRC/dgemqrt.f

@@ -160,7 +160,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date November 2011
+*> \date November 2013
 *
 *> \ingroup doubleGEcomputational
 *
@@ -168,10 +168,10 @@
       SUBROUTINE DGEMQRT( SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT, 
      $                   C, LDC, WORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2011
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER SIDE, TRANS
@@ -225,7 +225,7 @@
          INFO = -4
       ELSE IF( K.LT.0 .OR. K.GT.Q ) THEN
          INFO = -5
-      ELSE IF( NB.LT.1 .OR. NB.GT.K ) THEN
+      ELSE IF( NB.LT.1 .OR. (NB.GT.K .AND. K.GT.0)) THEN
          INFO = -6
       ELSE IF( LDV.LT.MAX( 1, Q ) ) THEN
          INFO = -8

lapack-netlib/SRC/dgeqrt.f

@@ -108,7 +108,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date November 2011
+*> \date November 2013
 *
 *> \ingroup doubleGEcomputational
 *
@@ -141,10 +141,10 @@
 *  =====================================================================
       SUBROUTINE DGEQRT( M, N, NB, A, LDA, T, LDT, WORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2011
+*     November 2013
 *
 *     .. Scalar Arguments ..
       INTEGER INFO, LDA, LDT, M, N, NB
@@ -173,7 +173,7 @@
          INFO = -1
       ELSE IF( N.LT.0 ) THEN
          INFO = -2
-      ELSE IF( NB.LT.1 .OR. NB.GT.MIN(M,N) ) THEN
+      ELSE IF( NB.LT.1 .OR. ( NB.GT.MIN(M,N) .AND. MIN(M,N).GT.0 ) )THEN
          INFO = -3
       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
          INFO = -5

lapack-netlib/SRC/dgesdd.f

@@ -175,8 +175,7 @@
 *>            LWORK >= 3*min(M,N) + 
 *>                     max(max(M,N),5*min(M,N)*min(M,N)+4*min(M,N)).
 *>          If JOBZ = 'S' or 'A'
-*>            LWORK >= 3*min(M,N) +
-*>                     max(max(M,N),4*min(M,N)*min(M,N)+3*min(M,N)+max(M,N)).
+*>            LWORK >= min(M,N)*(6+4*min(M,N))+max(M,N)
 *>          For good performance, LWORK should generally be larger.
 *>          If LWORK = -1 but other input arguments are legal, WORK(1)
 *>          returns the optimal LWORK.
@@ -203,7 +202,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date September 2012
+*> \date November 2013
 *
 *> \ingroup doubleGEsing
 *
@@ -217,10 +216,10 @@
       SUBROUTINE DGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,
      $                   LWORK, IWORK, INFO )
 *
-*  -- LAPACK driver routine (version 3.4.2) --
+*  -- LAPACK driver routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     September 2012
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBZ

lapack-netlib/SRC/dgetc2.f

@@ -98,7 +98,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date September 2012
+*> \date November 2013
 *
 *> \ingroup doubleGEauxiliary
 *
@@ -111,10 +111,10 @@
 *  =====================================================================
       SUBROUTINE DGETC2( N, A, LDA, IPIV, JPIV, INFO )
 *
-*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK auxiliary routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     September 2012
+*     November 2013
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, N
@@ -203,6 +203,11 @@
          INFO = N
          A( N, N ) = SMIN
       END IF
+*
+*     Set last pivots to N
+*
+      IPIV( N ) = N
+      JPIV( N ) = N
 *
       RETURN
 *

lapack-netlib/SRC/dhgeqz.f

@@ -282,7 +282,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date April 2012
+*> \date November 2013
 *
 *> \ingroup doubleGEcomputational
 *
@@ -304,10 +304,10 @@
      $                   ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDZ, WORK,
      $                   LWORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.1) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     April 2012
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          COMPQ, COMPZ, JOB
@@ -739,9 +739,9 @@
 *           Exceptional shift.  Chosen for no particularly good reason.
 *           (Single shift only.)
 *
-            IF( ( DBLE( MAXIT )*SAFMIN )*ABS( H( ILAST-1, ILAST ) ).LT.
+            IF( ( DBLE( MAXIT )*SAFMIN )*ABS( H( ILAST, ILAST-1 ) ).LT.
      $          ABS( T( ILAST-1, ILAST-1 ) ) ) THEN
-               ESHIFT = ESHIFT + H( ILAST, ILAST-1 ) /
+               ESHIFT = H( ILAST, ILAST-1 ) /
      $                  T( ILAST-1, ILAST-1 )
             ELSE
                ESHIFT = ESHIFT + ONE / ( SAFMIN*DBLE( MAXIT ) )
@@ -759,6 +759,16 @@
      $                  T( ILAST-1, ILAST-1 ), LDT, SAFMIN*SAFETY, S1,
      $                  S2, WR, WR2, WI )
 *
+            IF ( ABS( (WR/S1)*T( ILAST, ILAST ) - H( ILAST, ILAST ) )
+     $         .GT. ABS( (WR2/S2)*T( ILAST, ILAST ) 
+     $         - H( ILAST, ILAST ) ) ) THEN
+               TEMP = WR
+               WR = WR2
+               WR2 = TEMP
+               TEMP = S1
+               S1 = S2
+               S2 = TEMP
+            END IF
             TEMP = MAX( S1, SAFMIN*MAX( ONE, ABS( WR ), ABS( WI ) ) )
             IF( WI.NE.ZERO )
      $         GO TO 200

lapack-netlib/SRC/dhsein.f

@@ -108,6 +108,7 @@
 *> \verbatim
 *>          H is DOUBLE PRECISION array, dimension (LDH,N)
 *>          The upper Hessenberg matrix H.
+*>          If a NaN is detected in H, the routine will return with INFO=-6.
 *> \endverbatim
 *>
 *> \param[in] LDH
@@ -243,7 +244,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date November 2011
+*> \date November 2013
 *
 *> \ingroup doubleOTHERcomputational
 *
@@ -262,10 +263,10 @@
      $                   VL, LDVL, VR, LDVR, MM, M, WORK, IFAILL,
      $                   IFAILR, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2011
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          EIGSRC, INITV, SIDE
@@ -291,9 +292,9 @@
      $                   WKR
 *     ..
 *     .. External Functions ..
-      LOGICAL            LSAME
+      LOGICAL            LSAME, DISNAN
       DOUBLE PRECISION   DLAMCH, DLANHS
-      EXTERNAL           LSAME, DLAMCH, DLANHS
+      EXTERNAL           LSAME, DLAMCH, DLANHS, DISNAN
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           DLAEIN, XERBLA
@@ -423,7 +424,10 @@
 *              has not ben computed before.
 *
                HNORM = DLANHS( 'I', KR-KL+1, H( KL, KL ), LDH, WORK )
-               IF( HNORM.GT.ZERO ) THEN
+               IF( DISNAN( HNORM ) ) THEN
+                  INFO = -6
+                  RETURN
+               ELSE IF( HNORM.GT.ZERO ) THEN
                   EPS3 = HNORM*ULP
                ELSE
                   EPS3 = SMLNUM

lapack-netlib/SRC/dladiv.f

@@ -36,8 +36,9 @@
 *>            p + i*q = ---------
 *>                       c + i*d
 *>
-*> The algorithm is due to Robert L. Smith and can be found
-*> in D. Knuth, The art of Computer Programming, Vol.2, p.195
+*> The algorithm is due to Michael Baudin and Robert L. Smith
+*> and can be found in the paper
+*> "A Robust Complex Division in Scilab"
 *> \endverbatim
 *
 *  Arguments:
@@ -83,17 +84,17 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date September 2012
+*> \date January 2013
 *
 *> \ingroup auxOTHERauxiliary
 *
 *  =====================================================================
       SUBROUTINE DLADIV( A, B, C, D, P, Q )
 *
-*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK auxiliary routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     September 2012
+*     January 2013
 *
 *     .. Scalar Arguments ..
       DOUBLE PRECISION   A, B, C, D, P, Q
@@ -101,28 +102,152 @@
 *
 *  =====================================================================
 *
+*     .. Parameters ..
+      DOUBLE PRECISION   BS
+      PARAMETER          ( BS = 2.0D0 )
+      DOUBLE PRECISION   HALF
+      PARAMETER          ( HALF = 0.5D0 )
+      DOUBLE PRECISION   TWO
+      PARAMETER          ( TWO = 2.0D0 )
+*
 *     .. Local Scalars ..
-      DOUBLE PRECISION   E, F
+      DOUBLE PRECISION   AA, BB, CC, DD, AB, CD, S, OV, UN, BE, EPS
+*     ..
+*     .. External Functions ..
+      DOUBLE PRECISION   DLAMCH
+      EXTERNAL           DLAMCH
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DLADIV1
 *     ..
 *     .. Intrinsic Functions ..
-      INTRINSIC          ABS
+      INTRINSIC          ABS, MAX
 *     ..
 *     .. Executable Statements ..
 *
-      IF( ABS( D ).LT.ABS( C ) ) THEN
-         E = D / C
-         F = C + D*E
-         P = ( A+B*E ) / F
-         Q = ( B-A*E ) / F
+      AA = A
+      BB = B
+      CC = C
+      DD = D
+      AB = MAX( ABS(A), ABS(B) )
+      CD = MAX( ABS(C), ABS(D) )
+      S = 1.0D0
+      
+      OV = DLAMCH( 'Overflow threshold' )
+      UN = DLAMCH( 'Safe minimum' )
+      EPS = DLAMCH( 'Epsilon' )
+      BE = BS / (EPS*EPS)
+      
+      IF( AB >= HALF*OV ) THEN
+         AA = HALF * AA
+         BB = HALF * BB
+         S  = TWO * S
+      END IF
+      IF( CD >= HALF*OV ) THEN
+         CC = HALF * CC
+         DD = HALF * DD
+         S  = HALF * S
+      END IF
+      IF( AB <= UN*BS/EPS ) THEN
+         AA = AA * BE
+         BB = BB * BE
+         S  = S / BE
+      END IF
+      IF( CD <= UN*BS/EPS ) THEN
+         CC = CC * BE
+         DD = DD * BE
+         S  = S * BE
+      END IF
+      IF( ABS( D ).LE.ABS( C ) ) THEN
+         CALL DLADIV1(AA, BB, CC, DD, P, Q)
       ELSE
-         E = C / D
-         F = D + C*E
-         P = ( B+A*E ) / F
-         Q = ( -A+B*E ) / F
+         CALL DLADIV1(BB, AA, DD, CC, P, Q)
+         Q = -Q
       END IF
+      P = P * S
+      Q = Q * S
 *
       RETURN
 *
 *     End of DLADIV
 *
       END
+
+      
+
+      SUBROUTINE DLADIV1( A, B, C, D, P, Q )
+*
+*  -- LAPACK auxiliary routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     January 2013
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION   A, B, C, D, P, Q
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ONE
+      PARAMETER          ( ONE = 1.0D0 )
+*
+*     .. Local Scalars ..
+      DOUBLE PRECISION   R, T
+*     ..
+*     .. External Functions ..
+      DOUBLE PRECISION   DLADIV2
+      EXTERNAL           DLADIV2
+*     ..
+*     .. Executable Statements ..
+*
+      R = D / C
+      T = ONE / (C + D * R)
+      P = DLADIV2(A, B, C, D, R, T)
+      A = -A
+      Q = DLADIV2(B, A, C, D, R, T)
+*
+      RETURN
+*
+*     End of DLADIV1
+*
+      END
+
+      DOUBLE PRECISION FUNCTION DLADIV2( A, B, C, D, R, T )
+*
+*  -- LAPACK auxiliary routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     January 2013
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION   A, B, C, D, R, T
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ZERO
+      PARAMETER          ( ZERO = 0.0D0 )
+*
+*     .. Local Scalars ..
+      DOUBLE PRECISION   BR
+*     ..
+*     .. Executable Statements ..
+*
+      IF( R.NE.ZERO ) THEN
+         BR = B * R
+         if( BR.NE.ZERO ) THEN
+            DLADIV2 = (A + BR) * T
+         ELSE
+            DLADIV2 = A * T + (B * T) * R
+         END IF
+      ELSE
+         DLADIV2 = (A + D * (B / C)) * T
+      END IF
+*
+      RETURN
+*
+*     End of DLADIV12
+*
+      END

lapack-netlib/SRC/dlaqp2.f

@@ -122,7 +122,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date September 2012
+*> \date November 2013
 *
 *> \ingroup doubleOTHERauxiliary
 *
@@ -149,10 +149,10 @@
       SUBROUTINE DLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2,
      $                   WORK )
 *
-*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK auxiliary routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     September 2012
+*     November 2013
 *
 *     .. Scalar Arguments ..
       INTEGER            LDA, M, N, OFFSET
@@ -217,7 +217,7 @@
             CALL DLARFG( 1, A( M, I ), A( M, I ), 1, TAU( I ) )
          END IF
 *
-         IF( I.LE.N ) THEN
+         IF( I.LT.N ) THEN
 *
 *           Apply H(i)**T to A(offset+i:m,i+1:n) from the left.
 *

lapack-netlib/SRC/dlarfb.f

@@ -159,7 +159,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date September 2012
+*> \date June 2013
 *
 *> \ingroup doubleOTHERauxiliary
 *
@@ -195,10 +195,10 @@
       SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,
      $                   T, LDT, C, LDC, WORK, LDWORK )
 *
-*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK auxiliary routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     September 2012
+*     June 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          DIRECT, SIDE, STOREV, TRANS
@@ -217,12 +217,11 @@
 *     ..
 *     .. Local Scalars ..
       CHARACTER          TRANST
-      INTEGER            I, J, LASTV, LASTC, lastv2
+      INTEGER            I, J
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
-      INTEGER            ILADLR, ILADLC
-      EXTERNAL           LSAME, ILADLR, ILADLC
+      EXTERNAL           LSAME
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           DCOPY, DGEMM, DTRMM
@@ -252,58 +251,53 @@
 *
 *              Form  H * C  or  H**T * C  where  C = ( C1 )
 *                                                    ( C2 )
-*
-               LASTV = MAX( K, ILADLR( M, K, V, LDV ) )
-               LASTC = ILADLC( LASTV, N, C, LDC )
 *
 *              W := C**T * V  =  (C1**T * V1 + C2**T * V2)  (stored in WORK)
 *
 *              W := C1**T
 *
                DO 10 J = 1, K
-                  CALL DCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
+                  CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
    10          CONTINUE
 *
 *              W := W * V1
 *
-               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
-     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
-               IF( LASTV.GT.K ) THEN
+               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', N,
+     $                     K, ONE, V, LDV, WORK, LDWORK )
+               IF( M.GT.K ) THEN
 *
-*                 W := W + C2**T *V2
+*                 W := W + C2**T * V2
 *
-                  CALL DGEMM( 'Transpose', 'No transpose',
-     $                 LASTC, K, LASTV-K,
-     $                 ONE, C( K+1, 1 ), LDC, V( K+1, 1 ), LDV,
-     $                 ONE, WORK, LDWORK )
+                  CALL DGEMM( 'Transpose', 'No transpose', N, K, M-K,
+     $                        ONE, C( K+1, 1 ), LDC, V( K+1, 1 ), LDV,
+     $                        ONE, WORK, LDWORK )
                END IF
 *
 *              W := W * T**T  or  W * T
 *
-               CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
-     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
+               CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit', N, K,
+     $                     ONE, T, LDT, WORK, LDWORK )
 *
 *              C := C - V * W**T
 *
-               IF( LASTV.GT.K ) THEN
+               IF( M.GT.K ) THEN
 *
 *                 C2 := C2 - V2 * W**T
 *
-                  CALL DGEMM( 'No transpose', 'Transpose',
-     $                 LASTV-K, LASTC, K,
-     $                 -ONE, V( K+1, 1 ), LDV, WORK, LDWORK, ONE,
-     $                 C( K+1, 1 ), LDC )
+                  CALL DGEMM( 'No transpose', 'Transpose', M-K, N, K,
+     $                        -ONE, V( K+1, 1 ), LDV, WORK, LDWORK, ONE,
+     $                        C( K+1, 1 ), LDC )
                END IF
 *
 *              W := W * V1**T
 *
-               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',
-     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
+               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', N, K,
+     $                     ONE, V, LDV, WORK, LDWORK )
 *
 *              C1 := C1 - W**T
 *
                DO 30 J = 1, K
-                  DO 20 I = 1, LASTC
+                  DO 20 I = 1, N
                      C( J, I ) = C( J, I ) - WORK( I, J )
    20             CONTINUE
    30          CONTINUE
@@ -311,58 +305,53 @@
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
 *              Form  C * H  or  C * H**T  where  C = ( C1  C2 )
-*
-               LASTV = MAX( K, ILADLR( N, K, V, LDV ) )
-               LASTC = ILADLR( M, LASTV, C, LDC )
 *
 *              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)
 *
 *              W := C1
 *
                DO 40 J = 1, K
-                  CALL DCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )
+                  CALL DCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 )
    40          CONTINUE
 *
 *              W := W * V1
 *
-               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
-     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
-               IF( LASTV.GT.K ) THEN
+               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', M,
+     $                     K, ONE, V, LDV, WORK, LDWORK )
+               IF( N.GT.K ) THEN
 *
 *                 W := W + C2 * V2
 *
-                  CALL DGEMM( 'No transpose', 'No transpose',
-     $                 LASTC, K, LASTV-K,
-     $                 ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV,
-     $                 ONE, WORK, LDWORK )
+                  CALL DGEMM( 'No transpose', 'No transpose', M, K, N-K,
+     $                        ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV,
+     $                        ONE, WORK, LDWORK )
                END IF
 *
 *              W := W * T  or  W * T**T
 *
-               CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit',
-     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
+               CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit', M, K,
+     $                     ONE, T, LDT, WORK, LDWORK )
 *
 *              C := C - W * V**T
 *
-               IF( LASTV.GT.K ) THEN
+               IF( N.GT.K ) THEN
 *
 *                 C2 := C2 - W * V2**T
 *
-                  CALL DGEMM( 'No transpose', 'Transpose',
-     $                 LASTC, LASTV-K, K,
-     $                 -ONE, WORK, LDWORK, V( K+1, 1 ), LDV, ONE,
-     $                 C( 1, K+1 ), LDC )
+                  CALL DGEMM( 'No transpose', 'Transpose', M, N-K, K,
+     $                        -ONE, WORK, LDWORK, V( K+1, 1 ), LDV, ONE,
+     $                        C( 1, K+1 ), LDC )
                END IF
 *
 *              W := W * V1**T
 *
-               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',
-     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
+               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', M, K,
+     $                     ONE, V, LDV, WORK, LDWORK )
 *
 *              C1 := C1 - W
 *
                DO 60 J = 1, K
-                  DO 50 I = 1, LASTC
+                  DO 50 I = 1, M
                      C( I, J ) = C( I, J ) - WORK( I, J )
    50             CONTINUE
    60          CONTINUE
@@ -378,36 +367,31 @@
 *
 *              Form  H * C  or  H**T * C  where  C = ( C1 )
 *                                                    ( C2 )
-*
-               LASTC = ILADLC( M, N, C, LDC )
 *
 *              W := C**T * V  =  (C1**T * V1 + C2**T * V2)  (stored in WORK)
 *
 *              W := C2**T
 *
                DO 70 J = 1, K
-                  CALL DCOPY( LASTC, C( M-K+J, 1 ), LDC,
-     $                 WORK( 1, J ), 1 )
+                  CALL DCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 )
    70          CONTINUE
 *
 *              W := W * V2
 *
-               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
-     $              LASTC, K, ONE, V( M-K+1, 1 ), LDV,
-     $              WORK, LDWORK )
+               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', N,
+     $                     K, ONE, V( M-K+1, 1 ), LDV, WORK, LDWORK )
                IF( M.GT.K ) THEN
 *
-*                 W := W + C1**T*V1
+*                 W := W + C1**T * V1
 *
-                  CALL DGEMM( 'Transpose', 'No transpose',
-     $                 LASTC, K, M-K, ONE, C, LDC, V, LDV,
-     $                 ONE, WORK, LDWORK )
+                  CALL DGEMM( 'Transpose', 'No transpose', N, K, M-K,
+     $                        ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
                END IF
 *
 *              W := W * T**T  or  W * T
 *
-               CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
-     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
+               CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K,
+     $                     ONE, T, LDT, WORK, LDWORK )
 *
 *              C := C - V * W**T
 *
@@ -415,57 +399,51 @@
 *
 *                 C1 := C1 - V1 * W**T
 *
-                  CALL DGEMM( 'No transpose', 'Transpose',
-     $                 M-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,
-     $                 ONE, C, LDC )
+                  CALL DGEMM( 'No transpose', 'Transpose', M-K, N, K,
+     $                        -ONE, V, LDV, WORK, LDWORK, ONE, C, LDC )
                END IF
 *
 *              W := W * V2**T
 *
-               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
-     $              LASTC, K, ONE, V( M-K+1, 1 ), LDV,
-     $              WORK, LDWORK )
+               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', N, K,
+     $                     ONE, V( M-K+1, 1 ), LDV, WORK, LDWORK )
 *
 *              C2 := C2 - W**T
 *
                DO 90 J = 1, K
-                  DO 80 I = 1, LASTC
-                     C( M-K+J, I ) = C( M-K+J, I ) - WORK(I, J)
+                  DO 80 I = 1, N
+                     C( M-K+J, I ) = C( M-K+J, I ) - WORK( I, J )
    80             CONTINUE
    90          CONTINUE
 *
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
 *              Form  C * H  or  C * H**T  where  C = ( C1  C2 )
-*
-               LASTC = ILADLR( M, N, C, LDC )
 *
 *              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)
 *
 *              W := C2
 *
                DO 100 J = 1, K
-                  CALL DCOPY( LASTC, C( 1, N-K+J ), 1, WORK( 1, J ), 1 )
+                  CALL DCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 )
   100          CONTINUE
 *
 *              W := W * V2
 *
-               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
-     $              LASTC, K, ONE, V( N-K+1, 1 ), LDV,
-     $              WORK, LDWORK )
+               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', M,
+     $                     K, ONE, V( N-K+1, 1 ), LDV, WORK, LDWORK )
                IF( N.GT.K ) THEN
 *
 *                 W := W + C1 * V1
 *
-                  CALL DGEMM( 'No transpose', 'No transpose',
-     $                 LASTC, K, N-K, ONE, C, LDC, V, LDV,
-     $                 ONE, WORK, LDWORK )
+                  CALL DGEMM( 'No transpose', 'No transpose', M, K, N-K,
+     $                        ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
                END IF
 *
 *              W := W * T  or  W * T**T
 *
-               CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
-     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
+               CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K,
+     $                     ONE, T, LDT, WORK, LDWORK )
 *
 *              C := C - W * V**T
 *
@@ -473,22 +451,20 @@
 *
 *                 C1 := C1 - W * V1**T
 *
-                  CALL DGEMM( 'No transpose', 'Transpose',
-     $                 LASTC, N-K, K, -ONE, WORK, LDWORK, V, LDV,
-     $                 ONE, C, LDC )
+                  CALL DGEMM( 'No transpose', 'Transpose', M, N-K, K,
+     $                        -ONE, WORK, LDWORK, V, LDV, ONE, C, LDC )
                END IF
 *
 *              W := W * V2**T
 *
-               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
-     $              LASTC, K, ONE, V( N-K+1, 1 ), LDV,
-     $              WORK, LDWORK )
+               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', M, K,
+     $                     ONE, V( N-K+1, 1 ), LDV, WORK, LDWORK )
 *
 *              C2 := C2 - W
 *
                DO 120 J = 1, K
-                  DO 110 I = 1, LASTC
-                     C( I, N-K+J ) = C( I, N-K+J ) - WORK(I, J)
+                  DO 110 I = 1, M
+                     C( I, N-K+J ) = C( I, N-K+J ) - WORK( I, J )
   110             CONTINUE
   120          CONTINUE
             END IF
@@ -505,58 +481,53 @@
 *
 *              Form  H * C  or  H**T * C  where  C = ( C1 )
 *                                                    ( C2 )
-*
-               LASTV = MAX( K, ILADLC( K, M, V, LDV ) )
-               LASTC = ILADLC( LASTV, N, C, LDC )
 *
 *              W := C**T * V**T  =  (C1**T * V1**T + C2**T * V2**T) (stored in WORK)
 *
 *              W := C1**T
 *
                DO 130 J = 1, K
-                  CALL DCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
+                  CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
   130          CONTINUE
 *
 *              W := W * V1**T
 *
-               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
-     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
-               IF( LASTV.GT.K ) THEN
+               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', N, K,
+     $                     ONE, V, LDV, WORK, LDWORK )
+               IF( M.GT.K ) THEN
 *
-*                 W := W + C2**T*V2**T
+*                 W := W + C2**T * V2**T
 *
-                  CALL DGEMM( 'Transpose', 'Transpose',
-     $                 LASTC, K, LASTV-K,
-     $                 ONE, C( K+1, 1 ), LDC, V( 1, K+1 ), LDV,
-     $                 ONE, WORK, LDWORK )
+                  CALL DGEMM( 'Transpose', 'Transpose', N, K, M-K, ONE,
+     $                        C( K+1, 1 ), LDC, V( 1, K+1 ), LDV, ONE,
+     $                        WORK, LDWORK )
                END IF
 *
 *              W := W * T**T  or  W * T
 *
-               CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
-     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
+               CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit', N, K,
+     $                     ONE, T, LDT, WORK, LDWORK )
 *
 *              C := C - V**T * W**T
 *
-               IF( LASTV.GT.K ) THEN
+               IF( M.GT.K ) THEN
 *
 *                 C2 := C2 - V2**T * W**T
 *
-                  CALL DGEMM( 'Transpose', 'Transpose',
-     $                 LASTV-K, LASTC, K,
-     $                 -ONE, V( 1, K+1 ), LDV, WORK, LDWORK,
-     $                 ONE, C( K+1, 1 ), LDC )
+                  CALL DGEMM( 'Transpose', 'Transpose', M-K, N, K, -ONE,
+     $                        V( 1, K+1 ), LDV, WORK, LDWORK, ONE,
+     $                        C( K+1, 1 ), LDC )
                END IF
 *
 *              W := W * V1
 *
-               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
-     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
+               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', N,
+     $                     K, ONE, V, LDV, WORK, LDWORK )
 *
 *              C1 := C1 - W**T
 *
                DO 150 J = 1, K
-                  DO 140 I = 1, LASTC
+                  DO 140 I = 1, N
                      C( J, I ) = C( J, I ) - WORK( I, J )
   140             CONTINUE
   150          CONTINUE
@@ -564,58 +535,53 @@
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
 *              Form  C * H  or  C * H**T  where  C = ( C1  C2 )
-*
-               LASTV = MAX( K, ILADLC( K, N, V, LDV ) )
-               LASTC = ILADLR( M, LASTV, C, LDC )
 *
 *              W := C * V**T  =  (C1*V1**T + C2*V2**T)  (stored in WORK)
 *
 *              W := C1
 *
                DO 160 J = 1, K
-                  CALL DCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )
+                  CALL DCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 )
   160          CONTINUE
 *
 *              W := W * V1**T
 *
-               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
-     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
-               IF( LASTV.GT.K ) THEN
+               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', M, K,
+     $                     ONE, V, LDV, WORK, LDWORK )
+               IF( N.GT.K ) THEN
 *
 *                 W := W + C2 * V2**T
 *
-                  CALL DGEMM( 'No transpose', 'Transpose',
-     $                 LASTC, K, LASTV-K,
-     $                 ONE, C( 1, K+1 ), LDC, V( 1, K+1 ), LDV,
-     $                 ONE, WORK, LDWORK )
+                  CALL DGEMM( 'No transpose', 'Transpose', M, K, N-K,
+     $                        ONE, C( 1, K+1 ), LDC, V( 1, K+1 ), LDV,
+     $                        ONE, WORK, LDWORK )
                END IF
 *
 *              W := W * T  or  W * T**T
 *
-               CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit',
-     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
+               CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit', M, K,
+     $                     ONE, T, LDT, WORK, LDWORK )
 *
 *              C := C - W * V
 *
-               IF( LASTV.GT.K ) THEN
+               IF( N.GT.K ) THEN
 *
 *                 C2 := C2 - W * V2
 *
-                  CALL DGEMM( 'No transpose', 'No transpose',
-     $                 LASTC, LASTV-K, K,
-     $                 -ONE, WORK, LDWORK, V( 1, K+1 ), LDV,
-     $                 ONE, C( 1, K+1 ), LDC )
+                  CALL DGEMM( 'No transpose', 'No transpose', M, N-K, K,
+     $                        -ONE, WORK, LDWORK, V( 1, K+1 ), LDV, ONE,
+     $                        C( 1, K+1 ), LDC )
                END IF
 *
 *              W := W * V1
 *
-               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
-     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
+               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', M,
+     $                     K, ONE, V, LDV, WORK, LDWORK )
 *
 *              C1 := C1 - W
 *
                DO 180 J = 1, K
-                  DO 170 I = 1, LASTC
+                  DO 170 I = 1, M
                      C( I, J ) = C( I, J ) - WORK( I, J )
   170             CONTINUE
   180          CONTINUE
@@ -631,36 +597,31 @@
 *
 *              Form  H * C  or  H**T * C  where  C = ( C1 )
 *                                                    ( C2 )
-*
-               LASTC = ILADLC( M, N, C, LDC )
 *
 *              W := C**T * V**T  =  (C1**T * V1**T + C2**T * V2**T) (stored in WORK)
 *
 *              W := C2**T
 *
                DO 190 J = 1, K
-                  CALL DCOPY( LASTC, C( M-K+J, 1 ), LDC,
-     $                 WORK( 1, J ), 1 )
+                  CALL DCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 )
   190          CONTINUE
 *
 *              W := W * V2**T
 *
-               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',
-     $              LASTC, K, ONE, V( 1, M-K+1 ), LDV,
-     $              WORK, LDWORK )
+               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', N, K,
+     $                     ONE, V( 1, M-K+1 ), LDV, WORK, LDWORK )
                IF( M.GT.K ) THEN
 *
 *                 W := W + C1**T * V1**T
 *
-                  CALL DGEMM( 'Transpose', 'Transpose',
-     $                 LASTC, K, M-K, ONE, C, LDC, V, LDV,
-     $                 ONE, WORK, LDWORK )
+                  CALL DGEMM( 'Transpose', 'Transpose', N, K, M-K, ONE,
+     $                        C, LDC, V, LDV, ONE, WORK, LDWORK )
                END IF
 *
 *              W := W * T**T  or  W * T
 *
-               CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
-     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
+               CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K,
+     $                     ONE, T, LDT, WORK, LDWORK )
 *
 *              C := C - V**T * W**T
 *
@@ -668,58 +629,51 @@
 *
 *                 C1 := C1 - V1**T * W**T
 *
-                  CALL DGEMM( 'Transpose', 'Transpose',
-     $                 M-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,
-     $                 ONE, C, LDC )
+                  CALL DGEMM( 'Transpose', 'Transpose', M-K, N, K, -ONE,
+     $                        V, LDV, WORK, LDWORK, ONE, C, LDC )
                END IF
 *
 *              W := W * V2
 *
-               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
-     $              LASTC, K, ONE, V( 1, M-K+1 ), LDV,
-     $              WORK, LDWORK )
+               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', N,
+     $                     K, ONE, V( 1, M-K+1 ), LDV, WORK, LDWORK )
 *
 *              C2 := C2 - W**T
 *
                DO 210 J = 1, K
-                  DO 200 I = 1, LASTC
-                     C( M-K+J, I ) = C( M-K+J, I ) - WORK(I, J)
+                  DO 200 I = 1, N
+                     C( M-K+J, I ) = C( M-K+J, I ) - WORK( I, J )
   200             CONTINUE
   210          CONTINUE
 *
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )
-*
-               LASTC = ILADLR( M, N, C, LDC )
+*              Form  C * H  or  C * H'  where  C = ( C1  C2 )
 *
 *              W := C * V**T  =  (C1*V1**T + C2*V2**T)  (stored in WORK)
 *
 *              W := C2
 *
                DO 220 J = 1, K
-                  CALL DCOPY( LASTC, C( 1, N-K+J ), 1,
-     $                 WORK( 1, J ), 1 )
+                  CALL DCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 )
   220          CONTINUE
 *
 *              W := W * V2**T
 *
-               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',
-     $              LASTC, K, ONE, V( 1, N-K+1 ), LDV,
-     $              WORK, LDWORK )
+               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', M, K,
+     $                     ONE, V( 1, N-K+1 ), LDV, WORK, LDWORK )
                IF( N.GT.K ) THEN
 *
 *                 W := W + C1 * V1**T
 *
-                  CALL DGEMM( 'No transpose', 'Transpose',
-     $                 LASTC, K, N-K, ONE, C, LDC, V, LDV,
-     $                 ONE, WORK, LDWORK )
+                  CALL DGEMM( 'No transpose', 'Transpose', M, K, N-K,
+     $                        ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
                END IF
 *
 *              W := W * T  or  W * T**T
 *
-               CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
-     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
+               CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K,
+     $                     ONE, T, LDT, WORK, LDWORK )
 *
 *              C := C - W * V
 *
@@ -727,22 +681,20 @@
 *
 *                 C1 := C1 - W * V1
 *
-                  CALL DGEMM( 'No transpose', 'No transpose',
-     $                 LASTC, N-K, K, -ONE, WORK, LDWORK, V, LDV,
-     $                 ONE, C, LDC )
+                  CALL DGEMM( 'No transpose', 'No transpose', M, N-K, K,
+     $                        -ONE, WORK, LDWORK, V, LDV, ONE, C, LDC )
                END IF
 *
 *              W := W * V2
 *
-               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
-     $              LASTC, K, ONE, V( 1, N-K+1 ), LDV,
-     $              WORK, LDWORK )
+               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', M,
+     $                     K, ONE, V( 1, N-K+1 ), LDV, WORK, LDWORK )
 *
 *              C1 := C1 - W
 *
                DO 240 J = 1, K
-                  DO 230 I = 1, LASTC
-                     C( I, N-K+J ) = C( I, N-K+J ) - WORK(I, J)
+                  DO 230 I = 1, M
+                     C( I, N-K+J ) = C( I, N-K+J ) - WORK( I, J )
   230             CONTINUE
   240          CONTINUE
 *

lapack-netlib/SRC/dlasd4.f

@@ -140,7 +140,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date September 2012
+*> \date November 2013
 *
 *> \ingroup auxOTHERauxiliary
 *
@@ -153,10 +153,10 @@
 *  =====================================================================
       SUBROUTINE DLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )
 *
-*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK auxiliary routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     September 2012
+*     November 2013
 *
 *     .. Scalar Arguments ..
       INTEGER            I, INFO, N

lapack-netlib/SRC/dlasyf.f

@@ -1,25 +1,25 @@
-*> \brief \b DLASYF computes a partial factorization of a real symmetric matrix, using the diagonal pivoting method.
+*> \brief \b DLASYF computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method.
 *
 *  =========== DOCUMENTATION ===========
 *
-* Online html documentation available at 
-*            http://www.netlib.org/lapack/explore-html/ 
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
 *
 *> \htmlonly
-*> Download DLASYF + dependencies 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasyf.f"> 
-*> [TGZ]</a> 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasyf.f"> 
-*> [ZIP]</a> 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasyf.f"> 
+*> Download DLASYF + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasyf.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasyf.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasyf.f">
 *> [TXT]</a>
-*> \endhtmlonly 
+*> \endhtmlonly
 *
 *  Definition:
 *  ===========
 *
 *       SUBROUTINE DLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
-* 
+*
 *       .. Scalar Arguments ..
 *       CHARACTER          UPLO
 *       INTEGER            INFO, KB, LDA, LDW, N, NB
@@ -28,7 +28,7 @@
 *       INTEGER            IPIV( * )
 *       DOUBLE PRECISION   A( LDA, * ), W( LDW, * )
 *       ..
-*  
+*
 *
 *> \par Purpose:
 *  =============
@@ -109,16 +109,26 @@
 *> \verbatim
 *>          IPIV is INTEGER array, dimension (N)
 *>          Details of the interchanges and the block structure of D.
-*>          If UPLO = 'U', only the last KB elements of IPIV are set;
-*>          if UPLO = 'L', only the first KB elements are set.
 *>
-*>          If IPIV(k) > 0, then rows and columns k and IPIV(k) were
-*>          interchanged and D(k,k) is a 1-by-1 diagonal block.
-*>          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
-*>          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
-*>          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
-*>          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
-*>          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*>          If UPLO = 'U':
+*>             Only the last KB elements of IPIV are set.
+*>
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k-1) < 0, then rows and columns
+*>             k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
+*>             is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>             Only the first KB elements of IPIV are set.
+*>
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k+1) < 0, then rows and columns
+*>             k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1)
+*>             is a 2-by-2 diagonal block.
 *> \endverbatim
 *>
 *> \param[out] W
@@ -144,22 +154,32 @@
 *  Authors:
 *  ========
 *
-*> \author Univ. of Tennessee 
-*> \author Univ. of California Berkeley 
-*> \author Univ. of Colorado Denver 
-*> \author NAG Ltd. 
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
 *
-*> \date September 2012
+*> \date November 2013
 *
 *> \ingroup doubleSYcomputational
 *
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>  November 2013,  Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*> \endverbatim
+*
 *  =====================================================================
       SUBROUTINE DLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.2) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     September 2012
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          UPLO
@@ -237,7 +257,8 @@
          ABSAKK = ABS( W( K, KW ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.GT.1 ) THEN
             IMAX = IDAMAX( K-1, W( 1, KW ), 1 )
@@ -248,7 +269,7 @@
 *
          IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
 *
-*           Column K is zero: set INFO and continue
+*           Column K is zero or underflow: set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
@@ -293,7 +314,7 @@
 *
                   KP = IMAX
 *
-*                 copy column KW-1 of W to column KW
+*                 copy column KW-1 of W to column KW of W
 *
                   CALL DCOPY( K, W( 1, KW-1 ), 1, W( 1, KW ), 1 )
                ELSE
@@ -305,60 +326,118 @@
                   KSTEP = 2
                END IF
             END IF
+*
+*           ============================================================
+*
+*           KK is the column of A where pivoting step stopped
 *
             KK = K - KSTEP + 1
+*
+*           KKW is the column of W which corresponds to column KK of A
+*
             KKW = NB + KK - N
 *
-*           Updated column KP is already stored in column KKW of W
+*           Interchange rows and columns KP and KK.
+*           Updated column KP is already stored in column KKW of W.
 *
             IF( KP.NE.KK ) THEN
 *
-*              Copy non-updated column KK to column KP
+*              Copy non-updated column KK to column KP of submatrix A
+*              at step K. No need to copy element into column K
+*              (or K and K-1 for 2-by-2 pivot) of A, since these columns
+*              will be later overwritten.
 *
-               A( KP, K ) = A( KK, K )
-               CALL DCOPY( K-1-KP, A( KP+1, KK ), 1, A( KP, KP+1 ),
+               A( KP, KP ) = A( KK, KK )
+               CALL DCOPY( KK-1-KP, A( KP+1, KK ), 1, A( KP, KP+1 ),
      $                     LDA )
-               CALL DCOPY( KP, A( 1, KK ), 1, A( 1, KP ), 1 )
+               IF( KP.GT.1 )
+     $            CALL DCOPY( KP-1, A( 1, KK ), 1, A( 1, KP ), 1 )
 *
-*              Interchange rows KK and KP in last KK columns of A and W
+*              Interchange rows KK and KP in last K+1 to N columns of A
+*              (columns K (or K and K-1 for 2-by-2 pivot) of A will be
+*              later overwritten). Interchange rows KK and KP
+*              in last KKW to NB columns of W.
 *
-               CALL DSWAP( N-KK+1, A( KK, KK ), LDA, A( KP, KK ), LDA )
+               IF( K.LT.N )
+     $            CALL DSWAP( N-K, A( KK, K+1 ), LDA, A( KP, K+1 ),
+     $                        LDA )
                CALL DSWAP( N-KK+1, W( KK, KKW ), LDW, W( KP, KKW ),
      $                     LDW )
             END IF
 *
             IF( KSTEP.EQ.1 ) THEN
 *
-*              1-by-1 pivot block D(k): column KW of W now holds
+*              1-by-1 pivot block D(k): column kw of W now holds
 *
-*              W(k) = U(k)*D(k)
+*              W(kw) = U(k)*D(k),
 *
 *              where U(k) is the k-th column of U
 *
-*              Store U(k) in column k of A
+*              Store subdiag. elements of column U(k)
+*              and 1-by-1 block D(k) in column k of A.
+*              NOTE: Diagonal element U(k,k) is a UNIT element
+*              and not stored.
+*                 A(k,k) := D(k,k) = W(k,kw)
+*                 A(1:k-1,k) := U(1:k-1,k) = W(1:k-1,kw)/D(k,k)
 *
                CALL DCOPY( K, W( 1, KW ), 1, A( 1, K ), 1 )
                R1 = ONE / A( K, K )
                CALL DSCAL( K-1, R1, A( 1, K ), 1 )
+*
             ELSE
 *
-*              2-by-2 pivot block D(k): columns KW and KW-1 of W now
-*              hold
+*              2-by-2 pivot block D(k): columns kw and kw-1 of W now hold
 *
-*              ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
+*              ( W(kw-1) W(kw) ) = ( U(k-1) U(k) )*D(k)
 *
 *              where U(k) and U(k-1) are the k-th and (k-1)-th columns
 *              of U
+*
+*              Store U(1:k-2,k-1) and U(1:k-2,k) and 2-by-2
+*              block D(k-1:k,k-1:k) in columns k-1 and k of A.
+*              NOTE: 2-by-2 diagonal block U(k-1:k,k-1:k) is a UNIT
+*              block and not stored.
+*                 A(k-1:k,k-1:k) := D(k-1:k,k-1:k) = W(k-1:k,kw-1:kw)
+*                 A(1:k-2,k-1:k) := U(1:k-2,k:k-1:k) =
+*                 = W(1:k-2,kw-1:kw) * ( D(k-1:k,k-1:k)**(-1) )
 *
                IF( K.GT.2 ) THEN
 *
-*                 Store U(k) and U(k-1) in columns k and k-1 of A
+*                 Compose the columns of the inverse of 2-by-2 pivot
+*                 block D in the following way to reduce the number
+*                 of FLOPS when we myltiply panel ( W(kw-1) W(kw) ) by
+*                 this inverse
+*
+*                 D**(-1) = ( d11 d21 )**(-1) =
+*                           ( d21 d22 )
+*
+*                 = 1/(d11*d22-d21**2) * ( ( d22 ) (-d21 ) ) =
+*                                        ( (-d21 ) ( d11 ) )
+*
+*                 = 1/d21 * 1/((d11/d21)*(d22/d21)-1) *
+*
+*                   * ( ( d22/d21 ) (      -1 ) ) =
+*                     ( (      -1 ) ( d11/d21 ) )
+*
+*                 = 1/d21 * 1/(D22*D11-1) * ( ( D11 ) (  -1 ) ) =
+*                                           ( ( -1  ) ( D22 ) )
+*
+*                 = 1/d21 * T * ( ( D11 ) (  -1 ) )
+*                               ( (  -1 ) ( D22 ) )
+*
+*                 = D21 * ( ( D11 ) (  -1 ) )
+*                         ( (  -1 ) ( D22 ) )
 *
                   D21 = W( K-1, KW )
                   D11 = W( K, KW ) / D21
                   D22 = W( K-1, KW-1 ) / D21
                   T = ONE / ( D11*D22-ONE )
                   D21 = T / D21
+*
+*                 Update elements in columns A(k-1) and A(k) as
+*                 dot products of rows of ( W(kw-1) W(kw) ) and columns
+*                 of D**(-1)
+*
                   DO 20 J = 1, K - 2
                      A( J, K-1 ) = D21*( D11*W( J, KW-1 )-W( J, KW ) )
                      A( J, K ) = D21*( D22*W( J, KW )-W( J, KW-1 ) )
@@ -370,7 +449,9 @@
                A( K-1, K-1 ) = W( K-1, KW-1 )
                A( K-1, K ) = W( K-1, KW )
                A( K, K ) = W( K, KW )
+*
             END IF
+*
          END IF
 *
 *        Store details of the interchanges in IPIV
@@ -414,20 +495,28 @@
    50    CONTINUE
 *
 *        Put U12 in standard form by partially undoing the interchanges
-*        in columns k+1:n
+*        in columns k+1:n looping backwards from k+1 to n
 *
          J = K + 1
    60    CONTINUE
-         JJ = J
-         JP = IPIV( J )
-         IF( JP.LT.0 ) THEN
-            JP = -JP
+*
+*           Undo the interchanges (if any) of rows JJ and JP at each
+*           step J
+*
+*           (Here, J is a diagonal index)
+            JJ = J
+            JP = IPIV( J )
+            IF( JP.LT.0 ) THEN
+               JP = -JP
+*              (Here, J is a diagonal index)
+               J = J + 1
+            END IF
+*           (NOTE: Here, J is used to determine row length. Length N-J+1
+*           of the rows to swap back doesn't include diagonal element)
             J = J + 1
-         END IF
-         J = J + 1
-         IF( JP.NE.JJ .AND. J.LE.N )
-     $      CALL DSWAP( N-J+1, A( JP, J ), LDA, A( JJ, J ), LDA )
-         IF( J.LE.N )
+            IF( JP.NE.JJ .AND. J.LE.N )
+     $         CALL DSWAP( N-J+1, A( JP, J ), LDA, A( JJ, J ), LDA )
+         IF( J.LT.N )
      $      GO TO 60
 *
 *        Set KB to the number of columns factorized
@@ -464,7 +553,8 @@
          ABSAKK = ABS( W( K, K ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.LT.N ) THEN
             IMAX = K + IDAMAX( N-K, W( K+1, K ), 1 )
@@ -475,7 +565,7 @@
 *
          IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
 *
-*           Column K is zero: set INFO and continue
+*           Column K is zero or underflow: set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
@@ -518,7 +608,7 @@
 *
                   KP = IMAX
 *
-*                 copy column K+1 of W to column K
+*                 copy column K+1 of W to column K of W
 *
                   CALL DCOPY( N-K+1, W( K, K+1 ), 1, W( K, K ), 1 )
                ELSE
@@ -530,22 +620,36 @@
                   KSTEP = 2
                END IF
             END IF
+*
+*           ============================================================
+*
+*           KK is the column of A where pivoting step stopped
 *
             KK = K + KSTEP - 1
 *
-*           Updated column KP is already stored in column KK of W
+*           Interchange rows and columns KP and KK.
+*           Updated column KP is already stored in column KK of W.
 *
             IF( KP.NE.KK ) THEN
 *
-*              Copy non-updated column KK to column KP
+*              Copy non-updated column KK to column KP of submatrix A
+*              at step K. No need to copy element into column K
+*              (or K and K+1 for 2-by-2 pivot) of A, since these columns
+*              will be later overwritten.
 *
-               A( KP, K ) = A( KK, K )
-               CALL DCOPY( KP-K-1, A( K+1, KK ), 1, A( KP, K+1 ), LDA )
-               CALL DCOPY( N-KP+1, A( KP, KK ), 1, A( KP, KP ), 1 )
+               A( KP, KP ) = A( KK, KK )
+               CALL DCOPY( KP-KK-1, A( KK+1, KK ), 1, A( KP, KK+1 ),
+     $                     LDA )
+               IF( KP.LT.N )
+     $            CALL DCOPY( N-KP, A( KP+1, KK ), 1, A( KP+1, KP ), 1 )
 *
-*              Interchange rows KK and KP in first KK columns of A and W
+*              Interchange rows KK and KP in first K-1 columns of A
+*              (columns K (or K and K+1 for 2-by-2 pivot) of A will be
+*              later overwritten). Interchange rows KK and KP
+*              in first KK columns of W.
 *
-               CALL DSWAP( KK, A( KK, 1 ), LDA, A( KP, 1 ), LDA )
+               IF( K.GT.1 )
+     $            CALL DSWAP( K-1, A( KK, 1 ), LDA, A( KP, 1 ), LDA )
                CALL DSWAP( KK, W( KK, 1 ), LDW, W( KP, 1 ), LDW )
             END IF
 *
@@ -553,17 +657,23 @@
 *
 *              1-by-1 pivot block D(k): column k of W now holds
 *
-*              W(k) = L(k)*D(k)
+*              W(k) = L(k)*D(k),
 *
 *              where L(k) is the k-th column of L
 *
-*              Store L(k) in column k of A
+*              Store subdiag. elements of column L(k)
+*              and 1-by-1 block D(k) in column k of A.
+*              (NOTE: Diagonal element L(k,k) is a UNIT element
+*              and not stored)
+*                 A(k,k) := D(k,k) = W(k,k)
+*                 A(k+1:N,k) := L(k+1:N,k) = W(k+1:N,k)/D(k,k)
 *
                CALL DCOPY( N-K+1, W( K, K ), 1, A( K, K ), 1 )
                IF( K.LT.N ) THEN
                   R1 = ONE / A( K, K )
                   CALL DSCAL( N-K, R1, A( K+1, K ), 1 )
                END IF
+*
             ELSE
 *
 *              2-by-2 pivot block D(k): columns k and k+1 of W now hold
@@ -572,16 +682,52 @@
 *
 *              where L(k) and L(k+1) are the k-th and (k+1)-th columns
 *              of L
+*
+*              Store L(k+2:N,k) and L(k+2:N,k+1) and 2-by-2
+*              block D(k:k+1,k:k+1) in columns k and k+1 of A.
+*              (NOTE: 2-by-2 diagonal block L(k:k+1,k:k+1) is a UNIT
+*              block and not stored)
+*                 A(k:k+1,k:k+1) := D(k:k+1,k:k+1) = W(k:k+1,k:k+1)
+*                 A(k+2:N,k:k+1) := L(k+2:N,k:k+1) =
+*                 = W(k+2:N,k:k+1) * ( D(k:k+1,k:k+1)**(-1) )
 *
                IF( K.LT.N-1 ) THEN
 *
-*                 Store L(k) and L(k+1) in columns k and k+1 of A
+*                 Compose the columns of the inverse of 2-by-2 pivot
+*                 block D in the following way to reduce the number
+*                 of FLOPS when we myltiply panel ( W(k) W(k+1) ) by
+*                 this inverse
+*
+*                 D**(-1) = ( d11 d21 )**(-1) =
+*                           ( d21 d22 )
+*
+*                 = 1/(d11*d22-d21**2) * ( ( d22 ) (-d21 ) ) =
+*                                        ( (-d21 ) ( d11 ) )
+*
+*                 = 1/d21 * 1/((d11/d21)*(d22/d21)-1) *
+*
+*                   * ( ( d22/d21 ) (      -1 ) ) =
+*                     ( (      -1 ) ( d11/d21 ) )
+*
+*                 = 1/d21 * 1/(D22*D11-1) * ( ( D11 ) (  -1 ) ) =
+*                                           ( ( -1  ) ( D22 ) )
+*
+*                 = 1/d21 * T * ( ( D11 ) (  -1 ) )
+*                               ( (  -1 ) ( D22 ) )
+*
+*                 = D21 * ( ( D11 ) (  -1 ) )
+*                         ( (  -1 ) ( D22 ) )
 *
                   D21 = W( K+1, K )
                   D11 = W( K+1, K+1 ) / D21
                   D22 = W( K, K ) / D21
                   T = ONE / ( D11*D22-ONE )
                   D21 = T / D21
+*
+*                 Update elements in columns A(k) and A(k+1) as
+*                 dot products of rows of ( W(k) W(k+1) ) and columns
+*                 of D**(-1)
+*
                   DO 80 J = K + 2, N
                      A( J, K ) = D21*( D11*W( J, K )-W( J, K+1 ) )
                      A( J, K+1 ) = D21*( D22*W( J, K+1 )-W( J, K ) )
@@ -593,7 +739,9 @@
                A( K, K ) = W( K, K )
                A( K+1, K ) = W( K+1, K )
                A( K+1, K+1 ) = W( K+1, K+1 )
+*
             END IF
+*
          END IF
 *
 *        Store details of the interchanges in IPIV
@@ -638,20 +786,28 @@
   110    CONTINUE
 *
 *        Put L21 in standard form by partially undoing the interchanges
-*        in columns 1:k-1
+*        of rows in columns 1:k-1 looping backwards from k-1 to 1
 *
          J = K - 1
   120    CONTINUE
-         JJ = J
-         JP = IPIV( J )
-         IF( JP.LT.0 ) THEN
-            JP = -JP
+*
+*           Undo the interchanges (if any) of rows JJ and JP at each
+*           step J
+*
+*           (Here, J is a diagonal index)
+            JJ = J
+            JP = IPIV( J )
+            IF( JP.LT.0 ) THEN
+               JP = -JP
+*              (Here, J is a diagonal index)
+               J = J - 1
+            END IF
+*           (NOTE: Here, J is used to determine row length. Length J
+*           of the rows to swap back doesn't include diagonal element)
             J = J - 1
-         END IF
-         J = J - 1
-         IF( JP.NE.JJ .AND. J.GE.1 )
-     $      CALL DSWAP( J, A( JP, 1 ), LDA, A( JJ, 1 ), LDA )
-         IF( J.GE.1 )
+            IF( JP.NE.JJ .AND. J.GE.1 )
+     $         CALL DSWAP( J, A( JP, 1 ), LDA, A( JJ, 1 ), LDA )
+         IF( J.GT.1 )
      $      GO TO 120
 *
 *        Set KB to the number of columns factorized

lapack-netlib/SRC/dlasyf_rook.f

@@ -0,0 +1,892 @@
+*> \brief \b DLASYF_ROOK *> DLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLASYF_ROOK + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasyf_rook.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasyf_rook.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasyf_rook.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLASYF_ROOK( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
+*
+*       .. Scalar Arguments ..
+*       CHARADLATER          UPLO
+*       INTEGER            INFO, KB, LDA, LDW, N, NB
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       DOUBLE PRECISION   A( LDA, * ), W( LDW, * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLASYF_ROOK computes a partial factorization of a real symmetric
+*> matrix A using the bounded Bunch-Kaufman ("rook") diagonal
+*> pivoting method. The partial factorization has the form:
+*>
+*> A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
+*>       ( 0  U22 ) (  0   D  ) ( U12**T U22**T )
+*>
+*> A  =  ( L11  0 ) (  D   0  ) ( L11**T L21**T )  if UPLO = 'L'
+*>       ( L21  I ) (  0  A22 ) (  0       I    )
+*>
+*> where the order of D is at most NB. The actual order is returned in
+*> the argument KB, and is either NB or NB-1, or N if N <= NB.
+*>
+*> DLASYF_ROOK is an auxiliary routine called by DSYTRF_ROOK. It uses
+*> blocked code (calling Level 3 BLAS) to update the submatrix
+*> A11 (if UPLO = 'U') or A22 (if UPLO = 'L').
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          Specifies whether the upper or lower triangular part of the
+*>          symmetric matrix A is stored:
+*>          = 'U':  Upper triangular
+*>          = 'L':  Lower triangular
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NB
+*> \verbatim
+*>          NB is INTEGER
+*>          The maximum number of columns of the matrix A that should be
+*>          factored.  NB should be at least 2 to allow for 2-by-2 pivot
+*>          blocks.
+*> \endverbatim
+*>
+*> \param[out] KB
+*> \verbatim
+*>          KB is INTEGER
+*>          The number of columns of A that were actually factored.
+*>          KB is either NB-1 or NB, or N if N <= NB.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is DOUBLE PRECISION array, dimension (LDA,N)
+*>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
+*>          n-by-n upper triangular part of A contains the upper
+*>          triangular part of the matrix A, and the strictly lower
+*>          triangular part of A is not referenced.  If UPLO = 'L', the
+*>          leading n-by-n lower triangular part of A contains the lower
+*>          triangular part of the matrix A, and the strictly upper
+*>          triangular part of A is not referenced.
+*>          On exit, A contains details of the partial factorization.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          Details of the interchanges and the block structure of D.
+*>
+*>          If UPLO = 'U':
+*>             Only the last KB elements of IPIV are set.
+*>
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
+*>             columns k and -IPIV(k) were interchanged and rows and
+*>             columns k-1 and -IPIV(k-1) were inerchaged,
+*>             D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>             Only the first KB elements of IPIV are set.
+*>
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k)
+*>             were interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
+*>             columns k and -IPIV(k) were interchanged and rows and
+*>             columns k+1 and -IPIV(k+1) were inerchaged,
+*>             D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*> \endverbatim
+*>
+*> \param[out] W
+*> \verbatim
+*>          W is DOUBLE PRECISION array, dimension (LDW,NB)
+*> \endverbatim
+*>
+*> \param[in] LDW
+*> \verbatim
+*>          LDW is INTEGER
+*>          The leading dimension of the array W.  LDW >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0: successful exit
+*>          > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
+*>               has been completed, but the block diagonal matrix D is
+*>               exactly singular.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2013
+*
+*> \ingroup doubleSYcomputational
+*
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>  November 2013,     Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*>
+*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*>                  School of Mathematics,
+*>                  University of Manchester
+*>
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE DLASYF_ROOK( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW,
+     $                        INFO )
+*
+*  -- LAPACK computational routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2013
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, KB, LDA, LDW, N, NB
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      DOUBLE PRECISION   A( LDA, * ), W( LDW, * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ZERO, ONE
+      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
+      DOUBLE PRECISION   EIGHT, SEVTEN
+      PARAMETER          ( EIGHT = 8.0D+0, SEVTEN = 17.0D+0 )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            DONE
+      INTEGER            IMAX, ITEMP, J, JB, JJ, JMAX, JP1, JP2, K, KK,
+     $                   KW, KKW, KP, KSTEP, P, II
+
+      DOUBLE PRECISION   ABSAKK, ALPHA, COLMAX, D11, D12, D21, D22,
+     $                   DTEMP, R1, ROWMAX, T, SFMIN
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      INTEGER            IDAMAX
+      DOUBLE PRECISION   DLAMCH
+      EXTERNAL           LSAME, IDAMAX, DLAMCH
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DCOPY, DGEMM, DGEMV, DSCAL, DSWAP
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, MAX, MIN, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+      INFO = 0
+*
+*     Initialize ALPHA for use in choosing pivot block size.
+*
+      ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT
+*
+*     Compute machine safe minimum
+*
+      SFMIN = DLAMCH( 'S' )
+*
+      IF( LSAME( UPLO, 'U' ) ) THEN
+*
+*        Factorize the trailing columns of A using the upper triangle
+*        of A and working backwards, and compute the matrix W = U12*D
+*        for use in updating A11
+*
+*        K is the main loop index, decreasing from N in steps of 1 or 2
+*
+         K = N
+   10    CONTINUE
+*
+*        KW is the column of W which corresponds to column K of A
+*
+         KW = NB + K - N
+*
+*        Exit from loop
+*
+         IF( ( K.LE.N-NB+1 .AND. NB.LT.N ) .OR. K.LT.1 )
+     $      GO TO 30
+*
+         KSTEP = 1
+         P = K
+*
+*        Copy column K of A to column KW of W and update it
+*
+         CALL DCOPY( K, A( 1, K ), 1, W( 1, KW ), 1 )
+         IF( K.LT.N )
+     $      CALL DGEMV( 'No transpose', K, N-K, -ONE, A( 1, K+1 ),
+     $                  LDA, W( K, KW+1 ), LDW, ONE, W( 1, KW ), 1 )
+*
+*        Determine rows and columns to be interchanged and whether
+*        a 1-by-1 or 2-by-2 pivot block will be used
+*
+         ABSAKK = ABS( W( K, KW ) )
+*
+*        IMAX is the row-index of the largest off-diagonal element in
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
+*
+         IF( K.GT.1 ) THEN
+            IMAX = IDAMAX( K-1, W( 1, KW ), 1 )
+            COLMAX = ABS( W( IMAX, KW ) )
+         ELSE
+            COLMAX = ZERO
+         END IF
+*
+         IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
+*
+*           Column K is zero or underflow: set INFO and continue
+*
+            IF( INFO.EQ.0 )
+     $         INFO = K
+            KP = K
+            CALL DCOPY( K, W( 1, KW ), 1, A( 1, K ), 1 )
+         ELSE
+*
+*           ============================================================
+*
+*           Test for interchange
+*
+*           Equivalent to testing for ABSAKK.GE.ALPHA*COLMAX
+*           (used to handle NaN and Inf)
+*
+            IF( .NOT.( ABSAKK.LT.ALPHA*COLMAX ) ) THEN
+*
+*              no interchange, use 1-by-1 pivot block
+*
+               KP = K
+*
+            ELSE
+*
+               DONE = .FALSE.
+*
+*              Loop until pivot found
+*
+   12          CONTINUE
+*
+*                 Begin pivot search loop body
+*
+*
+*                 Copy column IMAX to column KW-1 of W and update it
+*
+                  CALL DCOPY( IMAX, A( 1, IMAX ), 1, W( 1, KW-1 ), 1 )
+                  CALL DCOPY( K-IMAX, A( IMAX, IMAX+1 ), LDA,
+     $                        W( IMAX+1, KW-1 ), 1 )
+*
+                  IF( K.LT.N )
+     $               CALL DGEMV( 'No transpose', K, N-K, -ONE,
+     $                           A( 1, K+1 ), LDA, W( IMAX, KW+1 ), LDW,
+     $                           ONE, W( 1, KW-1 ), 1 )
+*
+*                 JMAX is the column-index of the largest off-diagonal
+*                 element in row IMAX, and ROWMAX is its absolute value.
+*                 Determine both ROWMAX and JMAX.
+*
+                  IF( IMAX.NE.K ) THEN
+                     JMAX = IMAX + IDAMAX( K-IMAX, W( IMAX+1, KW-1 ),
+     $                                     1 )
+                     ROWMAX = ABS( W( JMAX, KW-1 ) )
+                  ELSE
+                     ROWMAX = ZERO
+                  END IF
+*
+                  IF( IMAX.GT.1 ) THEN
+                     ITEMP = IDAMAX( IMAX-1, W( 1, KW-1 ), 1 )
+                     DTEMP = ABS( W( ITEMP, KW-1 ) )
+                     IF( DTEMP.GT.ROWMAX ) THEN
+                        ROWMAX = DTEMP
+                        JMAX = ITEMP
+                     END IF
+                  END IF
+*
+*                 Equivalent to testing for
+*                 ABS( W( IMAX, KW-1 ) ).GE.ALPHA*ROWMAX
+*                 (used to handle NaN and Inf)
+*
+                  IF( .NOT.(ABS( W( IMAX, KW-1 ) ).LT.ALPHA*ROWMAX ) )
+     $            THEN
+*
+*                    interchange rows and columns K and IMAX,
+*                    use 1-by-1 pivot block
+*
+                     KP = IMAX
+*
+*                    copy column KW-1 of W to column KW of W
+*
+                     CALL DCOPY( K, W( 1, KW-1 ), 1, W( 1, KW ), 1 )
+*
+                     DONE = .TRUE.
+*
+*                 Equivalent to testing for ROWMAX.EQ.COLMAX,
+*                 (used to handle NaN and Inf)
+*
+                  ELSE IF( ( P.EQ.JMAX ) .OR. ( ROWMAX.LE.COLMAX ) )
+     $            THEN
+*
+*                    interchange rows and columns K-1 and IMAX,
+*                    use 2-by-2 pivot block
+*
+                     KP = IMAX
+                     KSTEP = 2
+                     DONE = .TRUE.
+                  ELSE
+*
+*                    Pivot not found: set params and repeat
+*
+                     P = IMAX
+                     COLMAX = ROWMAX
+                     IMAX = JMAX
+*
+*                    Copy updated JMAXth (next IMAXth) column to Kth of W
+*
+                     CALL DCOPY( K, W( 1, KW-1 ), 1, W( 1, KW ), 1 )
+*
+                  END IF
+*
+*                 End pivot search loop body
+*
+               IF( .NOT. DONE ) GOTO 12
+*
+            END IF
+*
+*           ============================================================
+*
+            KK = K - KSTEP + 1
+*
+*           KKW is the column of W which corresponds to column KK of A
+*
+            KKW = NB + KK - N
+*
+            IF( ( KSTEP.EQ.2 ) .AND. ( P.NE.K ) ) THEN
+*
+*              Copy non-updated column K to column P
+*
+               CALL DCOPY( K-P, A( P+1, K ), 1, A( P, P+1 ), LDA )
+               CALL DCOPY( P, A( 1, K ), 1, A( 1, P ), 1 )
+*
+*              Interchange rows K and P in last N-K+1 columns of A
+*              and last N-K+2 columns of W
+*
+               CALL DSWAP( N-K+1, A( K, K ), LDA, A( P, K ), LDA )
+               CALL DSWAP( N-KK+1, W( K, KKW ), LDW, W( P, KKW ), LDW )
+            END IF
+*
+*           Updated column KP is already stored in column KKW of W
+*
+            IF( KP.NE.KK ) THEN
+*
+*              Copy non-updated column KK to column KP
+*
+               A( KP, K ) = A( KK, K )
+               CALL DCOPY( K-1-KP, A( KP+1, KK ), 1, A( KP, KP+1 ),
+     $                     LDA )
+               CALL DCOPY( KP, A( 1, KK ), 1, A( 1, KP ), 1 )
+*
+*              Interchange rows KK and KP in last N-KK+1 columns
+*              of A and W
+*
+               CALL DSWAP( N-KK+1, A( KK, KK ), LDA, A( KP, KK ), LDA )
+               CALL DSWAP( N-KK+1, W( KK, KKW ), LDW, W( KP, KKW ),
+     $                     LDW )
+            END IF
+*
+            IF( KSTEP.EQ.1 ) THEN
+*
+*              1-by-1 pivot block D(k): column KW of W now holds
+*
+*              W(k) = U(k)*D(k)
+*
+*              where U(k) is the k-th column of U
+*
+*              Store U(k) in column k of A
+*
+               CALL DCOPY( K, W( 1, KW ), 1, A( 1, K ), 1 )
+               IF( K.GT.1 ) THEN
+                  IF( ABS( A( K, K ) ).GE.SFMIN ) THEN
+                     R1 = ONE / A( K, K )
+                     CALL DSCAL( K-1, R1, A( 1, K ), 1 )
+                  ELSE IF( A( K, K ).NE.ZERO ) THEN
+                     DO 14 II = 1, K - 1
+                        A( II, K ) = A( II, K ) / A( K, K )
+   14                CONTINUE
+                  END IF
+               END IF
+*
+            ELSE
+*
+*              2-by-2 pivot block D(k): columns KW and KW-1 of W now
+*              hold
+*
+*              ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
+*
+*              where U(k) and U(k-1) are the k-th and (k-1)-th columns
+*              of U
+*
+               IF( K.GT.2 ) THEN
+*
+*                 Store U(k) and U(k-1) in columns k and k-1 of A
+*
+                  D12 = W( K-1, KW )
+                  D11 = W( K, KW ) / D12
+                  D22 = W( K-1, KW-1 ) / D12
+                  T = ONE / ( D11*D22-ONE )
+                  DO 20 J = 1, K - 2
+                     A( J, K-1 ) = T*( (D11*W( J, KW-1 )-W( J, KW ) ) /
+     $                             D12 )
+                     A( J, K ) = T*( ( D22*W( J, KW )-W( J, KW-1 ) ) /
+     $                           D12 )
+   20             CONTINUE
+               END IF
+*
+*              Copy D(k) to A
+*
+               A( K-1, K-1 ) = W( K-1, KW-1 )
+               A( K-1, K ) = W( K-1, KW )
+               A( K, K ) = W( K, KW )
+            END IF
+         END IF
+*
+*        Store details of the interchanges in IPIV
+*
+         IF( KSTEP.EQ.1 ) THEN
+            IPIV( K ) = KP
+         ELSE
+            IPIV( K ) = -P
+            IPIV( K-1 ) = -KP
+         END IF
+*
+*        Decrease K and return to the start of the main loop
+*
+         K = K - KSTEP
+         GO TO 10
+*
+   30    CONTINUE
+*
+*        Update the upper triangle of A11 (= A(1:k,1:k)) as
+*
+*        A11 := A11 - U12*D*U12**T = A11 - U12*W**T
+*
+*        computing blocks of NB columns at a time
+*
+         DO 50 J = ( ( K-1 ) / NB )*NB + 1, 1, -NB
+            JB = MIN( NB, K-J+1 )
+*
+*           Update the upper triangle of the diagonal block
+*
+            DO 40 JJ = J, J + JB - 1
+               CALL DGEMV( 'No transpose', JJ-J+1, N-K, -ONE,
+     $                     A( J, K+1 ), LDA, W( JJ, KW+1 ), LDW, ONE,
+     $                     A( J, JJ ), 1 )
+   40       CONTINUE
+*
+*           Update the rectangular superdiagonal block
+*
+            IF( J.GE.2 )
+     $         CALL DGEMM( 'No transpose', 'Transpose', J-1, JB,
+     $                  N-K, -ONE, A( 1, K+1 ), LDA, W( J, KW+1 ), LDW,
+     $                  ONE, A( 1, J ), LDA )
+   50    CONTINUE
+*
+*        Put U12 in standard form by partially undoing the interchanges
+*        in columns k+1:n
+*
+         J = K + 1
+   60    CONTINUE
+*
+            KSTEP = 1
+            JP1 = 1
+            JJ = J
+            JP2 = IPIV( J )
+            IF( JP2.LT.0 ) THEN
+               JP2 = -JP2
+               J = J + 1
+               JP1 = -IPIV( J )
+               KSTEP = 2
+            END IF
+*
+            J = J + 1
+            IF( JP2.NE.JJ .AND. J.LE.N )
+     $         CALL DSWAP( N-J+1, A( JP2, J ), LDA, A( JJ, J ), LDA )
+            JJ = J - 1
+            IF( JP1.NE.JJ .AND. KSTEP.EQ.2 )
+     $         CALL DSWAP( N-J+1, A( JP1, J ), LDA, A( JJ, J ), LDA )
+         IF( J.LE.N )
+     $      GO TO 60
+*
+*        Set KB to the number of columns factorized
+*
+         KB = N - K
+*
+      ELSE
+*
+*        Factorize the leading columns of A using the lower triangle
+*        of A and working forwards, and compute the matrix W = L21*D
+*        for use in updating A22
+*
+*        K is the main loop index, increasing from 1 in steps of 1 or 2
+*
+         K = 1
+   70   CONTINUE
+*
+*        Exit from loop
+*
+         IF( ( K.GE.NB .AND. NB.LT.N ) .OR. K.GT.N )
+     $      GO TO 90
+*
+         KSTEP = 1
+         P = K
+*
+*        Copy column K of A to column K of W and update it
+*
+         CALL DCOPY( N-K+1, A( K, K ), 1, W( K, K ), 1 )
+         IF( K.GT.1 )
+     $      CALL DGEMV( 'No transpose', N-K+1, K-1, -ONE, A( K, 1 ),
+     $                  LDA, W( K, 1 ), LDW, ONE, W( K, K ), 1 )
+*
+*        Determine rows and columns to be interchanged and whether
+*        a 1-by-1 or 2-by-2 pivot block will be used
+*
+         ABSAKK = ABS( W( K, K ) )
+*
+*        IMAX is the row-index of the largest off-diagonal element in
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
+*
+         IF( K.LT.N ) THEN
+            IMAX = K + IDAMAX( N-K, W( K+1, K ), 1 )
+            COLMAX = ABS( W( IMAX, K ) )
+         ELSE
+            COLMAX = ZERO
+         END IF
+*
+         IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
+*
+*           Column K is zero or underflow: set INFO and continue
+*
+            IF( INFO.EQ.0 )
+     $         INFO = K
+            KP = K
+            CALL DCOPY( N-K+1, W( K, K ), 1, A( K, K ), 1 )
+         ELSE
+*
+*           ============================================================
+*
+*           Test for interchange
+*
+*           Equivalent to testing for ABSAKK.GE.ALPHA*COLMAX
+*           (used to handle NaN and Inf)
+*
+            IF( .NOT.( ABSAKK.LT.ALPHA*COLMAX ) ) THEN
+*
+*              no interchange, use 1-by-1 pivot block
+*
+               KP = K
+*
+            ELSE
+*
+               DONE = .FALSE.
+*
+*              Loop until pivot found
+*
+   72          CONTINUE
+*
+*                 Begin pivot search loop body
+*
+*
+*                 Copy column IMAX to column K+1 of W and update it
+*
+                  CALL DCOPY( IMAX-K, A( IMAX, K ), LDA, W( K, K+1 ), 1)
+                  CALL DCOPY( N-IMAX+1, A( IMAX, IMAX ), 1,
+     $                        W( IMAX, K+1 ), 1 )
+                  IF( K.GT.1 )
+     $               CALL DGEMV( 'No transpose', N-K+1, K-1, -ONE,
+     $                           A( K, 1 ), LDA, W( IMAX, 1 ), LDW,
+     $                           ONE, W( K, K+1 ), 1 )
+*
+*                 JMAX is the column-index of the largest off-diagonal
+*                 element in row IMAX, and ROWMAX is its absolute value.
+*                 Determine both ROWMAX and JMAX.
+*
+                  IF( IMAX.NE.K ) THEN
+                     JMAX = K - 1 + IDAMAX( IMAX-K, W( K, K+1 ), 1 )
+                     ROWMAX = ABS( W( JMAX, K+1 ) )
+                  ELSE
+                     ROWMAX = ZERO
+                  END IF
+*
+                  IF( IMAX.LT.N ) THEN
+                     ITEMP = IMAX + IDAMAX( N-IMAX, W( IMAX+1, K+1 ), 1)
+                     DTEMP = ABS( W( ITEMP, K+1 ) )
+                     IF( DTEMP.GT.ROWMAX ) THEN
+                        ROWMAX = DTEMP
+                        JMAX = ITEMP
+                     END IF
+                  END IF
+*
+*                 Equivalent to testing for
+*                 ABS( W( IMAX, K+1 ) ).GE.ALPHA*ROWMAX
+*                 (used to handle NaN and Inf)
+*
+                  IF( .NOT.( ABS( W( IMAX, K+1 ) ).LT.ALPHA*ROWMAX ) )
+     $            THEN
+*
+*                    interchange rows and columns K and IMAX,
+*                    use 1-by-1 pivot block
+*
+                     KP = IMAX
+*
+*                    copy column K+1 of W to column K of W
+*
+                     CALL DCOPY( N-K+1, W( K, K+1 ), 1, W( K, K ), 1 )
+*
+                     DONE = .TRUE.
+*
+*                 Equivalent to testing for ROWMAX.EQ.COLMAX,
+*                 (used to handle NaN and Inf)
+*
+                  ELSE IF( ( P.EQ.JMAX ) .OR. ( ROWMAX.LE.COLMAX ) )
+     $            THEN
+*
+*                    interchange rows and columns K+1 and IMAX,
+*                    use 2-by-2 pivot block
+*
+                     KP = IMAX
+                     KSTEP = 2
+                     DONE = .TRUE.
+                  ELSE
+*
+*                    Pivot not found: set params and repeat
+*
+                     P = IMAX
+                     COLMAX = ROWMAX
+                     IMAX = JMAX
+*
+*                    Copy updated JMAXth (next IMAXth) column to Kth of W
+*
+                     CALL DCOPY( N-K+1, W( K, K+1 ), 1, W( K, K ), 1 )
+*
+                  END IF
+*
+*                 End pivot search loop body
+*
+               IF( .NOT. DONE ) GOTO 72
+*
+            END IF
+*
+*           ============================================================
+*
+            KK = K + KSTEP - 1
+*
+            IF( ( KSTEP.EQ.2 ) .AND. ( P.NE.K ) ) THEN
+*
+*              Copy non-updated column K to column P
+*
+               CALL DCOPY( P-K, A( K, K ), 1, A( P, K ), LDA )
+               CALL DCOPY( N-P+1, A( P, K ), 1, A( P, P ), 1 )
+*
+*              Interchange rows K and P in first K columns of A
+*              and first K+1 columns of W
+*
+               CALL DSWAP( K, A( K, 1 ), LDA, A( P, 1 ), LDA )
+               CALL DSWAP( KK, W( K, 1 ), LDW, W( P, 1 ), LDW )
+            END IF
+*
+*           Updated column KP is already stored in column KK of W
+*
+            IF( KP.NE.KK ) THEN
+*
+*              Copy non-updated column KK to column KP
+*
+               A( KP, K ) = A( KK, K )
+               CALL DCOPY( KP-K-1, A( K+1, KK ), 1, A( KP, K+1 ), LDA )
+               CALL DCOPY( N-KP+1, A( KP, KK ), 1, A( KP, KP ), 1 )
+*
+*              Interchange rows KK and KP in first KK columns of A and W
+*
+               CALL DSWAP( KK, A( KK, 1 ), LDA, A( KP, 1 ), LDA )
+               CALL DSWAP( KK, W( KK, 1 ), LDW, W( KP, 1 ), LDW )
+            END IF
+*
+            IF( KSTEP.EQ.1 ) THEN
+*
+*              1-by-1 pivot block D(k): column k of W now holds
+*
+*              W(k) = L(k)*D(k)
+*
+*              where L(k) is the k-th column of L
+*
+*              Store L(k) in column k of A
+*
+               CALL DCOPY( N-K+1, W( K, K ), 1, A( K, K ), 1 )
+               IF( K.LT.N ) THEN
+                  IF( ABS( A( K, K ) ).GE.SFMIN ) THEN
+                     R1 = ONE / A( K, K )
+                     CALL DSCAL( N-K, R1, A( K+1, K ), 1 )
+                  ELSE IF( A( K, K ).NE.ZERO ) THEN
+                     DO 74 II = K + 1, N
+                        A( II, K ) = A( II, K ) / A( K, K )
+   74                CONTINUE
+                  END IF
+               END IF
+*
+            ELSE
+*
+*              2-by-2 pivot block D(k): columns k and k+1 of W now hold
+*
+*              ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k)
+*
+*              where L(k) and L(k+1) are the k-th and (k+1)-th columns
+*              of L
+*
+               IF( K.LT.N-1 ) THEN
+*
+*                 Store L(k) and L(k+1) in columns k and k+1 of A
+*
+                  D21 = W( K+1, K )
+                  D11 = W( K+1, K+1 ) / D21
+                  D22 = W( K, K ) / D21
+                  T = ONE / ( D11*D22-ONE )
+                  DO 80 J = K + 2, N
+                     A( J, K ) = T*( ( D11*W( J, K )-W( J, K+1 ) ) /
+     $                           D21 )
+                     A( J, K+1 ) = T*( ( D22*W( J, K+1 )-W( J, K ) ) /
+     $                             D21 )
+   80             CONTINUE
+               END IF
+*
+*              Copy D(k) to A
+*
+               A( K, K ) = W( K, K )
+               A( K+1, K ) = W( K+1, K )
+               A( K+1, K+1 ) = W( K+1, K+1 )
+            END IF
+         END IF
+*
+*        Store details of the interchanges in IPIV
+*
+         IF( KSTEP.EQ.1 ) THEN
+            IPIV( K ) = KP
+         ELSE
+            IPIV( K ) = -P
+            IPIV( K+1 ) = -KP
+         END IF
+*
+*        Increase K and return to the start of the main loop
+*
+         K = K + KSTEP
+         GO TO 70
+*
+   90    CONTINUE
+*
+*        Update the lower triangle of A22 (= A(k:n,k:n)) as
+*
+*        A22 := A22 - L21*D*L21**T = A22 - L21*W**T
+*
+*        computing blocks of NB columns at a time
+*
+         DO 110 J = K, N, NB
+            JB = MIN( NB, N-J+1 )
+*
+*           Update the lower triangle of the diagonal block
+*
+            DO 100 JJ = J, J + JB - 1
+               CALL DGEMV( 'No transpose', J+JB-JJ, K-1, -ONE,
+     $                     A( JJ, 1 ), LDA, W( JJ, 1 ), LDW, ONE,
+     $                     A( JJ, JJ ), 1 )
+  100       CONTINUE
+*
+*           Update the rectangular subdiagonal block
+*
+            IF( J+JB.LE.N )
+     $         CALL DGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB,
+     $                     K-1, -ONE, A( J+JB, 1 ), LDA, W( J, 1 ), LDW,
+     $                     ONE, A( J+JB, J ), LDA )
+  110    CONTINUE
+*
+*        Put L21 in standard form by partially undoing the interchanges
+*        in columns 1:k-1
+*
+         J = K - 1
+  120    CONTINUE
+*
+            KSTEP = 1
+            JP1 = 1
+            JJ = J
+            JP2 = IPIV( J )
+            IF( JP2.LT.0 ) THEN
+               JP2 = -JP2
+               J = J - 1
+               JP1 = -IPIV( J )
+               KSTEP = 2
+            END IF
+*
+            J = J - 1
+            IF( JP2.NE.JJ .AND. J.GE.1 )
+     $         CALL DSWAP( J, A( JP2, 1 ), LDA, A( JJ, 1 ), LDA )
+            JJ = J + 1
+            IF( JP1.NE.JJ .AND. KSTEP.EQ.2 )
+     $         CALL DSWAP( J, A( JP1, 1 ), LDA, A( JJ, 1 ), LDA )
+         IF( J.GE.1 )
+     $      GO TO 120
+*
+*        Set KB to the number of columns factorized
+*
+         KB = K - 1
+*
+      END IF
+      RETURN
+*
+*     End of DLASYF_ROOK
+*
+      END

lapack-netlib/SRC/dorbdb.f

@@ -255,7 +255,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date November 2011
+*> \date November 2013
 *
 *> \ingroup doubleOTHERcomputational
 *
@@ -287,10 +287,10 @@
      $                   X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
      $                   TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2011
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          SIGNS, TRANS
@@ -415,19 +415,36 @@
             THETA(I) = ATAN2( DNRM2( M-P-I+1, X21(I,I), 1 ),
      $                 DNRM2( P-I+1, X11(I,I), 1 ) )
 *
-            CALL DLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) )
+            IF( P .GT. I ) THEN
+               CALL DLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) )
+            ELSE IF( P .EQ. I ) THEN
+               CALL DLARFGP( P-I+1, X11(I,I), X11(I,I), 1, TAUP1(I) )
+            END IF
             X11(I,I) = ONE
-            CALL DLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1, TAUP2(I) )
+            IF ( M-P .GT. I ) THEN
+               CALL DLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1,
+     $                       TAUP2(I) )
+            ELSE IF ( M-P .EQ. I ) THEN
+               CALL DLARFGP( M-P-I+1, X21(I,I), X21(I,I), 1, TAUP2(I) )
+            END IF
             X21(I,I) = ONE
 *
-            CALL DLARF( 'L', P-I+1, Q-I, X11(I,I), 1, TAUP1(I),
-     $                  X11(I,I+1), LDX11, WORK )
-            CALL DLARF( 'L', P-I+1, M-Q-I+1, X11(I,I), 1, TAUP1(I),
-     $                  X12(I,I), LDX12, WORK )
-            CALL DLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1, TAUP2(I),
-     $                  X21(I,I+1), LDX21, WORK )
-            CALL DLARF( 'L', M-P-I+1, M-Q-I+1, X21(I,I), 1, TAUP2(I),
-     $                  X22(I,I), LDX22, WORK )
+            IF ( Q .GT. I ) THEN
+               CALL DLARF( 'L', P-I+1, Q-I, X11(I,I), 1, TAUP1(I),
+     $                     X11(I,I+1), LDX11, WORK )
+            END IF
+            IF ( M-Q+1 .GT. I ) THEN
+               CALL DLARF( 'L', P-I+1, M-Q-I+1, X11(I,I), 1, TAUP1(I),
+     $                     X12(I,I), LDX12, WORK )
+            END IF
+            IF ( Q .GT. I ) THEN
+               CALL DLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1, TAUP2(I),
+     $                     X21(I,I+1), LDX21, WORK )
+            END IF
+            IF ( M-Q+1 .GT. I ) THEN
+               CALL DLARF( 'L', M-P-I+1, M-Q-I+1, X21(I,I), 1, TAUP2(I),
+     $                     X22(I,I), LDX22, WORK )
+            END IF
 *
             IF( I .LT. Q ) THEN
                CALL DSCAL( Q-I, -Z1*Z3*SIN(THETA(I)), X11(I,I+1),
@@ -444,12 +461,24 @@
      $                  DNRM2( M-Q-I+1, X12(I,I), LDX12 ) )
 *
             IF( I .LT. Q ) THEN
-               CALL DLARFGP( Q-I, X11(I,I+1), X11(I,I+2), LDX11,
-     $                       TAUQ1(I) )
+               IF ( Q-I .EQ. 1 ) THEN
+                  CALL DLARFGP( Q-I, X11(I,I+1), X11(I,I+1), LDX11,
+     $                          TAUQ1(I) )
+               ELSE
+                  CALL DLARFGP( Q-I, X11(I,I+1), X11(I,I+2), LDX11,
+     $                          TAUQ1(I) )
+               END IF
                X11(I,I+1) = ONE
             END IF
-            CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12,
-     $                    TAUQ2(I) )
+            IF ( Q+I-1 .LT. M ) THEN
+               IF ( M-Q .EQ. I ) THEN
+                  CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I,I), LDX12,
+     $                          TAUQ2(I) )
+               ELSE
+                  CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12,
+     $                          TAUQ2(I) )
+               END IF
+            END IF
             X12(I,I) = ONE
 *
             IF( I .LT. Q ) THEN
@@ -458,10 +487,14 @@
                CALL DLARF( 'R', M-P-I, Q-I, X11(I,I+1), LDX11, TAUQ1(I),
      $                     X21(I+1,I+1), LDX21, WORK )
             END IF
-            CALL DLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
-     $                  X12(I+1,I), LDX12, WORK )
-            CALL DLARF( 'R', M-P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
-     $                  X22(I+1,I), LDX22, WORK )
+            IF ( P .GT. I ) THEN
+               CALL DLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
+     $                     X12(I+1,I), LDX12, WORK )
+            END IF
+            IF ( M-P .GT. I ) THEN
+               CALL DLARF( 'R', M-P-I, M-Q-I+1, X12(I,I), LDX12,
+     $                     TAUQ2(I), X22(I+1,I), LDX22, WORK )
+            END IF
 *
          END DO
 *
@@ -470,12 +503,19 @@
          DO I = Q + 1, P
 *
             CALL DSCAL( M-Q-I+1, -Z1*Z4, X12(I,I), LDX12 )
-            CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12,
-     $                    TAUQ2(I) )
+            IF ( I .GE. M-Q ) THEN
+               CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I,I), LDX12,
+     $                       TAUQ2(I) )
+            ELSE
+               CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12,
+     $                       TAUQ2(I) )
+            END IF
             X12(I,I) = ONE
 *
-            CALL DLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
-     $                  X12(I+1,I), LDX12, WORK )
+            IF ( P. GT. I ) THEN
+               CALL DLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
+     $                     X12(I+1,I), LDX12, WORK )
+            END IF
             IF( M-P-Q .GE. 1 )
      $         CALL DLARF( 'R', M-P-Q, M-Q-I+1, X12(I,I), LDX12,
      $                     TAUQ2(I), X22(Q+1,I), LDX22, WORK )
@@ -487,11 +527,18 @@
          DO I = 1, M - P - Q
 *
             CALL DSCAL( M-P-Q-I+1, Z2*Z4, X22(Q+I,P+I), LDX22 )
-            CALL DLARFGP( M-P-Q-I+1, X22(Q+I,P+I), X22(Q+I,P+I+1),
-     $                    LDX22, TAUQ2(P+I) )
+            IF ( I .EQ. M-P-Q ) THEN
+               CALL DLARFGP( M-P-Q-I+1, X22(Q+I,P+I), X22(Q+I,P+I),
+     $                       LDX22, TAUQ2(P+I) )
+            ELSE
+               CALL DLARFGP( M-P-Q-I+1, X22(Q+I,P+I), X22(Q+I,P+I+1),
+     $                       LDX22, TAUQ2(P+I) )
+            END IF
             X22(Q+I,P+I) = ONE
-            CALL DLARF( 'R', M-P-Q-I, M-P-Q-I+1, X22(Q+I,P+I), LDX22,
-     $                  TAUQ2(P+I), X22(Q+I+1,P+I), LDX22, WORK )
+            IF ( I .LT. M-P-Q ) THEN
+               CALL DLARF( 'R', M-P-Q-I, M-P-Q-I+1, X22(Q+I,P+I), LDX22,
+     $                     TAUQ2(P+I), X22(Q+I+1,P+I), LDX22, WORK )
+            END IF
 *
          END DO
 *
@@ -521,18 +568,31 @@
 *
             CALL DLARFGP( P-I+1, X11(I,I), X11(I,I+1), LDX11, TAUP1(I) )
             X11(I,I) = ONE
-            CALL DLARFGP( M-P-I+1, X21(I,I), X21(I,I+1), LDX21,
+            IF ( I .EQ. M-P ) THEN
+               CALL DLARFGP( M-P-I+1, X21(I,I), X21(I,I), LDX21,
+     $                    TAUP2(I) )
+            ELSE
+               CALL DLARFGP( M-P-I+1, X21(I,I), X21(I,I+1), LDX21,
      $                    TAUP2(I) )
+            END IF
             X21(I,I) = ONE
 *
-            CALL DLARF( 'R', Q-I, P-I+1, X11(I,I), LDX11, TAUP1(I),
-     $                  X11(I+1,I), LDX11, WORK )
-            CALL DLARF( 'R', M-Q-I+1, P-I+1, X11(I,I), LDX11, TAUP1(I),
-     $                  X12(I,I), LDX12, WORK )
-            CALL DLARF( 'R', Q-I, M-P-I+1, X21(I,I), LDX21, TAUP2(I),
-     $                  X21(I+1,I), LDX21, WORK )
-            CALL DLARF( 'R', M-Q-I+1, M-P-I+1, X21(I,I), LDX21,
-     $                  TAUP2(I), X22(I,I), LDX22, WORK )
+            IF ( Q .GT. I ) THEN
+               CALL DLARF( 'R', Q-I, P-I+1, X11(I,I), LDX11, TAUP1(I),
+     $                     X11(I+1,I), LDX11, WORK )
+            END IF
+            IF ( M-Q+1 .GT. I ) THEN
+               CALL DLARF( 'R', M-Q-I+1, P-I+1, X11(I,I), LDX11,
+     $                     TAUP1(I), X12(I,I), LDX12, WORK )
+            END IF
+            IF ( Q .GT. I ) THEN
+               CALL DLARF( 'R', Q-I, M-P-I+1, X21(I,I), LDX21, TAUP2(I),
+     $                     X21(I+1,I), LDX21, WORK )
+            END IF
+            IF ( M-Q+1 .GT. I ) THEN
+               CALL DLARF( 'R', M-Q-I+1, M-P-I+1, X21(I,I), LDX21,
+     $                     TAUP2(I), X22(I,I), LDX22, WORK )
+            END IF
 *
             IF( I .LT. Q ) THEN
                CALL DSCAL( Q-I, -Z1*Z3*SIN(THETA(I)), X11(I+1,I), 1 )
@@ -548,10 +608,22 @@
      $                  DNRM2( M-Q-I+1, X12(I,I), 1 ) )
 *
             IF( I .LT. Q ) THEN
-               CALL DLARFGP( Q-I, X11(I+1,I), X11(I+2,I), 1, TAUQ1(I) )
+               IF ( Q-I .EQ. 1) THEN
+                  CALL DLARFGP( Q-I, X11(I+1,I), X11(I+1,I), 1,
+     $                          TAUQ1(I) )
+               ELSE
+                  CALL DLARFGP( Q-I, X11(I+1,I), X11(I+2,I), 1,
+     $                          TAUQ1(I) )
+               END IF
                X11(I+1,I) = ONE
             END IF
-            CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, TAUQ2(I) )
+            IF ( M-Q .GT. I ) THEN
+               CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, 
+     $                       TAUQ2(I) )
+            ELSE
+               CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I,I), 1, 
+     $                       TAUQ2(I) )
+            END IF               
             X12(I,I) = ONE
 *
             IF( I .LT. Q ) THEN
@@ -562,8 +634,10 @@
             END IF
             CALL DLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1, TAUQ2(I),
      $                  X12(I,I+1), LDX12, WORK )
-            CALL DLARF( 'L', M-Q-I+1, M-P-I, X12(I,I), 1, TAUQ2(I),
-     $                  X22(I,I+1), LDX22, WORK )
+            IF ( M-P-I .GT. 0 ) THEN
+               CALL DLARF( 'L', M-Q-I+1, M-P-I, X12(I,I), 1, TAUQ2(I),
+     $                     X22(I,I+1), LDX22, WORK )
+            END IF
 *
          END DO
 *
@@ -575,8 +649,10 @@
             CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, TAUQ2(I) )
             X12(I,I) = ONE
 *
-            CALL DLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1, TAUQ2(I),
+            IF ( P .GT. I ) THEN 
+               CALL DLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1, TAUQ2(I),
      $                  X12(I,I+1), LDX12, WORK )
+            END IF
             IF( M-P-Q .GE. 1 )
      $         CALL DLARF( 'L', M-Q-I+1, M-P-Q, X12(I,I), 1, TAUQ2(I),
      $                     X22(I,Q+1), LDX22, WORK )
@@ -588,12 +664,16 @@
          DO I = 1, M - P - Q
 *
             CALL DSCAL( M-P-Q-I+1, Z2*Z4, X22(P+I,Q+I), 1 )
-            CALL DLARFGP( M-P-Q-I+1, X22(P+I,Q+I), X22(P+I+1,Q+I), 1,
-     $                    TAUQ2(P+I) )
-            X22(P+I,Q+I) = ONE
-*
-            CALL DLARF( 'L', M-P-Q-I+1, M-P-Q-I, X22(P+I,Q+I), 1,
+            IF ( M-P-Q .EQ. I ) THEN
+               CALL DLARFGP( M-P-Q-I+1, X22(P+I,Q+I), X22(P+I,Q+I), 1,
+     $                       TAUQ2(P+I) )
+            ELSE
+               CALL DLARFGP( M-P-Q-I+1, X22(P+I,Q+I), X22(P+I+1,Q+I), 1,
+     $                       TAUQ2(P+I) )
+               CALL DLARF( 'L', M-P-Q-I+1, M-P-Q-I, X22(P+I,Q+I), 1,
      $                  TAUQ2(P+I), X22(P+I,Q+I+1), LDX22, WORK )
+            END IF
+            X22(P+I,Q+I) = ONE
 *
          END DO
 *

lapack-netlib/SRC/dorbdb1.f

@@ -0,0 +1,324 @@
+*> \brief \b DORBDB1
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DORBDB1 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorbdb1.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorbdb1.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorbdb1.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DORBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
+*                           TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            INFO, LWORK, M, P, Q, LDX11, LDX21
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   PHI(*), THETA(*)
+*       DOUBLE PRECISION   TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*),
+*      $                   X11(LDX11,*), X21(LDX21,*)
+*       ..
+*  
+* 
+*> \par Purpose:
+*> =============
+*>
+*>\verbatim
+*>
+*> DORBDB1 simultaneously bidiagonalizes the blocks of a tall and skinny
+*> matrix X with orthonomal columns:
+*>
+*>                            [ B11 ]
+*>      [ X11 ]   [ P1 |    ] [  0  ]
+*>      [-----] = [---------] [-----] Q1**T .
+*>      [ X21 ]   [    | P2 ] [ B21 ]
+*>                            [  0  ]
+*>
+*> X11 is P-by-Q, and X21 is (M-P)-by-Q. Q must be no larger than P,
+*> M-P, or M-Q. Routines DORBDB2, DORBDB3, and DORBDB4 handle cases in
+*> which Q is not the minimum dimension.
+*>
+*> The orthogonal matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P),
+*> and (M-Q)-by-(M-Q), respectively. They are represented implicitly by
+*> Householder vectors.
+*>
+*> B11 and B12 are Q-by-Q bidiagonal matrices represented implicitly by
+*> angles THETA, PHI.
+*>
+*>\endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>           The number of rows X11 plus the number of rows in X21.
+*> \endverbatim
+*>
+*> \param[in] P
+*> \verbatim
+*>          P is INTEGER
+*>           The number of rows in X11. 0 <= P <= M.
+*> \endverbatim
+*>
+*> \param[in] Q
+*> \verbatim
+*>          Q is INTEGER
+*>           The number of columns in X11 and X21. 0 <= Q <=
+*>           MIN(P,M-P,M-Q).
+*> \endverbatim
+*>
+*> \param[in,out] X11
+*> \verbatim
+*>          X11 is DOUBLE PRECISION array, dimension (LDX11,Q)
+*>           On entry, the top block of the matrix X to be reduced. On
+*>           exit, the columns of tril(X11) specify reflectors for P1 and
+*>           the rows of triu(X11,1) specify reflectors for Q1.
+*> \endverbatim
+*>
+*> \param[in] LDX11
+*> \verbatim
+*>          LDX11 is INTEGER
+*>           The leading dimension of X11. LDX11 >= P.
+*> \endverbatim
+*>
+*> \param[in,out] X21
+*> \verbatim
+*>          X21 is DOUBLE PRECISION array, dimension (LDX21,Q)
+*>           On entry, the bottom block of the matrix X to be reduced. On
+*>           exit, the columns of tril(X21) specify reflectors for P2.
+*> \endverbatim
+*>
+*> \param[in] LDX21
+*> \verbatim
+*>          LDX21 is INTEGER
+*>           The leading dimension of X21. LDX21 >= M-P.
+*> \endverbatim
+*>
+*> \param[out] THETA
+*> \verbatim
+*>          THETA is DOUBLE PRECISION array, dimension (Q)
+*>           The entries of the bidiagonal blocks B11, B21 are defined by
+*>           THETA and PHI. See Further Details.
+*> \endverbatim
+*>
+*> \param[out] PHI
+*> \verbatim
+*>          PHI is DOUBLE PRECISION array, dimension (Q-1)
+*>           The entries of the bidiagonal blocks B11, B21 are defined by
+*>           THETA and PHI. See Further Details.
+*> \endverbatim
+*>
+*> \param[out] TAUP1
+*> \verbatim
+*>          TAUP1 is DOUBLE PRECISION array, dimension (P)
+*>           The scalar factors of the elementary reflectors that define
+*>           P1.
+*> \endverbatim
+*>
+*> \param[out] TAUP2
+*> \verbatim
+*>          TAUP2 is DOUBLE PRECISION array, dimension (M-P)
+*>           The scalar factors of the elementary reflectors that define
+*>           P2.
+*> \endverbatim
+*>
+*> \param[out] TAUQ1
+*> \verbatim
+*>          TAUQ1 is DOUBLE PRECISION array, dimension (Q)
+*>           The scalar factors of the elementary reflectors that define
+*>           Q1.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is DOUBLE PRECISION array, dimension (LWORK)
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>           The dimension of the array WORK. LWORK >= M-Q.
+*> 
+*>           If LWORK = -1, then a workspace query is assumed; the routine
+*>           only calculates the optimal size of the WORK array, returns
+*>           this value as the first entry of the WORK array, and no error
+*>           message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>           = 0:  successful exit.
+*>           < 0:  if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*>
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date July 2012
+*
+*> \ingroup doubleOTHERcomputational
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  The upper-bidiagonal blocks B11, B21 are represented implicitly by
+*>  angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry
+*>  in each bidiagonal band is a product of a sine or cosine of a THETA
+*>  with a sine or cosine of a PHI. See [1] or DORCSD for details.
+*>
+*>  P1, P2, and Q1 are represented as products of elementary reflectors.
+*>  See DORCSD2BY1 for details on generating P1, P2, and Q1 using DORGQR
+*>  and DORGLQ.
+*> \endverbatim
+*
+*> \par References:
+*  ================
+*>
+*>  [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
+*>      Algorithms, 50(1):33-65, 2009.
+*>
+*  =====================================================================
+      SUBROUTINE DORBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
+     $                    TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO )
+*
+*  -- LAPACK computational routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     July 2012
+*
+*     .. Scalar Arguments ..
+      INTEGER            INFO, LWORK, M, P, Q, LDX11, LDX21
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   PHI(*), THETA(*)
+      DOUBLE PRECISION   TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*),
+     $                   X11(LDX11,*), X21(LDX21,*)
+*     ..
+*
+*  ====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ONE
+      PARAMETER          ( ONE = 1.0D0 )
+*     ..
+*     .. Local Scalars ..
+      DOUBLE PRECISION   C, S
+      INTEGER            CHILDINFO, I, ILARF, IORBDB5, LLARF, LORBDB5,
+     $                   LWORKMIN, LWORKOPT
+      LOGICAL            LQUERY
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DLARF, DLARFGP, DORBDB5, DROT, XERBLA
+*     ..
+*     .. External Functions ..
+      DOUBLE PRECISION   DNRM2
+      EXTERNAL           DNRM2
+*     ..
+*     .. Intrinsic Function ..
+      INTRINSIC          ATAN2, COS, MAX, SIN, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+*     Test input arguments
+*
+      INFO = 0
+      LQUERY = LWORK .EQ. -1
+*
+      IF( M .LT. 0 ) THEN
+         INFO = -1
+      ELSE IF( P .LT. Q .OR. M-P .LT. Q ) THEN
+         INFO = -2
+      ELSE IF( Q .LT. 0 .OR. M-Q .LT. Q ) THEN
+         INFO = -3
+      ELSE IF( LDX11 .LT. MAX( 1, P ) ) THEN
+         INFO = -5
+      ELSE IF( LDX21 .LT. MAX( 1, M-P ) ) THEN
+         INFO = -7
+      END IF
+*
+*     Compute workspace
+*
+      IF( INFO .EQ. 0 ) THEN
+         ILARF = 2
+         LLARF = MAX( P-1, M-P-1, Q-1 )
+         IORBDB5 = 2
+         LORBDB5 = Q-2
+         LWORKOPT = MAX( ILARF+LLARF-1, IORBDB5+LORBDB5-1 )
+         LWORKMIN = LWORKOPT
+         WORK(1) = LWORKOPT
+         IF( LWORK .LT. LWORKMIN .AND. .NOT.LQUERY ) THEN
+           INFO = -14
+         END IF
+      END IF
+      IF( INFO .NE. 0 ) THEN
+         CALL XERBLA( 'DORBDB1', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+*
+*     Reduce columns 1, ..., Q of X11 and X21
+*
+      DO I = 1, Q
+*
+         CALL DLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) )
+         CALL DLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1, TAUP2(I) )
+         THETA(I) = ATAN2( X21(I,I), X11(I,I) )
+         C = COS( THETA(I) )
+         S = SIN( THETA(I) )
+         X11(I,I) = ONE
+         X21(I,I) = ONE
+         CALL DLARF( 'L', P-I+1, Q-I, X11(I,I), 1, TAUP1(I), X11(I,I+1),
+     $               LDX11, WORK(ILARF) )
+         CALL DLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1, TAUP2(I),
+     $               X21(I,I+1), LDX21, WORK(ILARF) )
+*
+         IF( I .LT. Q ) THEN
+            CALL DROT( Q-I, X11(I,I+1), LDX11, X21(I,I+1), LDX21, C, S )
+            CALL DLARFGP( Q-I, X21(I,I+1), X21(I,I+2), LDX21, TAUQ1(I) )
+            S = X21(I,I+1)
+            X21(I,I+1) = ONE
+            CALL DLARF( 'R', P-I, Q-I, X21(I,I+1), LDX21, TAUQ1(I),
+     $                  X11(I+1,I+1), LDX11, WORK(ILARF) )
+            CALL DLARF( 'R', M-P-I, Q-I, X21(I,I+1), LDX21, TAUQ1(I),
+     $                  X21(I+1,I+1), LDX21, WORK(ILARF) )
+            C = SQRT( DNRM2( P-I, X11(I+1,I+1), 1, X11(I+1,I+1),
+     $          1 )**2 + DNRM2( M-P-I, X21(I+1,I+1), 1, X21(I+1,I+1),
+     $          1 )**2 )
+            PHI(I) = ATAN2( S, C )
+            CALL DORBDB5( P-I, M-P-I, Q-I-1, X11(I+1,I+1), 1,
+     $                    X21(I+1,I+1), 1, X11(I+1,I+2), LDX11,
+     $                    X21(I+1,I+2), LDX21, WORK(IORBDB5), LORBDB5,
+     $                    CHILDINFO )
+         END IF
+*
+      END DO
+*
+      RETURN
+*
+*     End of DORBDB1
+*
+      END
+

lapack-netlib/SRC/dorbdb2.f

@@ -0,0 +1,333 @@
+*> \brief \b DORBDB2
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DORBDB2 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorbdb2.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorbdb2.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorbdb2.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DORBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
+*                           TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            INFO, LWORK, M, P, Q, LDX11, LDX21
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   PHI(*), THETA(*)
+*       DOUBLE PRECISION   TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*),
+*      $                   X11(LDX11,*), X21(LDX21,*)
+*       ..
+*  
+* 
+*> \par Purpose:
+*> =============
+*>
+*>\verbatim
+*>
+*> DORBDB2 simultaneously bidiagonalizes the blocks of a tall and skinny
+*> matrix X with orthonomal columns:
+*>
+*>                            [ B11 ]
+*>      [ X11 ]   [ P1 |    ] [  0  ]
+*>      [-----] = [---------] [-----] Q1**T .
+*>      [ X21 ]   [    | P2 ] [ B21 ]
+*>                            [  0  ]
+*>
+*> X11 is P-by-Q, and X21 is (M-P)-by-Q. P must be no larger than M-P,
+*> Q, or M-Q. Routines DORBDB1, DORBDB3, and DORBDB4 handle cases in
+*> which P is not the minimum dimension.
+*>
+*> The orthogonal matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P),
+*> and (M-Q)-by-(M-Q), respectively. They are represented implicitly by
+*> Householder vectors.
+*>
+*> B11 and B12 are P-by-P bidiagonal matrices represented implicitly by
+*> angles THETA, PHI.
+*>
+*>\endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>           The number of rows X11 plus the number of rows in X21.
+*> \endverbatim
+*>
+*> \param[in] P
+*> \verbatim
+*>          P is INTEGER
+*>           The number of rows in X11. 0 <= P <= min(M-P,Q,M-Q).
+*> \endverbatim
+*>
+*> \param[in] Q
+*> \verbatim
+*>          Q is INTEGER
+*>           The number of columns in X11 and X21. 0 <= Q <= M.
+*> \endverbatim
+*>
+*> \param[in,out] X11
+*> \verbatim
+*>          X11 is DOUBLE PRECISION array, dimension (LDX11,Q)
+*>           On entry, the top block of the matrix X to be reduced. On
+*>           exit, the columns of tril(X11) specify reflectors for P1 and
+*>           the rows of triu(X11,1) specify reflectors for Q1.
+*> \endverbatim
+*>
+*> \param[in] LDX11
+*> \verbatim
+*>          LDX11 is INTEGER
+*>           The leading dimension of X11. LDX11 >= P.
+*> \endverbatim
+*>
+*> \param[in,out] X21
+*> \verbatim
+*>          X21 is DOUBLE PRECISION array, dimension (LDX21,Q)
+*>           On entry, the bottom block of the matrix X to be reduced. On
+*>           exit, the columns of tril(X21) specify reflectors for P2.
+*> \endverbatim
+*>
+*> \param[in] LDX21
+*> \verbatim
+*>          LDX21 is INTEGER
+*>           The leading dimension of X21. LDX21 >= M-P.
+*> \endverbatim
+*>
+*> \param[out] THETA
+*> \verbatim
+*>          THETA is DOUBLE PRECISION array, dimension (Q)
+*>           The entries of the bidiagonal blocks B11, B21 are defined by
+*>           THETA and PHI. See Further Details.
+*> \endverbatim
+*>
+*> \param[out] PHI
+*> \verbatim
+*>          PHI is DOUBLE PRECISION array, dimension (Q-1)
+*>           The entries of the bidiagonal blocks B11, B21 are defined by
+*>           THETA and PHI. See Further Details.
+*> \endverbatim
+*>
+*> \param[out] TAUP1
+*> \verbatim
+*>          TAUP1 is DOUBLE PRECISION array, dimension (P)
+*>           The scalar factors of the elementary reflectors that define
+*>           P1.
+*> \endverbatim
+*>
+*> \param[out] TAUP2
+*> \verbatim
+*>          TAUP2 is DOUBLE PRECISION array, dimension (M-P)
+*>           The scalar factors of the elementary reflectors that define
+*>           P2.
+*> \endverbatim
+*>
+*> \param[out] TAUQ1
+*> \verbatim
+*>          TAUQ1 is DOUBLE PRECISION array, dimension (Q)
+*>           The scalar factors of the elementary reflectors that define
+*>           Q1.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is DOUBLE PRECISION array, dimension (LWORK)
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>           The dimension of the array WORK. LWORK >= M-Q.
+*> 
+*>           If LWORK = -1, then a workspace query is assumed; the routine
+*>           only calculates the optimal size of the WORK array, returns
+*>           this value as the first entry of the WORK array, and no error
+*>           message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>           = 0:  successful exit.
+*>           < 0:  if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*>
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date July 2012
+*
+*> \ingroup doubleOTHERcomputational
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  The upper-bidiagonal blocks B11, B21 are represented implicitly by
+*>  angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry
+*>  in each bidiagonal band is a product of a sine or cosine of a THETA
+*>  with a sine or cosine of a PHI. See [1] or DORCSD for details.
+*>
+*>  P1, P2, and Q1 are represented as products of elementary reflectors.
+*>  See DORCSD2BY1 for details on generating P1, P2, and Q1 using DORGQR
+*>  and DORGLQ.
+*> \endverbatim
+*
+*> \par References:
+*  ================
+*>
+*>  [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
+*>      Algorithms, 50(1):33-65, 2009.
+*>
+*  =====================================================================
+      SUBROUTINE DORBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
+     $                    TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO )
+*
+*  -- LAPACK computational routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     July 2012
+*
+*     .. Scalar Arguments ..
+      INTEGER            INFO, LWORK, M, P, Q, LDX11, LDX21
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   PHI(*), THETA(*)
+      DOUBLE PRECISION   TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*),
+     $                   X11(LDX11,*), X21(LDX21,*)
+*     ..
+*
+*  ====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   NEGONE, ONE
+      PARAMETER          ( NEGONE = -1.0D0, ONE = 1.0D0 )
+*     ..
+*     .. Local Scalars ..
+      DOUBLE PRECISION   C, S
+      INTEGER            CHILDINFO, I, ILARF, IORBDB5, LLARF, LORBDB5,
+     $                   LWORKMIN, LWORKOPT
+      LOGICAL            LQUERY
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DLARF, DLARFGP, DORBDB5, DROT, DSCAL, XERBLA
+*     ..
+*     .. External Functions ..
+      DOUBLE PRECISION   DNRM2
+      EXTERNAL           DNRM2
+*     ..
+*     .. Intrinsic Function ..
+      INTRINSIC          ATAN2, COS, MAX, SIN, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+*     Test input arguments
+*
+      INFO = 0
+      LQUERY = LWORK .EQ. -1
+*
+      IF( M .LT. 0 ) THEN
+         INFO = -1
+      ELSE IF( P .LT. 0 .OR. P .GT. M-P ) THEN
+         INFO = -2
+      ELSE IF( Q .LT. 0 .OR. Q .LT. P .OR. M-Q .LT. P ) THEN
+         INFO = -3
+      ELSE IF( LDX11 .LT. MAX( 1, P ) ) THEN
+         INFO = -5
+      ELSE IF( LDX21 .LT. MAX( 1, M-P ) ) THEN
+         INFO = -7
+      END IF
+*
+*     Compute workspace
+*
+      IF( INFO .EQ. 0 ) THEN
+         ILARF = 2
+         LLARF = MAX( P-1, M-P, Q-1 )
+         IORBDB5 = 2
+         LORBDB5 = Q-1
+         LWORKOPT = MAX( ILARF+LLARF-1, IORBDB5+LORBDB5-1 )
+         LWORKMIN = LWORKOPT
+         WORK(1) = LWORKOPT
+         IF( LWORK .LT. LWORKMIN .AND. .NOT.LQUERY ) THEN
+           INFO = -14
+         END IF
+      END IF
+      IF( INFO .NE. 0 ) THEN
+         CALL XERBLA( 'DORBDB2', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+*
+*     Reduce rows 1, ..., P of X11 and X21
+*
+      DO I = 1, P
+*      
+         IF( I .GT. 1 ) THEN
+            CALL DROT( Q-I+1, X11(I,I), LDX11, X21(I-1,I), LDX21, C, S )
+         END IF
+         CALL DLARFGP( Q-I+1, X11(I,I), X11(I,I+1), LDX11, TAUQ1(I) )
+         C = X11(I,I)
+         X11(I,I) = ONE
+         CALL DLARF( 'R', P-I, Q-I+1, X11(I,I), LDX11, TAUQ1(I),
+     $               X11(I+1,I), LDX11, WORK(ILARF) )
+         CALL DLARF( 'R', M-P-I+1, Q-I+1, X11(I,I), LDX11, TAUQ1(I),
+     $               X21(I,I), LDX21, WORK(ILARF) )
+         S = SQRT( DNRM2( P-I, X11(I+1,I), 1, X11(I+1,I),
+     $       1 )**2 + DNRM2( M-P-I+1, X21(I,I), 1, X21(I,I), 1 )**2 )
+         THETA(I) = ATAN2( S, C )
+*
+         CALL DORBDB5( P-I, M-P-I+1, Q-I, X11(I+1,I), 1, X21(I,I), 1,
+     $                 X11(I+1,I+1), LDX11, X21(I,I+1), LDX21,
+     $                 WORK(IORBDB5), LORBDB5, CHILDINFO )
+         CALL DSCAL( P-I, NEGONE, X11(I+1,I), 1 )
+         CALL DLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1, TAUP2(I) )
+         IF( I .LT. P ) THEN
+            CALL DLARFGP( P-I, X11(I+1,I), X11(I+2,I), 1, TAUP1(I) )
+            PHI(I) = ATAN2( X11(I+1,I), X21(I,I) )
+            C = COS( PHI(I) )
+            S = SIN( PHI(I) )
+            X11(I+1,I) = ONE
+            CALL DLARF( 'L', P-I, Q-I, X11(I+1,I), 1, TAUP1(I),
+     $                  X11(I+1,I+1), LDX11, WORK(ILARF) )
+         END IF
+         X21(I,I) = ONE
+         CALL DLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1, TAUP2(I),
+     $               X21(I,I+1), LDX21, WORK(ILARF) )
+*
+      END DO
+*
+*     Reduce the bottom-right portion of X21 to the identity matrix
+*
+      DO I = P + 1, Q
+         CALL DLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1, TAUP2(I) )
+         X21(I,I) = ONE
+         CALL DLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1, TAUP2(I),
+     $               X21(I,I+1), LDX21, WORK(ILARF) )
+      END DO
+*
+      RETURN
+*
+*     End of DORBDB2
+*
+      END
+

lapack-netlib/SRC/dorbdb3.f

@@ -0,0 +1,332 @@
+*> \brief \b DORBDB3
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DORBDB3 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorbdb3.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorbdb3.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorbdb3.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DORBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
+*                           TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            INFO, LWORK, M, P, Q, LDX11, LDX21
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   PHI(*), THETA(*)
+*       DOUBLE PRECISION   TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*),
+*      $                   X11(LDX11,*), X21(LDX21,*)
+*       ..
+*  
+* 
+*> \par Purpose:
+*> =============
+*>
+*>\verbatim
+*>
+*> DORBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny
+*> matrix X with orthonomal columns:
+*>
+*>                            [ B11 ]
+*>      [ X11 ]   [ P1 |    ] [  0  ]
+*>      [-----] = [---------] [-----] Q1**T .
+*>      [ X21 ]   [    | P2 ] [ B21 ]
+*>                            [  0  ]
+*>
+*> X11 is P-by-Q, and X21 is (M-P)-by-Q. M-P must be no larger than P,
+*> Q, or M-Q. Routines DORBDB1, DORBDB2, and DORBDB4 handle cases in
+*> which M-P is not the minimum dimension.
+*>
+*> The orthogonal matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P),
+*> and (M-Q)-by-(M-Q), respectively. They are represented implicitly by
+*> Householder vectors.
+*>
+*> B11 and B12 are (M-P)-by-(M-P) bidiagonal matrices represented
+*> implicitly by angles THETA, PHI.
+*>
+*>\endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>           The number of rows X11 plus the number of rows in X21.
+*> \endverbatim
+*>
+*> \param[in] P
+*> \verbatim
+*>          P is INTEGER
+*>           The number of rows in X11. 0 <= P <= M. M-P <= min(P,Q,M-Q).
+*> \endverbatim
+*>
+*> \param[in] Q
+*> \verbatim
+*>          Q is INTEGER
+*>           The number of columns in X11 and X21. 0 <= Q <= M.
+*> \endverbatim
+*>
+*> \param[in,out] X11
+*> \verbatim
+*>          X11 is DOUBLE PRECISION array, dimension (LDX11,Q)
+*>           On entry, the top block of the matrix X to be reduced. On
+*>           exit, the columns of tril(X11) specify reflectors for P1 and
+*>           the rows of triu(X11,1) specify reflectors for Q1.
+*> \endverbatim
+*>
+*> \param[in] LDX11
+*> \verbatim
+*>          LDX11 is INTEGER
+*>           The leading dimension of X11. LDX11 >= P.
+*> \endverbatim
+*>
+*> \param[in,out] X21
+*> \verbatim
+*>          X21 is DOUBLE PRECISION array, dimension (LDX21,Q)
+*>           On entry, the bottom block of the matrix X to be reduced. On
+*>           exit, the columns of tril(X21) specify reflectors for P2.
+*> \endverbatim
+*>
+*> \param[in] LDX21
+*> \verbatim
+*>          LDX21 is INTEGER
+*>           The leading dimension of X21. LDX21 >= M-P.
+*> \endverbatim
+*>
+*> \param[out] THETA
+*> \verbatim
+*>          THETA is DOUBLE PRECISION array, dimension (Q)
+*>           The entries of the bidiagonal blocks B11, B21 are defined by
+*>           THETA and PHI. See Further Details.
+*> \endverbatim
+*>
+*> \param[out] PHI
+*> \verbatim
+*>          PHI is DOUBLE PRECISION array, dimension (Q-1)
+*>           The entries of the bidiagonal blocks B11, B21 are defined by
+*>           THETA and PHI. See Further Details.
+*> \endverbatim
+*>
+*> \param[out] TAUP1
+*> \verbatim
+*>          TAUP1 is DOUBLE PRECISION array, dimension (P)
+*>           The scalar factors of the elementary reflectors that define
+*>           P1.
+*> \endverbatim
+*>
+*> \param[out] TAUP2
+*> \verbatim
+*>          TAUP2 is DOUBLE PRECISION array, dimension (M-P)
+*>           The scalar factors of the elementary reflectors that define
+*>           P2.
+*> \endverbatim
+*>
+*> \param[out] TAUQ1
+*> \verbatim
+*>          TAUQ1 is DOUBLE PRECISION array, dimension (Q)
+*>           The scalar factors of the elementary reflectors that define
+*>           Q1.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is DOUBLE PRECISION array, dimension (LWORK)
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>           The dimension of the array WORK. LWORK >= M-Q.
+*> 
+*>           If LWORK = -1, then a workspace query is assumed; the routine
+*>           only calculates the optimal size of the WORK array, returns
+*>           this value as the first entry of the WORK array, and no error
+*>           message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>           = 0:  successful exit.
+*>           < 0:  if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date July 2012
+*
+*> \ingroup doubleOTHERcomputational
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  The upper-bidiagonal blocks B11, B21 are represented implicitly by
+*>  angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry
+*>  in each bidiagonal band is a product of a sine or cosine of a THETA
+*>  with a sine or cosine of a PHI. See [1] or DORCSD for details.
+*>
+*>  P1, P2, and Q1 are represented as products of elementary reflectors.
+*>  See DORCSD2BY1 for details on generating P1, P2, and Q1 using DORGQR
+*>  and DORGLQ.
+*> \endverbatim
+*
+*> \par References:
+*  ================
+*>
+*>  [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
+*>      Algorithms, 50(1):33-65, 2009.
+*>
+*  =====================================================================
+      SUBROUTINE DORBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
+     $                    TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO )
+*
+*  -- LAPACK computational routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     July 2012
+*
+*     .. Scalar Arguments ..
+      INTEGER            INFO, LWORK, M, P, Q, LDX11, LDX21
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   PHI(*), THETA(*)
+      DOUBLE PRECISION   TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*),
+     $                   X11(LDX11,*), X21(LDX21,*)
+*     ..
+*
+*  ====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ONE
+      PARAMETER          ( ONE = 1.0D0 )
+*     ..
+*     .. Local Scalars ..
+      DOUBLE PRECISION   C, S
+      INTEGER            CHILDINFO, I, ILARF, IORBDB5, LLARF, LORBDB5,
+     $                   LWORKMIN, LWORKOPT
+      LOGICAL            LQUERY
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DLARF, DLARFGP, DORBDB5, DROT, XERBLA
+*     ..
+*     .. External Functions ..
+      DOUBLE PRECISION   DNRM2
+      EXTERNAL           DNRM2
+*     ..
+*     .. Intrinsic Function ..
+      INTRINSIC          ATAN2, COS, MAX, SIN, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+*     Test input arguments
+*
+      INFO = 0
+      LQUERY = LWORK .EQ. -1
+*
+      IF( M .LT. 0 ) THEN
+         INFO = -1
+      ELSE IF( 2*P .LT. M .OR. P .GT. M ) THEN
+         INFO = -2
+      ELSE IF( Q .LT. M-P .OR. M-Q .LT. M-P ) THEN
+         INFO = -3
+      ELSE IF( LDX11 .LT. MAX( 1, P ) ) THEN
+         INFO = -5
+      ELSE IF( LDX21 .LT. MAX( 1, M-P ) ) THEN
+         INFO = -7
+      END IF
+*
+*     Compute workspace
+*
+      IF( INFO .EQ. 0 ) THEN
+         ILARF = 2
+         LLARF = MAX( P, M-P-1, Q-1 )
+         IORBDB5 = 2
+         LORBDB5 = Q-1
+         LWORKOPT = MAX( ILARF+LLARF-1, IORBDB5+LORBDB5-1 )
+         LWORKMIN = LWORKOPT
+         WORK(1) = LWORKOPT
+         IF( LWORK .LT. LWORKMIN .AND. .NOT.LQUERY ) THEN
+           INFO = -14
+         END IF
+      END IF
+      IF( INFO .NE. 0 ) THEN
+         CALL XERBLA( 'DORBDB3', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+*
+*     Reduce rows 1, ..., M-P of X11 and X21
+*
+      DO I = 1, M-P
+*      
+         IF( I .GT. 1 ) THEN
+            CALL DROT( Q-I+1, X11(I-1,I), LDX11, X21(I,I), LDX11, C, S )
+         END IF
+*
+         CALL DLARFGP( Q-I+1, X21(I,I), X21(I,I+1), LDX21, TAUQ1(I) )
+         S = X21(I,I)
+         X21(I,I) = ONE
+         CALL DLARF( 'R', P-I+1, Q-I+1, X21(I,I), LDX21, TAUQ1(I),
+     $               X11(I,I), LDX11, WORK(ILARF) )
+         CALL DLARF( 'R', M-P-I, Q-I+1, X21(I,I), LDX21, TAUQ1(I),
+     $               X21(I+1,I), LDX21, WORK(ILARF) )
+         C = SQRT( DNRM2( P-I+1, X11(I,I), 1, X11(I,I),
+     $       1 )**2 + DNRM2( M-P-I, X21(I+1,I), 1, X21(I+1,I), 1 )**2 )
+         THETA(I) = ATAN2( S, C )
+*
+         CALL DORBDB5( P-I+1, M-P-I, Q-I, X11(I,I), 1, X21(I+1,I), 1,
+     $                 X11(I,I+1), LDX11, X21(I+1,I+1), LDX21,
+     $                 WORK(IORBDB5), LORBDB5, CHILDINFO )
+         CALL DLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) )
+         IF( I .LT. M-P ) THEN
+            CALL DLARFGP( M-P-I, X21(I+1,I), X21(I+2,I), 1, TAUP2(I) )
+            PHI(I) = ATAN2( X21(I+1,I), X11(I,I) )
+            C = COS( PHI(I) )
+            S = SIN( PHI(I) )
+            X21(I+1,I) = ONE
+            CALL DLARF( 'L', M-P-I, Q-I, X21(I+1,I), 1, TAUP2(I),
+     $                  X21(I+1,I+1), LDX21, WORK(ILARF) )
+         END IF
+         X11(I,I) = ONE
+         CALL DLARF( 'L', P-I+1, Q-I, X11(I,I), 1, TAUP1(I), X11(I,I+1),
+     $               LDX11, WORK(ILARF) )
+*
+      END DO
+*
+*     Reduce the bottom-right portion of X11 to the identity matrix
+*
+      DO I = M-P + 1, Q
+         CALL DLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) )
+         X11(I,I) = ONE
+         CALL DLARF( 'L', P-I+1, Q-I, X11(I,I), 1, TAUP1(I), X11(I,I+1),
+     $               LDX11, WORK(ILARF) )
+      END DO
+*
+      RETURN
+*
+*     End of DORBDB3
+*
+      END
+

lapack-netlib/SRC/dorbdb4.f

@@ -0,0 +1,378 @@
+*> \brief \b DORBDB4
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DORBDB4 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorbdb4.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorbdb4.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorbdb4.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DORBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
+*                           TAUP1, TAUP2, TAUQ1, PHANTOM, WORK, LWORK,
+*                           INFO )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            INFO, LWORK, M, P, Q, LDX11, LDX21
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   PHI(*), THETA(*)
+*       DOUBLE PRECISION   PHANTOM(*), TAUP1(*), TAUP2(*), TAUQ1(*),
+*      $                   WORK(*), X11(LDX11,*), X21(LDX21,*)
+*       ..
+*  
+* 
+*> \par Purpose:
+*> =============
+*>
+*>\verbatim
+*>
+*> DORBDB4 simultaneously bidiagonalizes the blocks of a tall and skinny
+*> matrix X with orthonomal columns:
+*>
+*>                            [ B11 ]
+*>      [ X11 ]   [ P1 |    ] [  0  ]
+*>      [-----] = [---------] [-----] Q1**T .
+*>      [ X21 ]   [    | P2 ] [ B21 ]
+*>                            [  0  ]
+*>
+*> X11 is P-by-Q, and X21 is (M-P)-by-Q. M-Q must be no larger than P,
+*> M-P, or Q. Routines DORBDB1, DORBDB2, and DORBDB3 handle cases in
+*> which M-Q is not the minimum dimension.
+*>
+*> The orthogonal matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P),
+*> and (M-Q)-by-(M-Q), respectively. They are represented implicitly by
+*> Householder vectors.
+*>
+*> B11 and B12 are (M-Q)-by-(M-Q) bidiagonal matrices represented
+*> implicitly by angles THETA, PHI.
+*>
+*>\endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>           The number of rows X11 plus the number of rows in X21.
+*> \endverbatim
+*>
+*> \param[in] P
+*> \verbatim
+*>          P is INTEGER
+*>           The number of rows in X11. 0 <= P <= M.
+*> \endverbatim
+*>
+*> \param[in] Q
+*> \verbatim
+*>          Q is INTEGER
+*>           The number of columns in X11 and X21. 0 <= Q <= M and
+*>           M-Q <= min(P,M-P,Q).
+*> \endverbatim
+*>
+*> \param[in,out] X11
+*> \verbatim
+*>          X11 is DOUBLE PRECISION array, dimension (LDX11,Q)
+*>           On entry, the top block of the matrix X to be reduced. On
+*>           exit, the columns of tril(X11) specify reflectors for P1 and
+*>           the rows of triu(X11,1) specify reflectors for Q1.
+*> \endverbatim
+*>
+*> \param[in] LDX11
+*> \verbatim
+*>          LDX11 is INTEGER
+*>           The leading dimension of X11. LDX11 >= P.
+*> \endverbatim
+*>
+*> \param[in,out] X21
+*> \verbatim
+*>          X21 is DOUBLE PRECISION array, dimension (LDX21,Q)
+*>           On entry, the bottom block of the matrix X to be reduced. On
+*>           exit, the columns of tril(X21) specify reflectors for P2.
+*> \endverbatim
+*>
+*> \param[in] LDX21
+*> \verbatim
+*>          LDX21 is INTEGER
+*>           The leading dimension of X21. LDX21 >= M-P.
+*> \endverbatim
+*>
+*> \param[out] THETA
+*> \verbatim
+*>          THETA is DOUBLE PRECISION array, dimension (Q)
+*>           The entries of the bidiagonal blocks B11, B21 are defined by
+*>           THETA and PHI. See Further Details.
+*> \endverbatim
+*>
+*> \param[out] PHI
+*> \verbatim
+*>          PHI is DOUBLE PRECISION array, dimension (Q-1)
+*>           The entries of the bidiagonal blocks B11, B21 are defined by
+*>           THETA and PHI. See Further Details.
+*> \endverbatim
+*>
+*> \param[out] TAUP1
+*> \verbatim
+*>          TAUP1 is DOUBLE PRECISION array, dimension (P)
+*>           The scalar factors of the elementary reflectors that define
+*>           P1.
+*> \endverbatim
+*>
+*> \param[out] TAUP2
+*> \verbatim
+*>          TAUP2 is DOUBLE PRECISION array, dimension (M-P)
+*>           The scalar factors of the elementary reflectors that define
+*>           P2.
+*> \endverbatim
+*>
+*> \param[out] TAUQ1
+*> \verbatim
+*>          TAUQ1 is DOUBLE PRECISION array, dimension (Q)
+*>           The scalar factors of the elementary reflectors that define
+*>           Q1.
+*> \endverbatim
+*>
+*> \param[out] PHANTOM
+*> \verbatim
+*>          PHANTOM is DOUBLE PRECISION array, dimension (M)
+*>           The routine computes an M-by-1 column vector Y that is
+*>           orthogonal to the columns of [ X11; X21 ]. PHANTOM(1:P) and
+*>           PHANTOM(P+1:M) contain Householder vectors for Y(1:P) and
+*>           Y(P+1:M), respectively.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is DOUBLE PRECISION array, dimension (LWORK)
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>           The dimension of the array WORK. LWORK >= M-Q.
+*> 
+*>           If LWORK = -1, then a workspace query is assumed; the routine
+*>           only calculates the optimal size of the WORK array, returns
+*>           this value as the first entry of the WORK array, and no error
+*>           message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>           = 0:  successful exit.
+*>           < 0:  if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date July 2012
+*
+*> \ingroup doubleOTHERcomputational
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  The upper-bidiagonal blocks B11, B21 are represented implicitly by
+*>  angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry
+*>  in each bidiagonal band is a product of a sine or cosine of a THETA
+*>  with a sine or cosine of a PHI. See [1] or DORCSD for details.
+*>
+*>  P1, P2, and Q1 are represented as products of elementary reflectors.
+*>  See DORCSD2BY1 for details on generating P1, P2, and Q1 using DORGQR
+*>  and DORGLQ.
+*> \endverbatim
+*
+*> \par References:
+*  ================
+*>
+*>  [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
+*>      Algorithms, 50(1):33-65, 2009.
+*>
+*  =====================================================================
+      SUBROUTINE DORBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
+     $                    TAUP1, TAUP2, TAUQ1, PHANTOM, WORK, LWORK,
+     $                    INFO )
+*
+*  -- LAPACK computational routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     July 2012
+*
+*     .. Scalar Arguments ..
+      INTEGER            INFO, LWORK, M, P, Q, LDX11, LDX21
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   PHI(*), THETA(*)
+      DOUBLE PRECISION   PHANTOM(*), TAUP1(*), TAUP2(*), TAUQ1(*),
+     $                   WORK(*), X11(LDX11,*), X21(LDX21,*)
+*     ..
+*
+*  ====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   NEGONE, ONE, ZERO
+      PARAMETER          ( NEGONE = -1.0D0, ONE = 1.0D0, ZERO = 0.0D0 )
+*     ..
+*     .. Local Scalars ..
+      DOUBLE PRECISION   C, S
+      INTEGER            CHILDINFO, I, ILARF, IORBDB5, J, LLARF,
+     $                   LORBDB5, LWORKMIN, LWORKOPT
+      LOGICAL            LQUERY
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DLARF, DLARFGP, DORBDB5, DROT, DSCAL, XERBLA
+*     ..
+*     .. External Functions ..
+      DOUBLE PRECISION   DNRM2
+      EXTERNAL           DNRM2
+*     ..
+*     .. Intrinsic Function ..
+      INTRINSIC          ATAN2, COS, MAX, SIN, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+*     Test input arguments
+*
+      INFO = 0
+      LQUERY = LWORK .EQ. -1
+*
+      IF( M .LT. 0 ) THEN
+         INFO = -1
+      ELSE IF( P .LT. M-Q .OR. M-P .LT. M-Q ) THEN
+         INFO = -2
+      ELSE IF( Q .LT. M-Q .OR. Q .GT. M ) THEN
+         INFO = -3
+      ELSE IF( LDX11 .LT. MAX( 1, P ) ) THEN
+         INFO = -5
+      ELSE IF( LDX21 .LT. MAX( 1, M-P ) ) THEN
+         INFO = -7
+      END IF
+*
+*     Compute workspace
+*
+      IF( INFO .EQ. 0 ) THEN
+         ILARF = 2
+         LLARF = MAX( Q-1, P-1, M-P-1 )
+         IORBDB5 = 2
+         LORBDB5 = Q
+         LWORKOPT = ILARF + LLARF - 1
+         LWORKOPT = MAX( LWORKOPT, IORBDB5 + LORBDB5 - 1 )
+         LWORKMIN = LWORKOPT
+         WORK(1) = LWORKOPT
+         IF( LWORK .LT. LWORKMIN .AND. .NOT.LQUERY ) THEN
+           INFO = -14
+         END IF
+      END IF
+      IF( INFO .NE. 0 ) THEN
+         CALL XERBLA( 'DORBDB4', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+*
+*     Reduce columns 1, ..., M-Q of X11 and X21
+*
+      DO I = 1, M-Q
+*
+         IF( I .EQ. 1 ) THEN
+            DO J = 1, M
+               PHANTOM(J) = ZERO
+            END DO
+            CALL DORBDB5( P, M-P, Q, PHANTOM(1), 1, PHANTOM(P+1), 1,
+     $                    X11, LDX11, X21, LDX21, WORK(IORBDB5),
+     $                    LORBDB5, CHILDINFO )
+            CALL DSCAL( P, NEGONE, PHANTOM(1), 1 )
+            CALL DLARFGP( P, PHANTOM(1), PHANTOM(2), 1, TAUP1(1) )
+            CALL DLARFGP( M-P, PHANTOM(P+1), PHANTOM(P+2), 1, TAUP2(1) )
+            THETA(I) = ATAN2( PHANTOM(1), PHANTOM(P+1) )
+            C = COS( THETA(I) )
+            S = SIN( THETA(I) )
+            PHANTOM(1) = ONE
+            PHANTOM(P+1) = ONE
+            CALL DLARF( 'L', P, Q, PHANTOM(1), 1, TAUP1(1), X11, LDX11,
+     $                  WORK(ILARF) )
+            CALL DLARF( 'L', M-P, Q, PHANTOM(P+1), 1, TAUP2(1), X21,
+     $                  LDX21, WORK(ILARF) )
+         ELSE
+            CALL DORBDB5( P-I+1, M-P-I+1, Q-I+1, X11(I,I-1), 1,
+     $                    X21(I,I-1), 1, X11(I,I), LDX11, X21(I,I),
+     $                    LDX21, WORK(IORBDB5), LORBDB5, CHILDINFO )
+            CALL DSCAL( P-I+1, NEGONE, X11(I,I-1), 1 )
+            CALL DLARFGP( P-I+1, X11(I,I-1), X11(I+1,I-1), 1, TAUP1(I) )
+            CALL DLARFGP( M-P-I+1, X21(I,I-1), X21(I+1,I-1), 1,
+     $                    TAUP2(I) )
+            THETA(I) = ATAN2( X11(I,I-1), X21(I,I-1) )
+            C = COS( THETA(I) )
+            S = SIN( THETA(I) )
+            X11(I,I-1) = ONE
+            X21(I,I-1) = ONE
+            CALL DLARF( 'L', P-I+1, Q-I+1, X11(I,I-1), 1, TAUP1(I),
+     $                  X11(I,I), LDX11, WORK(ILARF) )
+            CALL DLARF( 'L', M-P-I+1, Q-I+1, X21(I,I-1), 1, TAUP2(I),
+     $                  X21(I,I), LDX21, WORK(ILARF) )
+         END IF
+*
+         CALL DROT( Q-I+1, X11(I,I), LDX11, X21(I,I), LDX21, S, -C )
+         CALL DLARFGP( Q-I+1, X21(I,I), X21(I,I+1), LDX21, TAUQ1(I) )
+         C = X21(I,I)
+         X21(I,I) = ONE
+         CALL DLARF( 'R', P-I, Q-I+1, X21(I,I), LDX21, TAUQ1(I),
+     $               X11(I+1,I), LDX11, WORK(ILARF) )
+         CALL DLARF( 'R', M-P-I, Q-I+1, X21(I,I), LDX21, TAUQ1(I),
+     $               X21(I+1,I), LDX21, WORK(ILARF) )
+         IF( I .LT. M-Q ) THEN
+            S = SQRT( DNRM2( P-I, X11(I+1,I), 1, X11(I+1,I),
+     $          1 )**2 + DNRM2( M-P-I, X21(I+1,I), 1, X21(I+1,I),
+     $          1 )**2 )
+            PHI(I) = ATAN2( S, C )
+         END IF
+*
+      END DO
+*
+*     Reduce the bottom-right portion of X11 to [ I 0 ]
+*
+      DO I = M - Q + 1, P
+         CALL DLARFGP( Q-I+1, X11(I,I), X11(I,I+1), LDX11, TAUQ1(I) )
+         X11(I,I) = ONE
+         CALL DLARF( 'R', P-I, Q-I+1, X11(I,I), LDX11, TAUQ1(I),
+     $               X11(I+1,I), LDX11, WORK(ILARF) )
+         CALL DLARF( 'R', Q-P, Q-I+1, X11(I,I), LDX11, TAUQ1(I),
+     $               X21(M-Q+1,I), LDX21, WORK(ILARF) )
+      END DO
+*
+*     Reduce the bottom-right portion of X21 to [ 0 I ]
+*
+      DO I = P + 1, Q
+         CALL DLARFGP( Q-I+1, X21(M-Q+I-P,I), X21(M-Q+I-P,I+1), LDX21,
+     $                 TAUQ1(I) )
+         X21(M-Q+I-P,I) = ONE
+         CALL DLARF( 'R', Q-I, Q-I+1, X21(M-Q+I-P,I), LDX21, TAUQ1(I),
+     $               X21(M-Q+I-P+1,I), LDX21, WORK(ILARF) )
+      END DO
+*
+      RETURN
+*
+*     End of DORBDB4
+*
+      END
+

lapack-netlib/SRC/dorbdb5.f

@@ -0,0 +1,274 @@
+*> \brief \b DORBDB5
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DORBDB5 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorbdb5.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorbdb5.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorbdb5.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DORBDB5( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
+*                           LDQ2, WORK, LWORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            INCX1, INCX2, INFO, LDQ1, LDQ2, LWORK, M1, M2,
+*      $                   N
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*)
+*       ..
+*  
+* 
+*> \par Purpose:
+*> =============
+*>
+*>\verbatim
+*>
+*> DORBDB5 orthogonalizes the column vector
+*>      X = [ X1 ]
+*>          [ X2 ]
+*> with respect to the columns of
+*>      Q = [ Q1 ] .
+*>          [ Q2 ]
+*> The columns of Q must be orthonormal.
+*>
+*> If the projection is zero according to Kahan's "twice is enough"
+*> criterion, then some other vector from the orthogonal complement
+*> is returned. This vector is chosen in an arbitrary but deterministic
+*> way.
+*>
+*>\endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] M1
+*> \verbatim
+*>          M1 is INTEGER
+*>           The dimension of X1 and the number of rows in Q1. 0 <= M1.
+*> \endverbatim
+*>
+*> \param[in] M2
+*> \verbatim
+*>          M2 is INTEGER
+*>           The dimension of X2 and the number of rows in Q2. 0 <= M2.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>           The number of columns in Q1 and Q2. 0 <= N.
+*> \endverbatim
+*>
+*> \param[in,out] X1
+*> \verbatim
+*>          X1 is DOUBLE PRECISION array, dimension (M1)
+*>           On entry, the top part of the vector to be orthogonalized.
+*>           On exit, the top part of the projected vector.
+*> \endverbatim
+*>
+*> \param[in] INCX1
+*> \verbatim
+*>          INCX1 is INTEGER
+*>           Increment for entries of X1.
+*> \endverbatim
+*>
+*> \param[in,out] X2
+*> \verbatim
+*>          X2 is DOUBLE PRECISION array, dimension (M2)
+*>           On entry, the bottom part of the vector to be
+*>           orthogonalized. On exit, the bottom part of the projected
+*>           vector.
+*> \endverbatim
+*>
+*> \param[in] INCX2
+*> \verbatim
+*>          INCX2 is INTEGER
+*>           Increment for entries of X2.
+*> \endverbatim
+*>
+*> \param[in] Q1
+*> \verbatim
+*>          Q1 is DOUBLE PRECISION array, dimension (LDQ1, N)
+*>           The top part of the orthonormal basis matrix.
+*> \endverbatim
+*>
+*> \param[in] LDQ1
+*> \verbatim
+*>          LDQ1 is INTEGER
+*>           The leading dimension of Q1. LDQ1 >= M1.
+*> \endverbatim
+*>
+*> \param[in] Q2
+*> \verbatim
+*>          Q2 is DOUBLE PRECISION array, dimension (LDQ2, N)
+*>           The bottom part of the orthonormal basis matrix.
+*> \endverbatim
+*>
+*> \param[in] LDQ2
+*> \verbatim
+*>          LDQ2 is INTEGER
+*>           The leading dimension of Q2. LDQ2 >= M2.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is DOUBLE PRECISION array, dimension (LWORK)
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>           The dimension of the array WORK. LWORK >= N.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>           = 0:  successful exit.
+*>           < 0:  if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date July 2012
+*
+*> \ingroup doubleOTHERcomputational
+*
+*  =====================================================================
+      SUBROUTINE DORBDB5( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
+     $                    LDQ2, WORK, LWORK, INFO )
+*
+*  -- LAPACK computational routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     July 2012
+*
+*     .. Scalar Arguments ..
+      INTEGER            INCX1, INCX2, INFO, LDQ1, LDQ2, LWORK, M1, M2,
+     $                   N
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*)
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ONE, ZERO
+      PARAMETER          ( ONE = 1.0D0, ZERO = 0.0D0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            CHILDINFO, I, J
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DORBDB6, XERBLA
+*     ..
+*     .. External Functions ..
+      DOUBLE PRECISION   DNRM2
+      EXTERNAL           DNRM2
+*     ..
+*     .. Intrinsic Function ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+*     Test input arguments
+*
+      INFO = 0
+      IF( M1 .LT. 0 ) THEN
+         INFO = -1
+      ELSE IF( M2 .LT. 0 ) THEN
+         INFO = -2
+      ELSE IF( N .LT. 0 ) THEN
+         INFO = -3
+      ELSE IF( INCX1 .LT. 1 ) THEN
+         INFO = -5
+      ELSE IF( INCX2 .LT. 1 ) THEN
+         INFO = -7
+      ELSE IF( LDQ1 .LT. MAX( 1, M1 ) ) THEN
+         INFO = -9
+      ELSE IF( LDQ2 .LT. MAX( 1, M2 ) ) THEN
+         INFO = -11
+      ELSE IF( LWORK .LT. N ) THEN
+         INFO = -13
+      END IF
+*
+      IF( INFO .NE. 0 ) THEN
+         CALL XERBLA( 'DORBDB5', -INFO )
+         RETURN
+      END IF
+*
+*     Project X onto the orthogonal complement of Q
+*
+      CALL DORBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2, LDQ2,
+     $              WORK, LWORK, CHILDINFO )
+*
+*     If the projection is nonzero, then return
+*
+      IF( DNRM2(M1,X1,INCX1) .NE. ZERO
+     $    .OR. DNRM2(M2,X2,INCX2) .NE. ZERO ) THEN
+         RETURN
+      END IF
+*
+*     Project each standard basis vector e_1,...,e_M1 in turn, stopping
+*     when a nonzero projection is found
+*
+      DO I = 1, M1
+         DO J = 1, M1
+            X1(J) = ZERO
+         END DO
+         X1(I) = ONE
+         DO J = 1, M2
+            X2(J) = ZERO
+         END DO
+         CALL DORBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
+     $                 LDQ2, WORK, LWORK, CHILDINFO )
+         IF( DNRM2(M1,X1,INCX1) .NE. ZERO
+     $       .OR. DNRM2(M2,X2,INCX2) .NE. ZERO ) THEN
+            RETURN
+         END IF
+      END DO
+*
+*     Project each standard basis vector e_(M1+1),...,e_(M1+M2) in turn,
+*     stopping when a nonzero projection is found
+*
+      DO I = 1, M2
+         DO J = 1, M1
+            X1(J) = ZERO
+         END DO
+         DO J = 1, M2
+            X2(J) = ZERO
+         END DO
+         X2(I) = ONE
+         CALL DORBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
+     $                 LDQ2, WORK, LWORK, CHILDINFO )
+         IF( DNRM2(M1,X1,INCX1) .NE. ZERO
+     $       .OR. DNRM2(M2,X2,INCX2) .NE. ZERO ) THEN
+            RETURN
+         END IF
+      END DO
+*
+      RETURN
+*
+*     End of DORBDB5
+*      
+      END
+

lapack-netlib/SRC/dorbdb6.f

@@ -0,0 +1,312 @@
+*> \brief \b DORBDB6
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DORBDB6 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorbdb6.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorbdb6.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorbdb6.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DORBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
+*                           LDQ2, WORK, LWORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            INCX1, INCX2, INFO, LDQ1, LDQ2, LWORK, M1, M2,
+*      $                   N
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*)
+*       ..
+*  
+* 
+*> \par Purpose:
+*> =============
+*>
+*>\verbatim
+*>
+*> DORBDB6 orthogonalizes the column vector
+*>      X = [ X1 ]
+*>          [ X2 ]
+*> with respect to the columns of
+*>      Q = [ Q1 ] .
+*>          [ Q2 ]
+*> The columns of Q must be orthonormal.
+*>
+*> If the projection is zero according to Kahan's "twice is enough"
+*> criterion, then the zero vector is returned.
+*>
+*>\endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] M1
+*> \verbatim
+*>          M1 is INTEGER
+*>           The dimension of X1 and the number of rows in Q1. 0 <= M1.
+*> \endverbatim
+*>
+*> \param[in] M2
+*> \verbatim
+*>          M2 is INTEGER
+*>           The dimension of X2 and the number of rows in Q2. 0 <= M2.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>           The number of columns in Q1 and Q2. 0 <= N.
+*> \endverbatim
+*>
+*> \param[in,out] X1
+*> \verbatim
+*>          X1 is DOUBLE PRECISION array, dimension (M1)
+*>           On entry, the top part of the vector to be orthogonalized.
+*>           On exit, the top part of the projected vector.
+*> \endverbatim
+*>
+*> \param[in] INCX1
+*> \verbatim
+*>          INCX1 is INTEGER
+*>           Increment for entries of X1.
+*> \endverbatim
+*>
+*> \param[in,out] X2
+*> \verbatim
+*>          X2 is DOUBLE PRECISION array, dimension (M2)
+*>           On entry, the bottom part of the vector to be
+*>           orthogonalized. On exit, the bottom part of the projected
+*>           vector.
+*> \endverbatim
+*>
+*> \param[in] INCX2
+*> \verbatim
+*>          INCX2 is INTEGER
+*>           Increment for entries of X2.
+*> \endverbatim
+*>
+*> \param[in] Q1
+*> \verbatim
+*>          Q1 is DOUBLE PRECISION array, dimension (LDQ1, N)
+*>           The top part of the orthonormal basis matrix.
+*> \endverbatim
+*>
+*> \param[in] LDQ1
+*> \verbatim
+*>          LDQ1 is INTEGER
+*>           The leading dimension of Q1. LDQ1 >= M1.
+*> \endverbatim
+*>
+*> \param[in] Q2
+*> \verbatim
+*>          Q2 is DOUBLE PRECISION array, dimension (LDQ2, N)
+*>           The bottom part of the orthonormal basis matrix.
+*> \endverbatim
+*>
+*> \param[in] LDQ2
+*> \verbatim
+*>          LDQ2 is INTEGER
+*>           The leading dimension of Q2. LDQ2 >= M2.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is DOUBLE PRECISION array, dimension (LWORK)
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>           The dimension of the array WORK. LWORK >= N.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>           = 0:  successful exit.
+*>           < 0:  if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date July 2012
+*
+*> \ingroup doubleOTHERcomputational
+*
+*  =====================================================================
+      SUBROUTINE DORBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
+     $                    LDQ2, WORK, LWORK, INFO )
+*
+*  -- LAPACK computational routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     July 2012
+*
+*     .. Scalar Arguments ..
+      INTEGER            INCX1, INCX2, INFO, LDQ1, LDQ2, LWORK, M1, M2,
+     $                   N
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*)
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ALPHASQ, REALONE, REALZERO
+      PARAMETER          ( ALPHASQ = 0.01D0, REALONE = 1.0D0,
+     $                     REALZERO = 0.0D0 )
+      DOUBLE PRECISION   NEGONE, ONE, ZERO
+      PARAMETER          ( NEGONE = -1.0D0, ONE = 1.0D0, ZERO = 0.0D0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            I
+      DOUBLE PRECISION   NORMSQ1, NORMSQ2, SCL1, SCL2, SSQ1, SSQ2
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DGEMV, DLASSQ, XERBLA
+*     ..
+*     .. Intrinsic Function ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+*     Test input arguments
+*
+      INFO = 0
+      IF( M1 .LT. 0 ) THEN
+         INFO = -1
+      ELSE IF( M2 .LT. 0 ) THEN
+         INFO = -2
+      ELSE IF( N .LT. 0 ) THEN
+         INFO = -3
+      ELSE IF( INCX1 .LT. 1 ) THEN
+         INFO = -5
+      ELSE IF( INCX2 .LT. 1 ) THEN
+         INFO = -7
+      ELSE IF( LDQ1 .LT. MAX( 1, M1 ) ) THEN
+         INFO = -9
+      ELSE IF( LDQ2 .LT. MAX( 1, M2 ) ) THEN
+         INFO = -11
+      ELSE IF( LWORK .LT. N ) THEN
+         INFO = -13
+      END IF
+*
+      IF( INFO .NE. 0 ) THEN
+         CALL XERBLA( 'DORBDB6', -INFO )
+         RETURN
+      END IF
+*
+*     First, project X onto the orthogonal complement of Q's column
+*     space
+*
+      SCL1 = REALZERO
+      SSQ1 = REALONE
+      CALL DLASSQ( M1, X1, INCX1, SCL1, SSQ1 )
+      SCL2 = REALZERO
+      SSQ2 = REALONE
+      CALL DLASSQ( M2, X2, INCX2, SCL2, SSQ2 )
+      NORMSQ1 = SCL1**2*SSQ1 + SCL2**2*SSQ2
+*
+      IF( M1 .EQ. 0 ) THEN
+         DO I = 1, N
+            WORK(I) = ZERO
+         END DO
+      ELSE
+         CALL DGEMV( 'C', M1, N, ONE, Q1, LDQ1, X1, INCX1, ZERO, WORK,
+     $               1 )
+      END IF
+*
+      CALL DGEMV( 'C', M2, N, ONE, Q2, LDQ2, X2, INCX2, ONE, WORK, 1 )
+*
+      CALL DGEMV( 'N', M1, N, NEGONE, Q1, LDQ1, WORK, 1, ONE, X1,
+     $            INCX1 )
+      CALL DGEMV( 'N', M2, N, NEGONE, Q2, LDQ2, WORK, 1, ONE, X2,
+     $            INCX2 )
+*
+      SCL1 = REALZERO
+      SSQ1 = REALONE
+      CALL DLASSQ( M1, X1, INCX1, SCL1, SSQ1 )
+      SCL2 = REALZERO
+      SSQ2 = REALONE
+      CALL DLASSQ( M2, X2, INCX2, SCL2, SSQ2 )
+      NORMSQ2 = SCL1**2*SSQ1 + SCL2**2*SSQ2
+*
+*     If projection is sufficiently large in norm, then stop.
+*     If projection is zero, then stop.
+*     Otherwise, project again.
+*
+      IF( NORMSQ2 .GE. ALPHASQ*NORMSQ1 ) THEN
+         RETURN
+      END IF
+*
+      IF( NORMSQ2 .EQ. ZERO ) THEN
+         RETURN
+      END IF
+*      
+      NORMSQ1 = NORMSQ2
+*
+      DO I = 1, N
+         WORK(I) = ZERO
+      END DO
+*
+      IF( M1 .EQ. 0 ) THEN
+         DO I = 1, N
+            WORK(I) = ZERO
+         END DO
+      ELSE
+         CALL DGEMV( 'C', M1, N, ONE, Q1, LDQ1, X1, INCX1, ZERO, WORK,
+     $               1 )
+      END IF
+*
+      CALL DGEMV( 'C', M2, N, ONE, Q2, LDQ2, X2, INCX2, ONE, WORK, 1 )
+*
+      CALL DGEMV( 'N', M1, N, NEGONE, Q1, LDQ1, WORK, 1, ONE, X1,
+     $            INCX1 )
+      CALL DGEMV( 'N', M2, N, NEGONE, Q2, LDQ2, WORK, 1, ONE, X2,
+     $            INCX2 )
+*
+      SCL1 = REALZERO
+      SSQ1 = REALONE
+      CALL DLASSQ( M1, X1, INCX1, SCL1, SSQ1 )
+      SCL2 = REALZERO
+      SSQ2 = REALONE
+      CALL DLASSQ( M1, X1, INCX1, SCL1, SSQ1 )
+      NORMSQ2 = SCL1**2*SSQ1 + SCL2**2*SSQ2
+*
+*     If second projection is sufficiently large in norm, then do
+*     nothing more. Alternatively, if it shrunk significantly, then
+*     truncate it to zero.
+*
+      IF( NORMSQ2 .LT. ALPHASQ*NORMSQ1 ) THEN
+         DO I = 1, M1
+            X1(I) = ZERO
+         END DO
+         DO I = 1, M2
+            X2(I) = ZERO
+         END DO
+      END IF
+*
+      RETURN
+*      
+*     End of DORBDB6
+*
+      END
+

lapack-netlib/SRC/dorcsd.f

@@ -289,7 +289,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date November 2011
+*> \date November 2013
 *
 *> \ingroup doubleOTHERcomputational
 *
@@ -300,10 +300,10 @@
      $                             U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
      $                             LDV2T, WORK, LWORK, IWORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2011
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS
@@ -368,9 +368,22 @@
          INFO = -8
       ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN
          INFO = -9
-      ELSE IF( ( COLMAJOR .AND. LDX11 .LT. MAX(1,P) ) .OR.
-     $         ( .NOT.COLMAJOR .AND. LDX11 .LT. MAX(1,Q) ) ) THEN
-         INFO = -11
+      ELSE IF ( COLMAJOR .AND.  LDX11 .LT. MAX( 1, P ) ) THEN
+        INFO = -11
+      ELSE IF (.NOT. COLMAJOR .AND. LDX11 .LT. MAX( 1, Q ) ) THEN
+        INFO = -11
+      ELSE IF (COLMAJOR .AND. LDX12 .LT. MAX( 1, P ) ) THEN
+        INFO = -13
+      ELSE IF (.NOT. COLMAJOR .AND. LDX12 .LT. MAX( 1, M-Q ) ) THEN
+        INFO = -13
+      ELSE IF (COLMAJOR .AND. LDX21 .LT. MAX( 1, M-P ) ) THEN
+        INFO = -15
+      ELSE IF (.NOT. COLMAJOR .AND. LDX21 .LT. MAX( 1, Q ) ) THEN
+        INFO = -15
+      ELSE IF (COLMAJOR .AND. LDX22 .LT. MAX( 1, M-P ) ) THEN
+        INFO = -17
+      ELSE IF (.NOT. COLMAJOR .AND. LDX22 .LT. MAX( 1, M-Q ) ) THEN
+        INFO = -17
       ELSE IF( WANTU1 .AND. LDU1 .LT. P ) THEN
          INFO = -20
       ELSE IF( WANTU2 .AND. LDU2 .LT. M-P ) THEN
@@ -427,19 +440,19 @@
          ITAUQ1 = ITAUP2 + MAX( 1, M - P )
          ITAUQ2 = ITAUQ1 + MAX( 1, Q )
          IORGQR = ITAUQ2 + MAX( 1, M - Q )
-         CALL DORGQR( M-Q, M-Q, M-Q, 0, MAX(1,M-Q), 0, WORK, -1,
+         CALL DORGQR( M-Q, M-Q, M-Q, U1, MAX(1,M-Q), U1, WORK, -1,
      $                CHILDINFO )
          LORGQRWORKOPT = INT( WORK(1) )
          LORGQRWORKMIN = MAX( 1, M - Q )
          IORGLQ = ITAUQ2 + MAX( 1, M - Q )
-         CALL DORGLQ( M-Q, M-Q, M-Q, 0, MAX(1,M-Q), 0, WORK, -1,
+         CALL DORGLQ( M-Q, M-Q, M-Q, U1, MAX(1,M-Q), U1, WORK, -1,
      $                CHILDINFO )
          LORGLQWORKOPT = INT( WORK(1) )
          LORGLQWORKMIN = MAX( 1, M - Q )
          IORBDB = ITAUQ2 + MAX( 1, M - Q )
          CALL DORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
-     $                X21, LDX21, X22, LDX22, 0, 0, 0, 0, 0, 0, WORK,
-     $                -1, CHILDINFO )
+     $                X21, LDX21, X22, LDX22, THETA, V1T, U1, U2, V1T,
+     $                V2T, WORK, -1, CHILDINFO )
          LORBDBWORKOPT = INT( WORK(1) )
          LORBDBWORKMIN = LORBDBWORKOPT
          IB11D = ITAUQ2 + MAX( 1, M - Q )
@@ -451,9 +464,10 @@
          IB22D = IB21E + MAX( 1, Q - 1 )
          IB22E = IB22D + MAX( 1, Q )
          IBBCSD = IB22E + MAX( 1, Q - 1 )
-         CALL DBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, 0,
-     $                0, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, 0,
-     $                0, 0, 0, 0, 0, 0, 0, WORK, -1, CHILDINFO )
+         CALL DBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, 
+     $                THETA, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
+     $                LDV2T, U1, U1, U1, U1, U1, U1, U1, U1, WORK, -1,
+     $                CHILDINFO )
          LBBCSDWORKOPT = INT( WORK(1) )
          LBBCSDWORKMIN = LBBCSDWORKOPT
          LWORKOPT = MAX( IORGQR + LORGQRWORKOPT, IORGLQ + LORGLQWORKOPT,
@@ -514,10 +528,14 @@
          END IF
          IF( WANTV2T .AND. M-Q .GT. 0 ) THEN
             CALL DLACPY( 'U', P, M-Q, X12, LDX12, V2T, LDV2T )
-            CALL DLACPY( 'U', M-P-Q, M-P-Q, X22(Q+1,P+1), LDX22,
-     $                   V2T(P+1,P+1), LDV2T )
-            CALL DORGLQ( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2),
-     $                   WORK(IORGLQ), LORGLQWORK, INFO )
+            IF (M-P .GT. Q) Then
+               CALL DLACPY( 'U', M-P-Q, M-P-Q, X22(Q+1,P+1), LDX22,
+     $                      V2T(P+1,P+1), LDV2T )
+            END IF
+            IF (M .GT. Q) THEN
+               CALL DORGLQ( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2),
+     $                      WORK(IORGLQ), LORGLQWORK, INFO )
+            END IF
          END IF
       ELSE
          IF( WANTU1 .AND. P .GT. 0 ) THEN

lapack-netlib/SRC/dorcsd2by1.f

@@ -0,0 +1,715 @@
+*> \brief \b DORCSD2BY1
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DORCSD2BY1 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorcsd2by1.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorcsd2by1.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorcsd2by1.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DORCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11,
+*                              X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T,
+*                              LDV1T, WORK, LWORK, IWORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          JOBU1, JOBU2, JOBV1T
+*       INTEGER            INFO, LDU1, LDU2, LDV1T, LWORK, LDX11, LDX21,
+*      $                   M, P, Q
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   THETA(*)
+*       DOUBLE PRECISION   U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), WORK(*),
+*      $                   X11(LDX11,*), X21(LDX21,*)
+*       INTEGER            IWORK(*)
+*       ..
+*    
+* 
+*> \par Purpose:
+*> =============
+*>
+*>\verbatim
+*> Purpose:
+*> ========
+*>
+*> DORCSD2BY1 computes the CS decomposition of an M-by-Q matrix X with
+*> orthonormal columns that has been partitioned into a 2-by-1 block
+*> structure:
+*>
+*>                                [  I  0  0 ]
+*>                                [  0  C  0 ]
+*>          [ X11 ]   [ U1 |    ] [  0  0  0 ]
+*>      X = [-----] = [---------] [----------] V1**T .
+*>          [ X21 ]   [    | U2 ] [  0  0  0 ]
+*>                                [  0  S  0 ]
+*>                                [  0  0  I ]
+*> 
+*> X11 is P-by-Q. The orthogonal matrices U1, U2, V1, and V2 are P-by-P,
+*> (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are
+*> R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in
+*> which R = MIN(P,M-P,Q,M-Q).
+*>
+*>\endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] JOBU1
+*> \verbatim
+*>          JOBU1 is CHARACTER
+*>           = 'Y':      U1 is computed;
+*>           otherwise:  U1 is not computed.
+*> \endverbatim
+*>
+*> \param[in] JOBU2
+*> \verbatim
+*>          JOBU2 is CHARACTER
+*>           = 'Y':      U2 is computed;
+*>           otherwise:  U2 is not computed.
+*> \endverbatim
+*>
+*> \param[in] JOBV1T
+*> \verbatim
+*>          JOBV1T is CHARACTER
+*>           = 'Y':      V1T is computed;
+*>           otherwise:  V1T is not computed.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>           The number of rows and columns in X.
+*> \endverbatim
+*>
+*> \param[in] P
+*> \verbatim
+*>          P is INTEGER
+*>           The number of rows in X11 and X12. 0 <= P <= M.
+*> \endverbatim
+*>
+*> \param[in] Q
+*> \verbatim
+*>          Q is INTEGER
+*>           The number of columns in X11 and X21. 0 <= Q <= M.
+*> \endverbatim
+*>
+*> \param[in,out] X11
+*> \verbatim
+*>          X11 is DOUBLE PRECISION array, dimension (LDX11,Q)
+*>           On entry, part of the orthogonal matrix whose CSD is
+*>           desired.
+*> \endverbatim
+*>
+*> \param[in] LDX11
+*> \verbatim
+*>          LDX11 is INTEGER
+*>           The leading dimension of X11. LDX11 >= MAX(1,P).
+*> \endverbatim
+*>
+*> \param[in,out] X21
+*> \verbatim
+*>          X21 is DOUBLE PRECISION array, dimension (LDX21,Q)
+*>           On entry, part of the orthogonal matrix whose CSD is
+*>           desired.
+*> \endverbatim
+*>
+*> \param[in] LDX21
+*> \verbatim
+*>          LDX21 is INTEGER
+*>           The leading dimension of X21. LDX21 >= MAX(1,M-P).
+*> \endverbatim
+*>
+*> \param[out] THETA
+*> \verbatim
+*>          THETA is DOUBLE PRECISION array, dimension (R), in which R =
+*>           MIN(P,M-P,Q,M-Q).
+*>           C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and
+*>           S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ).
+*> \endverbatim
+*>
+*> \param[out] U1
+*> \verbatim
+*>          U1 is DOUBLE PRECISION array, dimension (P)
+*>           If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1.
+*> \endverbatim
+*>
+*> \param[in] LDU1
+*> \verbatim
+*>          LDU1 is INTEGER
+*>           The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
+*>           MAX(1,P).
+*> \endverbatim
+*>
+*> \param[out] U2
+*> \verbatim
+*>          U2 is DOUBLE PRECISION array, dimension (M-P)
+*>           If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal
+*>           matrix U2.
+*> \endverbatim
+*>
+*> \param[in] LDU2
+*> \verbatim
+*>          LDU2 is INTEGER
+*>           The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=
+*>           MAX(1,M-P).
+*> \endverbatim
+*>
+*> \param[out] V1T
+*> \verbatim
+*>          V1T is DOUBLE PRECISION array, dimension (Q)
+*>           If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal
+*>           matrix V1**T.
+*> \endverbatim
+*>
+*> \param[in] LDV1T
+*> \verbatim
+*>          LDV1T is INTEGER
+*>           The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
+*>           MAX(1,Q).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
+*>           On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*>           If INFO > 0 on exit, WORK(2:R) contains the values PHI(1),
+*>           ..., PHI(R-1) that, together with THETA(1), ..., THETA(R),
+*>           define the matrix in intermediate bidiagonal-block form
+*>           remaining after nonconvergence. INFO specifies the number
+*>           of nonzero PHI's.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>           The dimension of the array WORK.
+*> \endverbatim
+*>
+*>           If LWORK = -1, then a workspace query is assumed; the routine
+*>           only calculates the optimal size of the WORK array, returns
+*>           this value as the first entry of the work array, and no error
+*>           message related to LWORK is issued by XERBLA.
+*> \param[out] IWORK
+*> \verbatim
+*>          IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>           = 0:  successful exit.
+*>           < 0:  if INFO = -i, the i-th argument had an illegal value.
+*>           > 0:  DBBCSD did not converge. See the description of WORK
+*>                above for details.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date July 2012
+*
+*> \ingroup doubleOTHERcomputational
+*
+*> \par References:
+*  ================
+*>
+*>  [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
+*>      Algorithms, 50(1):33-65, 2009.
+*> \endverbatim
+*>
+*  =====================================================================
+      SUBROUTINE DORCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11,
+     $                       X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T,
+     $                       LDV1T, WORK, LWORK, IWORK, INFO )
+*
+*  -- LAPACK computational routine (3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     July 2012
+*
+*     .. Scalar Arguments ..
+      CHARACTER          JOBU1, JOBU2, JOBV1T
+      INTEGER            INFO, LDU1, LDU2, LDV1T, LWORK, LDX11, LDX21,
+     $                   M, P, Q
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   THETA(*)
+      DOUBLE PRECISION   U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), WORK(*),
+     $                   X11(LDX11,*), X21(LDX21,*)
+      INTEGER            IWORK(*)
+*     ..
+*  
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ONE, ZERO
+      PARAMETER          ( ONE = 1.0D0, ZERO = 0.0D0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            CHILDINFO, I, IB11D, IB11E, IB12D, IB12E,
+     $                   IB21D, IB21E, IB22D, IB22E, IBBCSD, IORBDB,
+     $                   IORGLQ, IORGQR, IPHI, ITAUP1, ITAUP2, ITAUQ1,
+     $                   J, LBBCSD, LORBDB, LORGLQ, LORGLQMIN,
+     $                   LORGLQOPT, LORGQR, LORGQRMIN, LORGQROPT,
+     $                   LWORKMIN, LWORKOPT, R
+      LOGICAL            LQUERY, WANTU1, WANTU2, WANTV1T
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DBBCSD, DCOPY, DLACPY, DLAPMR, DLAPMT, DORBDB1,
+     $                   DORBDB2, DORBDB3, DORBDB4, DORGLQ, DORGQR,
+     $                   XERBLA
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      EXTERNAL           LSAME
+*     ..
+*     .. Intrinsic Function ..
+      INTRINSIC          INT, MAX, MIN
+*     ..
+*     .. Executable Statements ..
+*
+*     Test input arguments
+*
+      INFO = 0
+      WANTU1 = LSAME( JOBU1, 'Y' )
+      WANTU2 = LSAME( JOBU2, 'Y' )
+      WANTV1T = LSAME( JOBV1T, 'Y' )
+      LQUERY = LWORK .EQ. -1
+*
+      IF( M .LT. 0 ) THEN
+         INFO = -4
+      ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN
+         INFO = -5
+      ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN
+         INFO = -6
+      ELSE IF( LDX11 .LT. MAX( 1, P ) ) THEN
+         INFO = -8
+      ELSE IF( LDX21 .LT. MAX( 1, M-P ) ) THEN
+         INFO = -10
+      ELSE IF( WANTU1 .AND. LDU1 .LT. P ) THEN
+         INFO = -13
+      ELSE IF( WANTU2 .AND. LDU2 .LT. M - P ) THEN
+         INFO = -15
+      ELSE IF( WANTV1T .AND. LDV1T .LT. Q ) THEN
+         INFO = -17
+      END IF
+*
+      R = MIN( P, M-P, Q, M-Q )
+*
+*     Compute workspace
+*
+*       WORK layout:
+*     |-------------------------------------------------------|
+*     | LWORKOPT (1)                                          |
+*     |-------------------------------------------------------|
+*     | PHI (MAX(1,R-1))                                      |
+*     |-------------------------------------------------------|
+*     | TAUP1 (MAX(1,P))                        | B11D (R)    |
+*     | TAUP2 (MAX(1,M-P))                      | B11E (R-1)  |
+*     | TAUQ1 (MAX(1,Q))                        | B12D (R)    |
+*     |-----------------------------------------| B12E (R-1)  |
+*     | DORBDB WORK | DORGQR WORK | DORGLQ WORK | B21D (R)    |
+*     |             |             |             | B21E (R-1)  |
+*     |             |             |             | B22D (R)    |
+*     |             |             |             | B22E (R-1)  |
+*     |             |             |             | DBBCSD WORK |
+*     |-------------------------------------------------------|
+*
+      IF( INFO .EQ. 0 ) THEN
+         IPHI = 2
+         IB11D = IPHI + MAX( 1, R-1 )
+         IB11E = IB11D + MAX( 1, R )
+         IB12D = IB11E + MAX( 1, R - 1 )
+         IB12E = IB12D + MAX( 1, R )
+         IB21D = IB12E + MAX( 1, R - 1 )
+         IB21E = IB21D + MAX( 1, R )
+         IB22D = IB21E + MAX( 1, R - 1 )
+         IB22E = IB22D + MAX( 1, R )
+         IBBCSD = IB22E + MAX( 1, R - 1 )
+         ITAUP1 = IPHI + MAX( 1, R-1 )
+         ITAUP2 = ITAUP1 + MAX( 1, P )
+         ITAUQ1 = ITAUP2 + MAX( 1, M-P )
+         IORBDB = ITAUQ1 + MAX( 1, Q )
+         IORGQR = ITAUQ1 + MAX( 1, Q )
+         IORGLQ = ITAUQ1 + MAX( 1, Q )
+         IF( R .EQ. Q ) THEN
+            CALL DORBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0,
+     $                    0, 0, WORK, -1, CHILDINFO )
+            LORBDB = INT( WORK(1) )
+            IF( P .GE. M-P ) THEN
+               CALL DORGQR( P, P, Q, U1, LDU1, 0, WORK(1), -1,
+     $                      CHILDINFO )
+               LORGQRMIN = MAX( 1, P )
+               LORGQROPT = INT( WORK(1) )
+            ELSE
+               CALL DORGQR( M-P, M-P, Q, U2, LDU2, 0, WORK(1), -1,
+     $                      CHILDINFO )
+               LORGQRMIN = MAX( 1, M-P )
+               LORGQROPT = INT( WORK(1) )
+            END IF
+            CALL DORGLQ( MAX(0,Q-1), MAX(0,Q-1), MAX(0,Q-1), V1T, LDV1T,
+     $                   0, WORK(1), -1, CHILDINFO )
+            LORGLQMIN = MAX( 1, Q-1 )
+            LORGLQOPT = INT( WORK(1) )
+            CALL DBBCSD( JOBU1, JOBU2, JOBV1T, 'N', 'N', M, P, Q, THETA,
+     $                   0, U1, LDU1, U2, LDU2, V1T, LDV1T, 0, 1, 0, 0,
+     $                   0, 0, 0, 0, 0, 0, WORK(1), -1, CHILDINFO )
+            LBBCSD = INT( WORK(1) )
+         ELSE IF( R .EQ. P ) THEN
+            CALL DORBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0,
+     $                    0, 0, WORK(1), -1, CHILDINFO )
+            LORBDB = INT( WORK(1) )
+            IF( P-1 .GE. M-P ) THEN
+               CALL DORGQR( P-1, P-1, P-1, U1(2,2), LDU1, 0, WORK(1),
+     $                      -1, CHILDINFO )
+               LORGQRMIN = MAX( 1, P-1 )
+               LORGQROPT = INT( WORK(1) )
+            ELSE
+               CALL DORGQR( M-P, M-P, Q, U2, LDU2, 0, WORK(1), -1,
+     $                      CHILDINFO )
+               LORGQRMIN = MAX( 1, M-P )
+               LORGQROPT = INT( WORK(1) )
+            END IF
+            CALL DORGLQ( Q, Q, R, V1T, LDV1T, 0, WORK(1), -1,
+     $                   CHILDINFO )
+            LORGLQMIN = MAX( 1, Q )
+            LORGLQOPT = INT( WORK(1) )
+            CALL DBBCSD( JOBV1T, 'N', JOBU1, JOBU2, 'T', M, Q, P, THETA,
+     $                   0, V1T, LDV1T, 0, 1, U1, LDU1, U2, LDU2, 0, 0,
+     $                   0, 0, 0, 0, 0, 0, WORK(1), -1, CHILDINFO )
+            LBBCSD = INT( WORK(1) )
+         ELSE IF( R .EQ. M-P ) THEN
+            CALL DORBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0,
+     $                    0, 0, WORK(1), -1, CHILDINFO )
+            LORBDB = INT( WORK(1) )
+            IF( P .GE. M-P-1 ) THEN
+               CALL DORGQR( P, P, Q, U1, LDU1, 0, WORK(1), -1,
+     $                      CHILDINFO )
+               LORGQRMIN = MAX( 1, P )
+               LORGQROPT = INT( WORK(1) )
+            ELSE
+               CALL DORGQR( M-P-1, M-P-1, M-P-1, U2(2,2), LDU2, 0,
+     $                      WORK(1), -1, CHILDINFO )
+               LORGQRMIN = MAX( 1, M-P-1 )
+               LORGQROPT = INT( WORK(1) )
+            END IF
+            CALL DORGLQ( Q, Q, R, V1T, LDV1T, 0, WORK(1), -1,
+     $                   CHILDINFO )
+            LORGLQMIN = MAX( 1, Q )
+            LORGLQOPT = INT( WORK(1) )
+            CALL DBBCSD( 'N', JOBV1T, JOBU2, JOBU1, 'T', M, M-Q, M-P,
+     $                   THETA, 0, 0, 1, V1T, LDV1T, U2, LDU2, U1, LDU1,
+     $                   0, 0, 0, 0, 0, 0, 0, 0, WORK(1), -1,
+     $                   CHILDINFO )
+            LBBCSD = INT( WORK(1) )
+         ELSE
+            CALL DORBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0,
+     $                    0, 0, 0, WORK(1), -1, CHILDINFO )
+            LORBDB = M + INT( WORK(1) )
+            IF( P .GE. M-P ) THEN
+               CALL DORGQR( P, P, M-Q, U1, LDU1, 0, WORK(1), -1,
+     $                      CHILDINFO )
+               LORGQRMIN = MAX( 1, P )
+               LORGQROPT = INT( WORK(1) )
+            ELSE
+               CALL DORGQR( M-P, M-P, M-Q, U2, LDU2, 0, WORK(1), -1,
+     $                      CHILDINFO )
+               LORGQRMIN = MAX( 1, M-P )
+               LORGQROPT = INT( WORK(1) )
+            END IF
+            CALL DORGLQ( Q, Q, Q, V1T, LDV1T, 0, WORK(1), -1,
+     $                   CHILDINFO )
+            LORGLQMIN = MAX( 1, Q )
+            LORGLQOPT = INT( WORK(1) )
+            CALL DBBCSD( JOBU2, JOBU1, 'N', JOBV1T, 'N', M, M-P, M-Q,
+     $                   THETA, 0, U2, LDU2, U1, LDU1, 0, 1, V1T, LDV1T,
+     $                   0, 0, 0, 0, 0, 0, 0, 0, WORK(1), -1,
+     $                   CHILDINFO )
+            LBBCSD = INT( WORK(1) )
+         END IF
+         LWORKMIN = MAX( IORBDB+LORBDB-1,
+     $                   IORGQR+LORGQRMIN-1,
+     $                   IORGLQ+LORGLQMIN-1,
+     $                   IBBCSD+LBBCSD-1 )
+         LWORKOPT = MAX( IORBDB+LORBDB-1,
+     $                   IORGQR+LORGQROPT-1,
+     $                   IORGLQ+LORGLQOPT-1,
+     $                   IBBCSD+LBBCSD-1 )
+         WORK(1) = LWORKOPT
+         IF( LWORK .LT. LWORKMIN .AND. .NOT.LQUERY ) THEN
+            INFO = -19
+         END IF
+      END IF
+      IF( INFO .NE. 0 ) THEN
+         CALL XERBLA( 'DORCSD2BY1', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+      LORGQR = LWORK-IORGQR+1
+      LORGLQ = LWORK-IORGLQ+1
+*
+*     Handle four cases separately: R = Q, R = P, R = M-P, and R = M-Q,
+*     in which R = MIN(P,M-P,Q,M-Q)
+*
+      IF( R .EQ. Q ) THEN
+*
+*        Case 1: R = Q
+*
+*        Simultaneously bidiagonalize X11 and X21
+*
+         CALL DORBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA,
+     $                 WORK(IPHI), WORK(ITAUP1), WORK(ITAUP2),
+     $                 WORK(ITAUQ1), WORK(IORBDB), LORBDB, CHILDINFO )
+*
+*        Accumulate Householder reflectors
+*
+         IF( WANTU1 .AND. P .GT. 0 ) THEN
+            CALL DLACPY( 'L', P, Q, X11, LDX11, U1, LDU1 )
+            CALL DORGQR( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGQR),
+     $                   LORGQR, CHILDINFO )
+         END IF
+         IF( WANTU2 .AND. M-P .GT. 0 ) THEN
+            CALL DLACPY( 'L', M-P, Q, X21, LDX21, U2, LDU2 )
+            CALL DORGQR( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2),
+     $                   WORK(IORGQR), LORGQR, CHILDINFO )
+         END IF
+         IF( WANTV1T .AND. Q .GT. 0 ) THEN
+            V1T(1,1) = ONE
+            DO J = 2, Q
+               V1T(1,J) = ZERO
+               V1T(J,1) = ZERO
+            END DO
+            CALL DLACPY( 'U', Q-1, Q-1, X21(1,2), LDX21, V1T(2,2),
+     $                   LDV1T )
+            CALL DORGLQ( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1),
+     $                   WORK(IORGLQ), LORGLQ, CHILDINFO )
+         END IF
+*   
+*        Simultaneously diagonalize X11 and X21.
+*   
+         CALL DBBCSD( JOBU1, JOBU2, JOBV1T, 'N', 'N', M, P, Q, THETA,
+     $                WORK(IPHI), U1, LDU1, U2, LDU2, V1T, LDV1T, 0, 1,
+     $                WORK(IB11D), WORK(IB11E), WORK(IB12D),
+     $                WORK(IB12E), WORK(IB21D), WORK(IB21E),
+     $                WORK(IB22D), WORK(IB22E), WORK(IBBCSD), LBBCSD,
+     $                CHILDINFO )
+*   
+*        Permute rows and columns to place zero submatrices in
+*        preferred positions
+*
+         IF( Q .GT. 0 .AND. WANTU2 ) THEN
+            DO I = 1, Q
+               IWORK(I) = M - P - Q + I
+            END DO
+            DO I = Q + 1, M - P
+               IWORK(I) = I - Q
+            END DO
+            CALL DLAPMT( .FALSE., M-P, M-P, U2, LDU2, IWORK )
+         END IF
+      ELSE IF( R .EQ. P ) THEN
+*
+*        Case 2: R = P
+*
+*        Simultaneously bidiagonalize X11 and X21
+*
+         CALL DORBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA,
+     $                 WORK(IPHI), WORK(ITAUP1), WORK(ITAUP2),
+     $                 WORK(ITAUQ1), WORK(IORBDB), LORBDB, CHILDINFO )
+*
+*        Accumulate Householder reflectors
+*
+         IF( WANTU1 .AND. P .GT. 0 ) THEN
+            U1(1,1) = ONE
+            DO J = 2, P
+               U1(1,J) = ZERO
+               U1(J,1) = ZERO
+            END DO
+            CALL DLACPY( 'L', P-1, P-1, X11(2,1), LDX11, U1(2,2), LDU1 )
+            CALL DORGQR( P-1, P-1, P-1, U1(2,2), LDU1, WORK(ITAUP1),
+     $                   WORK(IORGQR), LORGQR, CHILDINFO )
+         END IF
+         IF( WANTU2 .AND. M-P .GT. 0 ) THEN
+            CALL DLACPY( 'L', M-P, Q, X21, LDX21, U2, LDU2 )
+            CALL DORGQR( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2),
+     $                   WORK(IORGQR), LORGQR, CHILDINFO )
+         END IF
+         IF( WANTV1T .AND. Q .GT. 0 ) THEN
+            CALL DLACPY( 'U', P, Q, X11, LDX11, V1T, LDV1T )
+            CALL DORGLQ( Q, Q, R, V1T, LDV1T, WORK(ITAUQ1),
+     $                   WORK(IORGLQ), LORGLQ, CHILDINFO )
+         END IF
+*   
+*        Simultaneously diagonalize X11 and X21.
+*   
+         CALL DBBCSD( JOBV1T, 'N', JOBU1, JOBU2, 'T', M, Q, P, THETA,
+     $                WORK(IPHI), V1T, LDV1T, 0, 1, U1, LDU1, U2, LDU2,
+     $                WORK(IB11D), WORK(IB11E), WORK(IB12D),
+     $                WORK(IB12E), WORK(IB21D), WORK(IB21E),
+     $                WORK(IB22D), WORK(IB22E), WORK(IBBCSD), LBBCSD,
+     $                CHILDINFO )
+*   
+*        Permute rows and columns to place identity submatrices in
+*        preferred positions
+*
+         IF( Q .GT. 0 .AND. WANTU2 ) THEN
+            DO I = 1, Q
+               IWORK(I) = M - P - Q + I
+            END DO
+            DO I = Q + 1, M - P
+               IWORK(I) = I - Q
+            END DO
+            CALL DLAPMT( .FALSE., M-P, M-P, U2, LDU2, IWORK )
+         END IF
+      ELSE IF( R .EQ. M-P ) THEN
+*
+*        Case 3: R = M-P
+*
+*        Simultaneously bidiagonalize X11 and X21
+*
+         CALL DORBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA,
+     $                 WORK(IPHI), WORK(ITAUP1), WORK(ITAUP2),
+     $                 WORK(ITAUQ1), WORK(IORBDB), LORBDB, CHILDINFO )
+*
+*        Accumulate Householder reflectors
+*
+         IF( WANTU1 .AND. P .GT. 0 ) THEN
+            CALL DLACPY( 'L', P, Q, X11, LDX11, U1, LDU1 )
+            CALL DORGQR( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGQR),
+     $                   LORGQR, CHILDINFO )
+         END IF
+         IF( WANTU2 .AND. M-P .GT. 0 ) THEN
+            U2(1,1) = ONE
+            DO J = 2, M-P
+               U2(1,J) = ZERO
+               U2(J,1) = ZERO
+            END DO
+            CALL DLACPY( 'L', M-P-1, M-P-1, X21(2,1), LDX21, U2(2,2),
+     $                   LDU2 )
+            CALL DORGQR( M-P-1, M-P-1, M-P-1, U2(2,2), LDU2,
+     $                   WORK(ITAUP2), WORK(IORGQR), LORGQR, CHILDINFO )
+         END IF
+         IF( WANTV1T .AND. Q .GT. 0 ) THEN
+            CALL DLACPY( 'U', M-P, Q, X21, LDX21, V1T, LDV1T )
+            CALL DORGLQ( Q, Q, R, V1T, LDV1T, WORK(ITAUQ1),
+     $                   WORK(IORGLQ), LORGLQ, CHILDINFO )
+         END IF
+*   
+*        Simultaneously diagonalize X11 and X21.
+*   
+         CALL DBBCSD( 'N', JOBV1T, JOBU2, JOBU1, 'T', M, M-Q, M-P,
+     $                THETA, WORK(IPHI), 0, 1, V1T, LDV1T, U2, LDU2, U1,
+     $                LDU1, WORK(IB11D), WORK(IB11E), WORK(IB12D),
+     $                WORK(IB12E), WORK(IB21D), WORK(IB21E),
+     $                WORK(IB22D), WORK(IB22E), WORK(IBBCSD), LBBCSD,
+     $                CHILDINFO )
+*   
+*        Permute rows and columns to place identity submatrices in
+*        preferred positions
+*
+         IF( Q .GT. R ) THEN
+            DO I = 1, R
+               IWORK(I) = Q - R + I
+            END DO
+            DO I = R + 1, Q
+               IWORK(I) = I - R
+            END DO
+            IF( WANTU1 ) THEN
+               CALL DLAPMT( .FALSE., P, Q, U1, LDU1, IWORK )
+            END IF
+            IF( WANTV1T ) THEN
+               CALL DLAPMR( .FALSE., Q, Q, V1T, LDV1T, IWORK )
+            END IF
+         END IF
+      ELSE
+*
+*        Case 4: R = M-Q
+*
+*        Simultaneously bidiagonalize X11 and X21
+*
+         CALL DORBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA,
+     $                 WORK(IPHI), WORK(ITAUP1), WORK(ITAUP2),
+     $                 WORK(ITAUQ1), WORK(IORBDB), WORK(IORBDB+M),
+     $                 LORBDB-M, CHILDINFO )
+*
+*        Accumulate Householder reflectors
+*
+         IF( WANTU1 .AND. P .GT. 0 ) THEN
+            CALL DCOPY( P, WORK(IORBDB), 1, U1, 1 )
+            DO J = 2, P
+               U1(1,J) = ZERO
+            END DO
+            CALL DLACPY( 'L', P-1, M-Q-1, X11(2,1), LDX11, U1(2,2),
+     $                   LDU1 )
+            CALL DORGQR( P, P, M-Q, U1, LDU1, WORK(ITAUP1),
+     $                   WORK(IORGQR), LORGQR, CHILDINFO )
+         END IF
+         IF( WANTU2 .AND. M-P .GT. 0 ) THEN
+            CALL DCOPY( M-P, WORK(IORBDB+P), 1, U2, 1 )
+            DO J = 2, M-P
+               U2(1,J) = ZERO
+            END DO
+            CALL DLACPY( 'L', M-P-1, M-Q-1, X21(2,1), LDX21, U2(2,2),
+     $                   LDU2 )
+            CALL DORGQR( M-P, M-P, M-Q, U2, LDU2, WORK(ITAUP2),
+     $                   WORK(IORGQR), LORGQR, CHILDINFO )
+         END IF
+         IF( WANTV1T .AND. Q .GT. 0 ) THEN
+            CALL DLACPY( 'U', M-Q, Q, X21, LDX21, V1T, LDV1T )
+            CALL DLACPY( 'U', P-(M-Q), Q-(M-Q), X11(M-Q+1,M-Q+1), LDX11,
+     $                   V1T(M-Q+1,M-Q+1), LDV1T )
+            CALL DLACPY( 'U', -P+Q, Q-P, X21(M-Q+1,P+1), LDX21,
+     $                   V1T(P+1,P+1), LDV1T )
+            CALL DORGLQ( Q, Q, Q, V1T, LDV1T, WORK(ITAUQ1),
+     $                   WORK(IORGLQ), LORGLQ, CHILDINFO )
+         END IF
+*   
+*        Simultaneously diagonalize X11 and X21.
+*   
+         CALL DBBCSD( JOBU2, JOBU1, 'N', JOBV1T, 'N', M, M-P, M-Q,
+     $                THETA, WORK(IPHI), U2, LDU2, U1, LDU1, 0, 1, V1T,
+     $                LDV1T, WORK(IB11D), WORK(IB11E), WORK(IB12D),
+     $                WORK(IB12E), WORK(IB21D), WORK(IB21E),
+     $                WORK(IB22D), WORK(IB22E), WORK(IBBCSD), LBBCSD,
+     $                CHILDINFO )
+*   
+*        Permute rows and columns to place identity submatrices in
+*        preferred positions
+*
+         IF( P .GT. R ) THEN
+            DO I = 1, R
+               IWORK(I) = P - R + I
+            END DO
+            DO I = R + 1, P
+               IWORK(I) = I - R
+            END DO
+            IF( WANTU1 ) THEN
+               CALL DLAPMT( .FALSE., P, P, U1, LDU1, IWORK )
+            END IF
+            IF( WANTV1T ) THEN
+               CALL DLAPMR( .FALSE., P, Q, V1T, LDV1T, IWORK )
+            END IF
+         END IF
+      END IF
+*
+      RETURN
+*
+*     End of DORCSD2BY1
+*
+      END
+

lapack-netlib/SRC/dstemr.f

@@ -294,7 +294,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date September 2012
+*> \date November 2013
 *
 *> \ingroup doubleOTHERcomputational
 *
@@ -312,10 +312,10 @@
      $                   M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK,
      $                   IWORK, LIWORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.2) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     September 2012
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBZ, RANGE
@@ -391,6 +391,7 @@
       WU = ZERO
       IIL = 0
       IIU = 0
+      NSPLIT = 0
 
       IF( VALEIG ) THEN
 *        We do not reference VL, VU in the cases RANGE = 'I','A'

lapack-netlib/SRC/dsycon_rook.f

@@ -0,0 +1,258 @@
+*> \brief \b DSYCON_ROOK
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DSYCON_ROOK + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsycon_rook.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsycon_rook.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsycon_rook.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DSYCON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND,
+*                               WORK, IWORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, N
+*       DOUBLE PRECISION   ANORM, RCOND
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * ), IWORK( * )
+*       DOUBLE PRECISION   A( LDA, * ), WORK( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DSYCON_ROOK estimates the reciprocal of the condition number (in the
+*> 1-norm) of a real symmetric matrix A using the factorization
+*> A = U*D*U**T or A = L*D*L**T computed by DSYTRF_ROOK.
+*>
+*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
+*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          Specifies whether the details of the factorization are stored
+*>          as an upper or lower triangular matrix.
+*>          = 'U':  Upper triangular, form is A = U*D*U**T;
+*>          = 'L':  Lower triangular, form is A = L*D*L**T.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*>          A is DOUBLE PRECISION array, dimension (LDA,N)
+*>          The block diagonal matrix D and the multipliers used to
+*>          obtain the factor U or L as computed by DSYTRF_ROOK.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          Details of the interchanges and the block structure of D
+*>          as determined by DSYTRF_ROOK.
+*> \endverbatim
+*>
+*> \param[in] ANORM
+*> \verbatim
+*>          ANORM is DOUBLE PRECISION
+*>          The 1-norm of the original matrix A.
+*> \endverbatim
+*>
+*> \param[out] RCOND
+*> \verbatim
+*>          RCOND is DOUBLE PRECISION
+*>          The reciprocal of the condition number of the matrix A,
+*>          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
+*>          estimate of the 1-norm of inv(A) computed in this routine.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is DOUBLE PRECISION array, dimension (2*N)
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*>          IWORK is INTEGER array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0:  successful exit
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date April 2012
+*
+*> \ingroup doubleSYcomputational
+*
+*> \par Contributors:
+*  ==================
+*> \verbatim
+*>
+*>   April 2012, Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*>
+*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*>                  School of Mathematics,
+*>                  University of Manchester
+*>
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE DSYCON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
+     $                   IWORK, INFO )
+*
+*  -- LAPACK computational routine (version 3.4.1) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     April 2012
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, N
+      DOUBLE PRECISION   ANORM, RCOND
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * ), IWORK( * )
+      DOUBLE PRECISION   A( LDA, * ), WORK( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ONE, ZERO
+      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            UPPER
+      INTEGER            I, KASE
+      DOUBLE PRECISION   AINVNM
+*     ..
+*     .. Local Arrays ..
+      INTEGER            ISAVE( 3 )
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      EXTERNAL           LSAME
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DLACN2, DSYTRS_ROOK, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      UPPER = LSAME( UPLO, 'U' )
+      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -4
+      ELSE IF( ANORM.LT.ZERO ) THEN
+         INFO = -6
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'DSYCON_ROOK', -INFO )
+         RETURN
+      END IF
+*
+*     Quick return if possible
+*
+      RCOND = ZERO
+      IF( N.EQ.0 ) THEN
+         RCOND = ONE
+         RETURN
+      ELSE IF( ANORM.LE.ZERO ) THEN
+         RETURN
+      END IF
+*
+*     Check that the diagonal matrix D is nonsingular.
+*
+      IF( UPPER ) THEN
+*
+*        Upper triangular storage: examine D from bottom to top
+*
+         DO 10 I = N, 1, -1
+            IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
+     $         RETURN
+   10    CONTINUE
+      ELSE
+*
+*        Lower triangular storage: examine D from top to bottom.
+*
+         DO 20 I = 1, N
+            IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
+     $         RETURN
+   20    CONTINUE
+      END IF
+*
+*     Estimate the 1-norm of the inverse.
+*
+      KASE = 0
+   30 CONTINUE
+      CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
+      IF( KASE.NE.0 ) THEN
+*
+*        Multiply by inv(L*D*L**T) or inv(U*D*U**T).
+*
+         CALL DSYTRS_ROOK( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
+         GO TO 30
+      END IF
+*
+*     Compute the estimate of the reciprocal condition number.
+*
+      IF( AINVNM.NE.ZERO )
+     $   RCOND = ( ONE / AINVNM ) / ANORM
+*
+      RETURN
+*
+*     End of DSYCON_ROOK
+*
+      END

lapack-netlib/SRC/dsysv_rook.f

@@ -0,0 +1,293 @@
+*> \brief <b> DSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices</b>
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DSYSV_ROOK + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsysv_rook.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsysv_rook.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsysv_rook.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DSYSV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+*                         LWORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), WORK( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DSYSV_ROOK computes the solution to a real system of linear
+*> equations
+*>    A * X = B,
+*> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
+*> matrices.
+*>
+*> The diagonal pivoting method is used to factor A as
+*>    A = U * D * U**T,  if UPLO = 'U', or
+*>    A = L * D * L**T,  if UPLO = 'L',
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, and D is symmetric and block diagonal with
+*> 1-by-1 and 2-by-2 diagonal blocks.
+*>
+*> DSYTRF_ROOK is called to compute the factorization of a real
+*> symmetric matrix A using the bounded Bunch-Kaufman ("rook") diagonal
+*> pivoting method.
+*>
+*> The factored form of A is then used to solve the system 
+*> of equations A * X = B by calling DSYTRS_ROOK.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          = 'U':  Upper triangle of A is stored;
+*>          = 'L':  Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The number of linear equations, i.e., the order of the
+*>          matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*>          NRHS is INTEGER
+*>          The number of right hand sides, i.e., the number of columns
+*>          of the matrix B.  NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is DOUBLE PRECISION array, dimension (LDA,N)
+*>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
+*>          N-by-N upper triangular part of A contains the upper
+*>          triangular part of the matrix A, and the strictly lower
+*>          triangular part of A is not referenced.  If UPLO = 'L', the
+*>          leading N-by-N lower triangular part of A contains the lower
+*>          triangular part of the matrix A, and the strictly upper
+*>          triangular part of A is not referenced.
+*>
+*>          On exit, if INFO = 0, the block diagonal matrix D and the
+*>          multipliers used to obtain the factor U or L from the
+*>          factorization A = U*D*U**T or A = L*D*L**T as computed by
+*>          DSYTRF_ROOK.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          Details of the interchanges and the block structure of D,
+*>          as determined by DSYTRF_ROOK.
+*>
+*>          If UPLO = 'U':
+*>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
+*>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>               If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
+*>               columns k and -IPIV(k) were interchanged and rows and
+*>               columns k-1 and -IPIV(k-1) were inerchaged,
+*>               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
+*>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>               If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
+*>               columns k and -IPIV(k) were interchanged and rows and
+*>               columns k+1 and -IPIV(k+1) were inerchaged,
+*>               D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
+*>          On entry, the N-by-NRHS right hand side matrix B.
+*>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*>          LDB is INTEGER
+*>          The leading dimension of the array B.  LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
+*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>          The length of WORK.  LWORK >= 1, and for best performance
+*>          LWORK >= max(1,N*NB), where NB is the optimal blocksize for
+*>          DSYTRF_ROOK.
+*>          
+*>          TRS will be done with Level 2 BLAS
+*>
+*>          If LWORK = -1, then a workspace query is assumed; the routine
+*>          only calculates the optimal size of the WORK array, returns
+*>          this value as the first entry of the WORK array, and no error
+*>          message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0: successful exit
+*>          < 0: if INFO = -i, the i-th argument had an illegal value
+*>          > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
+*>               has been completed, but the block diagonal matrix D is
+*>               exactly singular, so the solution could not be computed.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date April 2012
+*
+*> \ingroup doubleSYsolve
+*
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>   April 2012, Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*>
+*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*>                  School of Mathematics,
+*>                  University of Manchester
+*>
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE DSYSV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+     $                  LWORK, INFO )
+*
+*  -- LAPACK driver routine (version 3.4.1) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     April 2012
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), WORK( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Local Scalars ..
+      LOGICAL            LQUERY
+      INTEGER            LWKOPT
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      EXTERNAL           LSAME
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           XERBLA, DSYTRF_ROOK, DSYTRS_ROOK
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      LQUERY = ( LWORK.EQ.-1 )
+      IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( NRHS.LT.0 ) THEN
+         INFO = -3
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -5
+      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+         INFO = -8
+      ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
+         INFO = -10
+      END IF
+*
+      IF( INFO.EQ.0 ) THEN
+         IF( N.EQ.0 ) THEN
+            LWKOPT = 1
+         ELSE
+            CALL DSYTRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, -1, INFO )
+            LWKOPT = WORK(1)
+         END IF
+         WORK( 1 ) = LWKOPT
+      END IF
+*
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'DSYSV_ROOK ', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+*
+*     Compute the factorization A = U*D*U**T or A = L*D*L**T.
+*
+      CALL DSYTRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+      IF( INFO.EQ.0 ) THEN
+*
+*        Solve the system A*X = B, overwriting B with X.
+*
+*        Solve with TRS_ROOK ( Use Level 2 BLAS)
+*
+         CALL DSYTRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
+*
+      END IF
+*
+      WORK( 1 ) = LWKOPT
+*
+      RETURN
+*
+*     End of DSYSV_ROOK
+*
+      END

lapack-netlib/SRC/dsytf2.f

@@ -90,13 +90,22 @@
 *> \verbatim
 *>          IPIV is INTEGER array, dimension (N)
 *>          Details of the interchanges and the block structure of D.
-*>          If IPIV(k) > 0, then rows and columns k and IPIV(k) were
-*>          interchanged and D(k,k) is a 1-by-1 diagonal block.
-*>          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
-*>          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
-*>          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
-*>          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
-*>          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'U':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k-1) < 0, then rows and columns
+*>             k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
+*>             is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k+1) < 0, then rows and columns
+*>             k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1)
+*>             is a 2-by-2 diagonal block.
 *> \endverbatim
 *>
 *> \param[out] INFO
@@ -118,7 +127,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date September 2012
+*> \date November 2013
 *
 *> \ingroup doubleSYcomputational
 *
@@ -185,10 +194,10 @@
 *  =====================================================================
       SUBROUTINE DSYTF2( UPLO, N, A, LDA, IPIV, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.2) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     September 2012
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          UPLO
@@ -268,7 +277,8 @@
          ABSAKK = ABS( A( K, K ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.GT.1 ) THEN
             IMAX = IDAMAX( K-1, A( 1, K ), 1 )
@@ -279,7 +289,8 @@
 *
          IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
 *
-*           Column K is zero or contains a NaN: set INFO and continue
+*           Column K is zero or underflow, or contains a NaN:
+*           set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
@@ -436,7 +447,8 @@
          ABSAKK = ABS( A( K, K ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.LT.N ) THEN
             IMAX = K + IDAMAX( N-K, A( K+1, K ), 1 )
@@ -447,7 +459,8 @@
 *
          IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
 *
-*           Column K is zero or contains a NaN: set INFO and continue
+*           Column K is zero or underflow, or contains a NaN:
+*           set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K

lapack-netlib/SRC/dsytf2_rook.f

@@ -0,0 +1,813 @@
+*> \brief \b DSYTF2_ROOK computes the factorization of a real symmetric indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (unblocked algorithm).
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DSYTF2_ROOK + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytf2_rook.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytf2_rook.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytf2_rook.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DSYTF2_ROOK( UPLO, N, A, LDA, IPIV, INFO )
+*
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, N
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       DOUBLE PRECISION   A( LDA, * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DSYTF2_ROOK computes the factorization of a real symmetric matrix A
+*> using the bounded Bunch-Kaufman ("rook") diagonal pivoting method:
+*>
+*>    A = U*D*U**T  or  A = L*D*L**T
+*>
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, U**T is the transpose of U, and D is symmetric and
+*> block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
+*>
+*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          Specifies whether the upper or lower triangular part of the
+*>          symmetric matrix A is stored:
+*>          = 'U':  Upper triangular
+*>          = 'L':  Lower triangular
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is DOUBLE PRECISION array, dimension (LDA,N)
+*>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
+*>          n-by-n upper triangular part of A contains the upper
+*>          triangular part of the matrix A, and the strictly lower
+*>          triangular part of A is not referenced.  If UPLO = 'L', the
+*>          leading n-by-n lower triangular part of A contains the lower
+*>          triangular part of the matrix A, and the strictly upper
+*>          triangular part of A is not referenced.
+*>
+*>          On exit, the block diagonal matrix D and the multipliers used
+*>          to obtain the factor U or L (see below for further details).
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          Details of the interchanges and the block structure of D.
+*>
+*>          If UPLO = 'U':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k)
+*>             were interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
+*>             columns k and -IPIV(k) were interchanged and rows and
+*>             columns k-1 and -IPIV(k-1) were inerchaged,
+*>             D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k)
+*>             were interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
+*>             columns k and -IPIV(k) were interchanged and rows and
+*>             columns k+1 and -IPIV(k+1) were inerchaged,
+*>             D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0: successful exit
+*>          < 0: if INFO = -k, the k-th argument had an illegal value
+*>          > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
+*>               has been completed, but the block diagonal matrix D is
+*>               exactly singular, and division by zero will occur if it
+*>               is used to solve a system of equations.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2013
+*
+*> \ingroup doubleSYcomputational
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  If UPLO = 'U', then A = U*D*U**T, where
+*>     U = P(n)*U(n)* ... *P(k)U(k)* ...,
+*>  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
+*>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
+*>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
+*>  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
+*>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
+*>
+*>             (   I    v    0   )   k-s
+*>     U(k) =  (   0    I    0   )   s
+*>             (   0    0    I   )   n-k
+*>                k-s   s   n-k
+*>
+*>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
+*>  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
+*>  and A(k,k), and v overwrites A(1:k-2,k-1:k).
+*>
+*>  If UPLO = 'L', then A = L*D*L**T, where
+*>     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
+*>  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
+*>  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
+*>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
+*>  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
+*>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
+*>
+*>             (   I    0     0   )  k-1
+*>     L(k) =  (   0    I     0   )  s
+*>             (   0    v     I   )  n-k-s+1
+*>                k-1   s  n-k-s+1
+*>
+*>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
+*>  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
+*>  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
+*> \endverbatim
+*
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>  November 2013,     Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*>
+*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*>                  School of Mathematics,
+*>                  University of Manchester
+*>
+*>  01-01-96 - Based on modifications by
+*>    J. Lewis, Boeing Computer Services Company
+*>    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville abd , USA
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE DSYTF2_ROOK( UPLO, N, A, LDA, IPIV, INFO )
+*
+*  -- LAPACK computational routine (version 3.5.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2013
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, N
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      DOUBLE PRECISION   A( LDA, * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ZERO, ONE
+      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
+      DOUBLE PRECISION   EIGHT, SEVTEN
+      PARAMETER          ( EIGHT = 8.0D+0, SEVTEN = 17.0D+0 )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            UPPER, DONE
+      INTEGER            I, IMAX, J, JMAX, ITEMP, K, KK, KP, KSTEP,
+     $                   P, II
+      DOUBLE PRECISION   ABSAKK, ALPHA, COLMAX, D11, D12, D21, D22,
+     $                   ROWMAX, DTEMP, T, WK, WKM1, WKP1, SFMIN
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      INTEGER            IDAMAX
+      DOUBLE PRECISION   DLAMCH
+      EXTERNAL           LSAME, IDAMAX, DLAMCH
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DSCAL, DSWAP, DSYR, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, MAX, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      UPPER = LSAME( UPLO, 'U' )
+      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -4
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'DSYTF2_ROOK', -INFO )
+         RETURN
+      END IF
+*
+*     Initialize ALPHA for use in choosing pivot block size.
+*
+      ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT
+*
+*     Compute machine safe minimum
+*
+      SFMIN = DLAMCH( 'S' )
+*
+      IF( UPPER ) THEN
+*
+*        Factorize A as U*D*U**T using the upper triangle of A
+*
+*        K is the main loop index, decreasing from N to 1 in steps of
+*        1 or 2
+*
+         K = N
+   10    CONTINUE
+*
+*        If K < 1, exit from loop
+*
+         IF( K.LT.1 )
+     $      GO TO 70
+         KSTEP = 1
+         P = K
+*
+*        Determine rows and columns to be interchanged and whether
+*        a 1-by-1 or 2-by-2 pivot block will be used
+*
+         ABSAKK = ABS( A( K, K ) )
+*
+*        IMAX is the row-index of the largest off-diagonal element in
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
+*
+         IF( K.GT.1 ) THEN
+            IMAX = IDAMAX( K-1, A( 1, K ), 1 )
+            COLMAX = ABS( A( IMAX, K ) )
+         ELSE
+            COLMAX = ZERO
+         END IF
+*
+         IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) ) THEN
+*
+*           Column K is zero or underflow: set INFO and continue
+*
+            IF( INFO.EQ.0 )
+     $         INFO = K
+            KP = K
+         ELSE
+*
+*           Test for interchange
+*
+*           Equivalent to testing for (used to handle NaN and Inf)
+*           ABSAKK.GE.ALPHA*COLMAX
+*
+            IF( .NOT.( ABSAKK.LT.ALPHA*COLMAX ) ) THEN
+*
+*              no interchange,
+*              use 1-by-1 pivot block
+*
+               KP = K
+            ELSE
+*
+               DONE = .FALSE.
+*
+*              Loop until pivot found
+*
+   12          CONTINUE
+*
+*                 Begin pivot search loop body
+*
+*                 JMAX is the column-index of the largest off-diagonal
+*                 element in row IMAX, and ROWMAX is its absolute value.
+*                 Determine both ROWMAX and JMAX.
+*
+                  IF( IMAX.NE.K ) THEN
+                     JMAX = IMAX + IDAMAX( K-IMAX, A( IMAX, IMAX+1 ),
+     $                                    LDA )
+                     ROWMAX = ABS( A( IMAX, JMAX ) )
+                  ELSE
+                     ROWMAX = ZERO
+                  END IF
+*
+                  IF( IMAX.GT.1 ) THEN
+                     ITEMP = IDAMAX( IMAX-1, A( 1, IMAX ), 1 )
+                     DTEMP = ABS( A( ITEMP, IMAX ) )
+                     IF( DTEMP.GT.ROWMAX ) THEN
+                        ROWMAX = DTEMP
+                        JMAX = ITEMP
+                     END IF
+                  END IF
+*
+*                 Equivalent to testing for (used to handle NaN and Inf)
+*                 ABS( A( IMAX, IMAX ) ).GE.ALPHA*ROWMAX
+*
+                  IF( .NOT.( ABS( A( IMAX, IMAX ) ).LT.ALPHA*ROWMAX ) )
+     $            THEN
+*
+*                    interchange rows and columns K and IMAX,
+*                    use 1-by-1 pivot block
+*
+                     KP = IMAX
+                     DONE = .TRUE.
+*
+*                 Equivalent to testing for ROWMAX .EQ. COLMAX,
+*                 used to handle NaN and Inf
+*
+                  ELSE IF( ( P.EQ.JMAX ).OR.( ROWMAX.LE.COLMAX ) ) THEN
+*
+*                    interchange rows and columns K+1 and IMAX,
+*                    use 2-by-2 pivot block
+*
+                     KP = IMAX
+                     KSTEP = 2
+                     DONE = .TRUE.
+                  ELSE
+*
+*                    Pivot NOT found, set variables and repeat
+*
+                     P = IMAX
+                     COLMAX = ROWMAX
+                     IMAX = JMAX
+                  END IF
+*
+*                 End pivot search loop body
+*
+               IF( .NOT. DONE ) GOTO 12
+*
+            END IF
+*
+*           Swap TWO rows and TWO columns
+*
+*           First swap
+*
+            IF( ( KSTEP.EQ.2 ) .AND. ( P.NE.K ) ) THEN
+*
+*              Interchange rows and column K and P in the leading
+*              submatrix A(1:k,1:k) if we have a 2-by-2 pivot
+*
+               IF( P.GT.1 )
+     $            CALL DSWAP( P-1, A( 1, K ), 1, A( 1, P ), 1 )
+               IF( P.LT.(K-1) )
+     $            CALL DSWAP( K-P-1, A( P+1, K ), 1, A( P, P+1 ),
+     $                     LDA )
+               T = A( K, K )
+               A( K, K ) = A( P, P )
+               A( P, P ) = T
+            END IF
+*
+*           Second swap
+*
+            KK = K - KSTEP + 1
+            IF( KP.NE.KK ) THEN
+*
+*              Interchange rows and columns KK and KP in the leading
+*              submatrix A(1:k,1:k)
+*
+               IF( KP.GT.1 )
+     $            CALL DSWAP( KP-1, A( 1, KK ), 1, A( 1, KP ), 1 )
+               IF( ( KK.GT.1 ) .AND. ( KP.LT.(KK-1) ) )
+     $            CALL DSWAP( KK-KP-1, A( KP+1, KK ), 1, A( KP, KP+1 ),
+     $                     LDA )
+               T = A( KK, KK )
+               A( KK, KK ) = A( KP, KP )
+               A( KP, KP ) = T
+               IF( KSTEP.EQ.2 ) THEN
+                  T = A( K-1, K )
+                  A( K-1, K ) = A( KP, K )
+                  A( KP, K ) = T
+               END IF
+            END IF
+*
+*           Update the leading submatrix
+*
+            IF( KSTEP.EQ.1 ) THEN
+*
+*              1-by-1 pivot block D(k): column k now holds
+*
+*              W(k) = U(k)*D(k)
+*
+*              where U(k) is the k-th column of U
+*
+               IF( K.GT.1 ) THEN
+*
+*                 Perform a rank-1 update of A(1:k-1,1:k-1) and
+*                 store U(k) in column k
+*
+                  IF( ABS( A( K, K ) ).GE.SFMIN ) THEN
+*
+*                    Perform a rank-1 update of A(1:k-1,1:k-1) as
+*                    A := A - U(k)*D(k)*U(k)**T
+*                       = A - W(k)*1/D(k)*W(k)**T
+*
+                     D11 = ONE / A( K, K )
+                     CALL DSYR( UPLO, K-1, -D11, A( 1, K ), 1, A, LDA )
+*
+*                    Store U(k) in column k
+*
+                     CALL DSCAL( K-1, D11, A( 1, K ), 1 )
+                  ELSE
+*
+*                    Store L(k) in column K
+*
+                     D11 = A( K, K )
+                     DO 16 II = 1, K - 1
+                        A( II, K ) = A( II, K ) / D11
+   16                CONTINUE
+*
+*                    Perform a rank-1 update of A(k+1:n,k+1:n) as
+*                    A := A - U(k)*D(k)*U(k)**T
+*                       = A - W(k)*(1/D(k))*W(k)**T
+*                       = A - (W(k)/D(k))*(D(k))*(W(k)/D(K))**T
+*
+                     CALL DSYR( UPLO, K-1, -D11, A( 1, K ), 1, A, LDA )
+                  END IF
+               END IF
+*
+            ELSE
+*
+*              2-by-2 pivot block D(k): columns k and k-1 now hold
+*
+*              ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
+*
+*              where U(k) and U(k-1) are the k-th and (k-1)-th columns
+*              of U
+*
+*              Perform a rank-2 update of A(1:k-2,1:k-2) as
+*
+*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T
+*                 = A - ( ( A(k-1)A(k) )*inv(D(k)) ) * ( A(k-1)A(k) )**T
+*
+*              and store L(k) and L(k+1) in columns k and k+1
+*
+               IF( K.GT.2 ) THEN
+*
+                  D12 = A( K-1, K )
+                  D22 = A( K-1, K-1 ) / D12
+                  D11 = A( K, K ) / D12
+                  T = ONE / ( D11*D22-ONE )
+*
+                  DO 30 J = K - 2, 1, -1
+*
+                     WKM1 = T*( D11*A( J, K-1 )-A( J, K ) )
+                     WK = T*( D22*A( J, K )-A( J, K-1 ) )
+*
+                     DO 20 I = J, 1, -1
+                        A( I, J ) = A( I, J ) - (A( I, K ) / D12 )*WK -
+     $                              ( A( I, K-1 ) / D12 )*WKM1
+   20                CONTINUE
+*
+*                    Store U(k) and U(k-1) in cols k and k-1 for row J
+*
+                     A( J, K ) = WK / D12
+                     A( J, K-1 ) = WKM1 / D12
+*
+   30             CONTINUE
+*
+               END IF
+*
+            END IF
+         END IF
+*
+*        Store details of the interchanges in IPIV
+*
+         IF( KSTEP.EQ.1 ) THEN
+            IPIV( K ) = KP
+         ELSE
+            IPIV( K ) = -P
+            IPIV( K-1 ) = -KP
+         END IF
+*
+*        Decrease K and return to the start of the main loop
+*
+         K = K - KSTEP
+         GO TO 10
+*
+      ELSE
+*
+*        Factorize A as L*D*L**T using the lower triangle of A
+*
+*        K is the main loop index, increasing from 1 to N in steps of
+*        1 or 2
+*
+         K = 1
+   40    CONTINUE
+*
+*        If K > N, exit from loop
+*
+         IF( K.GT.N )
+     $      GO TO 70
+         KSTEP = 1
+         P = K
+*
+*        Determine rows and columns to be interchanged and whether
+*        a 1-by-1 or 2-by-2 pivot block will be used
+*
+         ABSAKK = ABS( A( K, K ) )
+*
+*        IMAX is the row-index of the largest off-diagonal element in
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
+*
+         IF( K.LT.N ) THEN
+            IMAX = K + IDAMAX( N-K, A( K+1, K ), 1 )
+            COLMAX = ABS( A( IMAX, K ) )
+         ELSE
+            COLMAX = ZERO
+         END IF
+*
+         IF( ( MAX( ABSAKK, COLMAX ).EQ.ZERO ) ) THEN
+*
+*           Column K is zero or underflow: set INFO and continue
+*
+            IF( INFO.EQ.0 )
+     $         INFO = K
+            KP = K
+         ELSE
+*
+*           Test for interchange
+*
+*           Equivalent to testing for (used to handle NaN and Inf)
+*           ABSAKK.GE.ALPHA*COLMAX
+*
+            IF( .NOT.( ABSAKK.LT.ALPHA*COLMAX ) ) THEN
+*
+*              no interchange, use 1-by-1 pivot block
+*
+               KP = K
+            ELSE
+*
+               DONE = .FALSE.
+*
+*              Loop until pivot found
+*
+   42          CONTINUE
+*
+*                 Begin pivot search loop body
+*
+*                 JMAX is the column-index of the largest off-diagonal
+*                 element in row IMAX, and ROWMAX is its absolute value.
+*                 Determine both ROWMAX and JMAX.
+*
+                  IF( IMAX.NE.K ) THEN
+                     JMAX = K - 1 + IDAMAX( IMAX-K, A( IMAX, K ), LDA )
+                     ROWMAX = ABS( A( IMAX, JMAX ) )
+                  ELSE
+                     ROWMAX = ZERO
+                  END IF
+*
+                  IF( IMAX.LT.N ) THEN
+                     ITEMP = IMAX + IDAMAX( N-IMAX, A( IMAX+1, IMAX ),
+     $                                     1 )
+                     DTEMP = ABS( A( ITEMP, IMAX ) )
+                     IF( DTEMP.GT.ROWMAX ) THEN
+                        ROWMAX = DTEMP
+                        JMAX = ITEMP
+                     END IF
+                  END IF
+*
+*                 Equivalent to testing for (used to handle NaN and Inf)
+*                 ABS( A( IMAX, IMAX ) ).GE.ALPHA*ROWMAX
+*
+                  IF( .NOT.( ABS( A( IMAX, IMAX ) ).LT.ALPHA*ROWMAX ) )
+     $            THEN
+*
+*                    interchange rows and columns K and IMAX,
+*                    use 1-by-1 pivot block
+*
+                     KP = IMAX
+                     DONE = .TRUE.
+*
+*                 Equivalent to testing for ROWMAX .EQ. COLMAX,
+*                 used to handle NaN and Inf
+*
+                  ELSE IF( ( P.EQ.JMAX ).OR.( ROWMAX.LE.COLMAX ) ) THEN
+*
+*                    interchange rows and columns K+1 and IMAX,
+*                    use 2-by-2 pivot block
+*
+                     KP = IMAX
+                     KSTEP = 2
+                     DONE = .TRUE.
+                  ELSE
+*
+*                    Pivot NOT found, set variables and repeat
+*
+                     P = IMAX
+                     COLMAX = ROWMAX
+                     IMAX = JMAX
+                  END IF
+*
+*                 End pivot search loop body
+*
+               IF( .NOT. DONE ) GOTO 42
+*
+            END IF
+*
+*           Swap TWO rows and TWO columns
+*
+*           First swap
+*
+            IF( ( KSTEP.EQ.2 ) .AND. ( P.NE.K ) ) THEN
+*
+*              Interchange rows and column K and P in the trailing
+*              submatrix A(k:n,k:n) if we have a 2-by-2 pivot
+*
+               IF( P.LT.N )
+     $            CALL DSWAP( N-P, A( P+1, K ), 1, A( P+1, P ), 1 )
+               IF( P.GT.(K+1) )
+     $            CALL DSWAP( P-K-1, A( K+1, K ), 1, A( P, K+1 ), LDA )
+               T = A( K, K )
+               A( K, K ) = A( P, P )
+               A( P, P ) = T
+            END IF
+*
+*           Second swap
+*
+            KK = K + KSTEP - 1
+            IF( KP.NE.KK ) THEN
+*
+*              Interchange rows and columns KK and KP in the trailing
+*              submatrix A(k:n,k:n)
+*
+               IF( KP.LT.N )
+     $            CALL DSWAP( N-KP, A( KP+1, KK ), 1, A( KP+1, KP ), 1 )
+               IF( ( KK.LT.N ) .AND. ( KP.GT.(KK+1) ) )
+     $            CALL DSWAP( KP-KK-1, A( KK+1, KK ), 1, A( KP, KK+1 ),
+     $                     LDA )
+               T = A( KK, KK )
+               A( KK, KK ) = A( KP, KP )
+               A( KP, KP ) = T
+               IF( KSTEP.EQ.2 ) THEN
+                  T = A( K+1, K )
+                  A( K+1, K ) = A( KP, K )
+                  A( KP, K ) = T
+               END IF
+            END IF
+*
+*           Update the trailing submatrix
+*
+            IF( KSTEP.EQ.1 ) THEN
+*
+*              1-by-1 pivot block D(k): column k now holds
+*
+*              W(k) = L(k)*D(k)
+*
+*              where L(k) is the k-th column of L
+*
+               IF( K.LT.N ) THEN
+*
+*              Perform a rank-1 update of A(k+1:n,k+1:n) and
+*              store L(k) in column k
+*
+                  IF( ABS( A( K, K ) ).GE.SFMIN ) THEN
+*
+*                    Perform a rank-1 update of A(k+1:n,k+1:n) as
+*                    A := A - L(k)*D(k)*L(k)**T
+*                       = A - W(k)*(1/D(k))*W(k)**T
+*
+                     D11 = ONE / A( K, K )
+                     CALL DSYR( UPLO, N-K, -D11, A( K+1, K ), 1,
+     $                          A( K+1, K+1 ), LDA )
+*
+*                    Store L(k) in column k
+*
+                     CALL DSCAL( N-K, D11, A( K+1, K ), 1 )
+                  ELSE
+*
+*                    Store L(k) in column k
+*
+                     D11 = A( K, K )
+                     DO 46 II = K + 1, N
+                        A( II, K ) = A( II, K ) / D11
+   46                CONTINUE
+*
+*                    Perform a rank-1 update of A(k+1:n,k+1:n) as
+*                    A := A - L(k)*D(k)*L(k)**T
+*                       = A - W(k)*(1/D(k))*W(k)**T
+*                       = A - (W(k)/D(k))*(D(k))*(W(k)/D(K))**T
+*
+                     CALL DSYR( UPLO, N-K, -D11, A( K+1, K ), 1,
+     $                          A( K+1, K+1 ), LDA )
+                  END IF
+               END IF
+*
+            ELSE
+*
+*              2-by-2 pivot block D(k): columns k and k+1 now hold
+*
+*              ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k)
+*
+*              where L(k) and L(k+1) are the k-th and (k+1)-th columns
+*              of L
+*
+*
+*              Perform a rank-2 update of A(k+2:n,k+2:n) as
+*
+*              A := A - ( L(k) L(k+1) ) * D(k) * ( L(k) L(k+1) )**T
+*                 = A - ( ( A(k)A(k+1) )*inv(D(k) ) * ( A(k)A(k+1) )**T
+*
+*              and store L(k) and L(k+1) in columns k and k+1
+*
+               IF( K.LT.N-1 ) THEN
+*
+                  D21 = A( K+1, K )
+                  D11 = A( K+1, K+1 ) / D21
+                  D22 = A( K, K ) / D21
+                  T = ONE / ( D11*D22-ONE )
+*
+                  DO 60 J = K + 2, N
+*
+*                    Compute  D21 * ( W(k)W(k+1) ) * inv(D(k)) for row J
+*
+                     WK = T*( D11*A( J, K )-A( J, K+1 ) )
+                     WKP1 = T*( D22*A( J, K+1 )-A( J, K ) )
+*
+*                    Perform a rank-2 update of A(k+2:n,k+2:n)
+*
+                     DO 50 I = J, N
+                        A( I, J ) = A( I, J ) - ( A( I, K ) / D21 )*WK -
+     $                              ( A( I, K+1 ) / D21 )*WKP1
+   50                CONTINUE
+*
+*                    Store L(k) and L(k+1) in cols k and k+1 for row J
+*
+                     A( J, K ) = WK / D21
+                     A( J, K+1 ) = WKP1 / D21
+*
+   60             CONTINUE
+*
+               END IF
+*
+            END IF
+         END IF
+*
+*        Store details of the interchanges in IPIV
+*
+         IF( KSTEP.EQ.1 ) THEN
+            IPIV( K ) = KP
+         ELSE
+            IPIV( K ) = -P
+            IPIV( K+1 ) = -KP
+         END IF
+*
+*        Increase K and return to the start of the main loop
+*
+         K = K + KSTEP
+         GO TO 40
+*
+      END IF
+*
+   70 CONTINUE
+*
+      RETURN
+*
+*     End of DSYTF2_ROOK
+*
+      END

lapack-netlib/SRC/dsytrf_rook.f

@@ -0,0 +1,393 @@
+*> \brief \b DSYTRF_ROOK
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DSYTRF_ROOK + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytrf_rook.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytrf_rook.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytrf_rook.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DSYTRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, LWORK, N
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       DOUBLE PRECISION   A( LDA, * ), WORK( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DSYTRF_ROOK computes the factorization of a real symmetric matrix A
+*> using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
+*> The form of the factorization is
+*>
+*>    A = U*D*U**T  or  A = L*D*L**T
+*>
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, and D is symmetric and block diagonal with
+*> 1-by-1 and 2-by-2 diagonal blocks.
+*>
+*> This is the blocked version of the algorithm, calling Level 3 BLAS.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          = 'U':  Upper triangle of A is stored;
+*>          = 'L':  Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is DOUBLE PRECISION array, dimension (LDA,N)
+*>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
+*>          N-by-N upper triangular part of A contains the upper
+*>          triangular part of the matrix A, and the strictly lower
+*>          triangular part of A is not referenced.  If UPLO = 'L', the
+*>          leading N-by-N lower triangular part of A contains the lower
+*>          triangular part of the matrix A, and the strictly upper
+*>          triangular part of A is not referenced.
+*>
+*>          On exit, the block diagonal matrix D and the multipliers used
+*>          to obtain the factor U or L (see below for further details).
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          Details of the interchanges and the block structure of D.
+*>
+*>          If UPLO = 'U':
+*>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
+*>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>               If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
+*>               columns k and -IPIV(k) were interchanged and rows and
+*>               columns k-1 and -IPIV(k-1) were inerchaged,
+*>               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
+*>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>               If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
+*>               columns k and -IPIV(k) were interchanged and rows and
+*>               columns k+1 and -IPIV(k+1) were inerchaged,
+*>               D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)).
+*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>          The length of WORK.  LWORK >=1.  For best performance
+*>          LWORK >= N*NB, where NB is the block size returned by ILAENV.
+*>
+*>          If LWORK = -1, then a workspace query is assumed; the routine
+*>          only calculates the optimal size of the WORK array, returns
+*>          this value as the first entry of the WORK array, and no error
+*>          message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0:  successful exit
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value
+*>          > 0:  if INFO = i, D(i,i) is exactly zero.  The factorization
+*>                has been completed, but the block diagonal matrix D is
+*>                exactly singular, and division by zero will occur if it
+*>                is used to solve a system of equations.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date April 2012
+*
+*> \ingroup doubleSYcomputational
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  If UPLO = 'U', then A = U*D*U**T, where
+*>     U = P(n)*U(n)* ... *P(k)U(k)* ...,
+*>  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
+*>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
+*>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
+*>  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
+*>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
+*>
+*>             (   I    v    0   )   k-s
+*>     U(k) =  (   0    I    0   )   s
+*>             (   0    0    I   )   n-k
+*>                k-s   s   n-k
+*>
+*>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
+*>  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
+*>  and A(k,k), and v overwrites A(1:k-2,k-1:k).
+*>
+*>  If UPLO = 'L', then A = L*D*L**T, where
+*>     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
+*>  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
+*>  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
+*>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
+*>  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
+*>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
+*>
+*>             (   I    0     0   )  k-1
+*>     L(k) =  (   0    I     0   )  s
+*>             (   0    v     I   )  n-k-s+1
+*>                k-1   s  n-k-s+1
+*>
+*>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
+*>  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
+*>  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
+*> \endverbatim
+*
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>   April 2012, Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*>
+*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*>                  School of Mathematics,
+*>                  University of Manchester
+*>
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE DSYTRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+*
+*  -- LAPACK computational routine (version 3.4.1) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     April 2012
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, LWORK, N
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      DOUBLE PRECISION   A( LDA, * ), WORK( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Local Scalars ..
+      LOGICAL            LQUERY, UPPER
+      INTEGER            IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      INTEGER            ILAENV
+      EXTERNAL           LSAME, ILAENV
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DLASYF_ROOK, DSYTF2_ROOK, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      UPPER = LSAME( UPLO, 'U' )
+      LQUERY = ( LWORK.EQ.-1 )
+      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -4
+      ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
+         INFO = -7
+      END IF
+*
+      IF( INFO.EQ.0 ) THEN
+*
+*        Determine the block size
+*
+         NB = ILAENV( 1, 'DSYTRF_ROOK', UPLO, N, -1, -1, -1 )
+         LWKOPT = N*NB
+         WORK( 1 ) = LWKOPT
+      END IF
+*
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'DSYTRF_ROOK', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+*
+      NBMIN = 2
+      LDWORK = N
+      IF( NB.GT.1 .AND. NB.LT.N ) THEN
+         IWS = LDWORK*NB
+         IF( LWORK.LT.IWS ) THEN
+            NB = MAX( LWORK / LDWORK, 1 )
+            NBMIN = MAX( 2, ILAENV( 2, 'DSYTRF_ROOK',
+     $                              UPLO, N, -1, -1, -1 ) )
+         END IF
+      ELSE
+         IWS = 1
+      END IF
+      IF( NB.LT.NBMIN )
+     $   NB = N
+*
+      IF( UPPER ) THEN
+*
+*        Factorize A as U*D*U**T using the upper triangle of A
+*
+*        K is the main loop index, decreasing from N to 1 in steps of
+*        KB, where KB is the number of columns factorized by DLASYF_ROOK;
+*        KB is either NB or NB-1, or K for the last block
+*
+         K = N
+   10    CONTINUE
+*
+*        If K < 1, exit from loop
+*
+         IF( K.LT.1 )
+     $      GO TO 40
+*
+         IF( K.GT.NB ) THEN
+*
+*           Factorize columns k-kb+1:k of A and use blocked code to
+*           update columns 1:k-kb
+*
+            CALL DLASYF_ROOK( UPLO, K, NB, KB, A, LDA,
+     $                        IPIV, WORK, LDWORK, IINFO )
+         ELSE
+*
+*           Use unblocked code to factorize columns 1:k of A
+*
+            CALL DSYTF2_ROOK( UPLO, K, A, LDA, IPIV, IINFO )
+            KB = K
+         END IF
+*
+*        Set INFO on the first occurrence of a zero pivot
+*
+         IF( INFO.EQ.0 .AND. IINFO.GT.0 )
+     $      INFO = IINFO     
+*
+*        No need to adjust IPIV
+*
+*        Decrease K and return to the start of the main loop
+*
+         K = K - KB
+         GO TO 10
+*
+      ELSE
+*
+*        Factorize A as L*D*L**T using the lower triangle of A
+*
+*        K is the main loop index, increasing from 1 to N in steps of
+*        KB, where KB is the number of columns factorized by DLASYF_ROOK;
+*        KB is either NB or NB-1, or N-K+1 for the last block
+*
+         K = 1
+   20    CONTINUE
+*
+*        If K > N, exit from loop
+*
+         IF( K.GT.N )
+     $      GO TO 40
+*
+         IF( K.LE.N-NB ) THEN
+*
+*           Factorize columns k:k+kb-1 of A and use blocked code to
+*           update columns k+kb:n
+*
+            CALL DLASYF_ROOK( UPLO, N-K+1, NB, KB, A( K, K ), LDA,
+     $                        IPIV( K ), WORK, LDWORK, IINFO )
+         ELSE
+*
+*           Use unblocked code to factorize columns k:n of A
+*
+            CALL DSYTF2_ROOK( UPLO, N-K+1, A( K, K ), LDA, IPIV( K ),
+     $                   IINFO )
+            KB = N - K + 1
+         END IF
+*
+*        Set INFO on the first occurrence of a zero pivot
+*
+         IF( INFO.EQ.0 .AND. IINFO.GT.0 )
+     $      INFO = IINFO + K - 1
+*
+*        Adjust IPIV
+*
+         DO 30 J = K, K + KB - 1
+            IF( IPIV( J ).GT.0 ) THEN
+               IPIV( J ) = IPIV( J ) + K - 1
+            ELSE
+               IPIV( J ) = IPIV( J ) - K + 1
+            END IF
+   30    CONTINUE
+*
+*        Increase K and return to the start of the main loop
+*
+         K = K + KB
+         GO TO 20
+*
+      END IF
+*
+   40 CONTINUE
+      WORK( 1 ) = LWKOPT
+      RETURN
+*
+*     End of DSYTRF_ROOK
+*
+      END

lapack-netlib/SRC/dsytri_rook.f

@@ -0,0 +1,450 @@
+*> \brief \b DSYTRI_ROOK
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DSYTRI_ROOK + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytri_rook.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytri_rook.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytri_rook.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DSYTRI_ROOK( UPLO, N, A, LDA, IPIV, WORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, N
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       DOUBLE PRECISION   A( LDA, * ), WORK( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DSYTRI_ROOK computes the inverse of a real symmetric
+*> matrix A using the factorization A = U*D*U**T or A = L*D*L**T
+*> computed by DSYTRF_ROOK.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          Specifies whether the details of the factorization are stored
+*>          as an upper or lower triangular matrix.
+*>          = 'U':  Upper triangular, form is A = U*D*U**T;
+*>          = 'L':  Lower triangular, form is A = L*D*L**T.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is DOUBLE PRECISION array, dimension (LDA,N)
+*>          On entry, the block diagonal matrix D and the multipliers
+*>          used to obtain the factor U or L as computed by DSYTRF_ROOK.
+*>
+*>          On exit, if INFO = 0, the (symmetric) inverse of the original
+*>          matrix.  If UPLO = 'U', the upper triangular part of the
+*>          inverse is formed and the part of A below the diagonal is not
+*>          referenced; if UPLO = 'L' the lower triangular part of the
+*>          inverse is formed and the part of A above the diagonal is
+*>          not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          Details of the interchanges and the block structure of D
+*>          as determined by DSYTRF_ROOK.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is DOUBLE PRECISION array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0: successful exit
+*>          < 0: if INFO = -i, the i-th argument had an illegal value
+*>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
+*>               inverse could not be computed.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date April 2012
+*
+*> \ingroup doubleSYcomputational
+*
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>   April 2012, Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*>
+*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*>                  School of Mathematics,
+*>                  University of Manchester
+*>
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE DSYTRI_ROOK( UPLO, N, A, LDA, IPIV, WORK, INFO )
+*
+*  -- LAPACK computational routine (version 3.4.1) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     April 2012
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, N
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      DOUBLE PRECISION   A( LDA, * ), WORK( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ONE, ZERO
+      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            UPPER
+      INTEGER            K, KP, KSTEP
+      DOUBLE PRECISION   AK, AKKP1, AKP1, D, T, TEMP
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      DOUBLE PRECISION   DDOT
+      EXTERNAL           LSAME, DDOT
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DCOPY, DSWAP, DSYMV, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, MAX
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      UPPER = LSAME( UPLO, 'U' )
+      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -4
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'DSYTRI_ROOK', -INFO )
+         RETURN
+      END IF
+*
+*     Quick return if possible
+*
+      IF( N.EQ.0 )
+     $   RETURN
+*
+*     Check that the diagonal matrix D is nonsingular.
+*
+      IF( UPPER ) THEN
+*
+*        Upper triangular storage: examine D from bottom to top
+*
+         DO 10 INFO = N, 1, -1
+            IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO )
+     $         RETURN
+   10    CONTINUE
+      ELSE
+*
+*        Lower triangular storage: examine D from top to bottom.
+*
+         DO 20 INFO = 1, N
+            IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO )
+     $         RETURN
+   20    CONTINUE
+      END IF
+      INFO = 0
+*
+      IF( UPPER ) THEN
+*
+*        Compute inv(A) from the factorization A = U*D*U**T.
+*
+*        K is the main loop index, increasing from 1 to N in steps of
+*        1 or 2, depending on the size of the diagonal blocks.
+*
+         K = 1
+   30    CONTINUE
+*
+*        If K > N, exit from loop.
+*
+         IF( K.GT.N )
+     $      GO TO 40
+*
+         IF( IPIV( K ).GT.0 ) THEN
+*
+*           1 x 1 diagonal block
+*
+*           Invert the diagonal block.
+*
+            A( K, K ) = ONE / A( K, K )
+*
+*           Compute column K of the inverse.
+*
+            IF( K.GT.1 ) THEN
+               CALL DCOPY( K-1, A( 1, K ), 1, WORK, 1 )
+               CALL DSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
+     $                     A( 1, K ), 1 )
+               A( K, K ) = A( K, K ) - DDOT( K-1, WORK, 1, A( 1, K ),
+     $                     1 )
+            END IF
+            KSTEP = 1
+         ELSE
+*
+*           2 x 2 diagonal block
+*
+*           Invert the diagonal block.
+*
+            T = ABS( A( K, K+1 ) )
+            AK = A( K, K ) / T
+            AKP1 = A( K+1, K+1 ) / T
+            AKKP1 = A( K, K+1 ) / T
+            D = T*( AK*AKP1-ONE )
+            A( K, K ) = AKP1 / D
+            A( K+1, K+1 ) = AK / D
+            A( K, K+1 ) = -AKKP1 / D
+*
+*           Compute columns K and K+1 of the inverse.
+*
+            IF( K.GT.1 ) THEN
+               CALL DCOPY( K-1, A( 1, K ), 1, WORK, 1 )
+               CALL DSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
+     $                     A( 1, K ), 1 )
+               A( K, K ) = A( K, K ) - DDOT( K-1, WORK, 1, A( 1, K ),
+     $                     1 )
+               A( K, K+1 ) = A( K, K+1 ) -
+     $                       DDOT( K-1, A( 1, K ), 1, A( 1, K+1 ), 1 )
+               CALL DCOPY( K-1, A( 1, K+1 ), 1, WORK, 1 )
+               CALL DSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
+     $                     A( 1, K+1 ), 1 )
+               A( K+1, K+1 ) = A( K+1, K+1 ) -
+     $                         DDOT( K-1, WORK, 1, A( 1, K+1 ), 1 )
+            END IF
+            KSTEP = 2
+         END IF
+*
+         IF( KSTEP.EQ.1 ) THEN
+*
+*           Interchange rows and columns K and IPIV(K) in the leading
+*           submatrix A(1:k+1,1:k+1)
+*
+            KP = IPIV( K )
+            IF( KP.NE.K ) THEN
+               IF( KP.GT.1 )
+     $             CALL DSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
+               CALL DSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA )
+               TEMP = A( K, K )
+               A( K, K ) = A( KP, KP )
+               A( KP, KP ) = TEMP
+            END IF
+         ELSE
+*
+*           Interchange rows and columns K and K+1 with -IPIV(K) and
+*           -IPIV(K+1)in the leading submatrix A(1:k+1,1:k+1)
+*
+            KP = -IPIV( K )
+            IF( KP.NE.K ) THEN
+               IF( KP.GT.1 )
+     $            CALL DSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
+               CALL DSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA )
+*               
+               TEMP = A( K, K )
+               A( K, K ) = A( KP, KP )
+               A( KP, KP ) = TEMP
+               TEMP = A( K, K+1 )
+               A( K, K+1 ) = A( KP, K+1 )
+               A( KP, K+1 ) = TEMP
+            END IF
+*
+            K = K + 1
+            KP = -IPIV( K )
+            IF( KP.NE.K ) THEN
+               IF( KP.GT.1 )
+     $            CALL DSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
+               CALL DSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA )
+               TEMP = A( K, K )
+               A( K, K ) = A( KP, KP )
+               A( KP, KP ) = TEMP
+            END IF
+         END IF
+*
+         K = K + 1
+         GO TO 30
+   40    CONTINUE
+*
+      ELSE
+*
+*        Compute inv(A) from the factorization A = L*D*L**T.
+*
+*        K is the main loop index, increasing from 1 to N in steps of
+*        1 or 2, depending on the size of the diagonal blocks.
+*
+         K = N
+   50    CONTINUE
+*
+*        If K < 1, exit from loop.
+*
+         IF( K.LT.1 )
+     $      GO TO 60
+*
+         IF( IPIV( K ).GT.0 ) THEN
+*
+*           1 x 1 diagonal block
+*
+*           Invert the diagonal block.
+*
+            A( K, K ) = ONE / A( K, K )
+*
+*           Compute column K of the inverse.
+*
+            IF( K.LT.N ) THEN
+               CALL DCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
+               CALL DSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
+     $                     ZERO, A( K+1, K ), 1 )
+               A( K, K ) = A( K, K ) - DDOT( N-K, WORK, 1, A( K+1, K ),
+     $                     1 )
+            END IF
+            KSTEP = 1
+         ELSE
+*
+*           2 x 2 diagonal block
+*
+*           Invert the diagonal block.
+*
+            T = ABS( A( K, K-1 ) )
+            AK = A( K-1, K-1 ) / T
+            AKP1 = A( K, K ) / T
+            AKKP1 = A( K, K-1 ) / T
+            D = T*( AK*AKP1-ONE )
+            A( K-1, K-1 ) = AKP1 / D
+            A( K, K ) = AK / D
+            A( K, K-1 ) = -AKKP1 / D
+*
+*           Compute columns K-1 and K of the inverse.
+*
+            IF( K.LT.N ) THEN
+               CALL DCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
+               CALL DSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
+     $                     ZERO, A( K+1, K ), 1 )
+               A( K, K ) = A( K, K ) - DDOT( N-K, WORK, 1, A( K+1, K ),
+     $                     1 )
+               A( K, K-1 ) = A( K, K-1 ) -
+     $                       DDOT( N-K, A( K+1, K ), 1, A( K+1, K-1 ),
+     $                       1 )
+               CALL DCOPY( N-K, A( K+1, K-1 ), 1, WORK, 1 )
+               CALL DSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
+     $                     ZERO, A( K+1, K-1 ), 1 )
+               A( K-1, K-1 ) = A( K-1, K-1 ) -
+     $                         DDOT( N-K, WORK, 1, A( K+1, K-1 ), 1 )
+            END IF
+            KSTEP = 2
+         END IF  
+*
+         IF( KSTEP.EQ.1 ) THEN
+*
+*           Interchange rows and columns K and IPIV(K) in the trailing
+*           submatrix A(k-1:n,k-1:n)
+*
+            KP = IPIV( K )
+            IF( KP.NE.K ) THEN
+               IF( KP.LT.N )
+     $            CALL DSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
+               CALL DSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA )
+               TEMP = A( K, K )
+               A( K, K ) = A( KP, KP )
+               A( KP, KP ) = TEMP
+            END IF
+         ELSE
+*
+*           Interchange rows and columns K and K-1 with -IPIV(K) and
+*           -IPIV(K-1) in the trailing submatrix A(k-1:n,k-1:n)
+*
+            KP = -IPIV( K )
+            IF( KP.NE.K ) THEN
+               IF( KP.LT.N )
+     $            CALL DSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
+               CALL DSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA )
+*
+               TEMP = A( K, K )
+               A( K, K ) = A( KP, KP )
+               A( KP, KP ) = TEMP
+               TEMP = A( K, K-1 )
+               A( K, K-1 ) = A( KP, K-1 )
+               A( KP, K-1 ) = TEMP
+            END IF
+*
+            K = K - 1
+            KP = -IPIV( K )
+            IF( KP.NE.K ) THEN
+               IF( KP.LT.N )
+     $            CALL DSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
+               CALL DSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA )
+               TEMP = A( K, K )
+               A( K, K ) = A( KP, KP )
+               A( KP, KP ) = TEMP
+            END IF
+         END IF
+*
+         K = K - 1
+         GO TO 50
+   60    CONTINUE
+      END IF
+*
+      RETURN
+*
+*     End of DSYTRI_ROOK
+*
+      END

lapack-netlib/SRC/dsytrs_rook.f

@@ -0,0 +1,484 @@
+*> \brief \b DSYTRS_ROOK
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DSYTRS_ROOK + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytrs_rook.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytrs_rook.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytrs_rook.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DSYTRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, LDB, N, NRHS
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DSYTRS_ROOK solves a system of linear equations A*X = B with
+*> a real symmetric matrix A using the factorization A = U*D*U**T or
+*> A = L*D*L**T computed by DSYTRF_ROOK.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          Specifies whether the details of the factorization are stored
+*>          as an upper or lower triangular matrix.
+*>          = 'U':  Upper triangular, form is A = U*D*U**T;
+*>          = 'L':  Lower triangular, form is A = L*D*L**T.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*>          NRHS is INTEGER
+*>          The number of right hand sides, i.e., the number of columns
+*>          of the matrix B.  NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*>          A is DOUBLE PRECISION array, dimension (LDA,N)
+*>          The block diagonal matrix D and the multipliers used to
+*>          obtain the factor U or L as computed by DSYTRF_ROOK.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          Details of the interchanges and the block structure of D
+*>          as determined by DSYTRF_ROOK.
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
+*>          On entry, the right hand side matrix B.
+*>          On exit, the solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*>          LDB is INTEGER
+*>          The leading dimension of the array B.  LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0:  successful exit
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date April 2012
+*
+*> \ingroup doubleSYcomputational
+*
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>   April 2012, Igor Kozachenko,
+*>                  Computer Science Division,
+*>                  University of California, Berkeley
+*>
+*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*>                  School of Mathematics,
+*>                  University of Manchester
+*>
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE DSYTRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
+     $                        INFO )
+*
+*  -- LAPACK computational routine (version 3.4.1) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     April 2012
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, LDB, N, NRHS
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ONE
+      PARAMETER          ( ONE = 1.0D+0 )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            UPPER
+      INTEGER            J, K, KP
+      DOUBLE PRECISION   AK, AKM1, AKM1K, BK, BKM1, DENOM
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      EXTERNAL           LSAME
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DGEMV, DGER, DSCAL, DSWAP, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+      INFO = 0
+      UPPER = LSAME( UPLO, 'U' )
+      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( NRHS.LT.0 ) THEN
+         INFO = -3
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -5
+      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+         INFO = -8
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'DSYTRS_ROOK', -INFO )
+         RETURN
+      END IF
+*
+*     Quick return if possible
+*
+      IF( N.EQ.0 .OR. NRHS.EQ.0 )
+     $   RETURN
+*
+      IF( UPPER ) THEN
+*
+*        Solve A*X = B, where A = U*D*U**T.
+*
+*        First solve U*D*X = B, overwriting B with X.
+*
+*        K is the main loop index, decreasing from N to 1 in steps of
+*        1 or 2, depending on the size of the diagonal blocks.
+*
+         K = N
+   10    CONTINUE
+*
+*        If K < 1, exit from loop.
+*
+         IF( K.LT.1 )
+     $      GO TO 30
+*
+         IF( IPIV( K ).GT.0 ) THEN
+*
+*           1 x 1 diagonal block
+*
+*           Interchange rows K and IPIV(K).
+*
+            KP = IPIV( K )
+            IF( KP.NE.K )
+     $         CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+*
+*           Multiply by inv(U(K)), where U(K) is the transformation
+*           stored in column K of A.
+*
+            CALL DGER( K-1, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
+     $                 B( 1, 1 ), LDB )
+*
+*           Multiply by the inverse of the diagonal block.
+*
+            CALL DSCAL( NRHS, ONE / A( K, K ), B( K, 1 ), LDB )
+            K = K - 1
+         ELSE
+*
+*           2 x 2 diagonal block
+*
+*           Interchange rows K and -IPIV(K) THEN K-1 and -IPIV(K-1)
+*
+            KP = -IPIV( K )
+            IF( KP.NE.K )
+     $         CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+*
+            KP = -IPIV( K-1 )
+            IF( KP.NE.K-1 )
+     $         CALL DSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
+*
+*           Multiply by inv(U(K)), where U(K) is the transformation
+*           stored in columns K-1 and K of A.
+*
+            IF( K.GT.2 ) THEN
+               CALL DGER( K-2, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ),
+     $                    LDB, B( 1, 1 ), LDB )
+               CALL DGER( K-2, NRHS, -ONE, A( 1, K-1 ), 1, B( K-1, 1 ),
+     $                    LDB, B( 1, 1 ), LDB )
+            END IF
+*
+*           Multiply by the inverse of the diagonal block.
+*
+            AKM1K = A( K-1, K )
+            AKM1 = A( K-1, K-1 ) / AKM1K
+            AK = A( K, K ) / AKM1K
+            DENOM = AKM1*AK - ONE
+            DO 20 J = 1, NRHS
+               BKM1 = B( K-1, J ) / AKM1K
+               BK = B( K, J ) / AKM1K
+               B( K-1, J ) = ( AK*BKM1-BK ) / DENOM
+               B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM
+   20       CONTINUE
+            K = K - 2
+         END IF
+*
+         GO TO 10
+   30    CONTINUE
+*
+*        Next solve U**T *X = B, overwriting B with X.
+*
+*        K is the main loop index, increasing from 1 to N in steps of
+*        1 or 2, depending on the size of the diagonal blocks.
+*
+         K = 1
+   40    CONTINUE
+*
+*        If K > N, exit from loop.
+*
+         IF( K.GT.N )
+     $      GO TO 50
+*
+         IF( IPIV( K ).GT.0 ) THEN
+*
+*           1 x 1 diagonal block
+*
+*           Multiply by inv(U**T(K)), where U(K) is the transformation
+*           stored in column K of A.
+*
+            IF( K.GT.1 )
+     $         CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B,
+     $                     LDB, A( 1, K ), 1, ONE, B( K, 1 ), LDB )
+*
+*           Interchange rows K and IPIV(K).
+*
+            KP = IPIV( K )
+            IF( KP.NE.K )
+     $         CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+            K = K + 1
+         ELSE
+*
+*           2 x 2 diagonal block
+*
+*           Multiply by inv(U**T(K+1)), where U(K+1) is the transformation
+*           stored in columns K and K+1 of A.
+*
+            IF( K.GT.1 ) THEN
+               CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B,
+     $                     LDB, A( 1, K ), 1, ONE, B( K, 1 ), LDB )
+               CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B,
+     $                     LDB, A( 1, K+1 ), 1, ONE, B( K+1, 1 ), LDB )
+            END IF
+*
+*           Interchange rows K and -IPIV(K) THEN K+1 and -IPIV(K+1).
+*
+            KP = -IPIV( K )
+            IF( KP.NE.K )
+     $         CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+*
+            KP = -IPIV( K+1 )
+            IF( KP.NE.K+1 )
+     $         CALL DSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
+*
+            K = K + 2
+         END IF
+*
+         GO TO 40
+   50    CONTINUE
+*
+      ELSE
+*
+*        Solve A*X = B, where A = L*D*L**T.
+*
+*        First solve L*D*X = B, overwriting B with X.
+*
+*        K is the main loop index, increasing from 1 to N in steps of
+*        1 or 2, depending on the size of the diagonal blocks.
+*
+         K = 1
+   60    CONTINUE
+*
+*        If K > N, exit from loop.
+*
+         IF( K.GT.N )
+     $      GO TO 80
+*
+         IF( IPIV( K ).GT.0 ) THEN
+*
+*           1 x 1 diagonal block
+*
+*           Interchange rows K and IPIV(K).
+*
+            KP = IPIV( K )
+            IF( KP.NE.K )
+     $         CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+*
+*           Multiply by inv(L(K)), where L(K) is the transformation
+*           stored in column K of A.
+*
+            IF( K.LT.N )
+     $         CALL DGER( N-K, NRHS, -ONE, A( K+1, K ), 1, B( K, 1 ),
+     $                    LDB, B( K+1, 1 ), LDB )
+*
+*           Multiply by the inverse of the diagonal block.
+*
+            CALL DSCAL( NRHS, ONE / A( K, K ), B( K, 1 ), LDB )
+            K = K + 1
+         ELSE
+*
+*           2 x 2 diagonal block
+*
+*           Interchange rows K and -IPIV(K) THEN K+1 and -IPIV(K+1)
+*
+            KP = -IPIV( K )
+            IF( KP.NE.K )
+     $         CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+*
+            KP = -IPIV( K+1 )
+            IF( KP.NE.K+1 )
+     $         CALL DSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
+*
+*           Multiply by inv(L(K)), where L(K) is the transformation
+*           stored in columns K and K+1 of A.
+*
+            IF( K.LT.N-1 ) THEN
+               CALL DGER( N-K-1, NRHS, -ONE, A( K+2, K ), 1, B( K, 1 ),
+     $                    LDB, B( K+2, 1 ), LDB )
+               CALL DGER( N-K-1, NRHS, -ONE, A( K+2, K+1 ), 1,
+     $                    B( K+1, 1 ), LDB, B( K+2, 1 ), LDB )
+            END IF
+*
+*           Multiply by the inverse of the diagonal block.
+*
+            AKM1K = A( K+1, K )
+            AKM1 = A( K, K ) / AKM1K
+            AK = A( K+1, K+1 ) / AKM1K
+            DENOM = AKM1*AK - ONE
+            DO 70 J = 1, NRHS
+               BKM1 = B( K, J ) / AKM1K
+               BK = B( K+1, J ) / AKM1K
+               B( K, J ) = ( AK*BKM1-BK ) / DENOM
+               B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
+   70       CONTINUE
+            K = K + 2
+         END IF
+*
+         GO TO 60
+   80    CONTINUE
+*
+*        Next solve L**T *X = B, overwriting B with X.
+*
+*        K is the main loop index, decreasing from N to 1 in steps of
+*        1 or 2, depending on the size of the diagonal blocks.
+*
+         K = N
+   90    CONTINUE
+*
+*        If K < 1, exit from loop.
+*
+         IF( K.LT.1 )
+     $      GO TO 100
+*
+         IF( IPIV( K ).GT.0 ) THEN
+*
+*           1 x 1 diagonal block
+*
+*           Multiply by inv(L**T(K)), where L(K) is the transformation
+*           stored in column K of A.
+*
+            IF( K.LT.N )
+     $         CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
+     $                     LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB )
+*
+*           Interchange rows K and IPIV(K).
+*
+            KP = IPIV( K )
+            IF( KP.NE.K )
+     $         CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+            K = K - 1
+         ELSE
+*
+*           2 x 2 diagonal block
+*
+*           Multiply by inv(L**T(K-1)), where L(K-1) is the transformation
+*           stored in columns K-1 and K of A.
+*
+            IF( K.LT.N ) THEN
+               CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
+     $                     LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB )
+               CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
+     $                     LDB, A( K+1, K-1 ), 1, ONE, B( K-1, 1 ),
+     $                     LDB )
+            END IF
+*
+*           Interchange rows K and -IPIV(K) THEN K-1 and -IPIV(K-1)
+*
+            KP = -IPIV( K )
+            IF( KP.NE.K )
+     $         CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+*
+            KP = -IPIV( K-1 )
+            IF( KP.NE.K-1 )
+     $         CALL DSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
+*
+            K = K - 2
+         END IF
+*
+         GO TO 90
+  100    CONTINUE
+      END IF
+*
+      RETURN
+*
+*     End of DSYTRS_ROOK
+*
+      END

lapack-netlib/SRC/dtpmqrt.f

@@ -175,7 +175,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date April 2012
+*> \date November 2013
 *
 *> \ingroup doubleOTHERcomputational
 *
@@ -216,10 +216,10 @@
       SUBROUTINE DTPMQRT( SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT,
      $                    A, LDA, B, LDB, WORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.1) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     April 2012
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER SIDE, TRANS
@@ -235,7 +235,7 @@
 *     ..
 *     .. Local Scalars ..
       LOGICAL            LEFT, RIGHT, TRAN, NOTRAN
-      INTEGER            I, IB, MB, LB, KF, Q
+      INTEGER            I, IB, MB, LB, KF, LDAQ, LDVQ
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -257,10 +257,12 @@
       TRAN   = LSAME( TRANS, 'T' )
       NOTRAN = LSAME( TRANS, 'N' )
 *      
-      IF( LEFT ) THEN
-         Q = M
+      IF ( LEFT ) THEN
+         LDVQ = MAX( 1, M )
+         LDAQ = MAX( 1, K )
       ELSE IF ( RIGHT ) THEN
-         Q = N
+         LDVQ = MAX( 1, N )
+         LDAQ = MAX( 1, M )
       END IF
       IF( .NOT.LEFT .AND. .NOT.RIGHT ) THEN
          INFO = -1
@@ -274,13 +276,13 @@
          INFO = -5
       ELSE IF( L.LT.0 .OR. L.GT.K ) THEN
          INFO = -6         
-      ELSE IF( NB.LT.1 .OR. NB.GT.K ) THEN
+      ELSE IF( NB.LT.1 .OR. (NB.GT.K .AND. K.GT.0) ) THEN
          INFO = -7
-      ELSE IF( LDV.LT.MAX( 1, Q ) ) THEN
+      ELSE IF( LDV.LT.LDVQ ) THEN
          INFO = -9
       ELSE IF( LDT.LT.NB ) THEN
          INFO = -11
-      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
+      ELSE IF( LDA.LT.LDAQ ) THEN
          INFO = -13
       ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
          INFO = -15

lapack-netlib/SRC/dtpqrt.f

@@ -132,7 +132,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date April 2012
+*> \date November 2013
 *
 *> \ingroup doubleOTHERcomputational
 *
@@ -189,10 +189,10 @@
       SUBROUTINE DTPQRT( M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK,
      $                   INFO )
 *
-*  -- LAPACK computational routine (version 3.4.1) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     April 2012
+*     November 2013
 *
 *     .. Scalar Arguments ..
       INTEGER INFO, LDA, LDB, LDT, N, M, L, NB
@@ -219,9 +219,9 @@
          INFO = -1
       ELSE IF( N.LT.0 ) THEN
          INFO = -2
-      ELSE IF( L.LT.0 .OR. L.GT.MIN(M,N) ) THEN
+      ELSE IF( L.LT.0 .OR. (L.GT.MIN(M,N) .AND. MIN(M,N).GE.0)) THEN
          INFO = -3
-      ELSE IF( NB.LT.1 .OR. NB.GT.N ) THEN
+      ELSE IF( NB.LT.1 .OR. (NB.GT.N .AND. N.GT.0)) THEN
          INFO = -4
       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
          INFO = -6

lapack-netlib/SRC/ilaver.f

@@ -48,18 +48,18 @@
 *  =====================================================================
       SUBROUTINE ILAVER( VERS_MAJOR, VERS_MINOR, VERS_PATCH )
 *
-*  -- LAPACK computational routine (version 3.4.2) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     September 2012
+*     November 2013
 *
 *  =====================================================================
 *
       INTEGER VERS_MAJOR, VERS_MINOR, VERS_PATCH
 *  =====================================================================
       VERS_MAJOR = 3
-      VERS_MINOR = 4
-      VERS_PATCH = 2
+      VERS_MINOR = 5
+      VERS_PATCH = 0
 *  =====================================================================
 *
       RETURN

lapack-netlib/SRC/sbbcsd.f

@@ -322,7 +322,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date November 2011
+*> \date November 2013
 *
 *> \ingroup realOTHERcomputational
 *
@@ -332,10 +332,10 @@
      $                   V2T, LDV2T, B11D, B11E, B12D, B12E, B21D, B21E,
      $                   B22D, B22E, WORK, LWORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2011
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS
@@ -358,8 +358,8 @@
       PARAMETER          ( HUNDRED = 100.0E0, MEIGHTH = -0.125E0,
      $                     ONE = 1.0E0, PIOVER2 = 1.57079632679489662E0,
      $                     TEN = 10.0E0, ZERO = 0.0E0 )
-      REAL               NEGONECOMPLEX
-      PARAMETER          ( NEGONECOMPLEX = -1.0E0 )
+      REAL               NEGONE
+      PARAMETER          ( NEGONE = -1.0E0 )
 *     ..
 *     .. Local Scalars ..
       LOGICAL            COLMAJOR, LQUERY, RESTART11, RESTART12,
@@ -477,7 +477,10 @@
 *     Initial deflation
 *
       IMAX = Q
-      DO WHILE( ( IMAX .GT. 1 ) .AND. ( PHI(IMAX-1) .EQ. ZERO ) )
+      DO WHILE( IMAX .GT. 1 )
+         IF( PHI(IMAX-1) .NE. ZERO ) THEN
+            EXIT
+         END IF
          IMAX = IMAX - 1
       END DO
       IMIN = IMAX - 1
@@ -939,9 +942,9 @@
             B21D(IMAX) = -B21D(IMAX)
             IF( WANTV1T ) THEN
                IF( COLMAJOR ) THEN
-                  CALL SSCAL( Q, NEGONECOMPLEX, V1T(IMAX,1), LDV1T )
+                  CALL SSCAL( Q, NEGONE, V1T(IMAX,1), LDV1T )
                ELSE
-                  CALL SSCAL( Q, NEGONECOMPLEX, V1T(1,IMAX), 1 )
+                  CALL SSCAL( Q, NEGONE, V1T(1,IMAX), 1 )
                END IF
             END IF
          END IF
@@ -962,9 +965,9 @@
             B12D(IMAX) = -B12D(IMAX)
             IF( WANTU1 ) THEN
                IF( COLMAJOR ) THEN
-                  CALL SSCAL( P, NEGONECOMPLEX, U1(1,IMAX), 1 )
+                  CALL SSCAL( P, NEGONE, U1(1,IMAX), 1 )
                ELSE
-                  CALL SSCAL( P, NEGONECOMPLEX, U1(IMAX,1), LDU1 )
+                  CALL SSCAL( P, NEGONE, U1(IMAX,1), LDU1 )
                END IF
             END IF
          END IF
@@ -972,9 +975,9 @@
             B22D(IMAX) = -B22D(IMAX)
             IF( WANTU2 ) THEN
                IF( COLMAJOR ) THEN
-                  CALL SSCAL( M-P, NEGONECOMPLEX, U2(1,IMAX), 1 )
+                  CALL SSCAL( M-P, NEGONE, U2(1,IMAX), 1 )
                ELSE
-                  CALL SSCAL( M-P, NEGONECOMPLEX, U2(IMAX,1), LDU2 )
+                  CALL SSCAL( M-P, NEGONE, U2(IMAX,1), LDU2 )
                END IF
             END IF
          END IF
@@ -984,9 +987,9 @@
          IF( B12D(IMAX)+B22D(IMAX) .LT. 0 ) THEN
             IF( WANTV2T ) THEN
                IF( COLMAJOR ) THEN
-                  CALL SSCAL( M-Q, NEGONECOMPLEX, V2T(IMAX,1), LDV2T )
+                  CALL SSCAL( M-Q, NEGONE, V2T(IMAX,1), LDV2T )
                ELSE
-                  CALL SSCAL( M-Q, NEGONECOMPLEX, V2T(1,IMAX), 1 )
+                  CALL SSCAL( M-Q, NEGONE, V2T(1,IMAX), 1 )
                END IF
             END IF
          END IF

lapack-netlib/SRC/sgebal.f

@@ -121,7 +121,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date November 2011
+*> \date November 2013
 *
 *> \ingroup realGEcomputational
 *
@@ -160,10 +160,10 @@
 *  =====================================================================
       SUBROUTINE SGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2011
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOB
@@ -192,8 +192,8 @@
 *     .. External Functions ..
       LOGICAL            SISNAN, LSAME
       INTEGER            ISAMAX
-      REAL               SLAMCH
-      EXTERNAL           SISNAN, LSAME, ISAMAX, SLAMCH
+      REAL               SLAMCH, SNRM2
+      EXTERNAL           SISNAN, LSAME, ISAMAX, SLAMCH, SNRM2
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           SSCAL, SSWAP, XERBLA
@@ -316,15 +316,9 @@
       NOCONV = .FALSE.
 *
       DO 200 I = K, L
-         C = ZERO
-         R = ZERO
-*
-         DO 150 J = K, L
-            IF( J.EQ.I )
-     $         GO TO 150
-            C = C + ABS( A( J, I ) )
-            R = R + ABS( A( I, J ) )
-  150    CONTINUE
+*
+         C = SNRM2( L-K+1, A( K, I ), 1 )
+         R = SNRM2( L-K+1, A( I, K ), LDA )
          ICA = ISAMAX( L, A( 1, I ), 1 )
          CA = ABS( A( ICA, I ) )
          IRA = ISAMAX( N-K+1, A( I, K ), LDA )

lapack-netlib/SRC/sgemqrt.f

@@ -160,7 +160,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date November 2011
+*> \date November 2013
 *
 *> \ingroup realGEcomputational
 *
@@ -168,10 +168,10 @@
       SUBROUTINE SGEMQRT( SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT, 
      $                   C, LDC, WORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2011
+*     November 2013
 *
 *     .. Scalar Arguments ..
       CHARACTER SIDE, TRANS
@@ -225,7 +225,7 @@
          INFO = -4
       ELSE IF( K.LT.0 .OR. K.GT.Q ) THEN
          INFO = -5
-      ELSE IF( NB.LT.1 .OR. NB.GT.K ) THEN
+      ELSE IF( NB.LT.1 .OR. (NB.GT.K .AND. K.GT.0)) THEN
          INFO = -6
       ELSE IF( LDV.LT.MAX( 1, Q ) ) THEN
          INFO = -8

lapack-netlib/SRC/sgeqrt.f

@@ -108,7 +108,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \date November 2011
+*> \date November 2013
 *
 *> \ingroup realGEcomputational
 *
@@ -141,10 +141,10 @@
 *  =====================================================================
       SUBROUTINE SGEQRT( M, N, NB, A, LDA, T, LDT, WORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK computational routine (version 3.5.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2011
+*     November 2013
 *
 *     .. Scalar Arguments ..
       INTEGER INFO, LDA, LDT, M, N, NB
@@ -173,7 +173,7 @@
          INFO = -1
       ELSE IF( N.LT.0 ) THEN
          INFO = -2
-      ELSE IF( NB.LT.1 .OR. NB.GT.MIN(M,N) ) THEN
+      ELSE IF( NB.LT.1 .OR. ( NB.GT.MIN(M,N) .AND. MIN(M,N).GT.0 ) )THEN
          INFO = -3
       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
          INFO = -5