Update LAPACK to 3.9.0

lapack-netlib/TESTING/EIG/Makefile

@@ -1,5 +1,3 @@
-include ../../make.inc
-
 ########################################################################
 #  This is the makefile for the eigenvalue test program from LAPACK.
 #  The test files are organized as follows:
@@ -33,6 +31,9 @@ include ../../make.inc
 #
 ########################################################################
 
+TOPSRCDIR = ../..
+include $(TOPSRCDIR)/make.inc
+
 AEIGTST = \
    alahdg.o \
    alasum.o \
@@ -117,24 +118,26 @@ ZEIGTST = zchkee.o \
    zsgt01.o zslect.o \
    zstt21.o zstt22.o zunt01.o zunt03.o
 
+.PHONY: all
 all: single complex double complex16
 
+.PHONY: single complex double complex16
 single: xeigtsts
 complex: xeigtstc
 double: xeigtstd
 complex16: xeigtstz
 
-xeigtsts: $(SEIGTST) $(SCIGTST) $(AEIGTST) ../../$(TMGLIB) ../../$(LAPACKLIB) $(BLASLIB)
-	$(LOADER) $(LOADOPTS) -o $@ $^
+xeigtsts: $(SEIGTST) $(SCIGTST) $(AEIGTST) $(TMGLIB) $(LAPACKLIB) $(BLASLIB)
+	$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
 
-xeigtstc: $(CEIGTST) $(SCIGTST) $(AEIGTST) ../../$(TMGLIB) ../../$(LAPACKLIB) $(BLASLIB)
-	$(LOADER) $(LOADOPTS) -o $@ $^
+xeigtstc: $(CEIGTST) $(SCIGTST) $(AEIGTST) $(TMGLIB) $(LAPACKLIB) $(BLASLIB)
+	$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
 
-xeigtstd: $(DEIGTST) $(DZIGTST) $(AEIGTST) ../../$(TMGLIB) ../../$(LAPACKLIB) $(BLASLIB)
-	$(LOADER) $(LOADOPTS) -o $@ $^
+xeigtstd: $(DEIGTST) $(DZIGTST) $(AEIGTST) $(TMGLIB) $(LAPACKLIB) $(BLASLIB)
+	$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
 
-xeigtstz: $(ZEIGTST) $(DZIGTST) $(AEIGTST) ../../$(TMGLIB) ../../$(LAPACKLIB) $(BLASLIB)
-	$(LOADER) $(LOADOPTS) -o $@ $^
+xeigtstz: $(ZEIGTST) $(DZIGTST) $(AEIGTST) $(TMGLIB) $(LAPACKLIB) $(BLASLIB)
+	$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
 
 $(AEIGTST): $(FRC)
 $(SCIGTST): $(FRC)
@@ -147,6 +150,7 @@ $(ZEIGTST): $(FRC)
 FRC:
 	@FRC=$(FRC)
 
+.PHONY: clean cleanobj cleanexe
 clean: cleanobj cleanexe
 cleanobj:
 	rm -f *.o
@@ -154,13 +158,10 @@ cleanexe:
 	rm -f xeigtst*
 
 schkee.o: schkee.f
-	$(FORTRAN) $(DRVOPTS) -c -o $@ $<
+	$(FC) $(FFLAGS_DRV) -c -o $@ $<
 dchkee.o: dchkee.f
-	$(FORTRAN) $(DRVOPTS) -c -o $@ $<
+	$(FC) $(FFLAGS_DRV) -c -o $@ $<
 cchkee.o: cchkee.f
-	$(FORTRAN) $(DRVOPTS) -c -o $@ $<
+	$(FC) $(FFLAGS_DRV) -c -o $@ $<
 zchkee.o: zchkee.f
-	$(FORTRAN) $(DRVOPTS) -c -o $@ $<
-
-.f.o:
-	$(FORTRAN) $(OPTS) -c -o $@ $<
+	$(FC) $(FFLAGS_DRV) -c -o $@ $<

lapack-netlib/TESTING/EIG/cbdt05.f

@@ -52,6 +52,7 @@
 *> \verbatim
 *>          A is COMPLEX array, dimension (LDA,N)
 *>          The m by n matrix A.
+*> \endverbatim
 *>
 *> \param[in] LDA
 *> \verbatim

lapack-netlib/TESTING/EIG/cchkst.f

@@ -167,7 +167,7 @@
 *>                                              CSTEMR('V', 'I')
 *>
 *> Tests 29 through 34 are disable at present because CSTEMR
-*> does not handle partial specturm requests.
+*> does not handle partial spectrum requests.
 *>
 *> (29)    | S - Z D Z* | / ( |S| n ulp )    CSTEMR('V', 'I')
 *>

lapack-netlib/TESTING/EIG/cchkst2stg.f

@@ -188,7 +188,7 @@
 *>                                              CSTEMR('V', 'I')
 *>
 *> Tests 29 through 34 are disable at present because CSTEMR
-*> does not handle partial specturm requests.
+*> does not handle partial spectrum requests.
 *>
 *> (29)    | S - Z D Z* | / ( |S| n ulp )    CSTEMR('V', 'I')
 *>

lapack-netlib/TESTING/EIG/cdrgsx.f

@@ -737,7 +737,7 @@
       CALL CLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, A, LDA )
       CALL CLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA, B, LDA )
 *
-*     Compute the Schur factorization while swaping the
+*     Compute the Schur factorization while swapping the
 *     m-by-m (1,1)-blocks with n-by-n (2,2)-blocks.
 *
       CALL CGGESX( 'V', 'V', 'S', CLCTSX, 'B', MPLUSN, AI, LDA, BI, LDA,

lapack-netlib/TESTING/EIG/cdrvbd.f

@@ -33,8 +33,9 @@
 *>
 *> \verbatim
 *>
-*> CDRVBD checks the singular value decomposition (SVD) driver CGESVD
-*> and CGESDD.
+*> CDRVBD checks the singular value decomposition (SVD) driver CGESVD,
+*> CGESDD, CGESVJ, CGEJSV, CGESVDX, and CGESVDQ.
+*>
 *> CGESVD and CGESDD factors A = U diag(S) VT, where U and VT are
 *> unitary and diag(S) is diagonal with the entries of the array S on
 *> its diagonal. The entries of S are the singular values, nonnegative
@@ -73,81 +74,92 @@
 *>
 *> Test for CGESDD:
 *>
-*> (1)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )
+*> (8)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )
 *>
-*> (2)   | I - U'U | / ( M ulp )
+*> (9)   | I - U'U | / ( M ulp )
 *>
-*> (3)   | I - VT VT' | / ( N ulp )
+*> (10)  | I - VT VT' | / ( N ulp )
 *>
-*> (4)   S contains MNMIN nonnegative values in decreasing order.
+*> (11)  S contains MNMIN nonnegative values in decreasing order.
 *>       (Return 0 if true, 1/ULP if false.)
 *>
-*> (5)   | U - Upartial | / ( M ulp ) where Upartial is a partially
+*> (12)  | U - Upartial | / ( M ulp ) where Upartial is a partially
 *>       computed U.
 *>
-*> (6)   | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
+*> (13)  | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
 *>       computed VT.
 *>
-*> (7)   | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
+*> (14)  | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
 *>       vector of singular values from the partial SVD
 *>
+*> Test for CGESVDQ:
+*>
+*> (36)  | A - U diag(S) VT | / ( |A| max(M,N) ulp )
+*>
+*> (37)  | I - U'U | / ( M ulp )
+*>
+*> (38)  | I - VT VT' | / ( N ulp )
+*>
+*> (39)  S contains MNMIN nonnegative values in decreasing order.
+*>       (Return 0 if true, 1/ULP if false.)
+*>
 *> Test for CGESVJ:
 *>
-*> (1)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )
+*> (15)  | A - U diag(S) VT | / ( |A| max(M,N) ulp )
 *>
-*> (2)   | I - U'U | / ( M ulp )
+*> (16)  | I - U'U | / ( M ulp )
 *>
-*> (3)   | I - VT VT' | / ( N ulp )
+*> (17)  | I - VT VT' | / ( N ulp )
 *>
-*> (4)   S contains MNMIN nonnegative values in decreasing order.
+*> (18)  S contains MNMIN nonnegative values in decreasing order.
 *>       (Return 0 if true, 1/ULP if false.)
 *>
 *> Test for CGEJSV:
 *>
-*> (1)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )
+*> (19)  | A - U diag(S) VT | / ( |A| max(M,N) ulp )
 *>
-*> (2)   | I - U'U | / ( M ulp )
+*> (20)  | I - U'U | / ( M ulp )
 *>
-*> (3)   | I - VT VT' | / ( N ulp )
+*> (21)  | I - VT VT' | / ( N ulp )
 *>
-*> (4)   S contains MNMIN nonnegative values in decreasing order.
+*> (22)  S contains MNMIN nonnegative values in decreasing order.
 *>        (Return 0 if true, 1/ULP if false.)
 *>
 *> Test for CGESVDX( 'V', 'V', 'A' )/CGESVDX( 'N', 'N', 'A' )
 *>
-*> (1)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )
+*> (23)  | A - U diag(S) VT | / ( |A| max(M,N) ulp )
 *>
-*> (2)   | I - U'U | / ( M ulp )
+*> (24)  | I - U'U | / ( M ulp )
 *>
-*> (3)   | I - VT VT' | / ( N ulp )
+*> (25)  | I - VT VT' | / ( N ulp )
 *>
-*> (4)   S contains MNMIN nonnegative values in decreasing order.
+*> (26)  S contains MNMIN nonnegative values in decreasing order.
 *>       (Return 0 if true, 1/ULP if false.)
 *>
-*> (5)   | U - Upartial | / ( M ulp ) where Upartial is a partially
+*> (27)  | U - Upartial | / ( M ulp ) where Upartial is a partially
 *>       computed U.
 *>
-*> (6)   | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
+*> (28)  | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
 *>       computed VT.
 *>
-*> (7)   | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
+*> (29)  | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
 *>       vector of singular values from the partial SVD
 *>
 *> Test for CGESVDX( 'V', 'V', 'I' )
 *>
-*> (8)   | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )
+*> (30)  | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )
 *>
-*> (9)   | I - U'U | / ( M ulp )
+*> (31)  | I - U'U | / ( M ulp )
 *>
-*> (10)  | I - VT VT' | / ( N ulp )
+*> (32)  | I - VT VT' | / ( N ulp )
 *>
 *> Test for CGESVDX( 'V', 'V', 'V' )
 *>
-*> (11)   | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )
+*> (33)   | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )
 *>
-*> (12)   | I - U'U | / ( M ulp )
+*> (34)   | I - U'U | / ( M ulp )
 *>
-*> (13)   | I - VT VT' | / ( N ulp )
+*> (35)   | I - VT VT' | / ( N ulp )
 *>
 *> The "sizes" are specified by the arrays MM(1:NSIZES) and
 *> NN(1:NSIZES); the value of each element pair (MM(j),NN(j))
@@ -393,6 +405,8 @@
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     June 2016
+*
+      IMPLICIT NONE
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LDU, LDVT, LWORK, NOUNIT, NSIZES,
@@ -411,7 +425,7 @@
 *  =====================================================================
 *
 *     .. Parameters ..
-      REAL              ZERO, ONE, TWO, HALF
+      REAL               ZERO, ONE, TWO, HALF
       PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0,
      $                   HALF = 0.5E0 )
       COMPLEX            CZERO, CONE
@@ -431,10 +445,13 @@
       REAL               ANORM, DIF, DIV, OVFL, RTUNFL, ULP, ULPINV,
      $                   UNFL, VL, VU
 *     ..
+*     .. Local Scalars for CGESVDQ ..
+      INTEGER            LIWORK, NUMRANK
+*     ..
 *     .. Local Arrays ..
       CHARACTER          CJOB( 4 ), CJOBR( 3 ), CJOBV( 2 )
       INTEGER            IOLDSD( 4 ), ISEED2( 4 )
-      REAL               RESULT( 35 )
+      REAL               RESULT( 39 )
 *     ..
 *     .. External Functions ..
       REAL               SLAMCH, SLARND
@@ -442,8 +459,8 @@
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           ALASVM, XERBLA, CBDT01, CBDT05, CGESDD,
-     $                   CGESVD, CGESVJ, CGEJSV, CGESVDX, CLACPY,
-     $                   CLASET, CLATMS, CUNT01, CUNT03
+     $                   CGESVD, CGESVDQ, CGESVJ, CGEJSV, CGESVDX,
+     $                   CLACPY, CLASET, CLATMS, CUNT01, CUNT03
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          ABS, REAL, MAX, MIN
@@ -838,8 +855,64 @@
   130          CONTINUE
 
 *
-*              Test CGESVJ: Factorize A
-*              Note: CGESVJ does not work for M < N
+*              Test CGESVDQ
+*              Note: CGESVDQ only works for M >= N
+*
+               RESULT( 36 ) = ZERO
+               RESULT( 37 ) = ZERO
+               RESULT( 38 ) = ZERO
+               RESULT( 39 ) = ZERO
+*
+               IF( M.GE.N ) THEN
+                  IWTMP = 2*MNMIN*MNMIN + 2*MNMIN + MAX( M, N )
+                  LSWORK = IWTMP + ( IWSPC-1 )*( LWORK-IWTMP ) / 3
+                  LSWORK = MIN( LSWORK, LWORK )
+                  LSWORK = MAX( LSWORK, 1 )
+                  IF( IWSPC.EQ.4 )
+     $               LSWORK = LWORK
+*
+                  CALL CLACPY( 'F', M, N, ASAV, LDA, A, LDA )
+                  SRNAMT = 'CGESVDQ'
+*
+                  LRWORK = MAX(2, M, 5*N)
+                  LIWORK = MAX( N, 1 )
+                  CALL CGESVDQ( 'H', 'N', 'N', 'A', 'A', 
+     $                          M, N, A, LDA, SSAV, USAV, LDU,
+     $                          VTSAV, LDVT, NUMRANK, IWORK, LIWORK,
+     $                          WORK, LWORK, RWORK, LRWORK, IINFO )
+*
+                  IF( IINFO.NE.0 ) THEN
+                     WRITE( NOUNIT, FMT = 9995 )'CGESVDQ', IINFO, M, N,
+     $               JTYPE, LSWORK, IOLDSD
+                     INFO = ABS( IINFO )
+                     RETURN
+                  END IF
+*
+*                 Do tests 36--39
+*
+                  CALL CBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E,
+     $                         VTSAV, LDVT, WORK, RWORK, RESULT( 36 ) )
+                  IF( M.NE.0 .AND. N.NE.0 ) THEN
+                     CALL CUNT01( 'Columns', M, M, USAV, LDU, WORK,
+     $                            LWORK, RWORK, RESULT( 37 ) )
+                     CALL CUNT01( 'Rows', N, N, VTSAV, LDVT, WORK,
+     $                            LWORK, RWORK, RESULT( 38 ) )
+                  END IF
+                  RESULT( 39 ) = ZERO
+                  DO 199 I = 1, MNMIN - 1
+                     IF( SSAV( I ).LT.SSAV( I+1 ) )
+     $                  RESULT( 39 ) = ULPINV
+                     IF( SSAV( I ).LT.ZERO )
+     $                  RESULT( 39 ) = ULPINV
+  199             CONTINUE
+                  IF( MNMIN.GE.1 ) THEN
+                     IF( SSAV( MNMIN ).LT.ZERO )
+     $                  RESULT( 39 ) = ULPINV
+                  END IF
+               END IF
+*
+*              Test CGESVJ
+*              Note: CGESVJ only works for M >= N
 *
                RESULT( 15 ) = ZERO
                RESULT( 16 ) = ZERO
@@ -847,13 +920,13 @@
                RESULT( 18 ) = ZERO
 *
                IF( M.GE.N ) THEN
-               IWTMP = 2*MNMIN*MNMIN + 2*MNMIN + MAX( M, N )
-               LSWORK = IWTMP + ( IWSPC-1 )*( LWORK-IWTMP ) / 3
-               LSWORK = MIN( LSWORK, LWORK )
-               LSWORK = MAX( LSWORK, 1 )
-               LRWORK = MAX(6,N)
-               IF( IWSPC.EQ.4 )
-     $            LSWORK = LWORK
+                  IWTMP = 2*MNMIN*MNMIN + 2*MNMIN + MAX( M, N )
+                  LSWORK = IWTMP + ( IWSPC-1 )*( LWORK-IWTMP ) / 3
+                  LSWORK = MIN( LSWORK, LWORK )
+                  LSWORK = MAX( LSWORK, 1 )
+                  LRWORK = MAX(6,N)
+                  IF( IWSPC.EQ.4 )
+     $               LSWORK = LWORK
 *
                   CALL CLACPY( 'F', M, N, ASAV, LDA, USAV, LDA )
                   SRNAMT = 'CGESVJ'
@@ -861,8 +934,7 @@
      &                        0, A, LDVT, WORK, LWORK, RWORK,
      &                        LRWORK, IINFO )
 *
-*                 CGESVJ retuns V not VT, so we transpose to use the same
-*                 test suite.
+*                 CGESVJ returns V not VH
 *
                   DO J=1,N
                      DO I=1,N
@@ -900,31 +972,30 @@
                   END IF
                END IF
 *
-*              Test CGEJSV: Factorize A
-*              Note: CGEJSV does not work for M < N
+*              Test CGEJSV
+*              Note: CGEJSV only works for M >= N
 *
                RESULT( 19 ) = ZERO
                RESULT( 20 ) = ZERO
                RESULT( 21 ) = ZERO
                RESULT( 22 ) = ZERO
                IF( M.GE.N ) THEN
-               IWTMP = 2*MNMIN*MNMIN + 2*MNMIN + MAX( M, N )
-               LSWORK = IWTMP + ( IWSPC-1 )*( LWORK-IWTMP ) / 3
-               LSWORK = MIN( LSWORK, LWORK )
-               LSWORK = MAX( LSWORK, 1 )
-               IF( IWSPC.EQ.4 )
-     $            LSWORK = LWORK
-               LRWORK = MAX( 7, N + 2*M)
-*
-                 CALL CLACPY( 'F', M, N, ASAV, LDA, VTSAV, LDA )
+                  IWTMP = 2*MNMIN*MNMIN + 2*MNMIN + MAX( M, N )
+                  LSWORK = IWTMP + ( IWSPC-1 )*( LWORK-IWTMP ) / 3
+                  LSWORK = MIN( LSWORK, LWORK )
+                  LSWORK = MAX( LSWORK, 1 )
+                  IF( IWSPC.EQ.4 )
+     $               LSWORK = LWORK
+                  LRWORK = MAX( 7, N + 2*M)
+*
+                  CALL CLACPY( 'F', M, N, ASAV, LDA, VTSAV, LDA )
                   SRNAMT = 'CGEJSV'
                   CALL CGEJSV( 'G', 'U', 'V', 'R', 'N', 'N',
      &                   M, N, VTSAV, LDA, SSAV, USAV, LDU, A, LDVT,
      &                   WORK, LWORK, RWORK,
      &                   LRWORK, IWORK, IINFO )
 *
-*                 CGEJSV retuns V not VT, so we transpose to use the same
-*                 test suite.
+*                 CGEJSV returns V not VH
 *
                   DO 133 J=1,N
                      DO 132 I=1,N
@@ -933,7 +1004,7 @@
   133             END DO
 *
                   IF( IINFO.NE.0 ) THEN
-                     WRITE( NOUNIT, FMT = 9995 )'GESVJ', IINFO, M, N,
+                     WRITE( NOUNIT, FMT = 9995 )'GEJSV', IINFO, M, N,
      $               JTYPE, LSWORK, IOLDSD
                      INFO = ABS( IINFO )
                      RETURN
@@ -1160,7 +1231,7 @@
 *
                NTEST = 0
                NFAIL = 0
-               DO 190 J = 1, 35
+               DO 190 J = 1, 39
                   IF( RESULT( J ).GE.ZERO )
      $               NTEST = NTEST + 1
                   IF( RESULT( J ).GE.THRESH )
@@ -1175,7 +1246,7 @@
                   NTESTF = 2
                END IF
 *
-               DO 200 J = 1, 35
+               DO 200 J = 1, 39
                   IF( RESULT( J ).GE.THRESH ) THEN
                      WRITE( NOUNIT, FMT = 9997 )M, N, JTYPE, IWSPC,
      $                  IOLDSD, J, RESULT( J )
@@ -1251,6 +1322,12 @@
      $      / '33 = | U**T A VT**T - diag(S) | / ( |A| max(M,N) ulp )',
      $      / '34 = | I - U**T U | / ( M ulp ) ',
      $      / '35 = | I - VT VT**T | / ( N ulp ) ',
+     $      ' CGESVDQ(H,N,N,A,A',
+     $      / '36 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
+     $      / '37 = | I - U**T U | / ( M ulp ) ',
+     $      / '38 = | I - VT VT**T | / ( N ulp ) ',
+     $      / '39 = 0 if S contains min(M,N) nonnegative values in',
+     $      ' decreasing order, else 1/ulp',
      $      / / )
  9997 FORMAT( ' M=', I5, ', N=', I5, ', type ', I1, ', IWS=', I1,
      $      ', seed=', 4( I4, ',' ), ' test(', I2, ')=', G11.4 )

lapack-netlib/TESTING/EIG/cerred.f

@@ -36,6 +36,8 @@
 *>       CGEJSV   compute SVD of an M-by-N matrix A where M >= N
 *>       CGESVDX  compute SVD of an M-by-N matrix A(by bisection
 *>                and inverse iteration)
+*>       CGESVDQ  compute SVD of an M-by-N matrix A(with a 
+*>                QR-Preconditioned )
 *> \endverbatim
 *
 *  Arguments:
@@ -101,7 +103,7 @@
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           CHKXER, CGEES, CGEESX, CGEEV, CGEEVX, CGEJSV,
-     $                   CGESDD, CGESVD
+     $                   CGESDD, CGESVD, CGESVDX, CGESVDQ
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAMEN, CSLECT
@@ -495,6 +497,61 @@
          ELSE
             WRITE( NOUT, FMT = 9998 )
          END IF
+*
+*        Test CGESVDQ
+*
+         SRNAMT = 'CGESVDQ'
+         INFOT = 1
+         CALL CGESVDQ( 'X', 'P', 'T', 'A', 'A', 0, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'CGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 2
+         CALL CGESVDQ( 'A', 'X', 'T', 'A', 'A', 0, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'CGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 3
+         CALL CGESVDQ( 'A', 'P', 'X', 'A', 'A', 0, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'CGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 4
+         CALL CGESVDQ( 'A', 'P', 'T', 'X', 'A', 0, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'CGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 5
+         CALL CGESVDQ( 'A', 'P', 'T', 'A', 'X', 0, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'CGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 6
+         CALL CGESVDQ( 'A', 'P', 'T', 'A', 'A', -1, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'CGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 7
+         CALL CGESVDQ( 'A', 'P', 'T', 'A', 'A', 0, 1, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'CGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 9
+         CALL CGESVDQ( 'A', 'P', 'T', 'A', 'A', 1, 1, A, 0, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'CGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 12
+         CALL CGESVDQ( 'A', 'P', 'T', 'A', 'A', 1, 1, A, 1, S, U,
+     $                 -1, VT, 0, NS, IW, 1, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'CGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 14
+         CALL CGESVDQ( 'A', 'P', 'T', 'A', 'A', 1, 1, A, 1, S, U,
+     $                 1, VT, -1, NS, IW, 1, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'CGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 17
+         CALL CGESVDQ( 'A', 'P', 'T', 'A', 'A', 1, 1, A, 1, S, U,
+     $                 1, VT, 1, NS, IW, -5, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'CGESVDQ', INFOT, NOUT, LERR, OK )
+         NT = 11
+         IF( OK ) THEN
+            WRITE( NOUT, FMT = 9999 )SRNAMT( 1:LEN_TRIM( SRNAMT ) ),
+     $           NT
+         ELSE
+            WRITE( NOUT, FMT = 9998 )
+         END IF
       END IF
 *
 *     Print a summary line.

lapack-netlib/TESTING/EIG/cget51.f

@@ -29,12 +29,13 @@
 *>
 *>      CGET51  generally checks a decomposition of the form
 *>
-*>              A = U B VC>
-*>      where * means conjugate transpose and U and V are unitary.
+*>              A = U B V**H
+*>
+*>      where **H means conjugate transpose and U and V are unitary.
 *>
 *>      Specifically, if ITYPE=1
 *>
-*>              RESULT = | A - U B V* | / ( |A| n ulp )
+*>              RESULT = | A - U B V**H | / ( |A| n ulp )
 *>
 *>      If ITYPE=2, then:
 *>
@@ -42,7 +43,7 @@
 *>
 *>      If ITYPE=3, then:
 *>
-*>              RESULT = | I - UU* | / ( n ulp )
+*>              RESULT = | I - U U**H | / ( n ulp )
 *> \endverbatim
 *
 *  Arguments:
@@ -52,9 +53,9 @@
 *> \verbatim
 *>          ITYPE is INTEGER
 *>          Specifies the type of tests to be performed.
-*>          =1: RESULT = | A - U B V* | / ( |A| n ulp )
+*>          =1: RESULT = | A - U B V**H | / ( |A| n ulp )
 *>          =2: RESULT = | A - B | / ( |A| n ulp )
-*>          =3: RESULT = | I - UU* | / ( n ulp )
+*>          =3: RESULT = | I - U U**H | / ( n ulp )
 *> \endverbatim
 *>
 *> \param[in] N
@@ -218,7 +219,7 @@
 *
          IF( ITYPE.EQ.1 ) THEN
 *
-*           ITYPE=1: Compute W = A - UBV'
+*           ITYPE=1: Compute W = A - U B V**H
 *
             CALL CLACPY( ' ', N, N, A, LDA, WORK, N )
             CALL CGEMM( 'N', 'N', N, N, N, CONE, U, LDU, B, LDB, CZERO,
@@ -259,7 +260,7 @@
 *
 *        Tests not scaled by norm(A)
 *
-*        ITYPE=3: Compute  UU' - I
+*        ITYPE=3: Compute  U U**H - I
 *
          CALL CGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO,
      $               WORK, N )

lapack-netlib/TESTING/EIG/chbt21.f

@@ -28,14 +28,16 @@
 *>
 *> CHBT21  generally checks a decomposition of the form
 *>
-*>         A = U S UC>
-*> where * means conjugate transpose, A is hermitian banded, U is
+*>         A = U S U**H
+*>
+*> where **H means conjugate transpose, A is hermitian banded, U is
 *> unitary, and S is diagonal (if KS=0) or symmetric
 *> tridiagonal (if KS=1).
 *>
 *> Specifically:
 *>
-*>         RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC>         RESULT(2) = | I - UU* | / ( n ulp )
+*>         RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
+*>         RESULT(2) = | I - U U**H | / ( n ulp )
 *> \endverbatim
 *
 *  Arguments:
@@ -220,7 +222,7 @@
 *
       ANORM = MAX( CLANHB( '1', CUPLO, N, IKA, A, LDA, RWORK ), UNFL )
 *
-*     Compute error matrix:    Error = A - U S U*
+*     Compute error matrix:    Error = A - U S U**H
 *
 *     Copy A from SB to SP storage format.
 *
@@ -271,7 +273,7 @@
 *
 *     Do Test 2
 *
-*     Compute  UU* - I
+*     Compute  U U**H - I
 *
       CALL CGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO, WORK,
      $            N )

lapack-netlib/TESTING/EIG/chet21.f

@@ -29,8 +29,9 @@
 *>
 *> CHET21 generally checks a decomposition of the form
 *>
-*>    A = U S UC>
-*> where * means conjugate transpose, A is hermitian, U is unitary, and
+*>    A = U S U**H
+*>
+*> where **H means conjugate transpose, A is hermitian, U is unitary, and
 *> S is diagonal (if KBAND=0) or (real) symmetric tridiagonal (if
 *> KBAND=1).
 *>
@@ -42,18 +43,19 @@
 *>
 *> Specifically, if ITYPE=1, then:
 *>
-*>    RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC>    RESULT(2) = | I - UU* | / ( n ulp )
+*>    RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
+*>    RESULT(2) = | I - U U**H | / ( n ulp )
 *>
 *> If ITYPE=2, then:
 *>
-*>    RESULT(1) = | A - V S V* | / ( |A| n ulp )
+*>    RESULT(1) = | A - V S V**H | / ( |A| n ulp )
 *>
 *> If ITYPE=3, then:
 *>
-*>    RESULT(1) = | I - UV* | / ( n ulp )
+*>    RESULT(1) = | I - U V**H | / ( n ulp )
 *>
 *> For ITYPE > 1, the transformation U is expressed as a product
-*> V = H(1)...H(n-2),  where H(j) = I  -  tau(j) v(j) v(j)C> and each
+*> V = H(1)...H(n-2),  where H(j) = I  -  tau(j) v(j) v(j)**H and each
 *> vector v(j) has its first j elements 0 and the remaining n-j elements
 *> stored in V(j+1:n,j).
 *> \endverbatim
@@ -66,14 +68,15 @@
 *>          ITYPE is INTEGER
 *>          Specifies the type of tests to be performed.
 *>          1: U expressed as a dense unitary matrix:
-*>             RESULT(1) = | A - U S U* | / ( |A| n ulp )   *andC>             RESULT(2) = | I - UU* | / ( n ulp )
+*>             RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
+*>             RESULT(2) = | I - U U**H | / ( n ulp )
 *>
 *>          2: U expressed as a product V of Housholder transformations:
-*>             RESULT(1) = | A - V S V* | / ( |A| n ulp )
+*>             RESULT(1) = | A - V S V**H | / ( |A| n ulp )
 *>
 *>          3: U expressed both as a dense unitary matrix and
 *>             as a product of Housholder transformations:
-*>             RESULT(1) = | I - UV* | / ( n ulp )
+*>             RESULT(1) = | I - U V**H | / ( n ulp )
 *> \endverbatim
 *>
 *> \param[in] UPLO
@@ -171,7 +174,7 @@
 *> \verbatim
 *>          TAU is COMPLEX array, dimension (N)
 *>          If ITYPE >= 2, then TAU(j) is the scalar factor of
-*>          v(j) v(j)* in the Householder transformation H(j) of
+*>          v(j) v(j)**H in the Householder transformation H(j) of
 *>          the product  U = H(1)...H(n-2)
 *>          If ITYPE < 2, then TAU is not referenced.
 *> \endverbatim
@@ -294,7 +297,7 @@
 *
       IF( ITYPE.EQ.1 ) THEN
 *
-*        ITYPE=1: error = A - U S U*
+*        ITYPE=1: error = A - U S U**H
 *
          CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
          CALL CLACPY( CUPLO, N, N, A, LDA, WORK, N )
@@ -304,8 +307,7 @@
    10    CONTINUE
 *
          IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN
-CMK            DO 20 J = 1, N - 1
-            DO 20 J = 2, N - 1
+            DO 20 J = 1, N - 1
                CALL CHER2( CUPLO, N, -CMPLX( E( J ) ), U( 1, J ), 1,
      $                     U( 1, J-1 ), 1, WORK, N )
    20       CONTINUE
@@ -314,7 +316,7 @@ CMK            DO 20 J = 1, N - 1
 *
       ELSE IF( ITYPE.EQ.2 ) THEN
 *
-*        ITYPE=2: error = V S V* - A
+*        ITYPE=2: error = V S V**H - A
 *
          CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
 *
@@ -371,7 +373,7 @@ CMK            DO 20 J = 1, N - 1
 *
       ELSE IF( ITYPE.EQ.3 ) THEN
 *
-*        ITYPE=3: error = U V* - I
+*        ITYPE=3: error = U V**H - I
 *
          IF( N.LT.2 )
      $      RETURN
@@ -407,7 +409,7 @@ CMK            DO 20 J = 1, N - 1
 *
 *     Do Test 2
 *
-*     Compute  UU* - I
+*     Compute  U U**H - I
 *
       IF( ITYPE.EQ.1 ) THEN
          CALL CGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO,

lapack-netlib/TESTING/EIG/chet22.f

@@ -42,7 +42,8 @@
 *>
 *>      Specifically, if ITYPE=1, then:
 *>
-*>              RESULT(1) = | U' A U - S | / ( |A| m ulp ) *andC>              RESULT(2) = | I - U'U | / ( m ulp )
+*>              RESULT(1) = | U**H A U - S | / ( |A| m ulp ) and
+*>              RESULT(2) = | I - U**H U | / ( m ulp )
 *> \endverbatim
 *
 *  Arguments:
@@ -52,7 +53,8 @@
 *>  ITYPE   INTEGER
 *>          Specifies the type of tests to be performed.
 *>          1: U expressed as a dense orthogonal matrix:
-*>             RESULT(1) = | A - U S U' | / ( |A| n ulp )   *andC>             RESULT(2) = | I - UU' | / ( n ulp )
+*>             RESULT(1) = | A - U S U**H | / ( |A| n ulp )  and
+*>             RESULT(2) = | I - U U**H | / ( n ulp )
 *>
 *>  UPLO    CHARACTER
 *>          If UPLO='U', the upper triangle of A will be used and the
@@ -122,7 +124,7 @@
 *>
 *>  TAU     COMPLEX array, dimension (N)
 *>          If ITYPE >= 2, then TAU(j) is the scalar factor of
-*>          v(j) v(j)' in the Householder transformation H(j) of
+*>          v(j) v(j)**H in the Householder transformation H(j) of
 *>          the product  U = H(1)...H(n-2)
 *>          If ITYPE < 2, then TAU is not referenced.
 *>          Not modified.
@@ -215,7 +217,7 @@
 *
 *     Compute error matrix:
 *
-*     ITYPE=1: error = U' A U - S
+*     ITYPE=1: error = U**H A U - S
 *
       CALL CHEMM( 'L', UPLO, N, M, CONE, A, LDA, U, LDU, CZERO, WORK,
      $            N )
@@ -249,7 +251,7 @@
 *
 *     Do Test 2
 *
-*     Compute  U'U - I
+*     Compute  U**H U - I
 *
       IF( ITYPE.EQ.1 )
      $   CALL CUNT01( 'Columns', N, M, U, LDU, WORK, 2*N*N, RWORK,

lapack-netlib/TESTING/EIG/chpt21.f

@@ -29,8 +29,9 @@
 *>
 *> CHPT21  generally checks a decomposition of the form
 *>
-*>         A = U S UC>
-*> where * means conjugate transpose, A is hermitian, U is
+*>         A = U S U**H
+*>
+*> where **H means conjugate transpose, A is hermitian, U is
 *> unitary, and S is diagonal (if KBAND=0) or (real) symmetric
 *> tridiagonal (if KBAND=1).  If ITYPE=1, then U is represented as
 *> a dense matrix, otherwise the U is expressed as a product of
@@ -41,15 +42,16 @@
 *>
 *> Specifically, if ITYPE=1, then:
 *>
-*>         RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC>         RESULT(2) = | I - UU* | / ( n ulp )
+*>         RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
+*>         RESULT(2) = | I - U U**H | / ( n ulp )
 *>
 *> If ITYPE=2, then:
 *>
-*>         RESULT(1) = | A - V S V* | / ( |A| n ulp )
+*>         RESULT(1) = | A - V S V**H | / ( |A| n ulp )
 *>
 *> If ITYPE=3, then:
 *>
-*>         RESULT(1) = | I - UV* | / ( n ulp )
+*>         RESULT(1) = | I - U V**H | / ( n ulp )
 *>
 *> Packed storage means that, for example, if UPLO='U', then the columns
 *> of the upper triangle of A are stored one after another, so that
@@ -70,14 +72,16 @@
 *>
 *>    If UPLO='U', then  V = H(n-1)...H(1),  where
 *>
-*>        H(j) = I  -  tau(j) v(j) v(j)C>
+*>        H(j) = I  -  tau(j) v(j) v(j)**H
+*>
 *>    and the first j-1 elements of v(j) are stored in V(1:j-1,j+1),
 *>    (i.e., VP( j*(j+1)/2 + 1 : j*(j+1)/2 + j-1 ) ),
 *>    the j-th element is 1, and the last n-j elements are 0.
 *>
 *>    If UPLO='L', then  V = H(1)...H(n-1),  where
 *>
-*>        H(j) = I  -  tau(j) v(j) v(j)C>
+*>        H(j) = I  -  tau(j) v(j) v(j)**H
+*>
 *>    and the first j elements of v(j) are 0, the (j+1)-st is 1, and the
 *>    (j+2)-nd through n-th elements are stored in V(j+2:n,j) (i.e.,
 *>    in VP( (2*n-j)*(j-1)/2 + j+2 : (2*n-j)*(j-1)/2 + n ) .)
@@ -91,14 +95,15 @@
 *>          ITYPE is INTEGER
 *>          Specifies the type of tests to be performed.
 *>          1: U expressed as a dense unitary matrix:
-*>             RESULT(1) = | A - U S U* | / ( |A| n ulp )   *andC>             RESULT(2) = | I - UU* | / ( n ulp )
+*>             RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
+*>             RESULT(2) = | I - U U**H | / ( n ulp )
 *>
 *>          2: U expressed as a product V of Housholder transformations:
-*>             RESULT(1) = | A - V S V* | / ( |A| n ulp )
+*>             RESULT(1) = | A - V S V**H | / ( |A| n ulp )
 *>
 *>          3: U expressed both as a dense unitary matrix and
 *>             as a product of Housholder transformations:
-*>             RESULT(1) = | I - UV* | / ( n ulp )
+*>             RESULT(1) = | I - U V**H | / ( n ulp )
 *> \endverbatim
 *>
 *> \param[in] UPLO
@@ -181,7 +186,7 @@
 *> \verbatim
 *>          TAU is COMPLEX array, dimension (N)
 *>          If ITYPE >= 2, then TAU(j) is the scalar factor of
-*>          v(j) v(j)* in the Householder transformation H(j) of
+*>          v(j) v(j)**H in the Householder transformation H(j) of
 *>          the product  U = H(1)...H(n-2)
 *>          If ITYPE < 2, then TAU is not referenced.
 *> \endverbatim
@@ -313,7 +318,7 @@
 *
       IF( ITYPE.EQ.1 ) THEN
 *
-*        ITYPE=1: error = A - U S U*
+*        ITYPE=1: error = A - U S U**H
 *
          CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
          CALL CCOPY( LAP, AP, 1, WORK, 1 )
@@ -323,7 +328,7 @@
    10    CONTINUE
 *
          IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN
-            DO 20 J = 2, N - 1
+            DO 20 J = 1, N - 1
                CALL CHPR2( CUPLO, N, -CMPLX( E( J ) ), U( 1, J ), 1,
      $                     U( 1, J-1 ), 1, WORK )
    20       CONTINUE
@@ -332,7 +337,7 @@
 *
       ELSE IF( ITYPE.EQ.2 ) THEN
 *
-*        ITYPE=2: error = V S V* - A
+*        ITYPE=2: error = V S V**H - A
 *
          CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
 *
@@ -400,7 +405,7 @@
 *
       ELSE IF( ITYPE.EQ.3 ) THEN
 *
-*        ITYPE=3: error = U V* - I
+*        ITYPE=3: error = U V**H - I
 *
          IF( N.LT.2 )
      $      RETURN
@@ -431,7 +436,7 @@
 *
 *     Do Test 2
 *
-*     Compute  UU* - I
+*     Compute  U U**H - I
 *
       IF( ITYPE.EQ.1 ) THEN
          CALL CGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO,

lapack-netlib/TESTING/EIG/cstt21.f

@@ -28,14 +28,15 @@
 *>
 *> CSTT21  checks a decomposition of the form
 *>
-*>    A = U S UC>
-*> where * means conjugate transpose, A is real symmetric tridiagonal,
+*>    A = U S U**H
+*>
+*> where **H means conjugate transpose, A is real symmetric tridiagonal,
 *> U is unitary, and S is real and diagonal (if KBAND=0) or symmetric
 *> tridiagonal (if KBAND=1).  Two tests are performed:
 *>
-*>    RESULT(1) = | A - U S U* | / ( |A| n ulp )
+*>    RESULT(1) = | A - U S U**H | / ( |A| n ulp )
 *>
-*>    RESULT(2) = | I - UU* | / ( n ulp )
+*>    RESULT(2) = | I - U U**H | / ( n ulp )
 *> \endverbatim
 *
 *  Arguments:
@@ -201,7 +202,7 @@
       WORK( N**2 ) = AD( N )
       ANORM = MAX( ANORM, ABS( AD( N ) )+TEMP1, UNFL )
 *
-*     Norm of A - USU*
+*     Norm of A - U S U**H
 *
       DO 20 J = 1, N
          CALL CHER( 'L', N, -SD( J ), U( 1, J ), 1, WORK, N )
@@ -228,7 +229,7 @@
 *
 *     Do Test 2
 *
-*     Compute  UU* - I
+*     Compute  U U**H - I
 *
       CALL CGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO, WORK,
      $            N )

lapack-netlib/TESTING/EIG/dbdt05.f

@@ -52,6 +52,7 @@
 *> \verbatim
 *>          A is DOUBLE PRECISION array, dimension (LDA,N)
 *>          The m by n matrix A.
+*> \endverbatim
 *>
 *> \param[in] LDA
 *> \verbatim

lapack-netlib/TESTING/EIG/dchkst.f

@@ -166,7 +166,7 @@
 *>                                              DSTEMR('V', 'I')
 *>
 *> Tests 29 through 34 are disable at present because DSTEMR
-*> does not handle partial specturm requests.
+*> does not handle partial spectrum requests.
 *>
 *> (29)    | S - Z D Z' | / ( |S| n ulp )    DSTEMR('V', 'I')
 *>

lapack-netlib/TESTING/EIG/dchkst2stg.f

@@ -187,7 +187,7 @@
 *>                                              DSTEMR('V', 'I')
 *>
 *> Tests 29 through 34 are disable at present because DSTEMR
-*> does not handle partial specturm requests.
+*> does not handle partial spectrum requests.
 *>
 *> (29)    | S - Z D Z' | / ( |S| n ulp )    DSTEMR('V', 'I')
 *>

lapack-netlib/TESTING/EIG/ddrgsx.f

@@ -769,7 +769,7 @@
       CALL DLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, A, LDA )
       CALL DLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA, B, LDA )
 *
-*     Compute the Schur factorization while swaping the
+*     Compute the Schur factorization while swapping the
 *     m-by-m (1,1)-blocks with n-by-n (2,2)-blocks.
 *
       CALL DGGESX( 'V', 'V', 'S', DLCTSX, 'B', MPLUSN, AI, LDA, BI, LDA,

lapack-netlib/TESTING/EIG/ddrvbd.f

@@ -32,7 +32,7 @@
 *> \verbatim
 *>
 *> DDRVBD checks the singular value decomposition (SVD) drivers
-*> DGESVD, DGESDD, DGESVJ, and DGEJSV.
+*> DGESVD, DGESDD, DGESVDQ, DGESVJ, DGEJSV, and DGESVDX.
 *>
 *> Both DGESVD and DGESDD factor A = U diag(S) VT, where U and VT are
 *> orthogonal and diag(S) is diagonal with the entries of the array S
@@ -90,6 +90,17 @@
 *> (14)   | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
 *>        vector of singular values from the partial SVD
 *>
+*> Test for DGESVDQ:
+*>
+*> (36)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )
+*>
+*> (37)   | I - U'U | / ( M ulp )
+*>
+*> (38)   | I - VT VT' | / ( N ulp )
+*>
+*> (39)   S contains MNMIN nonnegative values in decreasing order.
+*>        (Return 0 if true, 1/ULP if false.)
+*>
 *> Test for DGESVJ:
 *>
 *> (15)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )
@@ -354,6 +365,8 @@
       SUBROUTINE DDRVBD( NSIZES, MM, NN, NTYPES, DOTYPE, ISEED, THRESH,
      $                   A, LDA, U, LDU, VT, LDVT, ASAV, USAV, VTSAV, S,
      $                   SSAV, E, WORK, LWORK, IWORK, NOUT, INFO )
+*
+      IMPLICIT NONE
 *
 *  -- LAPACK test routine (version 3.7.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
@@ -390,13 +403,19 @@
      $                   ITEMP, J, JSIZE, JTYPE, LSWORK, M, MINWRK,
      $                   MMAX, MNMAX, MNMIN, MTYPES, N, NFAIL,
      $                   NMAX, NS, NSI, NSV, NTEST
-      DOUBLE PRECISION  ANORM, DIF, DIV, OVFL, RTUNFL, ULP,
-     $                    ULPINV, UNFL, VL, VU
+      DOUBLE PRECISION   ANORM, DIF, DIV, OVFL, RTUNFL, ULP,
+     $                   ULPINV, UNFL, VL, VU
+*     ..
+*     .. Local Scalars for DGESVDQ ..
+      INTEGER            LIWORK, LRWORK, NUMRANK
+*     ..
+*     .. Local Arrays for DGESVDQ ..
+      DOUBLE PRECISION   RWORK( 2 )
 *     ..
 *     .. Local Arrays ..
       CHARACTER          CJOB( 4 ), CJOBR( 3 ), CJOBV( 2 )
       INTEGER            IOLDSD( 4 ), ISEED2( 4 )
-      DOUBLE PRECISION   RESULT( 40 )
+      DOUBLE PRECISION   RESULT( 39 )
 *     ..
 *     .. External Functions ..
       DOUBLE PRECISION   DLAMCH, DLARND
@@ -404,8 +423,8 @@
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           ALASVM, DBDT01, DGEJSV, DGESDD, DGESVD,
-     $                   DGESVDX, DGESVJ, DLABAD, DLACPY, DLASET,
-     $                   DLATMS, DORT01, DORT03, XERBLA
+     $                   DGESVDQ, DGESVDX, DGESVJ, DLABAD, DLACPY,
+     $                   DLASET, DLATMS, DORT01, DORT03, XERBLA
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          ABS, DBLE, INT, MAX, MIN
@@ -781,8 +800,64 @@
                   RESULT( 14 ) = MAX( RESULT( 14 ), DIF )
   110          CONTINUE
 *
-*              Test DGESVJ: Factorize A
-*              Note: DGESVJ does not work for M < N
+*              Test DGESVDQ
+*              Note: DGESVDQ only works for M >= N
+*
+               RESULT( 36 ) = ZERO
+               RESULT( 37 ) = ZERO
+               RESULT( 38 ) = ZERO
+               RESULT( 39 ) = ZERO
+*
+               IF( M.GE.N ) THEN
+                  IWTMP = 5*MNMIN*MNMIN + 9*MNMIN + MAX( M, N )
+                  LSWORK = IWTMP + ( IWS-1 )*( LWORK-IWTMP ) / 3
+                  LSWORK = MIN( LSWORK, LWORK )
+                  LSWORK = MAX( LSWORK, 1 )
+                  IF( IWS.EQ.4 )
+     $               LSWORK = LWORK
+*
+                  CALL DLACPY( 'F', M, N, ASAV, LDA, A, LDA )
+                  SRNAMT = 'DGESVDQ'
+*
+                  LRWORK = 2
+                  LIWORK = MAX( N, 1 )
+                  CALL DGESVDQ( 'H', 'N', 'N', 'A', 'A', 
+     $                          M, N, A, LDA, SSAV, USAV, LDU,
+     $                          VTSAV, LDVT, NUMRANK, IWORK, LIWORK,
+     $                          WORK, LWORK, RWORK, LRWORK, IINFO )
+*
+                  IF( IINFO.NE.0 ) THEN
+                     WRITE( NOUT, FMT = 9995 )'DGESVDQ', IINFO, M, N,
+     $               JTYPE, LSWORK, IOLDSD
+                     INFO = ABS( IINFO )
+                     RETURN
+                  END IF
+*
+*                 Do tests 36--39
+*
+                  CALL DBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E,
+     $                         VTSAV, LDVT, WORK, RESULT( 36 ) )
+                  IF( M.NE.0 .AND. N.NE.0 ) THEN
+                     CALL DORT01( 'Columns', M, M, USAV, LDU, WORK,
+     $                            LWORK, RESULT( 37 ) )
+                     CALL DORT01( 'Rows', N, N, VTSAV, LDVT, WORK,
+     $                            LWORK, RESULT( 38 ) )
+                  END IF
+                  RESULT( 39 ) = ZERO
+                  DO 199 I = 1, MNMIN - 1
+                     IF( SSAV( I ).LT.SSAV( I+1 ) )
+     $                  RESULT( 39 ) = ULPINV
+                     IF( SSAV( I ).LT.ZERO )
+     $                  RESULT( 39 ) = ULPINV
+  199             CONTINUE
+                  IF( MNMIN.GE.1 ) THEN
+                     IF( SSAV( MNMIN ).LT.ZERO )
+     $                  RESULT( 39 ) = ULPINV
+                  END IF
+               END IF
+*
+*              Test DGESVJ
+*              Note: DGESVJ only works for M >= N
 *
                RESULT( 15 ) = ZERO
                RESULT( 16 ) = ZERO
@@ -802,8 +877,7 @@
                   CALL DGESVJ( 'G', 'U', 'V', M, N, USAV, LDA, SSAV,
      &                        0, A, LDVT, WORK, LWORK, INFO )
 *
-*                 DGESVJ retuns V not VT, so we transpose to use the same
-*                 test suite.
+*                 DGESVJ returns V not VT
 *
                   DO J=1,N
                      DO I=1,N
@@ -841,8 +915,8 @@
                   END IF
                END IF
 *
-*              Test DGEJSV: Factorize A
-*              Note: DGEJSV does not work for M < N
+*              Test DGEJSV
+*              Note: DGEJSV only works for M >= N
 *
                RESULT( 19 ) = ZERO
                RESULT( 20 ) = ZERO
@@ -862,8 +936,7 @@
      &                   M, N, VTSAV, LDA, SSAV, USAV, LDU, A, LDVT,
      &                   WORK, LWORK, IWORK, INFO )
 *
-*                 DGEJSV retuns V not VT, so we transpose to use the same
-*                 test suite.
+*                 DGEJSV returns V not VT
 *
                   DO 140 J=1,N
                      DO 130 I=1,N
@@ -872,7 +945,7 @@
   140             END DO
 *
                   IF( IINFO.NE.0 ) THEN
-                     WRITE( NOUT, FMT = 9995 )'GESVJ', IINFO, M, N,
+                     WRITE( NOUT, FMT = 9995 )'GEJSV', IINFO, M, N,
      $               JTYPE, LSWORK, IOLDSD
                      INFO = ABS( IINFO )
                      RETURN
@@ -1086,7 +1159,7 @@
 *
 *              End of Loop -- Check for RESULT(j) > THRESH
 *
-               DO 210 J = 1, 35
+               DO 210 J = 1, 39
                   IF( RESULT( J ).GE.THRESH ) THEN
                      IF( NFAIL.EQ.0 ) THEN
                         WRITE( NOUT, FMT = 9999 )
@@ -1097,7 +1170,7 @@
                      NFAIL = NFAIL + 1
                   END IF
   210          CONTINUE
-               NTEST = NTEST + 35
+               NTEST = NTEST + 39
   220       CONTINUE
   230    CONTINUE
   240 CONTINUE
@@ -1158,6 +1231,12 @@
      $      ' DGESVDX(V,V,V) ',
      $      / '34 = | I - U**T U | / ( M ulp ) ',
      $      / '35 = | I - VT VT**T | / ( N ulp ) ',
+     $      ' DGESVDQ(H,N,N,A,A',
+     $      / '36 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
+     $      / '37 = | I - U**T U | / ( M ulp ) ',
+     $      / '38 = | I - VT VT**T | / ( N ulp ) ',
+     $      / '39 = 0 if S contains min(M,N) nonnegative values in',
+     $      ' decreasing order, else 1/ulp',
      $      / / )
  9997 FORMAT( ' M=', I5, ', N=', I5, ', type ', I1, ', IWS=', I1,
      $      ', seed=', 4( I4, ',' ), ' test(', I2, ')=', G11.4 )

lapack-netlib/TESTING/EIG/derred.f

@@ -36,6 +36,8 @@
 *>       DGEJSV   compute SVD of an M-by-N matrix A where M >= N
 *>       DGESVDX  compute SVD of an M-by-N matrix A(by bisection
 *>                and inverse iteration)
+*>       DGESVDQ  compute SVD of an M-by-N matrix A(with a 
+*>                QR-Preconditioned )
 *> \endverbatim
 *
 *  Arguments:
@@ -100,7 +102,7 @@
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           CHKXER, DGEES, DGEESX, DGEEV, DGEEVX, DGEJSV,
-     $                   DGESDD, DGESVD
+     $                   DGESDD, DGESVD, DGESVDX, DGESVQ
 *     ..
 *     .. External Functions ..
       LOGICAL            DSLECT, LSAMEN
@@ -486,6 +488,61 @@
          ELSE
             WRITE( NOUT, FMT = 9998 )
          END IF
+*
+*        Test DGESVDQ
+*
+         SRNAMT = 'DGESVDQ'
+         INFOT = 1
+         CALL DGESVDQ( 'X', 'P', 'T', 'A', 'A', 0, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, W, 1, INFO )
+         CALL CHKXER( 'DGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 2
+         CALL DGESVDQ( 'A', 'X', 'T', 'A', 'A', 0, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, W, 1, INFO )
+         CALL CHKXER( 'DGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 3
+         CALL DGESVDQ( 'A', 'P', 'X', 'A', 'A', 0, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, W, 1, INFO )
+         CALL CHKXER( 'DGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 4
+         CALL DGESVDQ( 'A', 'P', 'T', 'X', 'A', 0, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, W, 1, INFO )
+         CALL CHKXER( 'DGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 5
+         CALL DGESVDQ( 'A', 'P', 'T', 'A', 'X', 0, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, W, 1, INFO )
+         CALL CHKXER( 'DGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 6
+         CALL DGESVDQ( 'A', 'P', 'T', 'A', 'A', -1, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, W, 1, INFO )
+         CALL CHKXER( 'DGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 7
+         CALL DGESVDQ( 'A', 'P', 'T', 'A', 'A', 0, 1, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, W, 1, INFO )
+         CALL CHKXER( 'DGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 9
+         CALL DGESVDQ( 'A', 'P', 'T', 'A', 'A', 1, 1, A, 0, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, W, 1, INFO )
+         CALL CHKXER( 'DGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 12
+         CALL DGESVDQ( 'A', 'P', 'T', 'A', 'A', 1, 1, A, 1, S, U,
+     $                 -1, VT, 0, NS, IW, 1, W, 1, W, 1, INFO )
+         CALL CHKXER( 'DGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 14
+         CALL DGESVDQ( 'A', 'P', 'T', 'A', 'A', 1, 1, A, 1, S, U,
+     $                 1, VT, -1, NS, IW, 1, W, 1, W, 1, INFO )
+         CALL CHKXER( 'DGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 17
+         CALL DGESVDQ( 'A', 'P', 'T', 'A', 'A', 1, 1, A, 1, S, U,
+     $                 1, VT, 1, NS, IW, -5, W, 1, W, 1, INFO )
+         CALL CHKXER( 'DGESVDQ', INFOT, NOUT, LERR, OK )
+         NT = 11
+         IF( OK ) THEN
+            WRITE( NOUT, FMT = 9999 )SRNAMT( 1:LEN_TRIM( SRNAMT ) ),
+     $           NT
+         ELSE
+            WRITE( NOUT, FMT = 9998 )
+         END IF
       END IF
 *
 *     Print a summary line.

lapack-netlib/TESTING/EIG/dget39.f

@@ -194,7 +194,7 @@
       VM5( 2 ) = EPS
       VM5( 3 ) = SQRT( SMLNUM )
 *
-*     Initalization
+*     Initialization
 *
       KNT = 0
       RMAX = ZERO

lapack-netlib/TESTING/EIG/dsbt21.f

@@ -28,15 +28,16 @@
 *>
 *> DSBT21  generally checks a decomposition of the form
 *>
-*>         A = U S U'
+*>         A = U S U**T
 *>
-*> where ' means transpose, A is symmetric banded, U is
+*> where **T means transpose, A is symmetric banded, U is
 *> orthogonal, and S is diagonal (if KS=0) or symmetric
 *> tridiagonal (if KS=1).
 *>
 *> Specifically:
 *>
-*>         RESULT(1) = | A - U S U' | / ( |A| n ulp ) *andC>         RESULT(2) = | I - UU' | / ( n ulp )
+*>         RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
+*>         RESULT(2) = | I - U U**T | / ( n ulp )
 *> \endverbatim
 *
 *  Arguments:
@@ -214,7 +215,7 @@
 *
       ANORM = MAX( DLANSB( '1', CUPLO, N, IKA, A, LDA, WORK ), UNFL )
 *
-*     Compute error matrix:    Error = A - U S U'
+*     Compute error matrix:    Error = A - U S U**T
 *
 *     Copy A from SB to SP storage format.
 *
@@ -265,7 +266,7 @@
 *
 *     Do Test 2
 *
-*     Compute  UU' - I
+*     Compute  U U**T - I
 *
       CALL DGEMM( 'N', 'C', N, N, N, ONE, U, LDU, U, LDU, ZERO, WORK,
      $            N )

lapack-netlib/TESTING/EIG/dspt21.f

@@ -28,9 +28,9 @@
 *>
 *> DSPT21  generally checks a decomposition of the form
 *>
-*>         A = U S U'
+*>         A = U S U**T
 *>
-*> where ' means transpose, A is symmetric (stored in packed format), U
+*> where **T means transpose, A is symmetric (stored in packed format), U
 *> is orthogonal, and S is diagonal (if KBAND=0) or symmetric
 *> tridiagonal (if KBAND=1).  If ITYPE=1, then U is represented as a
 *> dense matrix, otherwise the U is expressed as a product of
@@ -41,15 +41,16 @@
 *>
 *> Specifically, if ITYPE=1, then:
 *>
-*>         RESULT(1) = | A - U S U' | / ( |A| n ulp ) *andC>         RESULT(2) = | I - UU' | / ( n ulp )
+*>         RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
+*>         RESULT(2) = | I - U U**T | / ( n ulp )
 *>
 *> If ITYPE=2, then:
 *>
-*>         RESULT(1) = | A - V S V' | / ( |A| n ulp )
+*>         RESULT(1) = | A - V S V**T | / ( |A| n ulp )
 *>
 *> If ITYPE=3, then:
 *>
-*>         RESULT(1) = | I - VU' | / ( n ulp )
+*>         RESULT(1) = | I - V U**T | / ( n ulp )
 *>
 *> Packed storage means that, for example, if UPLO='U', then the columns
 *> of the upper triangle of A are stored one after another, so that
@@ -70,7 +71,7 @@
 *>
 *>    If UPLO='U', then  V = H(n-1)...H(1),  where
 *>
-*>        H(j) = I  -  tau(j) v(j) v(j)'
+*>        H(j) = I  -  tau(j) v(j) v(j)**T
 *>
 *>    and the first j-1 elements of v(j) are stored in V(1:j-1,j+1),
 *>    (i.e., VP( j*(j+1)/2 + 1 : j*(j+1)/2 + j-1 ) ),
@@ -78,7 +79,7 @@
 *>
 *>    If UPLO='L', then  V = H(1)...H(n-1),  where
 *>
-*>        H(j) = I  -  tau(j) v(j) v(j)'
+*>        H(j) = I  -  tau(j) v(j) v(j)**T
 *>
 *>    and the first j elements of v(j) are 0, the (j+1)-st is 1, and the
 *>    (j+2)-nd through n-th elements are stored in V(j+2:n,j) (i.e.,
@@ -93,14 +94,15 @@
 *>          ITYPE is INTEGER
 *>          Specifies the type of tests to be performed.
 *>          1: U expressed as a dense orthogonal matrix:
-*>             RESULT(1) = | A - U S U' | / ( |A| n ulp )   *andC>             RESULT(2) = | I - UU' | / ( n ulp )
+*>             RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
+*>             RESULT(2) = | I - U U**T | / ( n ulp )
 *>
 *>          2: U expressed as a product V of Housholder transformations:
-*>             RESULT(1) = | A - V S V' | / ( |A| n ulp )
+*>             RESULT(1) = | A - V S V**T | / ( |A| n ulp )
 *>
 *>          3: U expressed both as a dense orthogonal matrix and
 *>             as a product of Housholder transformations:
-*>             RESULT(1) = | I - VU' | / ( n ulp )
+*>             RESULT(1) = | I - V U**T | / ( n ulp )
 *> \endverbatim
 *>
 *> \param[in] UPLO
@@ -183,7 +185,7 @@
 *> \verbatim
 *>          TAU is DOUBLE PRECISION array, dimension (N)
 *>          If ITYPE >= 2, then TAU(j) is the scalar factor of
-*>          v(j) v(j)' in the Householder transformation H(j) of
+*>          v(j) v(j)**T in the Householder transformation H(j) of
 *>          the product  U = H(1)...H(n-2)
 *>          If ITYPE < 2, then TAU is not referenced.
 *> \endverbatim
@@ -303,7 +305,7 @@
 *
       IF( ITYPE.EQ.1 ) THEN
 *
-*        ITYPE=1: error = A - U S U'
+*        ITYPE=1: error = A - U S U**T
 *
          CALL DLASET( 'Full', N, N, ZERO, ZERO, WORK, N )
          CALL DCOPY( LAP, AP, 1, WORK, 1 )
@@ -322,7 +324,7 @@
 *
       ELSE IF( ITYPE.EQ.2 ) THEN
 *
-*        ITYPE=2: error = V S V' - A
+*        ITYPE=2: error = V S V**T - A
 *
          CALL DLASET( 'Full', N, N, ZERO, ZERO, WORK, N )
 *
@@ -389,7 +391,7 @@
 *
       ELSE IF( ITYPE.EQ.3 ) THEN
 *
-*        ITYPE=3: error = U V' - I
+*        ITYPE=3: error = U V**T - I
 *
          IF( N.LT.2 )
      $      RETURN
@@ -420,7 +422,7 @@
 *
 *     Do Test 2
 *
-*     Compute  UU' - I
+*     Compute  U U**T - I
 *
       IF( ITYPE.EQ.1 ) THEN
          CALL DGEMM( 'N', 'C', N, N, N, ONE, U, LDU, U, LDU, ZERO, WORK,

lapack-netlib/TESTING/EIG/dsyt21.f

@@ -28,9 +28,9 @@
 *>
 *> DSYT21 generally checks a decomposition of the form
 *>
-*>    A = U S U'
+*>    A = U S U**T
 *>
-*> where ' means transpose, A is symmetric, U is orthogonal, and S is
+*> where **T means transpose, A is symmetric, U is orthogonal, and S is
 *> diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1).
 *>
 *> If ITYPE=1, then U is represented as a dense matrix; otherwise U is
@@ -41,18 +41,19 @@
 *>
 *> Specifically, if ITYPE=1, then:
 *>
-*>    RESULT(1) = | A - U S U' | / ( |A| n ulp ) *andC>    RESULT(2) = | I - UU' | / ( n ulp )
+*>    RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
+*>    RESULT(2) = | I - U U**T | / ( n ulp )
 *>
 *> If ITYPE=2, then:
 *>
-*>    RESULT(1) = | A - V S V' | / ( |A| n ulp )
+*>    RESULT(1) = | A - V S V**T | / ( |A| n ulp )
 *>
 *> If ITYPE=3, then:
 *>
-*>    RESULT(1) = | I - VU' | / ( n ulp )
+*>    RESULT(1) = | I - V U**T | / ( n ulp )
 *>
 *> For ITYPE > 1, the transformation U is expressed as a product
-*> V = H(1)...H(n-2),  where H(j) = I  -  tau(j) v(j) v(j)' and each
+*> V = H(1)...H(n-2),  where H(j) = I  -  tau(j) v(j) v(j)**T and each
 *> vector v(j) has its first j elements 0 and the remaining n-j elements
 *> stored in V(j+1:n,j).
 *> \endverbatim
@@ -65,14 +66,15 @@
 *>          ITYPE is INTEGER
 *>          Specifies the type of tests to be performed.
 *>          1: U expressed as a dense orthogonal matrix:
-*>             RESULT(1) = | A - U S U' | / ( |A| n ulp )   *andC>             RESULT(2) = | I - UU' | / ( n ulp )
+*>             RESULT(1) = | A - U S U**T | / ( |A| n ulp )  and
+*>             RESULT(2) = | I - U U**T | / ( n ulp )
 *>
 *>          2: U expressed as a product V of Housholder transformations:
-*>             RESULT(1) = | A - V S V' | / ( |A| n ulp )
+*>             RESULT(1) = | A - V S V**T | / ( |A| n ulp )
 *>
 *>          3: U expressed both as a dense orthogonal matrix and
 *>             as a product of Housholder transformations:
-*>             RESULT(1) = | I - VU' | / ( n ulp )
+*>             RESULT(1) = | I - V U**T | / ( n ulp )
 *> \endverbatim
 *>
 *> \param[in] UPLO
@@ -170,7 +172,7 @@
 *> \verbatim
 *>          TAU is DOUBLE PRECISION array, dimension (N)
 *>          If ITYPE >= 2, then TAU(j) is the scalar factor of
-*>          v(j) v(j)' in the Householder transformation H(j) of
+*>          v(j) v(j)**T in the Householder transformation H(j) of
 *>          the product  U = H(1)...H(n-2)
 *>          If ITYPE < 2, then TAU is not referenced.
 *> \endverbatim
@@ -283,7 +285,7 @@
 *
       IF( ITYPE.EQ.1 ) THEN
 *
-*        ITYPE=1: error = A - U S U'
+*        ITYPE=1: error = A - U S U**T
 *
          CALL DLASET( 'Full', N, N, ZERO, ZERO, WORK, N )
          CALL DLACPY( CUPLO, N, N, A, LDA, WORK, N )
@@ -302,7 +304,7 @@
 *
       ELSE IF( ITYPE.EQ.2 ) THEN
 *
-*        ITYPE=2: error = V S V' - A
+*        ITYPE=2: error = V S V**T - A
 *
          CALL DLASET( 'Full', N, N, ZERO, ZERO, WORK, N )
 *
@@ -359,7 +361,7 @@
 *
       ELSE IF( ITYPE.EQ.3 ) THEN
 *
-*        ITYPE=3: error = U V' - I
+*        ITYPE=3: error = U V**T - I
 *
          IF( N.LT.2 )
      $      RETURN
@@ -395,7 +397,7 @@
 *
 *     Do Test 2
 *
-*     Compute  UU' - I
+*     Compute  U U**T - I
 *
       IF( ITYPE.EQ.1 ) THEN
          CALL DGEMM( 'N', 'C', N, N, N, ONE, U, LDU, U, LDU, ZERO, WORK,

lapack-netlib/TESTING/EIG/dsyt22.f

@@ -41,7 +41,8 @@
 *>
 *>      Specifically, if ITYPE=1, then:
 *>
-*>              RESULT(1) = | U' A U - S | / ( |A| m ulp ) *andC>              RESULT(2) = | I - U'U | / ( m ulp )
+*>              RESULT(1) = | U**T A U - S | / ( |A| m ulp ) and
+*>              RESULT(2) = | I - U**T U | / ( m ulp )
 *> \endverbatim
 *
 *  Arguments:
@@ -51,7 +52,8 @@
 *>  ITYPE   INTEGER
 *>          Specifies the type of tests to be performed.
 *>          1: U expressed as a dense orthogonal matrix:
-*>             RESULT(1) = | A - U S U' | / ( |A| n ulp )   *andC>             RESULT(2) = | I - UU' | / ( n ulp )
+*>             RESULT(1) = | A - U S U**T | / ( |A| n ulp )  and
+*>             RESULT(2) = | I - U U**T | / ( n ulp )
 *>
 *>  UPLO    CHARACTER
 *>          If UPLO='U', the upper triangle of A will be used and the
@@ -122,7 +124,7 @@
 *>
 *>  TAU     DOUBLE PRECISION array, dimension (N)
 *>          If ITYPE >= 2, then TAU(j) is the scalar factor of
-*>          v(j) v(j)' in the Householder transformation H(j) of
+*>          v(j) v(j)**T in the Householder transformation H(j) of
 *>          the product  U = H(1)...H(n-2)
 *>          If ITYPE < 2, then TAU is not referenced.
 *>          Not modified.
@@ -207,7 +209,7 @@
 *
 *     Compute error matrix:
 *
-*     ITYPE=1: error = U' A U - S
+*     ITYPE=1: error = U**T A U - S
 *
       CALL DSYMM( 'L', UPLO, N, M, ONE, A, LDA, U, LDU, ZERO, WORK, N )
       NN = N*N
@@ -240,7 +242,7 @@
 *
 *     Do Test 2
 *
-*     Compute  U'U - I
+*     Compute  U**T U - I
 *
       IF( ITYPE.EQ.1 )
      $   CALL DORT01( 'Columns', N, M, U, LDU, WORK, 2*N*N,

lapack-netlib/TESTING/EIG/sbdt05.f

@@ -52,6 +52,7 @@
 *> \verbatim
 *>          A is REAL array, dimension (LDA,N)
 *>          The m by n matrix A.
+*> \endverbatim
 *>
 *> \param[in] LDA
 *> \verbatim

lapack-netlib/TESTING/EIG/schkst.f

@@ -166,7 +166,7 @@
 *>                                              SSTEMR('V', 'I')
 *>
 *> Tests 29 through 34 are disable at present because SSTEMR
-*> does not handle partial specturm requests.
+*> does not handle partial spectrum requests.
 *>
 *> (29)    | S - Z D Z' | / ( |S| n ulp )    SSTEMR('V', 'I')
 *>

lapack-netlib/TESTING/EIG/schkst2stg.f

@@ -187,7 +187,7 @@
 *>                                              SSTEMR('V', 'I')
 *>
 *> Tests 29 through 34 are disable at present because SSTEMR
-*> does not handle partial specturm requests.
+*> does not handle partial spectrum requests.
 *>
 *> (29)    | S - Z D Z' | / ( |S| n ulp )    SSTEMR('V', 'I')
 *>

lapack-netlib/TESTING/EIG/sdrgsx.f

@@ -770,7 +770,7 @@ c        MINWRK = MAX( 10*( NSIZE+1 ), 5*NSIZE*NSIZE / 2-2 )
       CALL SLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, A, LDA )
       CALL SLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA, B, LDA )
 *
-*     Compute the Schur factorization while swaping the
+*     Compute the Schur factorization while swapping the
 *     m-by-m (1,1)-blocks with n-by-n (2,2)-blocks.
 *
       CALL SGGESX( 'V', 'V', 'S', SLCTSX, 'B', MPLUSN, AI, LDA, BI, LDA,

lapack-netlib/TESTING/EIG/sdrvbd.f

@@ -32,7 +32,7 @@
 *> \verbatim
 *>
 *> SDRVBD checks the singular value decomposition (SVD) drivers
-*> SGESVD, SGESDD, SGESVJ, and SGEJSV.
+*> SGESVD, SGESDD, SGESVDQ, SGESVJ, SGEJSV, and DGESVDX.
 *>
 *> Both SGESVD and SGESDD factor A = U diag(S) VT, where U and VT are
 *> orthogonal and diag(S) is diagonal with the entries of the array S
@@ -90,6 +90,17 @@
 *> (14)   | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
 *>        vector of singular values from the partial SVD
 *>
+*> Test for SGESVDQ:
+*>
+*> (36)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )
+*>
+*> (37)   | I - U'U | / ( M ulp )
+*>
+*> (38)   | I - VT VT' | / ( N ulp )
+*>
+*> (39)   S contains MNMIN nonnegative values in decreasing order.
+*>        (Return 0 if true, 1/ULP if false.)
+*>
 *> Test for SGESVJ:
 *>
 *> (15)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )
@@ -359,6 +370,8 @@
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     June 2016
+*
+      IMPLICIT NONE
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LDU, LDVT, LWORK, NOUT, NSIZES,
@@ -391,12 +404,18 @@
      $                   MMAX, MNMAX, MNMIN, MTYPES, N, NFAIL,
      $                   NMAX, NS, NSI, NSV, NTEST
       REAL               ANORM, DIF, DIV, OVFL, RTUNFL, ULP,
-     $                    ULPINV, UNFL, VL, VU
+     $                   ULPINV, UNFL, VL, VU
+*     ..
+*     .. Local Scalars for DGESVDQ ..
+      INTEGER            LIWORK, LRWORK, NUMRANK
+*     ..
+*     .. Local Arrays for DGESVDQ ..
+      REAL               RWORK( 2 )
 *     ..
 *     .. Local Arrays ..
       CHARACTER          CJOB( 4 ), CJOBR( 3 ), CJOBV( 2 )
       INTEGER            IOLDSD( 4 ), ISEED2( 4 )
-      REAL               RESULT( 40 )
+      REAL               RESULT( 39 )
 *     ..
 *     .. External Functions ..
       REAL               SLAMCH, SLARND
@@ -404,8 +423,8 @@
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           ALASVM, SBDT01, SGEJSV, SGESDD, SGESVD,
-     $                   SGESVDX, SGESVJ, SLABAD, SLACPY, SLASET,
-     $                   SLATMS, SORT01, SORT03, XERBLA
+     $                   SGESVDQ, SGESVDX, SGESVJ, SLABAD, SLACPY,
+     $                   SLASET, SLATMS, SORT01, SORT03, XERBLA
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          ABS, REAL, INT, MAX, MIN
@@ -781,8 +800,64 @@
                   RESULT( 14 ) = MAX( RESULT( 14 ), DIF )
   110          CONTINUE
 *
-*              Test SGESVJ: Factorize A
-*              Note: SGESVJ does not work for M < N
+*              Test SGESVDQ
+*              Note: SGESVDQ only works for M >= N
+*
+               RESULT( 36 ) = ZERO
+               RESULT( 37 ) = ZERO
+               RESULT( 38 ) = ZERO
+               RESULT( 39 ) = ZERO
+*
+               IF( M.GE.N ) THEN
+                  IWTMP = 5*MNMIN*MNMIN + 9*MNMIN + MAX( M, N )
+                  LSWORK = IWTMP + ( IWS-1 )*( LWORK-IWTMP ) / 3
+                  LSWORK = MIN( LSWORK, LWORK )
+                  LSWORK = MAX( LSWORK, 1 )
+                  IF( IWS.EQ.4 )
+     $               LSWORK = LWORK
+*
+                  CALL SLACPY( 'F', M, N, ASAV, LDA, A, LDA )
+                  SRNAMT = 'SGESVDQ'
+*
+                  LRWORK = 2
+                  LIWORK = MAX( N, 1 )
+                  CALL SGESVDQ( 'H', 'N', 'N', 'A', 'A', 
+     $                          M, N, A, LDA, SSAV, USAV, LDU,
+     $                          VTSAV, LDVT, NUMRANK, IWORK, LIWORK,
+     $                          WORK, LWORK, RWORK, LRWORK, IINFO )
+*
+                  IF( IINFO.NE.0 ) THEN
+                     WRITE( NOUT, FMT = 9995 )'SGESVDQ', IINFO, M, N,
+     $               JTYPE, LSWORK, IOLDSD
+                     INFO = ABS( IINFO )
+                     RETURN
+                  END IF
+*
+*                 Do tests 36--39
+*
+                  CALL SBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E,
+     $                         VTSAV, LDVT, WORK, RESULT( 36 ) )
+                  IF( M.NE.0 .AND. N.NE.0 ) THEN
+                     CALL SORT01( 'Columns', M, M, USAV, LDU, WORK,
+     $                            LWORK, RESULT( 37 ) )
+                     CALL SORT01( 'Rows', N, N, VTSAV, LDVT, WORK,
+     $                            LWORK, RESULT( 38 ) )
+                  END IF
+                  RESULT( 39 ) = ZERO
+                  DO 199 I = 1, MNMIN - 1
+                     IF( SSAV( I ).LT.SSAV( I+1 ) )
+     $                  RESULT( 39 ) = ULPINV
+                     IF( SSAV( I ).LT.ZERO )
+     $                  RESULT( 39 ) = ULPINV
+  199             CONTINUE
+                  IF( MNMIN.GE.1 ) THEN
+                     IF( SSAV( MNMIN ).LT.ZERO )
+     $                  RESULT( 39 ) = ULPINV
+                  END IF
+               END IF
+*
+*              Test SGESVJ
+*              Note: SGESVJ only works for M >= N
 *
                RESULT( 15 ) = ZERO
                RESULT( 16 ) = ZERO
@@ -802,8 +877,7 @@
                   CALL SGESVJ( 'G', 'U', 'V', M, N, USAV, LDA, SSAV,
      &                        0, A, LDVT, WORK, LWORK, INFO )
 *
-*                 SGESVJ retuns V not VT, so we transpose to use the same
-*                 test suite.
+*                 SGESVJ returns V not VT
 *
                   DO J=1,N
                      DO I=1,N
@@ -841,8 +915,8 @@
                   END IF
                END IF
 *
-*              Test SGEJSV: Factorize A
-*              Note: SGEJSV does not work for M < N
+*              Test SGEJSV
+*              Note: SGEJSV only works for M >= N
 *
                RESULT( 19 ) = ZERO
                RESULT( 20 ) = ZERO
@@ -862,8 +936,7 @@
      &                   M, N, VTSAV, LDA, SSAV, USAV, LDU, A, LDVT,
      &                   WORK, LWORK, IWORK, INFO )
 *
-*                 SGEJSV retuns V not VT, so we transpose to use the same
-*                 test suite.
+*                 SGEJSV returns V not VT
 *
                   DO 140 J=1,N
                      DO 130 I=1,N
@@ -872,7 +945,7 @@
   140             END DO
 *
                   IF( IINFO.NE.0 ) THEN
-                     WRITE( NOUT, FMT = 9995 )'GESVJ', IINFO, M, N,
+                     WRITE( NOUT, FMT = 9995 )'GEJSV', IINFO, M, N,
      $               JTYPE, LSWORK, IOLDSD
                      INFO = ABS( IINFO )
                      RETURN
@@ -1086,7 +1159,7 @@
 *
 *              End of Loop -- Check for RESULT(j) > THRESH
 *
-               DO 210 J = 1, 35
+               DO 210 J = 1, 39
                   IF( RESULT( J ).GE.THRESH ) THEN
                      IF( NFAIL.EQ.0 ) THEN
                         WRITE( NOUT, FMT = 9999 )
@@ -1097,7 +1170,7 @@
                      NFAIL = NFAIL + 1
                   END IF
   210          CONTINUE
-               NTEST = NTEST + 35
+               NTEST = NTEST + 39
   220       CONTINUE
   230    CONTINUE
   240 CONTINUE
@@ -1158,6 +1231,12 @@
      $      ' SGESVDX(V,V,V) ',
      $      / '34 = | I - U**T U | / ( M ulp ) ',
      $      / '35 = | I - VT VT**T | / ( N ulp ) ',
+     $      ' SGESVDQ(H,N,N,A,A',
+     $      / '36 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
+     $      / '37 = | I - U**T U | / ( M ulp ) ',
+     $      / '38 = | I - VT VT**T | / ( N ulp ) ',
+     $      / '39 = 0 if S contains min(M,N) nonnegative values in',
+     $      ' decreasing order, else 1/ulp',
      $      / / )
  9997 FORMAT( ' M=', I5, ', N=', I5, ', type ', I1, ', IWS=', I1,
      $      ', seed=', 4( I4, ',' ), ' test(', I2, ')=', G11.4 )

lapack-netlib/TESTING/EIG/serred.f

@@ -36,6 +36,8 @@
 *>       SGEJSV   compute SVD of an M-by-N matrix A where M >= N
 *>       SGESVDX  compute SVD of an M-by-N matrix A(by bisection
 *>                and inverse iteration)
+*>       SGESVDQ  compute SVD of an M-by-N matrix A(with a 
+*>                QR-Preconditioned )
 *> \endverbatim
 *
 *  Arguments:
@@ -100,7 +102,7 @@
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           CHKXER, SGEES, SGEESX, SGEEV, SGEEVX, SGEJSV,
-     $                   SGESDD, SGESVD
+     $                   SGESDD, SGESVD, SGESVDX, SGESVDQ
 *     ..
 *     .. External Functions ..
       LOGICAL            SSLECT, LSAMEN
@@ -486,6 +488,61 @@
          ELSE
             WRITE( NOUT, FMT = 9998 )
          END IF
+*
+*        Test SGESVDQ
+*
+         SRNAMT = 'SGESVDQ'
+         INFOT = 1
+         CALL SGESVDQ( 'X', 'P', 'T', 'A', 'A', 0, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, W, 1, INFO )
+         CALL CHKXER( 'SGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 2
+         CALL SGESVDQ( 'A', 'X', 'T', 'A', 'A', 0, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, W, 1, INFO )
+         CALL CHKXER( 'SGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 3
+         CALL SGESVDQ( 'A', 'P', 'X', 'A', 'A', 0, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, W, 1, INFO )
+         CALL CHKXER( 'SGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 4
+         CALL SGESVDQ( 'A', 'P', 'T', 'X', 'A', 0, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, W, 1, INFO )
+         CALL CHKXER( 'SGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 5
+         CALL SGESVDQ( 'A', 'P', 'T', 'A', 'X', 0, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, W, 1, INFO )
+         CALL CHKXER( 'SGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 6
+         CALL SGESVDQ( 'A', 'P', 'T', 'A', 'A', -1, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, W, 1, INFO )
+         CALL CHKXER( 'SGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 7
+         CALL SGESVDQ( 'A', 'P', 'T', 'A', 'A', 0, 1, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, W, 1, INFO )
+         CALL CHKXER( 'SGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 9
+         CALL SGESVDQ( 'A', 'P', 'T', 'A', 'A', 1, 1, A, 0, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, W, 1, INFO )
+         CALL CHKXER( 'SGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 12
+         CALL SGESVDQ( 'A', 'P', 'T', 'A', 'A', 1, 1, A, 1, S, U,
+     $                 -1, VT, 0, NS, IW, 1, W, 1, W, 1, INFO )
+         CALL CHKXER( 'SGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 14
+         CALL SGESVDQ( 'A', 'P', 'T', 'A', 'A', 1, 1, A, 1, S, U,
+     $                 1, VT, -1, NS, IW, 1, W, 1, W, 1, INFO )
+         CALL CHKXER( 'SGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 17
+         CALL SGESVDQ( 'A', 'P', 'T', 'A', 'A', 1, 1, A, 1, S, U,
+     $                 1, VT, 1, NS, IW, -5, W, 1, W, 1, INFO )
+         CALL CHKXER( 'SGESVDQ', INFOT, NOUT, LERR, OK )
+         NT = 11
+         IF( OK ) THEN
+            WRITE( NOUT, FMT = 9999 )SRNAMT( 1:LEN_TRIM( SRNAMT ) ),
+     $           NT
+         ELSE
+            WRITE( NOUT, FMT = 9998 )
+         END IF
       END IF
 *
 *     Print a summary line.

lapack-netlib/TESTING/EIG/sget39.f

@@ -194,7 +194,7 @@
       VM5( 2 ) = EPS
       VM5( 3 ) = SQRT( SMLNUM )
 *
-*     Initalization
+*     Initialization
 *
       KNT = 0
       RMAX = ZERO

lapack-netlib/TESTING/EIG/ssbt21.f

@@ -28,15 +28,16 @@
 *>
 *> SSBT21  generally checks a decomposition of the form
 *>
-*>         A = U S U'
+*>         A = U S U**T
 *>
-*> where ' means transpose, A is symmetric banded, U is
+*> where **T means transpose, A is symmetric banded, U is
 *> orthogonal, and S is diagonal (if KS=0) or symmetric
 *> tridiagonal (if KS=1).
 *>
 *> Specifically:
 *>
-*>         RESULT(1) = | A - U S U' | / ( |A| n ulp ) *andC>         RESULT(2) = | I - UU' | / ( n ulp )
+*>         RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
+*>         RESULT(2) = | I - U U**T | / ( n ulp )
 *> \endverbatim
 *
 *  Arguments:
@@ -214,7 +215,7 @@
 *
       ANORM = MAX( SLANSB( '1', CUPLO, N, IKA, A, LDA, WORK ), UNFL )
 *
-*     Compute error matrix:    Error = A - U S U'
+*     Compute error matrix:    Error = A - U S U**T
 *
 *     Copy A from SB to SP storage format.
 *
@@ -265,7 +266,7 @@
 *
 *     Do Test 2
 *
-*     Compute  UU' - I
+*     Compute  U U**T - I
 *
       CALL SGEMM( 'N', 'C', N, N, N, ONE, U, LDU, U, LDU, ZERO, WORK,
      $            N )

lapack-netlib/TESTING/EIG/sspt21.f

@@ -28,9 +28,9 @@
 *>
 *> SSPT21  generally checks a decomposition of the form
 *>
-*>         A = U S U'
+*>         A = U S U**T
 *>
-*> where ' means transpose, A is symmetric (stored in packed format), U
+*> where **T means transpose, A is symmetric (stored in packed format), U
 *> is orthogonal, and S is diagonal (if KBAND=0) or symmetric
 *> tridiagonal (if KBAND=1).  If ITYPE=1, then U is represented as a
 *> dense matrix, otherwise the U is expressed as a product of
@@ -41,15 +41,16 @@
 *>
 *> Specifically, if ITYPE=1, then:
 *>
-*>         RESULT(1) = | A - U S U' | / ( |A| n ulp ) *andC>         RESULT(2) = | I - UU' | / ( n ulp )
+*>         RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
+*>         RESULT(2) = | I - U U**T | / ( n ulp )
 *>
 *> If ITYPE=2, then:
 *>
-*>         RESULT(1) = | A - V S V' | / ( |A| n ulp )
+*>         RESULT(1) = | A - V S V**T | / ( |A| n ulp )
 *>
 *> If ITYPE=3, then:
 *>
-*>         RESULT(1) = | I - VU' | / ( n ulp )
+*>         RESULT(1) = | I - V U**T | / ( n ulp )
 *>
 *> Packed storage means that, for example, if UPLO='U', then the columns
 *> of the upper triangle of A are stored one after another, so that
@@ -70,7 +71,7 @@
 *>
 *>    If UPLO='U', then  V = H(n-1)...H(1),  where
 *>
-*>        H(j) = I  -  tau(j) v(j) v(j)'
+*>        H(j) = I  -  tau(j) v(j) v(j)**T
 *>
 *>    and the first j-1 elements of v(j) are stored in V(1:j-1,j+1),
 *>    (i.e., VP( j*(j+1)/2 + 1 : j*(j+1)/2 + j-1 ) ),
@@ -78,7 +79,7 @@
 *>
 *>    If UPLO='L', then  V = H(1)...H(n-1),  where
 *>
-*>        H(j) = I  -  tau(j) v(j) v(j)'
+*>        H(j) = I  -  tau(j) v(j) v(j)**T
 *>
 *>    and the first j elements of v(j) are 0, the (j+1)-st is 1, and the
 *>    (j+2)-nd through n-th elements are stored in V(j+2:n,j) (i.e.,
@@ -93,14 +94,15 @@
 *>          ITYPE is INTEGER
 *>          Specifies the type of tests to be performed.
 *>          1: U expressed as a dense orthogonal matrix:
-*>             RESULT(1) = | A - U S U' | / ( |A| n ulp )   *andC>             RESULT(2) = | I - UU' | / ( n ulp )
+*>             RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
+*>             RESULT(2) = | I - U U**T | / ( n ulp )
 *>
 *>          2: U expressed as a product V of Housholder transformations:
-*>             RESULT(1) = | A - V S V' | / ( |A| n ulp )
+*>             RESULT(1) = | A - V S V**T | / ( |A| n ulp )
 *>
 *>          3: U expressed both as a dense orthogonal matrix and
 *>             as a product of Housholder transformations:
-*>             RESULT(1) = | I - VU' | / ( n ulp )
+*>             RESULT(1) = | I - V U**T | / ( n ulp )
 *> \endverbatim
 *>
 *> \param[in] UPLO
@@ -183,7 +185,7 @@
 *> \verbatim
 *>          TAU is REAL array, dimension (N)
 *>          If ITYPE >= 2, then TAU(j) is the scalar factor of
-*>          v(j) v(j)' in the Householder transformation H(j) of
+*>          v(j) v(j)**T in the Householder transformation H(j) of
 *>          the product  U = H(1)...H(n-2)
 *>          If ITYPE < 2, then TAU is not referenced.
 *> \endverbatim
@@ -303,7 +305,7 @@
 *
       IF( ITYPE.EQ.1 ) THEN
 *
-*        ITYPE=1: error = A - U S U'
+*        ITYPE=1: error = A - U S U**T
 *
          CALL SLASET( 'Full', N, N, ZERO, ZERO, WORK, N )
          CALL SCOPY( LAP, AP, 1, WORK, 1 )
@@ -322,7 +324,7 @@
 *
       ELSE IF( ITYPE.EQ.2 ) THEN
 *
-*        ITYPE=2: error = V S V' - A
+*        ITYPE=2: error = V S V**T - A
 *
          CALL SLASET( 'Full', N, N, ZERO, ZERO, WORK, N )
 *
@@ -389,7 +391,7 @@
 *
       ELSE IF( ITYPE.EQ.3 ) THEN
 *
-*        ITYPE=3: error = U V' - I
+*        ITYPE=3: error = U V**T - I
 *
          IF( N.LT.2 )
      $      RETURN
@@ -420,7 +422,7 @@
 *
 *     Do Test 2
 *
-*     Compute  UU' - I
+*     Compute  U U**T - I
 *
       IF( ITYPE.EQ.1 ) THEN
          CALL SGEMM( 'N', 'C', N, N, N, ONE, U, LDU, U, LDU, ZERO, WORK,

lapack-netlib/TESTING/EIG/ssyt21.f

@@ -28,9 +28,9 @@
 *>
 *> SSYT21 generally checks a decomposition of the form
 *>
-*>    A = U S U'
+*>    A = U S U**T
 *>
-*> where ' means transpose, A is symmetric, U is orthogonal, and S is
+*> where **T means transpose, A is symmetric, U is orthogonal, and S is
 *> diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1).
 *>
 *> If ITYPE=1, then U is represented as a dense matrix; otherwise U is
@@ -41,18 +41,19 @@
 *>
 *> Specifically, if ITYPE=1, then:
 *>
-*>    RESULT(1) = | A - U S U' | / ( |A| n ulp ) *andC>    RESULT(2) = | I - UU' | / ( n ulp )
+*>    RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
+*>    RESULT(2) = | I - U U**T | / ( n ulp )
 *>
 *> If ITYPE=2, then:
 *>
-*>    RESULT(1) = | A - V S V' | / ( |A| n ulp )
+*>    RESULT(1) = | A - V S V**T | / ( |A| n ulp )
 *>
 *> If ITYPE=3, then:
 *>
-*>    RESULT(1) = | I - VU' | / ( n ulp )
+*>    RESULT(1) = | I - V U**T | / ( n ulp )
 *>
 *> For ITYPE > 1, the transformation U is expressed as a product
-*> V = H(1)...H(n-2),  where H(j) = I  -  tau(j) v(j) v(j)' and each
+*> V = H(1)...H(n-2),  where H(j) = I  -  tau(j) v(j) v(j)**T and each
 *> vector v(j) has its first j elements 0 and the remaining n-j elements
 *> stored in V(j+1:n,j).
 *> \endverbatim
@@ -65,14 +66,15 @@
 *>          ITYPE is INTEGER
 *>          Specifies the type of tests to be performed.
 *>          1: U expressed as a dense orthogonal matrix:
-*>             RESULT(1) = | A - U S U' | / ( |A| n ulp )   *andC>             RESULT(2) = | I - UU' | / ( n ulp )
+*>             RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
+*>             RESULT(2) = | I - U U**T | / ( n ulp )
 *>
 *>          2: U expressed as a product V of Housholder transformations:
-*>             RESULT(1) = | A - V S V' | / ( |A| n ulp )
+*>             RESULT(1) = | A - V S V**T | / ( |A| n ulp )
 *>
 *>          3: U expressed both as a dense orthogonal matrix and
 *>             as a product of Housholder transformations:
-*>             RESULT(1) = | I - VU' | / ( n ulp )
+*>             RESULT(1) = | I - V U**T | / ( n ulp )
 *> \endverbatim
 *>
 *> \param[in] UPLO
@@ -170,7 +172,7 @@
 *> \verbatim
 *>          TAU is REAL array, dimension (N)
 *>          If ITYPE >= 2, then TAU(j) is the scalar factor of
-*>          v(j) v(j)' in the Householder transformation H(j) of
+*>          v(j) v(j)**T in the Householder transformation H(j) of
 *>          the product  U = H(1)...H(n-2)
 *>          If ITYPE < 2, then TAU is not referenced.
 *> \endverbatim
@@ -283,7 +285,7 @@
 *
       IF( ITYPE.EQ.1 ) THEN
 *
-*        ITYPE=1: error = A - U S U'
+*        ITYPE=1: error = A - U S U**T
 *
          CALL SLASET( 'Full', N, N, ZERO, ZERO, WORK, N )
          CALL SLACPY( CUPLO, N, N, A, LDA, WORK, N )
@@ -302,7 +304,7 @@
 *
       ELSE IF( ITYPE.EQ.2 ) THEN
 *
-*        ITYPE=2: error = V S V' - A
+*        ITYPE=2: error = V S V**T - A
 *
          CALL SLASET( 'Full', N, N, ZERO, ZERO, WORK, N )
 *
@@ -359,7 +361,7 @@
 *
       ELSE IF( ITYPE.EQ.3 ) THEN
 *
-*        ITYPE=3: error = U V' - I
+*        ITYPE=3: error = U V**T - I
 *
          IF( N.LT.2 )
      $      RETURN
@@ -395,7 +397,7 @@
 *
 *     Do Test 2
 *
-*     Compute  UU' - I
+*     Compute  U U**T - I
 *
       IF( ITYPE.EQ.1 ) THEN
          CALL SGEMM( 'N', 'C', N, N, N, ONE, U, LDU, U, LDU, ZERO, WORK,

lapack-netlib/TESTING/EIG/ssyt22.f

@@ -41,7 +41,8 @@
 *>
 *>      Specifically, if ITYPE=1, then:
 *>
-*>              RESULT(1) = | U' A U - S | / ( |A| m ulp ) *andC>              RESULT(2) = | I - U'U | / ( m ulp )
+*>              RESULT(1) = | U**T A U - S | / ( |A| m ulp ) and
+*>              RESULT(2) = | I - U**T U | / ( m ulp )
 *> \endverbatim
 *
 *  Arguments:
@@ -51,7 +52,8 @@
 *>  ITYPE   INTEGER
 *>          Specifies the type of tests to be performed.
 *>          1: U expressed as a dense orthogonal matrix:
-*>             RESULT(1) = | A - U S U' | / ( |A| n ulp )   *andC>             RESULT(2) = | I - UU' | / ( n ulp )
+*>             RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
+*>             RESULT(2) = | I - U U**T | / ( n ulp )
 *>
 *>  UPLO    CHARACTER
 *>          If UPLO='U', the upper triangle of A will be used and the
@@ -122,7 +124,7 @@
 *>
 *>  TAU     REAL array, dimension (N)
 *>          If ITYPE >= 2, then TAU(j) is the scalar factor of
-*>          v(j) v(j)' in the Householder transformation H(j) of
+*>          v(j) v(j)**T in the Householder transformation H(j) of
 *>          the product  U = H(1)...H(n-2)
 *>          If ITYPE < 2, then TAU is not referenced.
 *>          Not modified.
@@ -207,7 +209,7 @@
 *
 *     Compute error matrix:
 *
-*     ITYPE=1: error = U' A U - S
+*     ITYPE=1: error = U**T A U - S
 *
       CALL SSYMM( 'L', UPLO, N, M, ONE, A, LDA, U, LDU, ZERO, WORK, N )
       NN = N*N
@@ -240,7 +242,7 @@
 *
 *     Do Test 2
 *
-*     Compute  U'U - I
+*     Compute  U**T U - I
 *
       IF( ITYPE.EQ.1 )
      $   CALL SORT01( 'Columns', N, M, U, LDU, WORK, 2*N*N,

lapack-netlib/TESTING/EIG/zbdt05.f

@@ -52,6 +52,7 @@
 *> \verbatim
 *>          A is COMPLEX*16 array, dimension (LDA,N)
 *>          The m by n matrix A.
+*> \endverbatim
 *>
 *> \param[in] LDA
 *> \verbatim

lapack-netlib/TESTING/EIG/zchkst.f

@@ -167,7 +167,7 @@
 *>                                              ZSTEMR('V', 'I')
 *>
 *> Tests 29 through 34 are disable at present because ZSTEMR
-*> does not handle partial specturm requests.
+*> does not handle partial spectrum requests.
 *>
 *> (29)    | S - Z D Z* | / ( |S| n ulp )    ZSTEMR('V', 'I')
 *>

lapack-netlib/TESTING/EIG/zchkst2stg.f

@@ -188,7 +188,7 @@
 *>                                              ZSTEMR('V', 'I')
 *>
 *> Tests 29 through 34 are disable at present because ZSTEMR
-*> does not handle partial specturm requests.
+*> does not handle partial spectrum requests.
 *>
 *> (29)    | S - Z D Z* | / ( |S| n ulp )    ZSTEMR('V', 'I')
 *>

lapack-netlib/TESTING/EIG/zdrgev3.f

@@ -389,7 +389,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date Febuary 2015
+*> \date February 2015
 *
 *> \ingroup complex16_eig
 *

lapack-netlib/TESTING/EIG/zdrgsx.f

@@ -738,7 +738,7 @@
       CALL ZLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, A, LDA )
       CALL ZLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA, B, LDA )
 *
-*     Compute the Schur factorization while swaping the
+*     Compute the Schur factorization while swapping the
 *     m-by-m (1,1)-blocks with n-by-n (2,2)-blocks.
 *
       CALL ZGGESX( 'V', 'V', 'S', ZLCTSX, 'B', MPLUSN, AI, LDA, BI, LDA,

lapack-netlib/TESTING/EIG/zdrvbd.f

@@ -33,8 +33,9 @@
 *>
 *> \verbatim
 *>
-*> ZDRVBD checks the singular value decomposition (SVD) driver ZGESVD
-*> and ZGESDD.
+*> ZDRVBD checks the singular value decomposition (SVD) driver ZGESVD,
+*> ZGESDD, ZGESVJ, ZGEJSV, ZGESVDX, and ZGESVDQ.
+*>
 *> ZGESVD and ZGESDD factors A = U diag(S) VT, where U and VT are
 *> unitary and diag(S) is diagonal with the entries of the array S on
 *> its diagonal. The entries of S are the singular values, nonnegative
@@ -73,81 +74,92 @@
 *>
 *> Test for ZGESDD:
 *>
-*> (1)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )
+*> (8)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )
 *>
-*> (2)   | I - U'U | / ( M ulp )
+*> (9)   | I - U'U | / ( M ulp )
 *>
-*> (3)   | I - VT VT' | / ( N ulp )
+*> (10)  | I - VT VT' | / ( N ulp )
 *>
-*> (4)   S contains MNMIN nonnegative values in decreasing order.
+*> (11)  S contains MNMIN nonnegative values in decreasing order.
 *>       (Return 0 if true, 1/ULP if false.)
 *>
-*> (5)   | U - Upartial | / ( M ulp ) where Upartial is a partially
+*> (12)  | U - Upartial | / ( M ulp ) where Upartial is a partially
 *>       computed U.
 *>
-*> (6)   | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
+*> (13)  | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
 *>       computed VT.
 *>
-*> (7)   | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
+*> (14)  | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
 *>       vector of singular values from the partial SVD
 *>
+*> Test for ZGESVDQ:
+*>
+*> (36)  | A - U diag(S) VT | / ( |A| max(M,N) ulp )
+*>
+*> (37)  | I - U'U | / ( M ulp )
+*>
+*> (38)  | I - VT VT' | / ( N ulp )
+*>
+*> (39)  S contains MNMIN nonnegative values in decreasing order.
+*>       (Return 0 if true, 1/ULP if false.)
+*>
 *> Test for ZGESVJ:
 *>
-*> (1)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )
+*> (15)  | A - U diag(S) VT | / ( |A| max(M,N) ulp )
 *>
-*> (2)   | I - U'U | / ( M ulp )
+*> (16)  | I - U'U | / ( M ulp )
 *>
-*> (3)   | I - VT VT' | / ( N ulp )
+*> (17)  | I - VT VT' | / ( N ulp )
 *>
-*> (4)   S contains MNMIN nonnegative values in decreasing order.
+*> (18)  S contains MNMIN nonnegative values in decreasing order.
 *>       (Return 0 if true, 1/ULP if false.)
 *>
 *> Test for ZGEJSV:
 *>
-*> (1)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )
+*> (19)  | A - U diag(S) VT | / ( |A| max(M,N) ulp )
 *>
-*> (2)   | I - U'U | / ( M ulp )
+*> (20)  | I - U'U | / ( M ulp )
 *>
-*> (3)   | I - VT VT' | / ( N ulp )
+*> (21)  | I - VT VT' | / ( N ulp )
 *>
-*> (4)   S contains MNMIN nonnegative values in decreasing order.
+*> (22)  S contains MNMIN nonnegative values in decreasing order.
 *>        (Return 0 if true, 1/ULP if false.)
 *>
 *> Test for ZGESVDX( 'V', 'V', 'A' )/ZGESVDX( 'N', 'N', 'A' )
 *>
-*> (1)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )
+*> (23)  | A - U diag(S) VT | / ( |A| max(M,N) ulp )
 *>
-*> (2)   | I - U'U | / ( M ulp )
+*> (24)  | I - U'U | / ( M ulp )
 *>
-*> (3)   | I - VT VT' | / ( N ulp )
+*> (25)  | I - VT VT' | / ( N ulp )
 *>
-*> (4)   S contains MNMIN nonnegative values in decreasing order.
+*> (26)  S contains MNMIN nonnegative values in decreasing order.
 *>       (Return 0 if true, 1/ULP if false.)
 *>
-*> (5)   | U - Upartial | / ( M ulp ) where Upartial is a partially
+*> (27)  | U - Upartial | / ( M ulp ) where Upartial is a partially
 *>       computed U.
 *>
-*> (6)   | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
+*> (28)  | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
 *>       computed VT.
 *>
-*> (7)   | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
+*> (29)  | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
 *>       vector of singular values from the partial SVD
 *>
 *> Test for ZGESVDX( 'V', 'V', 'I' )
 *>
-*> (8)   | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )
+*> (30)  | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )
 *>
-*> (9)   | I - U'U | / ( M ulp )
+*> (31)  | I - U'U | / ( M ulp )
 *>
-*> (10)  | I - VT VT' | / ( N ulp )
+*> (32)  | I - VT VT' | / ( N ulp )
 *>
 *> Test for ZGESVDX( 'V', 'V', 'V' )
 *>
-*> (11)   | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )
+*> (33)   | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )
 *>
-*> (12)   | I - U'U | / ( M ulp )
+*> (34)   | I - U'U | / ( M ulp )
 *>
-*> (13)   | I - VT VT' | / ( N ulp )
+*> (35)   | I - VT VT' | / ( N ulp )
 *>
 *> The "sizes" are specified by the arrays MM(1:NSIZES) and
 *> NN(1:NSIZES); the value of each element pair (MM(j),NN(j))
@@ -393,6 +405,8 @@
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     June 2016
+*
+      IMPLICIT NONE
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LDU, LDVT, LWORK, NOUNIT, NSIZES,
@@ -411,7 +425,7 @@
 *  =====================================================================
 *
 *     .. Parameters ..
-      DOUBLE PRECISION  ZERO, ONE, TWO, HALF
+      DOUBLE PRECISION   ZERO, ONE, TWO, HALF
       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0,
      $                   HALF = 0.5D0 )
       COMPLEX*16         CZERO, CONE
@@ -431,10 +445,13 @@
       DOUBLE PRECISION   ANORM, DIF, DIV, OVFL, RTUNFL, ULP, ULPINV,
      $                   UNFL, VL, VU
 *     ..
+*     .. Local Scalars for ZGESVDQ ..
+      INTEGER            LIWORK, NUMRANK
+*     ..
 *     .. Local Arrays ..
       CHARACTER          CJOB( 4 ), CJOBR( 3 ), CJOBV( 2 )
       INTEGER            IOLDSD( 4 ), ISEED2( 4 )
-      DOUBLE PRECISION   RESULT( 35 )
+      DOUBLE PRECISION   RESULT( 39 )
 *     ..
 *     .. External Functions ..
       DOUBLE PRECISION   DLAMCH, DLARND
@@ -442,8 +459,8 @@
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           ALASVM, XERBLA, ZBDT01, ZBDT05, ZGESDD,
-     $                   ZGESVD, ZGESVJ, ZGEJSV, ZGESVDX, ZLACPY,
-     $                   ZLASET, ZLATMS, ZUNT01, ZUNT03
+     $                   ZGESVD, ZGESVDQ, ZGESVJ, ZGEJSV, ZGESVDX,
+     $                   ZLACPY, ZLASET, ZLATMS, ZUNT01, ZUNT03
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          ABS, DBLE, MAX, MIN
@@ -836,10 +853,65 @@
   120             CONTINUE
                   RESULT( 14 ) = MAX( RESULT( 14 ), DIF )
   130          CONTINUE
-
 *
-*              Test ZGESVJ: Factorize A
-*              Note: ZGESVJ does not work for M < N
+*              Test ZGESVDQ
+*              Note: ZGESVDQ only works for M >= N
+*
+               RESULT( 36 ) = ZERO
+               RESULT( 37 ) = ZERO
+               RESULT( 38 ) = ZERO
+               RESULT( 39 ) = ZERO
+*
+               IF( M.GE.N ) THEN
+                  IWTMP = 2*MNMIN*MNMIN + 2*MNMIN + MAX( M, N )
+                  LSWORK = IWTMP + ( IWSPC-1 )*( LWORK-IWTMP ) / 3
+                  LSWORK = MIN( LSWORK, LWORK )
+                  LSWORK = MAX( LSWORK, 1 )
+                  IF( IWSPC.EQ.4 )
+     $               LSWORK = LWORK
+*
+                  CALL ZLACPY( 'F', M, N, ASAV, LDA, A, LDA )
+                  SRNAMT = 'ZGESVDQ'
+*
+                  LRWORK = MAX(2, M, 5*N)
+                  LIWORK = MAX( N, 1 )
+                  CALL ZGESVDQ( 'H', 'N', 'N', 'A', 'A', 
+     $                          M, N, A, LDA, SSAV, USAV, LDU,
+     $                          VTSAV, LDVT, NUMRANK, IWORK, LIWORK,
+     $                          WORK, LWORK, RWORK, LRWORK, IINFO )
+*
+                  IF( IINFO.NE.0 ) THEN
+                     WRITE( NOUNIT, FMT = 9995 )'ZGESVDQ', IINFO, M, N,
+     $               JTYPE, LSWORK, IOLDSD
+                     INFO = ABS( IINFO )
+                     RETURN
+                  END IF
+*
+*                 Do tests 36--39
+*
+                  CALL ZBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E,
+     $                         VTSAV, LDVT, WORK, RWORK, RESULT( 36 ) )
+                  IF( M.NE.0 .AND. N.NE.0 ) THEN
+                     CALL ZUNT01( 'Columns', M, M, USAV, LDU, WORK,
+     $                            LWORK, RWORK, RESULT( 37 ) )
+                     CALL ZUNT01( 'Rows', N, N, VTSAV, LDVT, WORK,
+     $                            LWORK, RWORK, RESULT( 38 ) )
+                  END IF
+                  RESULT( 39 ) = ZERO
+                  DO 199 I = 1, MNMIN - 1
+                     IF( SSAV( I ).LT.SSAV( I+1 ) )
+     $                  RESULT( 39 ) = ULPINV
+                     IF( SSAV( I ).LT.ZERO )
+     $                  RESULT( 39 ) = ULPINV
+  199             CONTINUE
+                  IF( MNMIN.GE.1 ) THEN
+                     IF( SSAV( MNMIN ).LT.ZERO )
+     $                  RESULT( 39 ) = ULPINV
+                  END IF
+               END IF
+*
+*              Test ZGESVJ
+*              Note: ZGESVJ only works for M >= N
 *
                RESULT( 15 ) = ZERO
                RESULT( 16 ) = ZERO
@@ -847,13 +919,13 @@
                RESULT( 18 ) = ZERO
 *
                IF( M.GE.N ) THEN
-               IWTMP = 2*MNMIN*MNMIN + 2*MNMIN + MAX( M, N )
-               LSWORK = IWTMP + ( IWSPC-1 )*( LWORK-IWTMP ) / 3
-               LSWORK = MIN( LSWORK, LWORK )
-               LSWORK = MAX( LSWORK, 1 )
-               LRWORK = MAX(6,N)
-               IF( IWSPC.EQ.4 )
-     $            LSWORK = LWORK
+                  IWTMP = 2*MNMIN*MNMIN + 2*MNMIN + MAX( M, N )
+                  LSWORK = IWTMP + ( IWSPC-1 )*( LWORK-IWTMP ) / 3
+                  LSWORK = MIN( LSWORK, LWORK )
+                  LSWORK = MAX( LSWORK, 1 )
+                  LRWORK = MAX(6,N)
+                  IF( IWSPC.EQ.4 )
+     $               LSWORK = LWORK
 *
                   CALL ZLACPY( 'F', M, N, ASAV, LDA, USAV, LDA )
                   SRNAMT = 'ZGESVJ'
@@ -861,8 +933,7 @@
      &                        0, A, LDVT, WORK, LWORK, RWORK,
      &                        LRWORK, IINFO )
 *
-*                 ZGESVJ retuns V not VT, so we transpose to use the same
-*                 test suite.
+*                 ZGESVJ returns V not VH
 *
                   DO J=1,N
                      DO I=1,N
@@ -900,21 +971,21 @@
                   END IF
                END IF
 *
-*              Test ZGEJSV: Factorize A
-*              Note: ZGEJSV does not work for M < N
+*              Test ZGEJSV
+*              Note: ZGEJSV only works for M >= N
 *
                RESULT( 19 ) = ZERO
                RESULT( 20 ) = ZERO
                RESULT( 21 ) = ZERO
                RESULT( 22 ) = ZERO
                IF( M.GE.N ) THEN
-               IWTMP = 2*MNMIN*MNMIN + 2*MNMIN + MAX( M, N )
-               LSWORK = IWTMP + ( IWSPC-1 )*( LWORK-IWTMP ) / 3
-               LSWORK = MIN( LSWORK, LWORK )
-               LSWORK = MAX( LSWORK, 1 )
-               IF( IWSPC.EQ.4 )
-     $            LSWORK = LWORK
-               LRWORK = MAX( 7, N + 2*M)
+                  IWTMP = 2*MNMIN*MNMIN + 2*MNMIN + MAX( M, N )
+                  LSWORK = IWTMP + ( IWSPC-1 )*( LWORK-IWTMP ) / 3
+                  LSWORK = MIN( LSWORK, LWORK )
+                  LSWORK = MAX( LSWORK, 1 )
+                  IF( IWSPC.EQ.4 )
+     $               LSWORK = LWORK
+                  LRWORK = MAX( 7, N + 2*M)
 *
                   CALL ZLACPY( 'F', M, N, ASAV, LDA, VTSAV, LDA )
                   SRNAMT = 'ZGEJSV'
@@ -923,8 +994,7 @@
      &                   WORK, LWORK, RWORK,
      &                   LRWORK, IWORK, IINFO )
 *
-*                 ZGEJSV retuns V not VT, so we transpose to use the same
-*                 test suite.
+*                 ZGEJSV returns V not VH
 *
                   DO 133 J=1,N
                      DO 132 I=1,N
@@ -933,7 +1003,7 @@
   133             END DO
 *
                   IF( IINFO.NE.0 ) THEN
-                     WRITE( NOUNIT, FMT = 9995 )'GESVJ', IINFO, M, N,
+                     WRITE( NOUNIT, FMT = 9995 )'GEJSV', IINFO, M, N,
      $               JTYPE, LSWORK, IOLDSD
                      INFO = ABS( IINFO )
                      RETURN
@@ -1160,7 +1230,7 @@
 *
                NTEST = 0
                NFAIL = 0
-               DO 190 J = 1, 35
+               DO 190 J = 1, 39
                   IF( RESULT( J ).GE.ZERO )
      $               NTEST = NTEST + 1
                   IF( RESULT( J ).GE.THRESH )
@@ -1175,7 +1245,7 @@
                   NTESTF = 2
                END IF
 *
-               DO 200 J = 1, 35
+               DO 200 J = 1, 39
                   IF( RESULT( J ).GE.THRESH ) THEN
                      WRITE( NOUNIT, FMT = 9997 )M, N, JTYPE, IWSPC,
      $                  IOLDSD, J, RESULT( J )
@@ -1251,6 +1321,12 @@
      $      / '33 = | U**T A VT**T - diag(S) | / ( |A| max(M,N) ulp )',
      $      / '34 = | I - U**T U | / ( M ulp ) ',
      $      / '35 = | I - VT VT**T | / ( N ulp ) ',
+     $      ' ZGESVDQ(H,N,N,A,A',
+     $      / '36 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
+     $      / '37 = | I - U**T U | / ( M ulp ) ',
+     $      / '38 = | I - VT VT**T | / ( N ulp ) ',
+     $      / '39 = 0 if S contains min(M,N) nonnegative values in',
+     $      ' decreasing order, else 1/ulp',
      $      / / )
  9997 FORMAT( ' M=', I5, ', N=', I5, ', type ', I1, ', IWS=', I1,
      $      ', seed=', 4( I4, ',' ), ' test(', I2, ')=', G11.4 )

lapack-netlib/TESTING/EIG/zerred.f

@@ -36,6 +36,8 @@
 *>       ZGEJSV   compute SVD of an M-by-N matrix A where M >= N
 *>       ZGESVDX  compute SVD of an M-by-N matrix A(by bisection
 *>                and inverse iteration)
+*>       ZGESVDQ  compute SVD of an M-by-N matrix A(with a 
+*>                QR-Preconditioned )
 *> \endverbatim
 *
 *  Arguments:
@@ -101,7 +103,7 @@
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           CHKXER, ZGEES, ZGEESX, ZGEEV, ZGEEVX, ZGESVJ,
-     $                   ZGESDD, ZGESVD
+     $                   ZGESDD, ZGESVD, ZGESVDX, ZGESVQ
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAMEN, ZSLECT
@@ -495,6 +497,61 @@
          ELSE
             WRITE( NOUT, FMT = 9998 )
          END IF
+*
+*        Test ZGESVDQ
+*
+         SRNAMT = 'ZGESVDQ'
+         INFOT = 1
+         CALL ZGESVDQ( 'X', 'P', 'T', 'A', 'A', 0, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'ZGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 2
+         CALL ZGESVDQ( 'A', 'X', 'T', 'A', 'A', 0, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'ZGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 3
+         CALL ZGESVDQ( 'A', 'P', 'X', 'A', 'A', 0, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'ZGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 4
+         CALL ZGESVDQ( 'A', 'P', 'T', 'X', 'A', 0, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'ZGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 5
+         CALL ZGESVDQ( 'A', 'P', 'T', 'A', 'X', 0, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'ZGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 6
+         CALL ZGESVDQ( 'A', 'P', 'T', 'A', 'A', -1, 0, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'ZGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 7
+         CALL ZGESVDQ( 'A', 'P', 'T', 'A', 'A', 0, 1, A, 1, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'ZGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 9
+         CALL ZGESVDQ( 'A', 'P', 'T', 'A', 'A', 1, 1, A, 0, S, U,
+     $                 0, VT, 0, NS, IW, 1, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'ZGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 12
+         CALL ZGESVDQ( 'A', 'P', 'T', 'A', 'A', 1, 1, A, 1, S, U,
+     $                 -1, VT, 0, NS, IW, 1, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'ZGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 14
+         CALL ZGESVDQ( 'A', 'P', 'T', 'A', 'A', 1, 1, A, 1, S, U,
+     $                 1, VT, -1, NS, IW, 1, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'ZGESVDQ', INFOT, NOUT, LERR, OK )
+         INFOT = 17
+         CALL ZGESVDQ( 'A', 'P', 'T', 'A', 'A', 1, 1, A, 1, S, U,
+     $                 1, VT, 1, NS, IW, -5, W, 1, RW, 1, INFO )
+         CALL CHKXER( 'ZGESVDQ', INFOT, NOUT, LERR, OK )
+         NT = 11
+         IF( OK ) THEN
+            WRITE( NOUT, FMT = 9999 )SRNAMT( 1:LEN_TRIM( SRNAMT ) ),
+     $           NT
+         ELSE
+            WRITE( NOUT, FMT = 9998 )
+         END IF
       END IF
 *
 *     Print a summary line.

lapack-netlib/TESTING/EIG/zget51.f

@@ -29,12 +29,13 @@
 *>
 *>      ZGET51  generally checks a decomposition of the form
 *>
-*>              A = U B VC>
-*>      where * means conjugate transpose and U and V are unitary.
+*>              A = U B V**H
+*>
+*>      where **H means conjugate transpose and U and V are unitary.
 *>
 *>      Specifically, if ITYPE=1
 *>
-*>              RESULT = | A - U B V* | / ( |A| n ulp )
+*>              RESULT = | A - U B V**H | / ( |A| n ulp )
 *>
 *>      If ITYPE=2, then:
 *>
@@ -42,7 +43,7 @@
 *>
 *>      If ITYPE=3, then:
 *>
-*>              RESULT = | I - UU* | / ( n ulp )
+*>              RESULT = | I - U U**H | / ( n ulp )
 *> \endverbatim
 *
 *  Arguments:
@@ -52,9 +53,9 @@
 *> \verbatim
 *>          ITYPE is INTEGER
 *>          Specifies the type of tests to be performed.
-*>          =1: RESULT = | A - U B V* | / ( |A| n ulp )
+*>          =1: RESULT = | A - U B V**H | / ( |A| n ulp )
 *>          =2: RESULT = | A - B | / ( |A| n ulp )
-*>          =3: RESULT = | I - UU* | / ( n ulp )
+*>          =3: RESULT = | I - U U**H | / ( n ulp )
 *> \endverbatim
 *>
 *> \param[in] N
@@ -218,7 +219,7 @@
 *
          IF( ITYPE.EQ.1 ) THEN
 *
-*           ITYPE=1: Compute W = A - UBV'
+*           ITYPE=1: Compute W = A - U B V**H
 *
             CALL ZLACPY( ' ', N, N, A, LDA, WORK, N )
             CALL ZGEMM( 'N', 'N', N, N, N, CONE, U, LDU, B, LDB, CZERO,
@@ -259,7 +260,7 @@
 *
 *        Tests not scaled by norm(A)
 *
-*        ITYPE=3: Compute  UU' - I
+*        ITYPE=3: Compute  U U**H - I
 *
          CALL ZGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO,
      $               WORK, N )

lapack-netlib/TESTING/EIG/zhbt21.f

@@ -28,14 +28,16 @@
 *>
 *> ZHBT21  generally checks a decomposition of the form
 *>
-*>         A = U S UC>
-*> where * means conjugate transpose, A is hermitian banded, U is
+*>         A = U S U**H
+*>
+*> where **H means conjugate transpose, A is hermitian banded, U is
 *> unitary, and S is diagonal (if KS=0) or symmetric
 *> tridiagonal (if KS=1).
 *>
 *> Specifically:
 *>
-*>         RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC>         RESULT(2) = | I - UU* | / ( n ulp )
+*>         RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
+*>         RESULT(2) = | I - U U**H | / ( n ulp )
 *> \endverbatim
 *
 *  Arguments:
@@ -220,7 +222,7 @@
 *
       ANORM = MAX( ZLANHB( '1', CUPLO, N, IKA, A, LDA, RWORK ), UNFL )
 *
-*     Compute error matrix:    Error = A - U S U*
+*     Compute error matrix:    Error = A - U S U**H
 *
 *     Copy A from SB to SP storage format.
 *
@@ -271,7 +273,7 @@
 *
 *     Do Test 2
 *
-*     Compute  UU* - I
+*     Compute  U U**H - I
 *
       CALL ZGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO, WORK,
      $            N )

lapack-netlib/TESTING/EIG/zhet21.f

@@ -29,8 +29,9 @@
 *>
 *> ZHET21 generally checks a decomposition of the form
 *>
-*>    A = U S UC>
-*> where * means conjugate transpose, A is hermitian, U is unitary, and
+*>    A = U S U**H
+*>
+*> where **H means conjugate transpose, A is hermitian, U is unitary, and
 *> S is diagonal (if KBAND=0) or (real) symmetric tridiagonal (if
 *> KBAND=1).
 *>
@@ -42,18 +43,19 @@
 *>
 *> Specifically, if ITYPE=1, then:
 *>
-*>    RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC>    RESULT(2) = | I - UU* | / ( n ulp )
+*>    RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
+*>    RESULT(2) = | I - U U**H | / ( n ulp )
 *>
 *> If ITYPE=2, then:
 *>
-*>    RESULT(1) = | A - V S V* | / ( |A| n ulp )
+*>    RESULT(1) = | A - V S V**H | / ( |A| n ulp )
 *>
 *> If ITYPE=3, then:
 *>
-*>    RESULT(1) = | I - UV* | / ( n ulp )
+*>    RESULT(1) = | I - U V**H | / ( n ulp )
 *>
 *> For ITYPE > 1, the transformation U is expressed as a product
-*> V = H(1)...H(n-2),  where H(j) = I  -  tau(j) v(j) v(j)C> and each
+*> V = H(1)...H(n-2),  where H(j) = I  -  tau(j) v(j) v(j)**H and each
 *> vector v(j) has its first j elements 0 and the remaining n-j elements
 *> stored in V(j+1:n,j).
 *> \endverbatim
@@ -66,14 +68,15 @@
 *>          ITYPE is INTEGER
 *>          Specifies the type of tests to be performed.
 *>          1: U expressed as a dense unitary matrix:
-*>             RESULT(1) = | A - U S U* | / ( |A| n ulp )   *andC>             RESULT(2) = | I - UU* | / ( n ulp )
+*>             RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
+*>             RESULT(2) = | I - U U**H | / ( n ulp )
 *>
 *>          2: U expressed as a product V of Housholder transformations:
-*>             RESULT(1) = | A - V S V* | / ( |A| n ulp )
+*>             RESULT(1) = | A - V S V**H | / ( |A| n ulp )
 *>
 *>          3: U expressed both as a dense unitary matrix and
 *>             as a product of Housholder transformations:
-*>             RESULT(1) = | I - UV* | / ( n ulp )
+*>             RESULT(1) = | I - U V**H | / ( n ulp )
 *> \endverbatim
 *>
 *> \param[in] UPLO
@@ -171,7 +174,7 @@
 *> \verbatim
 *>          TAU is COMPLEX*16 array, dimension (N)
 *>          If ITYPE >= 2, then TAU(j) is the scalar factor of
-*>          v(j) v(j)* in the Householder transformation H(j) of
+*>          v(j) v(j)**H in the Householder transformation H(j) of
 *>          the product  U = H(1)...H(n-2)
 *>          If ITYPE < 2, then TAU is not referenced.
 *> \endverbatim
@@ -294,7 +297,7 @@
 *
       IF( ITYPE.EQ.1 ) THEN
 *
-*        ITYPE=1: error = A - U S U*
+*        ITYPE=1: error = A - U S U**H
 *
          CALL ZLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
          CALL ZLACPY( CUPLO, N, N, A, LDA, WORK, N )
@@ -304,8 +307,7 @@
    10    CONTINUE
 *
          IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN
-CMK            DO 20 J = 1, N - 1
-            DO 20 J = 2, N - 1
+            DO 20 J = 1, N - 1
                CALL ZHER2( CUPLO, N, -DCMPLX( E( J ) ), U( 1, J ), 1,
      $                     U( 1, J-1 ), 1, WORK, N )
    20       CONTINUE
@@ -314,7 +316,7 @@ CMK            DO 20 J = 1, N - 1
 *
       ELSE IF( ITYPE.EQ.2 ) THEN
 *
-*        ITYPE=2: error = V S V* - A
+*        ITYPE=2: error = V S V**H - A
 *
          CALL ZLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
 *
@@ -371,7 +373,7 @@ CMK            DO 20 J = 1, N - 1
 *
       ELSE IF( ITYPE.EQ.3 ) THEN
 *
-*        ITYPE=3: error = U V* - I
+*        ITYPE=3: error = U V**H - I
 *
          IF( N.LT.2 )
      $      RETURN
@@ -407,7 +409,7 @@ CMK            DO 20 J = 1, N - 1
 *
 *     Do Test 2
 *
-*     Compute  UU* - I
+*     Compute  U U**H - I
 *
       IF( ITYPE.EQ.1 ) THEN
          CALL ZGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO,

lapack-netlib/TESTING/EIG/zhet22.f

@@ -42,7 +42,8 @@
 *>
 *>      Specifically, if ITYPE=1, then:
 *>
-*>              RESULT(1) = | U' A U - S | / ( |A| m ulp ) *andC>              RESULT(2) = | I - U'U | / ( m ulp )
+*>              RESULT(1) = | U**H A U - S | / ( |A| m ulp ) and
+*>              RESULT(2) = | I - U**H U | / ( m ulp )
 *> \endverbatim
 *
 *  Arguments:
@@ -52,7 +53,8 @@
 *>  ITYPE   INTEGER
 *>          Specifies the type of tests to be performed.
 *>          1: U expressed as a dense orthogonal matrix:
-*>             RESULT(1) = | A - U S U' | / ( |A| n ulp )   *andC>             RESULT(2) = | I - UU' | / ( n ulp )
+*>             RESULT(1) = | A - U S U**H | / ( |A| n ulp )   *and
+*>             RESULT(2) = | I - U U**H | / ( n ulp )
 *>
 *>  UPLO    CHARACTER
 *>          If UPLO='U', the upper triangle of A will be used and the
@@ -122,7 +124,7 @@
 *>
 *>  TAU     COMPLEX*16 array, dimension (N)
 *>          If ITYPE >= 2, then TAU(j) is the scalar factor of
-*>          v(j) v(j)' in the Householder transformation H(j) of
+*>          v(j) v(j)**H in the Householder transformation H(j) of
 *>          the product  U = H(1)...H(n-2)
 *>          If ITYPE < 2, then TAU is not referenced.
 *>          Not modified.
@@ -215,7 +217,7 @@
 *
 *     Compute error matrix:
 *
-*     ITYPE=1: error = U' A U - S
+*     ITYPE=1: error = U**H A U - S
 *
       CALL ZHEMM( 'L', UPLO, N, M, CONE, A, LDA, U, LDU, CZERO, WORK,
      $            N )
@@ -249,7 +251,7 @@
 *
 *     Do Test 2
 *
-*     Compute  U'U - I
+*     Compute  U**H U - I
 *
       IF( ITYPE.EQ.1 )
      $   CALL ZUNT01( 'Columns', N, M, U, LDU, WORK, 2*N*N, RWORK,

lapack-netlib/TESTING/EIG/zhpt21.f

@@ -29,8 +29,9 @@
 *>
 *> ZHPT21  generally checks a decomposition of the form
 *>
-*>         A = U S UC>
-*> where * means conjugate transpose, A is hermitian, U is
+*>         A = U S U**H
+*>
+*> where **H means conjugate transpose, A is hermitian, U is
 *> unitary, and S is diagonal (if KBAND=0) or (real) symmetric
 *> tridiagonal (if KBAND=1).  If ITYPE=1, then U is represented as
 *> a dense matrix, otherwise the U is expressed as a product of
@@ -41,15 +42,16 @@
 *>
 *> Specifically, if ITYPE=1, then:
 *>
-*>         RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC>         RESULT(2) = | I - UU* | / ( n ulp )
+*>         RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
+*>         RESULT(2) = | I - U U**H | / ( n ulp )
 *>
 *> If ITYPE=2, then:
 *>
-*>         RESULT(1) = | A - V S V* | / ( |A| n ulp )
+*>         RESULT(1) = | A - V S V**H | / ( |A| n ulp )
 *>
 *> If ITYPE=3, then:
 *>
-*>         RESULT(1) = | I - UV* | / ( n ulp )
+*>         RESULT(1) = | I - U V**H | / ( n ulp )
 *>
 *> Packed storage means that, for example, if UPLO='U', then the columns
 *> of the upper triangle of A are stored one after another, so that
@@ -70,14 +72,16 @@
 *>
 *>    If UPLO='U', then  V = H(n-1)...H(1),  where
 *>
-*>        H(j) = I  -  tau(j) v(j) v(j)C>
+*>        H(j) = I  -  tau(j) v(j) v(j)**H
+*>
 *>    and the first j-1 elements of v(j) are stored in V(1:j-1,j+1),
 *>    (i.e., VP( j*(j+1)/2 + 1 : j*(j+1)/2 + j-1 ) ),
 *>    the j-th element is 1, and the last n-j elements are 0.
 *>
 *>    If UPLO='L', then  V = H(1)...H(n-1),  where
 *>
-*>        H(j) = I  -  tau(j) v(j) v(j)C>
+*>        H(j) = I  -  tau(j) v(j) v(j)**H
+*>
 *>    and the first j elements of v(j) are 0, the (j+1)-st is 1, and the
 *>    (j+2)-nd through n-th elements are stored in V(j+2:n,j) (i.e.,
 *>    in VP( (2*n-j)*(j-1)/2 + j+2 : (2*n-j)*(j-1)/2 + n ) .)
@@ -91,14 +95,15 @@
 *>          ITYPE is INTEGER
 *>          Specifies the type of tests to be performed.
 *>          1: U expressed as a dense unitary matrix:
-*>             RESULT(1) = | A - U S U* | / ( |A| n ulp )   *andC>             RESULT(2) = | I - UU* | / ( n ulp )
+*>             RESULT(1) = | A - U S U**H | / ( |A| n ulp )   and
+*>             RESULT(2) = | I - U U**H | / ( n ulp )
 *>
 *>          2: U expressed as a product V of Housholder transformations:
-*>             RESULT(1) = | A - V S V* | / ( |A| n ulp )
+*>             RESULT(1) = | A - V S V**H | / ( |A| n ulp )
 *>
 *>          3: U expressed both as a dense unitary matrix and
 *>             as a product of Housholder transformations:
-*>             RESULT(1) = | I - UV* | / ( n ulp )
+*>             RESULT(1) = | I - U V**H | / ( n ulp )
 *> \endverbatim
 *>
 *> \param[in] UPLO
@@ -181,7 +186,7 @@
 *> \verbatim
 *>          TAU is COMPLEX*16 array, dimension (N)
 *>          If ITYPE >= 2, then TAU(j) is the scalar factor of
-*>          v(j) v(j)* in the Householder transformation H(j) of
+*>          v(j) v(j)**H in the Householder transformation H(j) of
 *>          the product  U = H(1)...H(n-2)
 *>          If ITYPE < 2, then TAU is not referenced.
 *> \endverbatim
@@ -313,7 +318,7 @@
 *
       IF( ITYPE.EQ.1 ) THEN
 *
-*        ITYPE=1: error = A - U S U*
+*        ITYPE=1: error = A - U S U**H
 *
          CALL ZLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
          CALL ZCOPY( LAP, AP, 1, WORK, 1 )
@@ -323,8 +328,7 @@
    10    CONTINUE
 *
          IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN
-CMK            DO 20 J = 1, N - 1
-            DO 20 J = 2, N - 1
+            DO 20 J = 1, N - 1
                CALL ZHPR2( CUPLO, N, -DCMPLX( E( J ) ), U( 1, J ), 1,
      $                     U( 1, J-1 ), 1, WORK )
    20       CONTINUE
@@ -333,7 +337,7 @@ CMK            DO 20 J = 1, N - 1
 *
       ELSE IF( ITYPE.EQ.2 ) THEN
 *
-*        ITYPE=2: error = V S V* - A
+*        ITYPE=2: error = V S V**H - A
 *
          CALL ZLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
 *
@@ -401,7 +405,7 @@ CMK            DO 20 J = 1, N - 1
 *
       ELSE IF( ITYPE.EQ.3 ) THEN
 *
-*        ITYPE=3: error = U V* - I
+*        ITYPE=3: error = U V**H - I
 *
          IF( N.LT.2 )
      $      RETURN
@@ -432,7 +436,7 @@ CMK            DO 20 J = 1, N - 1
 *
 *     Do Test 2
 *
-*     Compute  UU* - I
+*     Compute  U U**H - I
 *
       IF( ITYPE.EQ.1 ) THEN
          CALL ZGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO,

lapack-netlib/TESTING/EIG/zstt21.f

@@ -28,14 +28,15 @@
 *>
 *> ZSTT21  checks a decomposition of the form
 *>
-*>    A = U S UC>
-*> where * means conjugate transpose, A is real symmetric tridiagonal,
+*>    A = U S U**H
+*>
+*> where **H means conjugate transpose, A is real symmetric tridiagonal,
 *> U is unitary, and S is real and diagonal (if KBAND=0) or symmetric
 *> tridiagonal (if KBAND=1).  Two tests are performed:
 *>
-*>    RESULT(1) = | A - U S U* | / ( |A| n ulp )
+*>    RESULT(1) = | A - U S U**H | / ( |A| n ulp )
 *>
-*>    RESULT(2) = | I - UU* | / ( n ulp )
+*>    RESULT(2) = | I - U U**H | / ( n ulp )
 *> \endverbatim
 *
 *  Arguments:
@@ -228,7 +229,7 @@
 *
 *     Do Test 2
 *
-*     Compute  UU* - I
+*     Compute  U U**H - I
 *
       CALL ZGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO, WORK,
      $            N )