Update LAPACK to 3.9.0

lapack-netlib/SRC/CMakeLists.txt

@@ -106,7 +106,7 @@ set(SLASRC
    slatbs.f slatdf.f slatps.f slatrd.f slatrs.f slatrz.f
    slauu2.f slauum.f sopgtr.f sopmtr.f sorg2l.f sorg2r.f
    sorgbr.f sorghr.f sorgl2.f sorglq.f sorgql.f sorgqr.f sorgr2.f
-   sorgrq.f sorgtr.f sorm2l.f sorm2r.f sorm22.f
+   sorgrq.f sorgtr.f sorgtsqr.f sorm2l.f sorm2r.f sorm22.f
    sormbr.f sormhr.f sorml2.f sormlq.f sormql.f sormqr.f sormr2.f
    sormr3.f sormrq.f sormrz.f sormtr.f spbcon.f spbequ.f spbrfs.f
    spbstf.f spbsv.f  spbsvx.f
@@ -148,9 +148,11 @@ set(SLASRC
    sgetsls.f sgeqr.f slatsqr.f slamtsqr.f sgemqr.f
    sgelq.f slaswlq.f slamswlq.f sgemlq.f
    stplqt.f stplqt2.f stpmlqt.f
+   sorhr_col.f slaorhr_col_getrfnp.f slaorhr_col_getrfnp2.f
    ssytrd_2stage.f ssytrd_sy2sb.f ssytrd_sb2st.F ssb2st_kernels.f
    ssyevd_2stage.f ssyev_2stage.f ssyevx_2stage.f ssyevr_2stage.f
-   ssbev_2stage.f ssbevx_2stage.f ssbevd_2stage.f ssygv_2stage.f)
+   ssbev_2stage.f ssbevx_2stage.f ssbevd_2stage.f ssygv_2stage.f
+   sgesvdq.f scombssq.f)
 
 set(DSLASRC spotrs.f sgetrs.f spotrf.f sgetrf.f)
 
@@ -233,7 +235,7 @@ set(CLASRC
    ctptrs.f ctrcon.f ctrevc.f ctrevc3.f ctrexc.f ctrrfs.f ctrsen.f ctrsna.f
    ctrsyl.f ctrti2.f ctrtri.f ctrtrs.f ctzrzf.f cung2l.f cung2r.f
    cungbr.f cunghr.f cungl2.f cunglq.f cungql.f cungqr.f cungr2.f
-   cungrq.f cungtr.f cunm2l.f cunm2r.f cunmbr.f cunmhr.f cunml2.f cunm22.f
+   cungrq.f cungtr.f cungtsqr.f cunm2l.f cunm2r.f cunmbr.f cunmhr.f cunml2.f cunm22.f
    cunmlq.f cunmql.f cunmqr.f cunmr2.f cunmr3.f cunmrq.f cunmrz.f
    cunmtr.f cupgtr.f cupmtr.f icmax1.f scsum1.f cstemr.f
    chfrk.f ctfttp.f clanhf.f cpftrf.f cpftri.f cpftrs.f ctfsm.f ctftri.f
@@ -247,9 +249,11 @@ set(CLASRC
    cgetsls.f cgeqr.f clatsqr.f clamtsqr.f cgemqr.f
    cgelq.f claswlq.f clamswlq.f cgemlq.f
    ctplqt.f ctplqt2.f ctpmlqt.f
+   cunhr_col.f claunhr_col_getrfnp.f claunhr_col_getrfnp2.f
    chetrd_2stage.f chetrd_he2hb.f chetrd_hb2st.F chb2st_kernels.f
    cheevd_2stage.f cheev_2stage.f cheevx_2stage.f cheevr_2stage.f
-   chbev_2stage.f chbevx_2stage.f chbevd_2stage.f chegv_2stage.f)
+   chbev_2stage.f chbevx_2stage.f chbevd_2stage.f chegv_2stage.f
+   cgesvdq.f)
 
 set(CXLASRC cgesvxx.f cgerfsx.f cla_gerfsx_extended.f cla_geamv.f
    cla_gercond_c.f cla_gercond_x.f cla_gerpvgrw.f
@@ -295,7 +299,7 @@ set(DLASRC
    dlatbs.f dlatdf.f dlatps.f dlatrd.f dlatrs.f dlatrz.f dlauu2.f
    dlauum.f dopgtr.f dopmtr.f dorg2l.f dorg2r.f
    dorgbr.f dorghr.f dorgl2.f dorglq.f dorgql.f dorgqr.f dorgr2.f
-   dorgrq.f dorgtr.f dorm2l.f dorm2r.f dorm22.f
+   dorgrq.f dorgtr.f dorgtsqr.f dorm2l.f dorm2r.f dorm22.f
    dormbr.f dormhr.f dorml2.f dormlq.f dormql.f dormqr.f dormr2.f
    dormr3.f dormrq.f dormrz.f dormtr.f dpbcon.f dpbequ.f dpbrfs.f
    dpbstf.f dpbsv.f  dpbsvx.f
@@ -339,9 +343,11 @@ set(DLASRC
    dgetsls.f dgeqr.f dlatsqr.f dlamtsqr.f dgemqr.f
    dgelq.f dlaswlq.f dlamswlq.f dgemlq.f
    dtplqt.f dtplqt2.f dtpmlqt.f
+   dorhr_col.f dlaorhr_col_getrfnp.f dlaorhr_col_getrfnp2.f
    dsytrd_2stage.f dsytrd_sy2sb.f dsytrd_sb2st.F dsb2st_kernels.f
    dsyevd_2stage.f dsyev_2stage.f dsyevx_2stage.f dsyevr_2stage.f
-   dsbev_2stage.f dsbevx_2stage.f dsbevd_2stage.f dsygv_2stage.f)
+   dsbev_2stage.f dsbevx_2stage.f dsbevd_2stage.f dsygv_2stage.f
+   dgesvdq.f dcombssq.f)
 
 set(DXLASRC dgesvxx.f dgerfsx.f dla_gerfsx_extended.f dla_geamv.f
    dla_gercond.f dla_gerpvgrw.f dsysvxx.f dsyrfsx.f
@@ -424,7 +430,7 @@ set(ZLASRC
    ztptrs.f ztrcon.f ztrevc.f ztrevc3.f ztrexc.f ztrrfs.f ztrsen.f ztrsna.f
    ztrsyl.f ztrti2.f ztrtri.f ztrtrs.f ztzrzf.f zung2l.f
    zung2r.f zungbr.f zunghr.f zungl2.f zunglq.f zungql.f zungqr.f zungr2.f
-   zungrq.f zungtr.f zunm2l.f zunm2r.f zunmbr.f zunmhr.f zunml2.f zunm22.f
+   zungrq.f zungtr.f zungtsqr.f zunm2l.f zunm2r.f zunmbr.f zunmhr.f zunml2.f zunm22.f
    zunmlq.f zunmql.f zunmqr.f zunmr2.f zunmr3.f zunmrq.f zunmrz.f
    zunmtr.f zupgtr.f
    zupmtr.f izmax1.f dzsum1.f zstemr.f
@@ -440,9 +446,11 @@ set(ZLASRC
    zgelqt.f zgelqt3.f zgemlqt.f
    zgetsls.f zgeqr.f zlatsqr.f zlamtsqr.f zgemqr.f
    zgelq.f zlaswlq.f zlamswlq.f zgemlq.f
+   zunhr_col.f zlaunhr_col_getrfnp.f zlaunhr_col_getrfnp2.f
    zhetrd_2stage.f zhetrd_he2hb.f zhetrd_hb2st.F zhb2st_kernels.f
    zheevd_2stage.f zheev_2stage.f zheevx_2stage.f zheevr_2stage.f
-   zhbev_2stage.f zhbevx_2stage.f zhbevd_2stage.f zhegv_2stage.f)
+   zhbev_2stage.f zhbevx_2stage.f zhbevd_2stage.f zhegv_2stage.f
+   zgesvdq.f)
 
 set(ZXLASRC zgesvxx.f zgerfsx.f zla_gerfsx_extended.f zla_geamv.f
    zla_gercond_c.f zla_gercond_x.f zla_gerpvgrw.f zsysvxx.f zsyrfsx.f
@@ -504,7 +512,7 @@ if(USE_XBLAS)
 endif()
 target_link_libraries(lapack PRIVATE ${BLAS_LIBRARIES})
 
-if (${CMAKE_BUILD_TYPE_UPPER} STREQUAL "COVERAGE")
+if(_is_coverage_build)
   target_link_libraries(lapack PRIVATE gcov)
   add_coverage(lapack)
 endif()

lapack-netlib/SRC/Makefile

@@ -1,5 +1,3 @@
-include ../make.inc
-
 #######################################################################
 #  This is the makefile to create a library for LAPACK.
 #  The files are organized as follows:
@@ -44,7 +42,7 @@ include ../make.inc
 #  and is created at the next higher directory level.
 #
 #  To remove the object files after the library is created, enter
-#       make clean
+#       make cleanobj
 #  On some systems, you can force the source files to be recompiled by
 #  entering (for example)
 #       make single FRC=FRC
@@ -56,6 +54,13 @@ include ../make.inc
 #
 #######################################################################
 
+TOPSRCDIR = ..
+include $(TOPSRCDIR)/make.inc
+
+.SUFFIXES: .F .o
+.F.o:
+	$(FC) $(FFLAGS) -c -o $@ $<
+
 ALLAUX_O = ilaenv.o ilaenv2stage.o ieeeck.o lsamen.o xerbla.o xerbla_array.o \
    iparmq.o iparam2stage.o \
    ilaprec.o ilatrans.o ilauplo.o iladiag.o chla_transtype.o \
@@ -128,7 +133,7 @@ SLASRC_O = \
    slatbs.o slatdf.o slatps.o slatrd.o slatrs.o slatrz.o \
    slauu2.o slauum.o sopgtr.o sopmtr.o sorg2l.o sorg2r.o \
    sorgbr.o sorghr.o sorgl2.o sorglq.o sorgql.o sorgqr.o sorgr2.o \
-   sorgrq.o sorgtr.o sorm2l.o sorm2r.o sorm22.o \
+   sorgrq.o sorgtr.o sorgtsqr.o sorm2l.o sorm2r.o sorm22.o \
    sormbr.o sormhr.o sorml2.o sormlq.o sormql.o sormqr.o sormr2.o \
    sormr3.o sormrq.o sormrz.o sormtr.o spbcon.o spbequ.o spbrfs.o \
    spbstf.o spbsv.o  spbsvx.o \
@@ -171,9 +176,11 @@ SLASRC_O = \
    sgetsls.o sgeqr.o slatsqr.o slamtsqr.o sgemqr.o \
    sgelq.o slaswlq.o slamswlq.o sgemlq.o \
    stplqt.o stplqt2.o stpmlqt.o \
+   sorhr_col.o slaorhr_col_getrfnp.o slaorhr_col_getrfnp2.o \
    ssytrd_2stage.o ssytrd_sy2sb.o ssytrd_sb2st.o ssb2st_kernels.o \
    ssyevd_2stage.o ssyev_2stage.o ssyevx_2stage.o ssyevr_2stage.o \
-   ssbev_2stage.o ssbevx_2stage.o ssbevd_2stage.o ssygv_2stage.o
+   ssbev_2stage.o ssbevx_2stage.o ssbevd_2stage.o ssygv_2stage.o \
+   sgesvdq.o scombssq.o
 
 DSLASRC_O = spotrs.o sgetrs.o spotrf.o sgetrf.o
 
@@ -258,7 +265,7 @@ CLASRC_O = \
    ctptrs.o ctrcon.o ctrevc.o ctrevc3.o ctrexc.o ctrrfs.o ctrsen.o ctrsna.o \
    ctrsyl.o ctrti2.o ctrtri.o ctrtrs.o ctzrzf.o cung2l.o cung2r.o \
    cungbr.o cunghr.o cungl2.o cunglq.o cungql.o cungqr.o cungr2.o \
-   cungrq.o cungtr.o cunm2l.o cunm2r.o cunmbr.o cunmhr.o cunml2.o cunm22.o \
+   cungrq.o cungtr.o cungtsqr.o cunm2l.o cunm2r.o cunmbr.o cunmhr.o cunml2.o cunm22.o \
    cunmlq.o cunmql.o cunmqr.o cunmr2.o cunmr3.o cunmrq.o cunmrz.o \
    cunmtr.o cupgtr.o cupmtr.o icmax1.o scsum1.o cstemr.o \
    chfrk.o ctfttp.o clanhf.o cpftrf.o cpftri.o cpftrs.o ctfsm.o ctftri.o \
@@ -272,9 +279,11 @@ CLASRC_O = \
    cgetsls.o cgeqr.o clatsqr.o clamtsqr.o cgemqr.o \
    cgelq.o claswlq.o clamswlq.o cgemlq.o \
    ctplqt.o ctplqt2.o ctpmlqt.o \
+   cunhr_col.o claunhr_col_getrfnp.o claunhr_col_getrfnp2.o \
    chetrd_2stage.o chetrd_he2hb.o chetrd_hb2st.o chb2st_kernels.o \
    cheevd_2stage.o cheev_2stage.o cheevx_2stage.o cheevr_2stage.o \
-   chbev_2stage.o chbevx_2stage.o chbevd_2stage.o chegv_2stage.o
+   chbev_2stage.o chbevx_2stage.o chbevd_2stage.o chegv_2stage.o \
+   cgesvdq.o
 
 ifdef USEXBLAS
 CXLASRC = cgesvxx.o cgerfsx.o cla_gerfsx_extended.o cla_geamv.o \
@@ -324,7 +333,7 @@ DLASRC_O = \
    dlatbs.o dlatdf.o dlatps.o dlatrd.o dlatrs.o dlatrz.o dlauu2.o \
    dlauum.o dopgtr.o dopmtr.o dorg2l.o dorg2r.o \
    dorgbr.o dorghr.o dorgl2.o dorglq.o dorgql.o dorgqr.o dorgr2.o \
-   dorgrq.o dorgtr.o dorm2l.o dorm2r.o dorm22.o \
+   dorgrq.o dorgtr.o dorgtsqr.o dorm2l.o dorm2r.o dorm22.o \
    dormbr.o dormhr.o dorml2.o dormlq.o dormql.o dormqr.o dormr2.o \
    dormr3.o dormrq.o dormrz.o dormtr.o dpbcon.o dpbequ.o dpbrfs.o \
    dpbstf.o dpbsv.o  dpbsvx.o \
@@ -368,9 +377,11 @@ DLASRC_O = \
    dgetsls.o dgeqr.o dlatsqr.o dlamtsqr.o dgemqr.o \
    dgelq.o dlaswlq.o dlamswlq.o dgemlq.o \
    dtplqt.o dtplqt2.o dtpmlqt.o \
+   dorhr_col.o dlaorhr_col_getrfnp.o dlaorhr_col_getrfnp2.o \
    dsytrd_2stage.o dsytrd_sy2sb.o dsytrd_sb2st.o dsb2st_kernels.o \
    dsyevd_2stage.o dsyev_2stage.o dsyevx_2stage.o dsyevr_2stage.o \
-   dsbev_2stage.o dsbevx_2stage.o dsbevd_2stage.o dsygv_2stage.o
+   dsbev_2stage.o dsbevx_2stage.o dsbevd_2stage.o dsygv_2stage.o \
+   dgesvdq.o dcombssq.o
 
 ifdef USEXBLAS
 DXLASRC = dgesvxx.o dgerfsx.o dla_gerfsx_extended.o dla_geamv.o \
@@ -456,7 +467,7 @@ ZLASRC_O = \
    ztptrs.o ztrcon.o ztrevc.o ztrevc3.o ztrexc.o ztrrfs.o ztrsen.o ztrsna.o \
    ztrsyl.o ztrti2.o ztrtri.o ztrtrs.o ztzrzf.o zung2l.o \
    zung2r.o zungbr.o zunghr.o zungl2.o zunglq.o zungql.o zungqr.o zungr2.o \
-   zungrq.o zungtr.o zunm2l.o zunm2r.o zunmbr.o zunmhr.o zunml2.o zunm22.o \
+   zungrq.o zungtr.o zungtsqr.o zunm2l.o zunm2r.o zunmbr.o zunmhr.o zunml2.o zunm22.o \
    zunmlq.o zunmql.o zunmqr.o zunmr2.o zunmr3.o zunmrq.o zunmrz.o \
    zunmtr.o zupgtr.o \
    zupmtr.o izmax1.o dzsum1.o zstemr.o \
@@ -472,9 +483,11 @@ ZLASRC_O = \
    zgelqt.o zgelqt3.o zgemlqt.o \
    zgetsls.o zgeqr.o zlatsqr.o zlamtsqr.o zgemqr.o \
    zgelq.o zlaswlq.o zlamswlq.o zgemlq.o \
+   zunhr_col.o zlaunhr_col_getrfnp.o zlaunhr_col_getrfnp2.o \
    zhetrd_2stage.o zhetrd_he2hb.o zhetrd_hb2st.o zhb2st_kernels.o \
    zheevd_2stage.o zheev_2stage.o zheevx_2stage.o zheevr_2stage.o \
-   zhbev_2stage.o zhbevx_2stage.o zhbevd_2stage.o zhegv_2stage.o
+   zhbev_2stage.o zhbevx_2stage.o zhbevd_2stage.o zhegv_2stage.o \
+   zgesvdq.o
 
 ifdef USEXBLAS
 ZXLASRC = zgesvxx.o zgerfsx.o zla_gerfsx_extended.o zla_geamv.o \
@@ -550,33 +563,29 @@ ifdef BUILD_DEPRECATED
 DEPRECATED = $(DEPRECSRC)
 endif
 
-all: ../$(LAPACKLIB)
+.PHONY: all
+all: $(LAPACKLIB)
 
-.PHONY: ../$(LAPACKLIB)
-
-../$(LAPACKLIB): $(ALLOBJ) $(ALLXOBJ) $(DEPRECATED)
-	$(ARCH) $(ARCHFLAGS) $@ $(ALLOBJ) $(ALLXOBJ) $(DEPRECATED)
+$(LAPACKLIB): $(ALLOBJ) $(ALLXOBJ) $(DEPRECATED)
+	$(AR) $(ARFLAGS) $@ $^
 	$(RANLIB) $@
 
+.PHONY: single complex double complex16
 single: $(SLASRC) $(DSLASRC) $(SXLASRC) $(SCLAUX) $(ALLAUX)
-	$(ARCH) $(ARCHFLAGS) ../$(LAPACKLIB) $(SLASRC) $(DSLASRC) \
-	$(SXLASRC) $(SCLAUX) $(ALLAUX)
-	$(RANLIB) ../$(LAPACKLIB)
+	$(AR) $(ARFLAGS) $(LAPACKLIB) $^
+	$(RANLIB) $(LAPACKLIB)
 
 complex: $(CLASRC) $(ZCLASRC) $(CXLASRC) $(SCLAUX) $(ALLAUX)
-	$(ARCH) $(ARCHFLAGS) ../$(LAPACKLIB) $(CLASRC) $(ZCLASRC) \
-	$(CXLASRC) $(SCLAUX) $(ALLAUX)
-	$(RANLIB) ../$(LAPACKLIB)
+	$(AR) $(ARFLAGS) $(LAPACKLIB) $^
+	$(RANLIB) $(LAPACKLIB)
 
 double: $(DLASRC) $(DSLASRC) $(DXLASRC) $(DZLAUX) $(ALLAUX)
-	$(ARCH) $(ARCHFLAGS) ../$(LAPACKLIB) $(DLASRC) $(DSLASRC) \
-	$(DXLASRC) $(DZLAUX) $(ALLAUX)
-	$(RANLIB) ../$(LAPACKLIB)
+	$(AR) $(ARFLAGS) $(LAPACKLIB) $^
+	$(RANLIB) $(LAPACKLIB)
 
 complex16: $(ZLASRC) $(ZCLASRC) $(ZXLASRC) $(DZLAUX) $(ALLAUX)
-	$(ARCH) $(ARCHFLAGS) ../$(LAPACKLIB) $(ZLASRC) $(ZCLASRC) \
-	$(ZXLASRC) $(DZLAUX) $(ALLAUX)
-	$(RANLIB) ../$(LAPACKLIB)
+	$(AR) $(ARFLAGS) $(LAPACKLIB) $^
+	$(RANLIB) $(LAPACKLIB)
 
 $(ALLAUX): $(FRC)
 $(SCLAUX): $(FRC)
@@ -597,18 +606,16 @@ endif
 FRC:
 	@FRC=$(FRC)
 
-clean:
+.PHONY: clean cleanobj cleanlib
+clean: cleanobj cleanlib
+cleanobj:
 	rm -f *.o DEPRECATED/*.o
-
-.f.o:
-	$(FORTRAN) $(OPTS) -c -o $@ $<
-
-.F.o:
-	$(FORTRAN) $(OPTS) -c $< -o $@
-	
-slaruv.o: slaruv.f ; $(FORTRAN) $(NOOPT) -c -o $@ $<
-dlaruv.o: dlaruv.f ; $(FORTRAN) $(NOOPT) -c -o $@ $<
-sla_wwaddw.o: sla_wwaddw.f ; $(FORTRAN) $(NOOPT) -c -o $@ $<
-dla_wwaddw.o: dla_wwaddw.f ; $(FORTRAN) $(NOOPT) -c -o $@ $<
-cla_wwaddw.o: cla_wwaddw.f ; $(FORTRAN) $(NOOPT) -c -o $@ $<
-zla_wwaddw.o: zla_wwaddw.f ; $(FORTRAN) $(NOOPT) -c -o $@ $<
+cleanlib:
+	rm -f $(LAPACKLIB)
+
+slaruv.o: slaruv.f ; $(FC) $(FFLAGS_NOOPT) -c -o $@ $<
+dlaruv.o: dlaruv.f ; $(FC) $(FFLAGS_NOOPT) -c -o $@ $<
+sla_wwaddw.o: sla_wwaddw.f ; $(FC) $(FFLAGS_NOOPT) -c -o $@ $<
+dla_wwaddw.o: dla_wwaddw.f ; $(FC) $(FFLAGS_NOOPT) -c -o $@ $<
+cla_wwaddw.o: cla_wwaddw.f ; $(FC) $(FFLAGS_NOOPT) -c -o $@ $<
+zla_wwaddw.o: zla_wwaddw.f ; $(FC) $(FFLAGS_NOOPT) -c -o $@ $<

lapack-netlib/SRC/cgbrfsx.f

@@ -75,7 +75,7 @@
 *>     Specifies the form of the system of equations:
 *>       = 'N':  A * X = B     (No transpose)
 *>       = 'T':  A**T * X = B  (Transpose)
-*>       = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
+*>       = 'C':  A**H * X = B  (Conjugate transpose)
 *> \endverbatim
 *>
 *> \param[in] EQUED
@@ -308,7 +308,7 @@
 *>     information as described below. There currently are up to three
 *>     pieces of information returned for each right-hand side. If
 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.
 *>
 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@@ -344,14 +344,14 @@
 *> \param[in] NPARAMS
 *> \verbatim
 *>          NPARAMS is INTEGER
-*>     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
+*>     Specifies the number of parameters set in PARAMS.  If <= 0, the
 *>     PARAMS array is never referenced and default values are used.
 *> \endverbatim
 *>
 *> \param[in,out] PARAMS
 *> \verbatim
 *>          PARAMS is REAL array, dimension NPARAMS
-*>     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
+*>     Specifies algorithm parameters.  If an entry is < 0.0, then
 *>     that entry will be filled with default value used for that
 *>     parameter.  Only positions up to NPARAMS are accessed; defaults
 *>     are used for higher-numbered parameters.
@@ -359,9 +359,9 @@
 *>       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
 *>            refinement or not.
 *>         Default: 1.0
-*>            = 0.0 : No refinement is performed, and no error bounds are
+*>            = 0.0:  No refinement is performed, and no error bounds are
 *>                    computed.
-*>            = 1.0 : Use the double-precision refinement algorithm,
+*>            = 1.0:  Use the double-precision refinement algorithm,
 *>                    possibly with doubled-single computations if the
 *>                    compilation environment does not support DOUBLE
 *>                    PRECISION.

lapack-netlib/SRC/cgbsvxx.f

@@ -431,7 +431,7 @@
 *>     information as described below. There currently are up to three
 *>     pieces of information returned for each right-hand side. If
 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.
 *>
 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@@ -467,14 +467,14 @@
 *> \param[in] NPARAMS
 *> \verbatim
 *>          NPARAMS is INTEGER
-*>     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
+*>     Specifies the number of parameters set in PARAMS.  If <= 0, the
 *>     PARAMS array is never referenced and default values are used.
 *> \endverbatim
 *>
 *> \param[in,out] PARAMS
 *> \verbatim
 *>          PARAMS is REAL array, dimension NPARAMS
-*>     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
+*>     Specifies algorithm parameters.  If an entry is < 0.0, then
 *>     that entry will be filled with default value used for that
 *>     parameter.  Only positions up to NPARAMS are accessed; defaults
 *>     are used for higher-numbered parameters.
@@ -482,9 +482,9 @@
 *>       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
 *>            refinement or not.
 *>         Default: 1.0
-*>            = 0.0 : No refinement is performed, and no error bounds are
+*>            = 0.0:  No refinement is performed, and no error bounds are
 *>                    computed.
-*>            = 1.0 : Use the double-precision refinement algorithm,
+*>            = 1.0:  Use the double-precision refinement algorithm,
 *>                    possibly with doubled-single computations if the
 *>                    compilation environment does not support DOUBLE
 *>                    PRECISION.

lapack-netlib/SRC/cgebak.f

@@ -48,10 +48,10 @@
 *> \verbatim
 *>          JOB is CHARACTER*1
 *>          Specifies the type of backward transformation required:
-*>          = 'N', do nothing, return immediately;
-*>          = 'P', do backward transformation for permutation only;
-*>          = 'S', do backward transformation for scaling only;
-*>          = 'B', do backward transformations for both permutation and
+*>          = 'N': do nothing, return immediately;
+*>          = 'P': do backward transformation for permutation only;
+*>          = 'S': do backward transformation for scaling only;
+*>          = 'B': do backward transformations for both permutation and
 *>                 scaling.
 *>          JOB must be the same as the argument JOB supplied to CGEBAL.
 *> \endverbatim

lapack-netlib/SRC/cgeev.f

@@ -157,7 +157,7 @@
 *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
 *>          > 0:  if INFO = i, the QR algorithm failed to compute all the
 *>                eigenvalues, and no eigenvectors have been computed;
-*>                elements and i+1:N of W contain eigenvalues which have
+*>                elements i+1:N of W contain eigenvalues which have
 *>                converged.
 *> \endverbatim
 *

lapack-netlib/SRC/cgejsv.f

@@ -80,13 +80,13 @@
 *>              desirable, then this option is advisable. The input matrix A
 *>              is preprocessed with QR factorization with FULL (row and
 *>              column) pivoting.
-*>       = 'G'  Computation as with 'F' with an additional estimate of the
+*>       = 'G': Computation as with 'F' with an additional estimate of the
 *>              condition number of B, where A=B*D. If A has heavily weighted
 *>              rows, then using this condition number gives too pessimistic
 *>              error bound.
 *>       = 'A': Small singular values are not well determined by the data 
 *>              and are considered as noisy; the matrix is treated as
-*>              numerically rank defficient. The error in the computed
+*>              numerically rank deficient. The error in the computed
 *>              singular values is bounded by f(m,n)*epsilon*||A||.
 *>              The computed SVD A = U * S * V^* restores A up to
 *>              f(m,n)*epsilon*||A||.
@@ -117,7 +117,7 @@
 *>       = 'V': N columns of V are returned in the array V; Jacobi rotations
 *>              are not explicitly accumulated.
 *>       = 'J': N columns of V are returned in the array V, but they are
-*>              computed as the product of Jacobi rotations, if JOBT .EQ. 'N'.
+*>              computed as the product of Jacobi rotations, if JOBT = 'N'.
 *>       = 'W': V may be used as workspace of length N*N. See the description
 *>              of V.
 *>       = 'N': V is not computed.
@@ -131,7 +131,7 @@
 *>         specified range. If A .NE. 0 is scaled so that the largest singular
 *>         value of c*A is around SQRT(BIG), BIG=SLAMCH('O'), then JOBR issues
 *>         the licence to kill columns of A whose norm in c*A is less than
-*>         SQRT(SFMIN) (for JOBR.EQ.'R'), or less than SMALL=SFMIN/EPSLN,
+*>         SQRT(SFMIN) (for JOBR = 'R'), or less than SMALL=SFMIN/EPSLN,
 *>         where SFMIN=SLAMCH('S'), EPSLN=SLAMCH('E').
 *>       = 'N': Do not kill small columns of c*A. This option assumes that
 *>              BLAS and QR factorizations and triangular solvers are
@@ -229,7 +229,7 @@
 *>          If JOBU = 'F', then U contains on exit the M-by-M matrix of
 *>                         the left singular vectors, including an ONB
 *>                         of the orthogonal complement of the Range(A).
-*>          If JOBU = 'W'  .AND. (JOBV.EQ.'V' .AND. JOBT.EQ.'T' .AND. M.EQ.N),
+*>          If JOBU = 'W'  .AND. (JOBV = 'V' .AND. JOBT = 'T' .AND. M = N),
 *>                         then U is used as workspace if the procedure
 *>                         replaces A with A^*. In that case, [V] is computed
 *>                         in U as left singular vectors of A^* and then
@@ -251,7 +251,7 @@
 *>          V is COMPLEX array, dimension ( LDV, N )
 *>          If JOBV = 'V', 'J' then V contains on exit the N-by-N matrix of
 *>                         the right singular vectors;
-*>          If JOBV = 'W', AND (JOBU.EQ.'U' AND JOBT.EQ.'T' AND M.EQ.N),
+*>          If JOBV = 'W', AND (JOBU = 'U' AND JOBT = 'T' AND M = N),
 *>                         then V is used as workspace if the pprocedure
 *>                         replaces A with A^*. In that case, [U] is computed
 *>                         in V as right singular vectors of A^* and then
@@ -282,7 +282,7 @@
 *>          Length of CWORK to confirm proper allocation of workspace.
 *>          LWORK depends on the job:
 *>
-*>          1. If only SIGMA is needed ( JOBU.EQ.'N', JOBV.EQ.'N' ) and
+*>          1. If only SIGMA is needed ( JOBU = 'N', JOBV = 'N' ) and
 *>            1.1 .. no scaled condition estimate required (JOBA.NE.'E'.AND.JOBA.NE.'G'):
 *>               LWORK >= 2*N+1. This is the minimal requirement.
 *>               ->> For optimal performance (blocked code) the optimal value
@@ -298,9 +298,9 @@
 *>               In general, the optimal length LWORK is computed as
 *>               LWORK >= max(N+LWORK(CGEQP3),N+LWORK(CGEQRF), LWORK(CGESVJ),
 *>                            N*N+LWORK(CPOCON)).
-*>          2. If SIGMA and the right singular vectors are needed (JOBV.EQ.'V'),
-*>             (JOBU.EQ.'N')
-*>            2.1   .. no scaled condition estimate requested (JOBE.EQ.'N'):    
+*>          2. If SIGMA and the right singular vectors are needed (JOBV = 'V'),
+*>             (JOBU = 'N')
+*>            2.1   .. no scaled condition estimate requested (JOBE = 'N'):    
 *>            -> the minimal requirement is LWORK >= 3*N.
 *>            -> For optimal performance, 
 *>               LWORK >= max(N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB,
@@ -318,10 +318,10 @@
 *>               LWORK >= max(N+LWORK(CGEQP3), LWORK(CPOCON), N+LWORK(CGESVJ),
 *>                       N+LWORK(CGELQF), 2*N+LWORK(CGEQRF), N+LWORK(CUNMLQ)).   
 *>          3. If SIGMA and the left singular vectors are needed
-*>            3.1  .. no scaled condition estimate requested (JOBE.EQ.'N'):
+*>            3.1  .. no scaled condition estimate requested (JOBE = 'N'):
 *>            -> the minimal requirement is LWORK >= 3*N.
 *>            -> For optimal performance:
-*>               if JOBU.EQ.'U' :: LWORK >= max(3*N, N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB,
+*>               if JOBU = 'U' :: LWORK >= max(3*N, N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB,
 *>               where NB is the optimal block size for CGEQP3, CGEQRF, CUNMQR.
 *>               In general, the optimal length LWORK is computed as
 *>               LWORK >= max(N+LWORK(CGEQP3), 2*N+LWORK(CGEQRF), N+LWORK(CUNMQR)). 
@@ -329,16 +329,16 @@
 *>               required (JOBA='E', or 'G').
 *>            -> the minimal requirement is LWORK >= 3*N.
 *>            -> For optimal performance:
-*>               if JOBU.EQ.'U' :: LWORK >= max(3*N, N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB,
+*>               if JOBU = 'U' :: LWORK >= max(3*N, N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB,
 *>               where NB is the optimal block size for CGEQP3, CGEQRF, CUNMQR.
 *>               In general, the optimal length LWORK is computed as
 *>               LWORK >= max(N+LWORK(CGEQP3),N+LWORK(CPOCON),
 *>                        2*N+LWORK(CGEQRF), N+LWORK(CUNMQR)).
 *>
-*>          4. If the full SVD is needed: (JOBU.EQ.'U' or JOBU.EQ.'F') and
-*>            4.1. if JOBV.EQ.'V'
+*>          4. If the full SVD is needed: (JOBU = 'U' or JOBU = 'F') and
+*>            4.1. if JOBV = 'V'
 *>               the minimal requirement is LWORK >= 5*N+2*N*N.
-*>            4.2. if JOBV.EQ.'J' the minimal requirement is
+*>            4.2. if JOBV = 'J' the minimal requirement is
 *>               LWORK >= 4*N+N*N.
 *>            In both cases, the allocated CWORK can accommodate blocked runs
 *>            of CGEQP3, CGEQRF, CGELQF, CUNMQR, CUNMLQ.
@@ -357,7 +357,7 @@
 *>                    of A. (See the description of SVA().)
 *>          RWORK(2) = See the description of RWORK(1).
 *>          RWORK(3) = SCONDA is an estimate for the condition number of
-*>                    column equilibrated A. (If JOBA .EQ. 'E' or 'G')
+*>                    column equilibrated A. (If JOBA = 'E' or 'G')
 *>                    SCONDA is an estimate of SQRT(||(R^* * R)^(-1)||_1).
 *>                    It is computed using SPOCON. It holds
 *>                    N^(-1/4) * SCONDA <= ||R^(-1)||_2 <= N^(1/4) * SCONDA
@@ -376,7 +376,7 @@
 *>                    triangular factor in the first QR factorization.
 *>          RWORK(5) = an estimate of the scaled condition number of the
 *>                    triangular factor in the second QR factorization.
-*>          The following two parameters are computed if JOBT .EQ. 'T'.
+*>          The following two parameters are computed if JOBT = 'T'.
 *>          They are provided for a developer/implementer who is familiar
 *>          with the details of the method.
 *>          RWORK(6) = the entropy of A^* * A :: this is the Shannon entropy
@@ -457,23 +457,23 @@
 *>                     of JOBA and JOBR.
 *>          IWORK(2) = the number of the computed nonzero singular values
 *>          IWORK(3) = if nonzero, a warning message:
-*>                     If IWORK(3).EQ.1 then some of the column norms of A
+*>                     If IWORK(3) = 1 then some of the column norms of A
 *>                     were denormalized floats. The requested high accuracy
 *>                     is not warranted by the data.
-*>          IWORK(4) = 1 or -1. If IWORK(4) .EQ. 1, then the procedure used A^* to
+*>          IWORK(4) = 1 or -1. If IWORK(4) = 1, then the procedure used A^* to
 *>                     do the job as specified by the JOB parameters.
-*>          If the call to CGEJSV is a workspace query (indicated by LWORK .EQ. -1 and 
-*>          LRWORK .EQ. -1), then on exit IWORK(1) contains the required length of 
+*>          If the call to CGEJSV is a workspace query (indicated by LWORK = -1 and 
+*>          LRWORK = -1), then on exit IWORK(1) contains the required length of 
 *>          IWORK for the job parameters used in the call.
 *> \endverbatim
 *>
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER
-*>           < 0  : if INFO = -i, then the i-th argument had an illegal value.
-*>           = 0 :  successful exit;
-*>           > 0 :  CGEJSV  did not converge in the maximal allowed number
-*>                  of sweeps. The computed values may be inaccurate.
+*>           < 0:  if INFO = -i, then the i-th argument had an illegal value.
+*>           = 0:  successful exit;
+*>           > 0:  CGEJSV  did not converge in the maximal allowed number
+*>                 of sweeps. The computed values may be inaccurate.
 *> \endverbatim
 *
 *  Authors:
@@ -1336,7 +1336,7 @@
       IF ( L2ABER ) THEN
 *        Standard absolute error bound suffices. All sigma_i with
 *        sigma_i < N*EPSLN*||A|| are flushed to zero. This is an
-*        agressive enforcement of lower numerical rank by introducing a
+*        aggressive enforcement of lower numerical rank by introducing a
 *        backward error of the order of N*EPSLN*||A||.
          TEMP1 = SQRT(REAL(N))*EPSLN
          DO 3001 p = 2, N
@@ -1348,9 +1348,9 @@
  3001    CONTINUE
  3002    CONTINUE
       ELSE IF ( L2RANK ) THEN
-*        .. similarly as above, only slightly more gentle (less agressive).
+*        .. similarly as above, only slightly more gentle (less aggressive).
 *        Sudden drop on the diagonal of R1 is used as the criterion for
-*        close-to-rank-defficient.
+*        close-to-rank-deficient.
          TEMP1 = SQRT(SFMIN)
          DO 3401 p = 2, N
             IF ( ( ABS(A(p,p)) .LT. (EPSLN*ABS(A(p-1,p-1))) ) .OR.
@@ -1718,7 +1718,7 @@
             CALL CPOCON('L',NR,CWORK(2*N+1),NR,ONE,TEMP1,
      $                   CWORK(2*N+NR*NR+1),RWORK,IERR)
             CONDR1 = ONE / SQRT(TEMP1)
-*           .. here need a second oppinion on the condition number
+*           .. here need a second opinion on the condition number
 *           .. then assume worst case scenario
 *           R1 is OK for inverse <=> CONDR1 .LT. REAL(N)
 *           more conservative    <=> CONDR1 .LT. SQRT(REAL(N))
@@ -1763,7 +1763,7 @@
             ELSE
 *
 *              .. ill-conditioned case: second QRF with pivoting
-*              Note that windowed pivoting would be equaly good
+*              Note that windowed pivoting would be equally good
 *              numerically, and more run-time efficient. So, in
 *              an optimal implementation, the next call to CGEQP3
 *              should be replaced with eg. CALL CGEQPX (ACM TOMS #782)
@@ -1821,7 +1821,7 @@
 *
                IF ( CONDR2 .GE. COND_OK ) THEN
 *                 .. save the Householder vectors used for Q3
-*                 (this overwrittes the copy of R2, as it will not be
+*                 (this overwrites the copy of R2, as it will not be
 *                 needed in this branch, but it does not overwritte the
 *                 Huseholder vectors of Q2.).
                   CALL CLACPY( 'U', NR, NR, V, LDV, CWORK(2*N+1), N )
@@ -2077,7 +2077,7 @@
 *
 *        This branch deploys a preconditioned Jacobi SVD with explicitly
 *        accumulated rotations. It is included as optional, mainly for
-*        experimental purposes. It does perfom well, and can also be used.
+*        experimental purposes. It does perform well, and can also be used.
 *        In this implementation, this branch will be automatically activated
 *        if the  condition number sigma_max(A) / sigma_min(A) is predicted
 *        to be greater than the overflow threshold. This is because the

lapack-netlib/SRC/cgelq.f

@@ -1,3 +1,4 @@
+*> \brief \b CGELQ
 *
 *  Definition:
 *  ===========
@@ -17,7 +18,17 @@
 *  =============
 *>
 *> \verbatim
-*> CGELQ computes a LQ factorization of an M-by-N matrix A.
+*>
+*> CGELQ computes an LQ factorization of a complex M-by-N matrix A:
+*>
+*>    A = ( L 0 ) *  Q
+*>
+*> where:
+*>
+*>    Q is a N-by-N orthogonal matrix;
+*>    L is an lower-triangular M-by-M matrix;
+*>    0 is a M-by-(N-M) zero matrix, if M < N.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -138,7 +149,7 @@
 *> \verbatim
 *>
 *> These details are particular for this LAPACK implementation. Users should not 
-*> take them for granted. These details may change in the future, and are unlikely not
+*> take them for granted. These details may change in the future, and are not likely
 *> true for another LAPACK implementation. These details are relevant if one wants
 *> to try to understand the code. They are not part of the interface.
 *>
@@ -159,10 +170,10 @@
       SUBROUTINE CGELQ( M, N, A, LDA, T, TSIZE, WORK, LWORK,
      $                  INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd. --
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N, TSIZE, LWORK

lapack-netlib/SRC/cgelq2.f

@@ -33,8 +33,16 @@
 *>
 *> \verbatim
 *>
-*> CGELQ2 computes an LQ factorization of a complex m by n matrix A:
-*> A = L * Q.
+*> CGELQ2 computes an LQ factorization of a complex m-by-n matrix A:
+*>
+*>    A = ( L 0 ) *  Q
+*>
+*> where:
+*>
+*>    Q is a n-by-n orthogonal matrix;
+*>    L is an lower-triangular m-by-m matrix;
+*>    0 is a m-by-(n-m) zero matrix, if m < n.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -96,7 +104,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date December 2016
+*> \date November 2019
 *
 *> \ingroup complexGEcomputational
 *
@@ -121,10 +129,10 @@
 *  =====================================================================
       SUBROUTINE CGELQ2( M, N, A, LDA, TAU, WORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N

lapack-netlib/SRC/cgelqf.f

@@ -34,7 +34,15 @@
 *> \verbatim
 *>
 *> CGELQF computes an LQ factorization of a complex M-by-N matrix A:
-*> A = L * Q.
+*>
+*>    A = ( L 0 ) *  Q
+*>
+*> where:
+*>
+*>    Q is a N-by-N orthogonal matrix;
+*>    L is an lower-triangular M-by-M matrix;
+*>    0 is a M-by-(N-M) zero matrix, if M < N.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -110,7 +118,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date December 2016
+*> \date November 2019
 *
 *> \ingroup complexGEcomputational
 *
@@ -135,10 +143,10 @@
 *  =====================================================================
       SUBROUTINE CGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LWORK, M, N

lapack-netlib/SRC/cgelqt.f

@@ -1,3 +1,4 @@
+*> \brief \b CGELQT
 *
 *  Definition:
 *  ===========

lapack-netlib/SRC/cgelqt3.f

@@ -1,3 +1,5 @@
+*> \brief \b CGELQT3
+*
 *  Definition:
 *  ===========
 *

lapack-netlib/SRC/cgemlq.f

@@ -1,3 +1,4 @@
+*> \brief \b CGEMLQ
 *
 *  Definition:
 *  ===========
@@ -143,7 +144,7 @@
 *> \verbatim
 *>
 *> These details are particular for this LAPACK implementation. Users should not 
-*> take them for granted. These details may change in the future, and are unlikely not
+*> take them for granted. These details may change in the future, and are not likely
 *> true for another LAPACK implementation. These details are relevant if one wants
 *> to try to understand the code. They are not part of the interface.
 *>

lapack-netlib/SRC/cgemlqt.f

@@ -1,3 +1,5 @@
+*> \brief \b CGEMLQT
+*
 *  Definition:
 *  ===========
 *

lapack-netlib/SRC/cgemqr.f

@@ -1,3 +1,4 @@
+*> \brief \b CGEMQR
 *
 *  Definition:
 *  ===========
@@ -144,7 +145,7 @@
 *> \verbatim
 *>
 *> These details are particular for this LAPACK implementation. Users should not 
-*> take them for granted. These details may change in the future, and are unlikely not
+*> take them for granted. These details may change in the future, and are not likely
 *> true for another LAPACK implementation. These details are relevant if one wants
 *> to try to understand the code. They are not part of the interface.
 *>

lapack-netlib/SRC/cgeqr.f

@@ -1,3 +1,4 @@
+*> \brief \b CGEQR
 *
 *  Definition:
 *  ===========
@@ -17,7 +18,18 @@
 *  =============
 *>
 *> \verbatim
-*> CGEQR computes a QR factorization of an M-by-N matrix A.
+*>
+*> CGEQR computes a QR factorization of a complex M-by-N matrix A:
+*>
+*>    A = Q * ( R ),
+*>            ( 0 )
+*>
+*> where:
+*>
+*>    Q is a M-by-M orthogonal matrix;
+*>    R is an upper-triangular N-by-N matrix;
+*>    0 is a (M-N)-by-N zero matrix, if M > N.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -138,7 +150,7 @@
 *> \verbatim
 *>
 *> These details are particular for this LAPACK implementation. Users should not 
-*> take them for granted. These details may change in the future, and are unlikely not
+*> take them for granted. These details may change in the future, and are not likely
 *> true for another LAPACK implementation. These details are relevant if one wants
 *> to try to understand the code. They are not part of the interface.
 *>
@@ -160,10 +172,10 @@
       SUBROUTINE CGEQR( M, N, A, LDA, T, TSIZE, WORK, LWORK,
      $                  INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd. --
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N, TSIZE, LWORK

lapack-netlib/SRC/cgeqr2.f

@@ -33,8 +33,17 @@
 *>
 *> \verbatim
 *>
-*> CGEQR2 computes a QR factorization of a complex m by n matrix A:
-*> A = Q * R.
+*> CGEQR2 computes a QR factorization of a complex m-by-n matrix A:
+*>
+*>    A = Q * ( R ),
+*>            ( 0 )
+*>
+*> where:
+*>
+*>    Q is a m-by-m orthogonal matrix;
+*>    R is an upper-triangular n-by-n matrix;
+*>    0 is a (m-n)-by-n zero matrix, if m > n.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -96,7 +105,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date December 2016
+*> \date November 2019
 *
 *> \ingroup complexGEcomputational
 *
@@ -121,10 +130,10 @@
 *  =====================================================================
       SUBROUTINE CGEQR2( M, N, A, LDA, TAU, WORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N

lapack-netlib/SRC/cgeqr2p.f

@@ -33,8 +33,18 @@
 *>
 *> \verbatim
 *>
-*> CGEQR2P computes a QR factorization of a complex m by n matrix A:
-*> A = Q * R. The diagonal entries of R are real and nonnegative.
+*> CGEQR2P computes a QR factorization of a complex m-by-n matrix A:
+*>
+*>    A = Q * ( R ),
+*>            ( 0 )
+*>
+*> where:
+*>
+*>    Q is a m-by-m orthogonal matrix;
+*>    R is an upper-triangular n-by-n matrix with nonnegative diagonal
+*>    entries;
+*>    0 is a (m-n)-by-n zero matrix, if m > n.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -97,7 +107,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date December 2016
+*> \date November 2019
 *
 *> \ingroup complexGEcomputational
 *
@@ -124,10 +134,10 @@
 *  =====================================================================
       SUBROUTINE CGEQR2P( M, N, A, LDA, TAU, WORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N

lapack-netlib/SRC/cgeqrf.f

@@ -34,7 +34,16 @@
 *> \verbatim
 *>
 *> CGEQRF computes a QR factorization of a complex M-by-N matrix A:
-*> A = Q * R.
+*>
+*>    A = Q * ( R ),
+*>            ( 0 )
+*>
+*> where:
+*>
+*>    Q is a M-by-M orthogonal matrix;
+*>    R is an upper-triangular N-by-N matrix;
+*>    0 is a (M-N)-by-N zero matrix, if M > N.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -111,7 +120,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date December 2016
+*> \date November 2019
 *
 *> \ingroup complexGEcomputational
 *
@@ -136,10 +145,10 @@
 *  =====================================================================
       SUBROUTINE CGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LWORK, M, N

lapack-netlib/SRC/cgeqrfp.f

@@ -33,8 +33,18 @@
 *>
 *> \verbatim
 *>
-*> CGEQRFP computes a QR factorization of a complex M-by-N matrix A:
-*> A = Q * R. The diagonal entries of R are real and nonnegative.
+*> CGEQR2P computes a QR factorization of a complex M-by-N matrix A:
+*>
+*>    A = Q * ( R ),
+*>            ( 0 )
+*>
+*> where:
+*>
+*>    Q is a M-by-M orthogonal matrix;
+*>    R is an upper-triangular N-by-N matrix with nonnegative diagonal
+*>    entries;
+*>    0 is a (M-N)-by-N zero matrix, if M > N.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -112,7 +122,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date December 2016
+*> \date November 2019
 *
 *> \ingroup complexGEcomputational
 *
@@ -139,10 +149,10 @@
 *  =====================================================================
       SUBROUTINE CGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LWORK, M, N

lapack-netlib/SRC/cgerfsx.f

@@ -74,7 +74,7 @@
 *>     Specifies the form of the system of equations:
 *>       = 'N':  A * X = B     (No transpose)
 *>       = 'T':  A**T * X = B  (Transpose)
-*>       = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
+*>       = 'C':  A**H * X = B  (Conjugate transpose)
 *> \endverbatim
 *>
 *> \param[in] EQUED
@@ -283,7 +283,7 @@
 *>     information as described below. There currently are up to three
 *>     pieces of information returned for each right-hand side. If
 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.
 *>
 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@@ -319,14 +319,14 @@
 *> \param[in] NPARAMS
 *> \verbatim
 *>          NPARAMS is INTEGER
-*>     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
+*>     Specifies the number of parameters set in PARAMS.  If <= 0, the
 *>     PARAMS array is never referenced and default values are used.
 *> \endverbatim
 *>
 *> \param[in,out] PARAMS
 *> \verbatim
 *>          PARAMS is REAL array, dimension NPARAMS
-*>     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
+*>     Specifies algorithm parameters.  If an entry is < 0.0, then
 *>     that entry will be filled with default value used for that
 *>     parameter.  Only positions up to NPARAMS are accessed; defaults
 *>     are used for higher-numbered parameters.
@@ -334,9 +334,9 @@
 *>       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
 *>            refinement or not.
 *>         Default: 1.0
-*>            = 0.0 : No refinement is performed, and no error bounds are
+*>            = 0.0:  No refinement is performed, and no error bounds are
 *>                    computed.
-*>            = 1.0 : Use the double-precision refinement algorithm,
+*>            = 1.0:  Use the double-precision refinement algorithm,
 *>                    possibly with doubled-single computations if the
 *>                    compilation environment does not support DOUBLE
 *>                    PRECISION.

lapack-netlib/SRC/cgesc2.f

@@ -91,7 +91,7 @@
 *> \verbatim
 *>          SCALE is REAL
 *>           On exit, SCALE contains the scale factor. SCALE is chosen
-*>           0 <= SCALE <= 1 to prevent owerflow in the solution.
+*>           0 <= SCALE <= 1 to prevent overflow in the solution.
 *> \endverbatim
 *
 *  Authors: