Mercurial > hg > qm-dsp
changeset 205:e81375fa6a33
Merge from branch clapack-included
| author | Chris Cannam |
|---|---|
| date | Fri, 30 Sep 2016 16:24:24 +0100 |
| parents | 6c0531397af8 (current diff) 214b31ec7e1a (diff) |
| children | 335be766a54d |
| files | |
| diffstat | 42 files changed, 15637 insertions(+), 8 deletions(-) [+] |
line wrap: on
line diff
--- a/build/general/Makefile.inc Thu May 26 14:17:00 2016 +0100 +++ b/build/general/Makefile.inc Fri Sep 30 16:24:24 2016 +0100 @@ -5,8 +5,45 @@ AR ?= ar RANLIB ?= ranlib -CFLAGS := $(CFLAGS) -I. -Iext/kissfft -Iext/kissfft/tools -Dkiss_fft_scalar=double -CXXFLAGS := $(CXXFLAGS) -I. -Iext/kissfft -Iext/kissfft/tools -Dkiss_fft_scalar=double +KISSFFT_CFLAGS := -Iext/kissfft -Iext/kissfft/tools -Dkiss_fft_scalar=double + +CFLAGS := $(CFLAGS) -I. -DNO_BLAS_WRAP -DADD_ -Iext/clapack/include -Iext/cblas/include $(KISSFFT_CFLAGS) +CXXFLAGS := $(CXXFLAGS) -I. $(KISSFFT_CFLAGS) + +CLAPACK_SRC := ext/clapack/src/dgetrf.c \ + ext/clapack/src/dgetri.c \ + ext/clapack/src/dgetf2.c \ + ext/clapack/src/xerbla.c \ + ext/clapack/src/dlaswp.c \ + ext/clapack/src/dtrtri.c \ + ext/clapack/src/ilaenv.c \ + ext/clapack/src/iparmq.c \ + ext/clapack/src/s_cat.c \ + ext/clapack/src/s_copy.c \ + ext/clapack/src/s_cmp.c \ + ext/clapack/src/pow_di.c \ + ext/clapack/src/ieeeck.c \ + ext/clapack/src/i_nint.c \ + ext/clapack/src/dtrti2.c \ + ext/clapack/src/f77_aloc.c \ + ext/clapack/src/exit_.c + +CBLAS_SRC := ext/cblas/src/dgemm.c \ + ext/cblas/src/ddot.c \ + ext/cblas/src/dgemv.c \ + ext/cblas/src/dswap.c \ + ext/cblas/src/dtrsm.c \ + ext/cblas/src/dger.c \ + ext/cblas/src/idamax.c \ + ext/cblas/src/dscal.c \ + ext/cblas/src/dtrmm.c \ + ext/cblas/src/lsame.c \ + ext/cblas/src/dlamch.c \ + ext/cblas/src/dtrmv.c \ + ext/cblas/src/cblas_globals.c \ + ext/cblas/src/cblas_dgemm.c \ + ext/cblas/src/cblas_ddot.c \ + ext/cblas/src/cblas_xerbla.c HEADERS := base/Pitch.h \ base/Window.h \ @@ -95,7 +132,9 @@ maths/pca/pca.c \ thread/Thread.cpp \ ext/kissfft/kiss_fft.c \ - ext/kissfft/tools/kiss_fftr.c + ext/kissfft/tools/kiss_fftr.c \ + $(CLAPACK_SRC) \ + $(CBLAS_SRC) OBJECTS := $(SOURCES:.cpp=.o) OBJECTS := $(OBJECTS:.c=.o) @@ -208,7 +247,7 @@ dsp/transforms/FFT.o: maths/nan-inf.h ext/kissfft/kiss_fft.h dsp/transforms/FFT.o: ext/kissfft/tools/kiss_fftr.h dsp/wavelet/Wavelet.o: dsp/wavelet/Wavelet.h -hmm/hmm.o: ./include/clapack.h maths/nan-inf.h ./include/cblas.h hmm/hmm.h +hmm/hmm.o: maths/nan-inf.h hmm/hmm.h maths/Correlation.o: maths/Correlation.h maths/CosineDistance.o: maths/CosineDistance.h maths/KLDivergence.o: maths/KLDivergence.h
--- a/build/linux/Makefile.linux64 Thu May 26 14:17:00 2016 +0100 +++ b/build/linux/Makefile.linux64 Fri Sep 30 16:24:24 2016 +0100 @@ -1,8 +1,8 @@ -#CFLAGS := -DNDEBUG -O3 -fPIC -ffast-math -msse -msse2 -mfpmath=sse -ftree-vectorize -DUSE_PTHREADS -Ibuild/linux/amd64 -CFLAGS := -DDEBUG -g -Wall -Wextra -Werror -fPIC -ffast-math -DUSE_PTHREADS -Ibuild/linux/amd64 +CFLAGS := -DNDEBUG -Wall -Wextra -Werror=implicit-function-declaration -O3 -fPIC -ffast-math -msse -msse2 -mfpmath=sse -ftree-vectorize -DUSE_PTHREADS +#CFLAGS := -DDEBUG -g -Wall -Wextra -Werror=implicit-function-declaration -fPIC -ffast-math -DUSE_PTHREADS -CXXFLAGS := $(CFLAGS) +CXXFLAGS := $(CFLAGS) -Werror include build/general/Makefile.inc
--- a/dsp/wavelet/Wavelet.cpp Thu May 26 14:17:00 2016 +0100 +++ b/dsp/wavelet/Wavelet.cpp Fri Sep 30 16:24:24 2016 +0100 @@ -1843,6 +1843,9 @@ break; } + // avoid compiler warning for unused value if assert is not compiled in: + (void)flength; + assert(flength == int(lpd.size())); assert(flength == int(hpd.size())); }
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/cblas/include/cblas.h Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,575 @@ +#ifndef CBLAS_H +#define CBLAS_H +#include <stddef.h> + +/* + * Enumerated and derived types + */ +#define CBLAS_INDEX size_t /* this may vary between platforms */ + +enum CBLAS_ORDER {CblasRowMajor=101, CblasColMajor=102}; +enum CBLAS_TRANSPOSE {CblasNoTrans=111, CblasTrans=112, CblasConjTrans=113}; +enum CBLAS_UPLO {CblasUpper=121, CblasLower=122}; +enum CBLAS_DIAG {CblasNonUnit=131, CblasUnit=132}; +enum CBLAS_SIDE {CblasLeft=141, CblasRight=142}; + +#ifdef __cplusplus +extern "C" { +#endif + +/* + * =========================================================================== + * Prototypes for level 1 BLAS functions (complex are recast as routines) + * =========================================================================== + */ +float cblas_sdsdot(const int N, const float alpha, const float *X, + const int incX, const float *Y, const int incY); +double cblas_dsdot(const int N, const float *X, const int incX, const float *Y, + const int incY); +float cblas_sdot(const int N, const float *X, const int incX, + const float *Y, const int incY); +double cblas_ddot(const int N, const double *X, const int incX, + const double *Y, const int incY); + +/* + * Functions having prefixes Z and C only + */ +void cblas_cdotu_sub(const int N, const void *X, const int incX, + const void *Y, const int incY, void *dotu); +void cblas_cdotc_sub(const int N, const void *X, const int incX, + const void *Y, const int incY, void *dotc); + +void cblas_zdotu_sub(const int N, const void *X, const int incX, + const void *Y, const int incY, void *dotu); +void cblas_zdotc_sub(const int N, const void *X, const int incX, + const void *Y, const int incY, void *dotc); + + +/* + * Functions having prefixes S D SC DZ + */ +float cblas_snrm2(const int N, const float *X, const int incX); +float cblas_sasum(const int N, const float *X, const int incX); + +double cblas_dnrm2(const int N, const double *X, const int incX); +double cblas_dasum(const int N, const double *X, const int incX); + +float cblas_scnrm2(const int N, const void *X, const int incX); +float cblas_scasum(const int N, const void *X, const int incX); + +double cblas_dznrm2(const int N, const void *X, const int incX); +double cblas_dzasum(const int N, const void *X, const int incX); + + +/* + * Functions having standard 4 prefixes (S D C Z) + */ +CBLAS_INDEX cblas_isamax(const int N, const float *X, const int incX); +CBLAS_INDEX cblas_idamax(const int N, const double *X, const int incX); +CBLAS_INDEX cblas_icamax(const int N, const void *X, const int incX); +CBLAS_INDEX cblas_izamax(const int N, const void *X, const int incX); + +/* + * =========================================================================== + * Prototypes for level 1 BLAS routines + * =========================================================================== + */ + +/* + * Routines with standard 4 prefixes (s, d, c, z) + */ +void cblas_sswap(const int N, float *X, const int incX, + float *Y, const int incY); +void cblas_scopy(const int N, const float *X, const int incX, + float *Y, const int incY); +void cblas_saxpy(const int N, const float alpha, const float *X, + const int incX, float *Y, const int incY); + +void cblas_dswap(const int N, double *X, const int incX, + double *Y, const int incY); +void cblas_dcopy(const int N, const double *X, const int incX, + double *Y, const int incY); +void cblas_daxpy(const int N, const double alpha, const double *X, + const int incX, double *Y, const int incY); + +void cblas_cswap(const int N, void *X, const int incX, + void *Y, const int incY); +void cblas_ccopy(const int N, const void *X, const int incX, + void *Y, const int incY); +void cblas_caxpy(const int N, const void *alpha, const void *X, + const int incX, void *Y, const int incY); + +void cblas_zswap(const int N, void *X, const int incX, + void *Y, const int incY); +void cblas_zcopy(const int N, const void *X, const int incX, + void *Y, const int incY); +void cblas_zaxpy(const int N, const void *alpha, const void *X, + const int incX, void *Y, const int incY); + + +/* + * Routines with S and D prefix only + */ +void cblas_srotg(float *a, float *b, float *c, float *s); +void cblas_srotmg(float *d1, float *d2, float *b1, const float b2, float *P); +void cblas_srot(const int N, float *X, const int incX, + float *Y, const int incY, const float c, const float s); +void cblas_srotm(const int N, float *X, const int incX, + float *Y, const int incY, const float *P); + +void cblas_drotg(double *a, double *b, double *c, double *s); +void cblas_drotmg(double *d1, double *d2, double *b1, const double b2, double *P); +void cblas_drot(const int N, double *X, const int incX, + double *Y, const int incY, const double c, const double s); +void cblas_drotm(const int N, double *X, const int incX, + double *Y, const int incY, const double *P); + + +/* + * Routines with S D C Z CS and ZD prefixes + */ +void cblas_sscal(const int N, const float alpha, float *X, const int incX); +void cblas_dscal(const int N, const double alpha, double *X, const int incX); +void cblas_cscal(const int N, const void *alpha, void *X, const int incX); +void cblas_zscal(const int N, const void *alpha, void *X, const int incX); +void cblas_csscal(const int N, const float alpha, void *X, const int incX); +void cblas_zdscal(const int N, const double alpha, void *X, const int incX); + +/* + * =========================================================================== + * Prototypes for level 2 BLAS + * =========================================================================== + */ + +/* + * Routines with standard 4 prefixes (S, D, C, Z) + */ +void cblas_sgemv(const enum CBLAS_ORDER order, + const enum CBLAS_TRANSPOSE TransA, const int M, const int N, + const float alpha, const float *A, const int lda, + const float *X, const int incX, const float beta, + float *Y, const int incY); +void cblas_sgbmv(const enum CBLAS_ORDER order, + const enum CBLAS_TRANSPOSE TransA, const int M, const int N, + const int KL, const int KU, const float alpha, + const float *A, const int lda, const float *X, + const int incX, const float beta, float *Y, const int incY); +void cblas_strmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const float *A, const int lda, + float *X, const int incX); +void cblas_stbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const int K, const float *A, const int lda, + float *X, const int incX); +void cblas_stpmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const float *Ap, float *X, const int incX); +void cblas_strsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const float *A, const int lda, float *X, + const int incX); +void cblas_stbsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const int K, const float *A, const int lda, + float *X, const int incX); +void cblas_stpsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const float *Ap, float *X, const int incX); + +void cblas_dgemv(const enum CBLAS_ORDER order, + const enum CBLAS_TRANSPOSE TransA, const int M, const int N, + const double alpha, const double *A, const int lda, + const double *X, const int incX, const double beta, + double *Y, const int incY); +void cblas_dgbmv(const enum CBLAS_ORDER order, + const enum CBLAS_TRANSPOSE TransA, const int M, const int N, + const int KL, const int KU, const double alpha, + const double *A, const int lda, const double *X, + const int incX, const double beta, double *Y, const int incY); +void cblas_dtrmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const double *A, const int lda, + double *X, const int incX); +void cblas_dtbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const int K, const double *A, const int lda, + double *X, const int incX); +void cblas_dtpmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const double *Ap, double *X, const int incX); +void cblas_dtrsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const double *A, const int lda, double *X, + const int incX); +void cblas_dtbsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const int K, const double *A, const int lda, + double *X, const int incX); +void cblas_dtpsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const double *Ap, double *X, const int incX); + +void cblas_cgemv(const enum CBLAS_ORDER order, + const enum CBLAS_TRANSPOSE TransA, const int M, const int N, + const void *alpha, const void *A, const int lda, + const void *X, const int incX, const void *beta, + void *Y, const int incY); +void cblas_cgbmv(const enum CBLAS_ORDER order, + const enum CBLAS_TRANSPOSE TransA, const int M, const int N, + const int KL, const int KU, const void *alpha, + const void *A, const int lda, const void *X, + const int incX, const void *beta, void *Y, const int incY); +void cblas_ctrmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const void *A, const int lda, + void *X, const int incX); +void cblas_ctbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const int K, const void *A, const int lda, + void *X, const int incX); +void cblas_ctpmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const void *Ap, void *X, const int incX); +void cblas_ctrsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const void *A, const int lda, void *X, + const int incX); +void cblas_ctbsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const int K, const void *A, const int lda, + void *X, const int incX); +void cblas_ctpsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const void *Ap, void *X, const int incX); + +void cblas_zgemv(const enum CBLAS_ORDER order, + const enum CBLAS_TRANSPOSE TransA, const int M, const int N, + const void *alpha, const void *A, const int lda, + const void *X, const int incX, const void *beta, + void *Y, const int incY); +void cblas_zgbmv(const enum CBLAS_ORDER order, + const enum CBLAS_TRANSPOSE TransA, const int M, const int N, + const int KL, const int KU, const void *alpha, + const void *A, const int lda, const void *X, + const int incX, const void *beta, void *Y, const int incY); +void cblas_ztrmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const void *A, const int lda, + void *X, const int incX); +void cblas_ztbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const int K, const void *A, const int lda, + void *X, const int incX); +void cblas_ztpmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const void *Ap, void *X, const int incX); +void cblas_ztrsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const void *A, const int lda, void *X, + const int incX); +void cblas_ztbsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const int K, const void *A, const int lda, + void *X, const int incX); +void cblas_ztpsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const void *Ap, void *X, const int incX); + + +/* + * Routines with S and D prefixes only + */ +void cblas_ssymv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const float alpha, const float *A, + const int lda, const float *X, const int incX, + const float beta, float *Y, const int incY); +void cblas_ssbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const int K, const float alpha, const float *A, + const int lda, const float *X, const int incX, + const float beta, float *Y, const int incY); +void cblas_sspmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const float alpha, const float *Ap, + const float *X, const int incX, + const float beta, float *Y, const int incY); +void cblas_sger(const enum CBLAS_ORDER order, const int M, const int N, + const float alpha, const float *X, const int incX, + const float *Y, const int incY, float *A, const int lda); +void cblas_ssyr(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const float alpha, const float *X, + const int incX, float *A, const int lda); +void cblas_sspr(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const float alpha, const float *X, + const int incX, float *Ap); +void cblas_ssyr2(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const float alpha, const float *X, + const int incX, const float *Y, const int incY, float *A, + const int lda); +void cblas_sspr2(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const float alpha, const float *X, + const int incX, const float *Y, const int incY, float *A); + +void cblas_dsymv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const double alpha, const double *A, + const int lda, const double *X, const int incX, + const double beta, double *Y, const int incY); +void cblas_dsbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const int K, const double alpha, const double *A, + const int lda, const double *X, const int incX, + const double beta, double *Y, const int incY); +void cblas_dspmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const double alpha, const double *Ap, + const double *X, const int incX, + const double beta, double *Y, const int incY); +void cblas_dger(const enum CBLAS_ORDER order, const int M, const int N, + const double alpha, const double *X, const int incX, + const double *Y, const int incY, double *A, const int lda); +void cblas_dsyr(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const double alpha, const double *X, + const int incX, double *A, const int lda); +void cblas_dspr(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const double alpha, const double *X, + const int incX, double *Ap); +void cblas_dsyr2(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const double alpha, const double *X, + const int incX, const double *Y, const int incY, double *A, + const int lda); +void cblas_dspr2(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const double alpha, const double *X, + const int incX, const double *Y, const int incY, double *A); + + +/* + * Routines with C and Z prefixes only + */ +void cblas_chemv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const void *alpha, const void *A, + const int lda, const void *X, const int incX, + const void *beta, void *Y, const int incY); +void cblas_chbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const int K, const void *alpha, const void *A, + const int lda, const void *X, const int incX, + const void *beta, void *Y, const int incY); +void cblas_chpmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const void *alpha, const void *Ap, + const void *X, const int incX, + const void *beta, void *Y, const int incY); +void cblas_cgeru(const enum CBLAS_ORDER order, const int M, const int N, + const void *alpha, const void *X, const int incX, + const void *Y, const int incY, void *A, const int lda); +void cblas_cgerc(const enum CBLAS_ORDER order, const int M, const int N, + const void *alpha, const void *X, const int incX, + const void *Y, const int incY, void *A, const int lda); +void cblas_cher(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const float alpha, const void *X, const int incX, + void *A, const int lda); +void cblas_chpr(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const float alpha, const void *X, + const int incX, void *A); +void cblas_cher2(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const int N, + const void *alpha, const void *X, const int incX, + const void *Y, const int incY, void *A, const int lda); +void cblas_chpr2(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const int N, + const void *alpha, const void *X, const int incX, + const void *Y, const int incY, void *Ap); + +void cblas_zhemv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const void *alpha, const void *A, + const int lda, const void *X, const int incX, + const void *beta, void *Y, const int incY); +void cblas_zhbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const int K, const void *alpha, const void *A, + const int lda, const void *X, const int incX, + const void *beta, void *Y, const int incY); +void cblas_zhpmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const void *alpha, const void *Ap, + const void *X, const int incX, + const void *beta, void *Y, const int incY); +void cblas_zgeru(const enum CBLAS_ORDER order, const int M, const int N, + const void *alpha, const void *X, const int incX, + const void *Y, const int incY, void *A, const int lda); +void cblas_zgerc(const enum CBLAS_ORDER order, const int M, const int N, + const void *alpha, const void *X, const int incX, + const void *Y, const int incY, void *A, const int lda); +void cblas_zher(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const double alpha, const void *X, const int incX, + void *A, const int lda); +void cblas_zhpr(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const double alpha, const void *X, + const int incX, void *A); +void cblas_zher2(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const int N, + const void *alpha, const void *X, const int incX, + const void *Y, const int incY, void *A, const int lda); +void cblas_zhpr2(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const int N, + const void *alpha, const void *X, const int incX, + const void *Y, const int incY, void *Ap); + +/* + * =========================================================================== + * Prototypes for level 3 BLAS + * =========================================================================== + */ + +/* + * Routines with standard 4 prefixes (S, D, C, Z) + */ +void cblas_sgemm(const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_TRANSPOSE TransB, const int M, const int N, + const int K, const float alpha, const float *A, + const int lda, const float *B, const int ldb, + const float beta, float *C, const int ldc); +void cblas_ssymm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const int M, const int N, + const float alpha, const float *A, const int lda, + const float *B, const int ldb, const float beta, + float *C, const int ldc); +void cblas_ssyrk(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const float alpha, const float *A, const int lda, + const float beta, float *C, const int ldc); +void cblas_ssyr2k(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const float alpha, const float *A, const int lda, + const float *B, const int ldb, const float beta, + float *C, const int ldc); +void cblas_strmm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_DIAG Diag, const int M, const int N, + const float alpha, const float *A, const int lda, + float *B, const int ldb); +void cblas_strsm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_DIAG Diag, const int M, const int N, + const float alpha, const float *A, const int lda, + float *B, const int ldb); + +void cblas_dgemm(const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_TRANSPOSE TransB, const int M, const int N, + const int K, const double alpha, const double *A, + const int lda, const double *B, const int ldb, + const double beta, double *C, const int ldc); +void cblas_dsymm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const int M, const int N, + const double alpha, const double *A, const int lda, + const double *B, const int ldb, const double beta, + double *C, const int ldc); +void cblas_dsyrk(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const double alpha, const double *A, const int lda, + const double beta, double *C, const int ldc); +void cblas_dsyr2k(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const double alpha, const double *A, const int lda, + const double *B, const int ldb, const double beta, + double *C, const int ldc); +void cblas_dtrmm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_DIAG Diag, const int M, const int N, + const double alpha, const double *A, const int lda, + double *B, const int ldb); +void cblas_dtrsm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_DIAG Diag, const int M, const int N, + const double alpha, const double *A, const int lda, + double *B, const int ldb); + +void cblas_cgemm(const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_TRANSPOSE TransB, const int M, const int N, + const int K, const void *alpha, const void *A, + const int lda, const void *B, const int ldb, + const void *beta, void *C, const int ldc); +void cblas_csymm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const int M, const int N, + const void *alpha, const void *A, const int lda, + const void *B, const int ldb, const void *beta, + void *C, const int ldc); +void cblas_csyrk(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const void *alpha, const void *A, const int lda, + const void *beta, void *C, const int ldc); +void cblas_csyr2k(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const void *alpha, const void *A, const int lda, + const void *B, const int ldb, const void *beta, + void *C, const int ldc); +void cblas_ctrmm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_DIAG Diag, const int M, const int N, + const void *alpha, const void *A, const int lda, + void *B, const int ldb); +void cblas_ctrsm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_DIAG Diag, const int M, const int N, + const void *alpha, const void *A, const int lda, + void *B, const int ldb); + +void cblas_zgemm(const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_TRANSPOSE TransB, const int M, const int N, + const int K, const void *alpha, const void *A, + const int lda, const void *B, const int ldb, + const void *beta, void *C, const int ldc); +void cblas_zsymm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const int M, const int N, + const void *alpha, const void *A, const int lda, + const void *B, const int ldb, const void *beta, + void *C, const int ldc); +void cblas_zsyrk(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const void *alpha, const void *A, const int lda, + const void *beta, void *C, const int ldc); +void cblas_zsyr2k(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const void *alpha, const void *A, const int lda, + const void *B, const int ldb, const void *beta, + void *C, const int ldc); +void cblas_ztrmm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_DIAG Diag, const int M, const int N, + const void *alpha, const void *A, const int lda, + void *B, const int ldb); +void cblas_ztrsm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_DIAG Diag, const int M, const int N, + const void *alpha, const void *A, const int lda, + void *B, const int ldb); + + +/* + * Routines with prefixes C and Z only + */ +void cblas_chemm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const int M, const int N, + const void *alpha, const void *A, const int lda, + const void *B, const int ldb, const void *beta, + void *C, const int ldc); +void cblas_cherk(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const float alpha, const void *A, const int lda, + const float beta, void *C, const int ldc); +void cblas_cher2k(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const void *alpha, const void *A, const int lda, + const void *B, const int ldb, const float beta, + void *C, const int ldc); + +void cblas_zhemm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const int M, const int N, + const void *alpha, const void *A, const int lda, + const void *B, const int ldb, const void *beta, + void *C, const int ldc); +void cblas_zherk(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const double alpha, const void *A, const int lda, + const double beta, void *C, const int ldc); +void cblas_zher2k(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const void *alpha, const void *A, const int lda, + const void *B, const int ldb, const double beta, + void *C, const int ldc); + +void cblas_xerbla(int p, const char *rout, const char *form, ...); + +#ifdef __cplusplus +} +#endif +#endif
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/cblas/include/cblas_f77.h Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,701 @@ +/* + * cblas_f77.h + * Written by Keita Teranishi + * + * Updated by Jeff Horner + * Merged cblas_f77.h and cblas_fortran_header.h + */ + +#ifndef CBLAS_F77_H +#define CBLAS_f77_H + +#ifdef CRAY + #include <fortran.h> + #define F77_CHAR _fcd + #define C2F_CHAR(a) ( _cptofcd( (a), 1 ) ) + #define C2F_STR(a, i) ( _cptofcd( (a), (i) ) ) + #define F77_STRLEN(a) (_fcdlen) +#endif + +#ifdef WeirdNEC + #define F77_INT long +#endif + +#ifdef F77_CHAR + #define FCHAR F77_CHAR +#else + #define FCHAR char * +#endif + +#ifdef F77_INT + #define FINT const F77_INT * + #define FINT2 F77_INT * +#else + #define FINT const int * + #define FINT2 int * +#endif + +#if defined(ADD_) +/* + * Level 1 BLAS + */ +#define F77_xerbla xerbla_ + #define F77_srotg srotg_ + #define F77_srotmg srotmg_ + #define F77_srot srot_ + #define F77_srotm srotm_ + #define F77_drotg drotg_ + #define F77_drotmg drotmg_ + #define F77_drot drot_ + #define F77_drotm drotm_ + #define F77_sswap sswap_ + #define F77_scopy scopy_ + #define F77_saxpy saxpy_ + #define F77_isamax_sub isamaxsub_ + #define F77_dswap dswap_ + #define F77_dcopy dcopy_ + #define F77_daxpy daxpy_ + #define F77_idamax_sub idamaxsub_ + #define F77_cswap cswap_ + #define F77_ccopy ccopy_ + #define F77_caxpy caxpy_ + #define F77_icamax_sub icamaxsub_ + #define F77_zswap zswap_ + #define F77_zcopy zcopy_ + #define F77_zaxpy zaxpy_ + #define F77_izamax_sub izamaxsub_ + #define F77_sdot_sub sdotsub_ + #define F77_ddot_sub ddotsub_ + #define F77_dsdot_sub dsdotsub_ + #define F77_sscal sscal_ + #define F77_dscal dscal_ + #define F77_cscal cscal_ + #define F77_zscal zscal_ + #define F77_csscal csscal_ + #define F77_zdscal zdscal_ + #define F77_cdotu_sub cdotusub_ + #define F77_cdotc_sub cdotcsub_ + #define F77_zdotu_sub zdotusub_ + #define F77_zdotc_sub zdotcsub_ + #define F77_snrm2_sub snrm2sub_ + #define F77_sasum_sub sasumsub_ + #define F77_dnrm2_sub dnrm2sub_ + #define F77_dasum_sub dasumsub_ + #define F77_scnrm2_sub scnrm2sub_ + #define F77_scasum_sub scasumsub_ + #define F77_dznrm2_sub dznrm2sub_ + #define F77_dzasum_sub dzasumsub_ + #define F77_sdsdot_sub sdsdotsub_ +/* + * Level 2 BLAS + */ + #define F77_ssymv ssymv_ + #define F77_ssbmv ssbmv_ + #define F77_sspmv sspmv_ + #define F77_sger sger_ + #define F77_ssyr ssyr_ + #define F77_sspr sspr_ + #define F77_ssyr2 ssyr2_ + #define F77_sspr2 sspr2_ + #define F77_dsymv dsymv_ + #define F77_dsbmv dsbmv_ + #define F77_dspmv dspmv_ + #define F77_dger dger_ + #define F77_dsyr dsyr_ + #define F77_dspr dspr_ + #define F77_dsyr2 dsyr2_ + #define F77_dspr2 dspr2_ + #define F77_chemv chemv_ + #define F77_chbmv chbmv_ + #define F77_chpmv chpmv_ + #define F77_cgeru cgeru_ + #define F77_cgerc cgerc_ + #define F77_cher cher_ + #define F77_chpr chpr_ + #define F77_cher2 cher2_ + #define F77_chpr2 chpr2_ + #define F77_zhemv zhemv_ + #define F77_zhbmv zhbmv_ + #define F77_zhpmv zhpmv_ + #define F77_zgeru zgeru_ + #define F77_zgerc zgerc_ + #define F77_zher zher_ + #define F77_zhpr zhpr_ + #define F77_zher2 zher2_ + #define F77_zhpr2 zhpr2_ + #define F77_sgemv sgemv_ + #define F77_sgbmv sgbmv_ + #define F77_strmv strmv_ + #define F77_stbmv stbmv_ + #define F77_stpmv stpmv_ + #define F77_strsv strsv_ + #define F77_stbsv stbsv_ + #define F77_stpsv stpsv_ + #define F77_dgemv dgemv_ + #define F77_dgbmv dgbmv_ + #define F77_dtrmv dtrmv_ + #define F77_dtbmv dtbmv_ + #define F77_dtpmv dtpmv_ + #define F77_dtrsv dtrsv_ + #define F77_dtbsv dtbsv_ + #define F77_dtpsv dtpsv_ + #define F77_cgemv cgemv_ + #define F77_cgbmv cgbmv_ + #define F77_ctrmv ctrmv_ + #define F77_ctbmv ctbmv_ + #define F77_ctpmv ctpmv_ + #define F77_ctrsv ctrsv_ + #define F77_ctbsv ctbsv_ + #define F77_ctpsv ctpsv_ + #define F77_zgemv zgemv_ + #define F77_zgbmv zgbmv_ + #define F77_ztrmv ztrmv_ + #define F77_ztbmv ztbmv_ + #define F77_ztpmv ztpmv_ + #define F77_ztrsv ztrsv_ + #define F77_ztbsv ztbsv_ + #define F77_ztpsv ztpsv_ +/* + * Level 3 BLAS + */ + #define F77_chemm chemm_ + #define F77_cherk cherk_ + #define F77_cher2k cher2k_ + #define F77_zhemm zhemm_ + #define F77_zherk zherk_ + #define F77_zher2k zher2k_ + #define F77_sgemm sgemm_ + #define F77_ssymm ssymm_ + #define F77_ssyrk ssyrk_ + #define F77_ssyr2k ssyr2k_ + #define F77_strmm strmm_ + #define F77_strsm strsm_ + #define F77_dgemm dgemm_ + #define F77_dsymm dsymm_ + #define F77_dsyrk dsyrk_ + #define F77_dsyr2k dsyr2k_ + #define F77_dtrmm dtrmm_ + #define F77_dtrsm dtrsm_ + #define F77_cgemm cgemm_ + #define F77_csymm csymm_ + #define F77_csyrk csyrk_ + #define F77_csyr2k csyr2k_ + #define F77_ctrmm ctrmm_ + #define F77_ctrsm ctrsm_ + #define F77_zgemm zgemm_ + #define F77_zsymm zsymm_ + #define F77_zsyrk zsyrk_ + #define F77_zsyr2k zsyr2k_ + #define F77_ztrmm ztrmm_ + #define F77_ztrsm ztrsm_ +#elif defined(UPCASE) +/* + * Level 1 BLAS + */ +#define F77_xerbla XERBLA + #define F77_srotg SROTG + #define F77_srotmg SROTMG + #define F77_srot SROT + #define F77_srotm SROTM + #define F77_drotg DROTG + #define F77_drotmg DROTMG + #define F77_drot DROT + #define F77_drotm DROTM + #define F77_sswap SSWAP + #define F77_scopy SCOPY + #define F77_saxpy SAXPY + #define F77_isamax_sub ISAMAXSUB + #define F77_dswap DSWAP + #define F77_dcopy DCOPY + #define F77_daxpy DAXPY + #define F77_idamax_sub IDAMAXSUB + #define F77_cswap CSWAP + #define F77_ccopy CCOPY + #define F77_caxpy CAXPY + #define F77_icamax_sub ICAMAXSUB + #define F77_zswap ZSWAP + #define F77_zcopy ZCOPY + #define F77_zaxpy ZAXPY + #define F77_izamax_sub IZAMAXSUB + #define F77_sdot_sub SDOTSUB + #define F77_ddot_sub DDOTSUB + #define F77_dsdot_sub DSDOTSUB + #define F77_sscal SSCAL + #define F77_dscal DSCAL + #define F77_cscal CSCAL + #define F77_zscal ZSCAL + #define F77_csscal CSSCAL + #define F77_zdscal ZDSCAL + #define F77_cdotu_sub CDOTUSUB + #define F77_cdotc_sub CDOTCSUB + #define F77_zdotu_sub ZDOTUSUB + #define F77_zdotc_sub ZDOTCSUB + #define F77_snrm2_sub SNRM2SUB + #define F77_sasum_sub SASUMSUB + #define F77_dnrm2_sub DNRM2SUB + #define F77_dasum_sub DASUMSUB + #define F77_scnrm2_sub SCNRM2SUB + #define F77_scasum_sub SCASUMSUB + #define F77_dznrm2_sub DZNRM2SUB + #define F77_dzasum_sub DZASUMSUB + #define F77_sdsdot_sub SDSDOTSUB +/* + * Level 2 BLAS + */ + #define F77_ssymv SSYMV + #define F77_ssbmv SSBMV + #define F77_sspmv SSPMV + #define F77_sger SGER + #define F77_ssyr SSYR + #define F77_sspr SSPR + #define F77_ssyr2 SSYR2 + #define F77_sspr2 SSPR2 + #define F77_dsymv DSYMV + #define F77_dsbmv DSBMV + #define F77_dspmv DSPMV + #define F77_dger DGER + #define F77_dsyr DSYR + #define F77_dspr DSPR + #define F77_dsyr2 DSYR2 + #define F77_dspr2 DSPR2 + #define F77_chemv CHEMV + #define F77_chbmv CHBMV + #define F77_chpmv CHPMV + #define F77_cgeru CGERU + #define F77_cgerc CGERC + #define F77_cher CHER + #define F77_chpr CHPR + #define F77_cher2 CHER2 + #define F77_chpr2 CHPR2 + #define F77_zhemv ZHEMV + #define F77_zhbmv ZHBMV + #define F77_zhpmv ZHPMV + #define F77_zgeru ZGERU + #define F77_zgerc ZGERC + #define F77_zher ZHER + #define F77_zhpr ZHPR + #define F77_zher2 ZHER2 + #define F77_zhpr2 ZHPR2 + #define F77_sgemv SGEMV + #define F77_sgbmv SGBMV + #define F77_strmv STRMV + #define F77_stbmv STBMV + #define F77_stpmv STPMV + #define F77_strsv STRSV + #define F77_stbsv STBSV + #define F77_stpsv STPSV + #define F77_dgemv DGEMV + #define F77_dgbmv DGBMV + #define F77_dtrmv DTRMV + #define F77_dtbmv DTBMV + #define F77_dtpmv DTPMV + #define F77_dtrsv DTRSV + #define F77_dtbsv DTBSV + #define F77_dtpsv DTPSV + #define F77_cgemv CGEMV + #define F77_cgbmv CGBMV + #define F77_ctrmv CTRMV + #define F77_ctbmv CTBMV + #define F77_ctpmv CTPMV + #define F77_ctrsv CTRSV + #define F77_ctbsv CTBSV + #define F77_ctpsv CTPSV + #define F77_zgemv ZGEMV + #define F77_zgbmv ZGBMV + #define F77_ztrmv ZTRMV + #define F77_ztbmv ZTBMV + #define F77_ztpmv ZTPMV + #define F77_ztrsv ZTRSV + #define F77_ztbsv ZTBSV + #define F77_ztpsv ZTPSV +/* + * Level 3 BLAS + */ + #define F77_chemm CHEMM + #define F77_cherk CHERK + #define F77_cher2k CHER2K + #define F77_zhemm ZHEMM + #define F77_zherk ZHERK + #define F77_zher2k ZHER2K + #define F77_sgemm SGEMM + #define F77_ssymm SSYMM + #define F77_ssyrk SSYRK + #define F77_ssyr2k SSYR2K + #define F77_strmm STRMM + #define F77_strsm STRSM + #define F77_dgemm DGEMM + #define F77_dsymm DSYMM + #define F77_dsyrk DSYRK + #define F77_dsyr2k DSYR2K + #define F77_dtrmm DTRMM + #define F77_dtrsm DTRSM + #define F77_cgemm CGEMM + #define F77_csymm CSYMM + #define F77_csyrk CSYRK + #define F77_csyr2k CSYR2K + #define F77_ctrmm CTRMM + #define F77_ctrsm CTRSM + #define F77_zgemm ZGEMM + #define F77_zsymm ZSYMM + #define F77_zsyrk ZSYRK + #define F77_zsyr2k ZSYR2K + #define F77_ztrmm ZTRMM + #define F77_ztrsm ZTRSM +#elif defined(NOCHANGE) +/* + * Level 1 BLAS + */ +#define F77_xerbla xerbla + #define F77_srotg srotg + #define F77_srotmg srotmg + #define F77_srot srot + #define F77_srotm srotm + #define F77_drotg drotg + #define F77_drotmg drotmg + #define F77_drot drot + #define F77_drotm drotm + #define F77_sswap sswap + #define F77_scopy scopy + #define F77_saxpy saxpy + #define F77_isamax_sub isamaxsub + #define F77_dswap dswap + #define F77_dcopy dcopy + #define F77_daxpy daxpy + #define F77_idamax_sub idamaxsub + #define F77_cswap cswap + #define F77_ccopy ccopy + #define F77_caxpy caxpy + #define F77_icamax_sub icamaxsub + #define F77_zswap zswap + #define F77_zcopy zcopy + #define F77_zaxpy zaxpy + #define F77_izamax_sub izamaxsub + #define F77_sdot_sub sdotsub + #define F77_ddot_sub ddotsub + #define F77_dsdot_sub dsdotsub + #define F77_sscal sscal + #define F77_dscal dscal + #define F77_cscal cscal + #define F77_zscal zscal + #define F77_csscal csscal + #define F77_zdscal zdscal + #define F77_cdotu_sub cdotusub + #define F77_cdotc_sub cdotcsub + #define F77_zdotu_sub zdotusub + #define F77_zdotc_sub zdotcsub + #define F77_snrm2_sub snrm2sub + #define F77_sasum_sub sasumsub + #define F77_dnrm2_sub dnrm2sub + #define F77_dasum_sub dasumsub + #define F77_scnrm2_sub scnrm2sub + #define F77_scasum_sub scasumsub + #define F77_dznrm2_sub dznrm2sub + #define F77_dzasum_sub dzasumsub + #define F77_sdsdot_sub sdsdotsub +/* + * Level 2 BLAS + */ + #define F77_ssymv ssymv + #define F77_ssbmv ssbmv + #define F77_sspmv sspmv + #define F77_sger sger + #define F77_ssyr ssyr + #define F77_sspr sspr + #define F77_ssyr2 ssyr2 + #define F77_sspr2 sspr2 + #define F77_dsymv dsymv + #define F77_dsbmv dsbmv + #define F77_dspmv dspmv + #define F77_dger dger + #define F77_dsyr dsyr + #define F77_dspr dspr + #define F77_dsyr2 dsyr2 + #define F77_dspr2 dspr2 + #define F77_chemv chemv + #define F77_chbmv chbmv + #define F77_chpmv chpmv + #define F77_cgeru cgeru + #define F77_cgerc cgerc + #define F77_cher cher + #define F77_chpr chpr + #define F77_cher2 cher2 + #define F77_chpr2 chpr2 + #define F77_zhemv zhemv + #define F77_zhbmv zhbmv + #define F77_zhpmv zhpmv + #define F77_zgeru zgeru + #define F77_zgerc zgerc + #define F77_zher zher + #define F77_zhpr zhpr + #define F77_zher2 zher2 + #define F77_zhpr2 zhpr2 + #define F77_sgemv sgemv + #define F77_sgbmv sgbmv + #define F77_strmv strmv + #define F77_stbmv stbmv + #define F77_stpmv stpmv + #define F77_strsv strsv + #define F77_stbsv stbsv + #define F77_stpsv stpsv + #define F77_dgemv dgemv + #define F77_dgbmv dgbmv + #define F77_dtrmv dtrmv + #define F77_dtbmv dtbmv + #define F77_dtpmv dtpmv + #define F77_dtrsv dtrsv + #define F77_dtbsv dtbsv + #define F77_dtpsv dtpsv + #define F77_cgemv cgemv + #define F77_cgbmv cgbmv + #define F77_ctrmv ctrmv + #define F77_ctbmv ctbmv + #define F77_ctpmv ctpmv + #define F77_ctrsv ctrsv + #define F77_ctbsv ctbsv + #define F77_ctpsv ctpsv + #define F77_zgemv zgemv + #define F77_zgbmv zgbmv + #define F77_ztrmv ztrmv + #define F77_ztbmv ztbmv + #define F77_ztpmv ztpmv + #define F77_ztrsv ztrsv + #define F77_ztbsv ztbsv + #define F77_ztpsv ztpsv +/* + * Level 3 BLAS + */ + #define F77_chemm chemm + #define F77_cherk cherk + #define F77_cher2k cher2k + #define F77_zhemm zhemm + #define F77_zherk zherk + #define F77_zher2k zher2k + #define F77_sgemm sgemm + #define F77_ssymm ssymm + #define F77_ssyrk ssyrk + #define F77_ssyr2k ssyr2k + #define F77_strmm strmm + #define F77_strsm strsm + #define F77_dgemm dgemm + #define F77_dsymm dsymm + #define F77_dsyrk dsyrk + #define F77_dsyr2k dsyr2k + #define F77_dtrmm dtrmm + #define F77_dtrsm dtrsm + #define F77_cgemm cgemm + #define F77_csymm csymm + #define F77_csyrk csyrk + #define F77_csyr2k csyr2k + #define F77_ctrmm ctrmm + #define F77_ctrsm ctrsm + #define F77_zgemm zgemm + #define F77_zsymm zsymm + #define F77_zsyrk zsyrk + #define F77_zsyr2k zsyr2k + #define F77_ztrmm ztrmm + #define F77_ztrsm ztrsm +#endif + +#ifdef __cplusplus +extern "C" { +#endif + + void F77_xerbla(FCHAR, void *); +/* + * Level 1 Fortran Prototypes + */ + +/* Single Precision */ + + void F77_srot(FINT, float *, FINT, float *, FINT, const float *, const float *); + void F77_srotg(float *,float *,float *,float *); + void F77_srotm( FINT, float *, FINT, float *, FINT, const float *); + void F77_srotmg(float *,float *,float *,const float *, float *); + void F77_sswap( FINT, float *, FINT, float *, FINT); + void F77_scopy( FINT, const float *, FINT, float *, FINT); + void F77_saxpy( FINT, const float *, const float *, FINT, float *, FINT); + void F77_sdot_sub(FINT, const float *, FINT, const float *, FINT, float *); + void F77_sdsdot_sub( FINT, const float *, const float *, FINT, const float *, FINT, float *); + void F77_sscal( FINT, const float *, float *, FINT); + void F77_snrm2_sub( FINT, const float *, FINT, float *); + void F77_sasum_sub( FINT, const float *, FINT, float *); + void F77_isamax_sub( FINT, const float * , FINT, FINT2); + +/* Double Precision */ + + void F77_drot(FINT, double *, FINT, double *, FINT, const double *, const double *); + void F77_drotg(double *,double *,double *,double *); + void F77_drotm( FINT, double *, FINT, double *, FINT, const double *); + void F77_drotmg(double *,double *,double *,const double *, double *); + void F77_dswap( FINT, double *, FINT, double *, FINT); + void F77_dcopy( FINT, const double *, FINT, double *, FINT); + void F77_daxpy( FINT, const double *, const double *, FINT, double *, FINT); + void F77_dswap( FINT, double *, FINT, double *, FINT); + void F77_dsdot_sub(FINT, const float *, FINT, const float *, FINT, double *); + void F77_ddot_sub( FINT, const double *, FINT, const double *, FINT, double *); + void F77_dscal( FINT, const double *, double *, FINT); + void F77_dnrm2_sub( FINT, const double *, FINT, double *); + void F77_dasum_sub( FINT, const double *, FINT, double *); + void F77_idamax_sub( FINT, const double * , FINT, FINT2); + +/* Single Complex Precision */ + + void F77_cswap( FINT, void *, FINT, void *, FINT); + void F77_ccopy( FINT, const void *, FINT, void *, FINT); + void F77_caxpy( FINT, const void *, const void *, FINT, void *, FINT); + void F77_cswap( FINT, void *, FINT, void *, FINT); + void F77_cdotc_sub( FINT, const void *, FINT, const void *, FINT, void *); + void F77_cdotu_sub( FINT, const void *, FINT, const void *, FINT, void *); + void F77_cscal( FINT, const void *, void *, FINT); + void F77_icamax_sub( FINT, const void *, FINT, FINT2); + void F77_csscal( FINT, const float *, void *, FINT); + void F77_scnrm2_sub( FINT, const void *, FINT, float *); + void F77_scasum_sub( FINT, const void *, FINT, float *); + +/* Double Complex Precision */ + + void F77_zswap( FINT, void *, FINT, void *, FINT); + void F77_zcopy( FINT, const void *, FINT, void *, FINT); + void F77_zaxpy( FINT, const void *, const void *, FINT, void *, FINT); + void F77_zswap( FINT, void *, FINT, void *, FINT); + void F77_zdotc_sub( FINT, const void *, FINT, const void *, FINT, void *); + void F77_zdotu_sub( FINT, const void *, FINT, const void *, FINT, void *); + void F77_zdscal( FINT, const double *, void *, FINT); + void F77_zscal( FINT, const void *, void *, FINT); + void F77_dznrm2_sub( FINT, const void *, FINT, double *); + void F77_dzasum_sub( FINT, const void *, FINT, double *); + void F77_izamax_sub( FINT, const void *, FINT, FINT2); + +/* + * Level 2 Fortran Prototypes + */ + +/* Single Precision */ + + void F77_sgemv(FCHAR, FINT, FINT, const float *, const float *, FINT, const float *, FINT, const float *, float *, FINT); + void F77_sgbmv(FCHAR, FINT, FINT, FINT, FINT, const float *, const float *, FINT, const float *, FINT, const float *, float *, FINT); + void F77_ssymv(FCHAR, FINT, const float *, const float *, FINT, const float *, FINT, const float *, float *, FINT); + void F77_ssbmv(FCHAR, FINT, FINT, const float *, const float *, FINT, const float *, FINT, const float *, float *, FINT); + void F77_sspmv(FCHAR, FINT, const float *, const float *, const float *, FINT, const float *, float *, FINT); + void F77_strmv( FCHAR, FCHAR, FCHAR, FINT, const float *, FINT, float *, FINT); + void F77_stbmv( FCHAR, FCHAR, FCHAR, FINT, FINT, const float *, FINT, float *, FINT); + void F77_strsv( FCHAR, FCHAR, FCHAR, FINT, const float *, FINT, float *, FINT); + void F77_stbsv( FCHAR, FCHAR, FCHAR, FINT, FINT, const float *, FINT, float *, FINT); + void F77_stpmv( FCHAR, FCHAR, FCHAR, FINT, const float *, float *, FINT); + void F77_stpsv( FCHAR, FCHAR, FCHAR, FINT, const float *, float *, FINT); + void F77_sger( FINT, FINT, const float *, const float *, FINT, const float *, FINT, float *, FINT); + void F77_ssyr(FCHAR, FINT, const float *, const float *, FINT, float *, FINT); + void F77_sspr(FCHAR, FINT, const float *, const float *, FINT, float *); + void F77_sspr2(FCHAR, FINT, const float *, const float *, FINT, const float *, FINT, float *); + void F77_ssyr2(FCHAR, FINT, const float *, const float *, FINT, const float *, FINT, float *, FINT); + +/* Double Precision */ + + void F77_dgemv(FCHAR, FINT, FINT, const double *, const double *, FINT, const double *, FINT, const double *, double *, FINT); + void F77_dgbmv(FCHAR, FINT, FINT, FINT, FINT, const double *, const double *, FINT, const double *, FINT, const double *, double *, FINT); + void F77_dsymv(FCHAR, FINT, const double *, const double *, FINT, const double *, FINT, const double *, double *, FINT); + void F77_dsbmv(FCHAR, FINT, FINT, const double *, const double *, FINT, const double *, FINT, const double *, double *, FINT); + void F77_dspmv(FCHAR, FINT, const double *, const double *, const double *, FINT, const double *, double *, FINT); + void F77_dtrmv( FCHAR, FCHAR, FCHAR, FINT, const double *, FINT, double *, FINT); + void F77_dtbmv( FCHAR, FCHAR, FCHAR, FINT, FINT, const double *, FINT, double *, FINT); + void F77_dtrsv( FCHAR, FCHAR, FCHAR, FINT, const double *, FINT, double *, FINT); + void F77_dtbsv( FCHAR, FCHAR, FCHAR, FINT, FINT, const double *, FINT, double *, FINT); + void F77_dtpmv( FCHAR, FCHAR, FCHAR, FINT, const double *, double *, FINT); + void F77_dtpsv( FCHAR, FCHAR, FCHAR, FINT, const double *, double *, FINT); + void F77_dger( FINT, FINT, const double *, const double *, FINT, const double *, FINT, double *, FINT); + void F77_dsyr(FCHAR, FINT, const double *, const double *, FINT, double *, FINT); + void F77_dspr(FCHAR, FINT, const double *, const double *, FINT, double *); + void F77_dspr2(FCHAR, FINT, const double *, const double *, FINT, const double *, FINT, double *); + void F77_dsyr2(FCHAR, FINT, const double *, const double *, FINT, const double *, FINT, double *, FINT); + +/* Single Complex Precision */ + + void F77_cgemv(FCHAR, FINT, FINT, const void *, const void *, FINT, const void *, FINT, const void *, void *, FINT); + void F77_cgbmv(FCHAR, FINT, FINT, FINT, FINT, const void *, const void *, FINT, const void *, FINT, const void *, void *, FINT); + void F77_chemv(FCHAR, FINT, const void *, const void *, FINT, const void *, FINT, const void *, void *, FINT); + void F77_chbmv(FCHAR, FINT, FINT, const void *, const void *, FINT, const void *, FINT, const void *, void *, FINT); + void F77_chpmv(FCHAR, FINT, const void *, const void *, const void *, FINT, const void *, void *, FINT); + void F77_ctrmv( FCHAR, FCHAR, FCHAR, FINT, const void *, FINT, void *, FINT); + void F77_ctbmv( FCHAR, FCHAR, FCHAR, FINT, FINT, const void *, FINT, void *, FINT); + void F77_ctpmv( FCHAR, FCHAR, FCHAR, FINT, const void *, void *, FINT); + void F77_ctrsv( FCHAR, FCHAR, FCHAR, FINT, const void *, FINT, void *, FINT); + void F77_ctbsv( FCHAR, FCHAR, FCHAR, FINT, FINT, const void *, FINT, void *, FINT); + void F77_ctpsv( FCHAR, FCHAR, FCHAR, FINT, const void *, void *,FINT); + void F77_cgerc( FINT, FINT, const void *, const void *, FINT, const void *, FINT, void *, FINT); + void F77_cgeru( FINT, FINT, const void *, const void *, FINT, const void *, FINT, void *, FINT); + void F77_cher(FCHAR, FINT, const float *, const void *, FINT, void *, FINT); + void F77_cher2(FCHAR, FINT, const void *, const void *, FINT, const void *, FINT, void *, FINT); + void F77_chpr(FCHAR, FINT, const float *, const void *, FINT, void *); + void F77_chpr2(FCHAR, FINT, const float *, const void *, FINT, const void *, FINT, void *); + +/* Double Complex Precision */ + + void F77_zgemv(FCHAR, FINT, FINT, const void *, const void *, FINT, const void *, FINT, const void *, void *, FINT); + void F77_zgbmv(FCHAR, FINT, FINT, FINT, FINT, const void *, const void *, FINT, const void *, FINT, const void *, void *, FINT); + void F77_zhemv(FCHAR, FINT, const void *, const void *, FINT, const void *, FINT, const void *, void *, FINT); + void F77_zhbmv(FCHAR, FINT, FINT, const void *, const void *, FINT, const void *, FINT, const void *, void *, FINT); + void F77_zhpmv(FCHAR, FINT, const void *, const void *, const void *, FINT, const void *, void *, FINT); + void F77_ztrmv( FCHAR, FCHAR, FCHAR, FINT, const void *, FINT, void *, FINT); + void F77_ztbmv( FCHAR, FCHAR, FCHAR, FINT, FINT, const void *, FINT, void *, FINT); + void F77_ztpmv( FCHAR, FCHAR, FCHAR, FINT, const void *, void *, FINT); + void F77_ztrsv( FCHAR, FCHAR, FCHAR, FINT, const void *, FINT, void *, FINT); + void F77_ztbsv( FCHAR, FCHAR, FCHAR, FINT, FINT, const void *, FINT, void *, FINT); + void F77_ztpsv( FCHAR, FCHAR, FCHAR, FINT, const void *, void *,FINT); + void F77_zgerc( FINT, FINT, const void *, const void *, FINT, const void *, FINT, void *, FINT); + void F77_zgeru( FINT, FINT, const void *, const void *, FINT, const void *, FINT, void *, FINT); + void F77_zher(FCHAR, FINT, const double *, const void *, FINT, void *, FINT); + void F77_zher2(FCHAR, FINT, const void *, const void *, FINT, const void *, FINT, void *, FINT); + void F77_zhpr(FCHAR, FINT, const double *, const void *, FINT, void *); + void F77_zhpr2(FCHAR, FINT, const double *, const void *, FINT, const void *, FINT, void *); + +/* + * Level 3 Fortran Prototypes + */ + +/* Single Precision */ + + void F77_sgemm(FCHAR, FCHAR, FINT, FINT, FINT, const float *, const float *, FINT, const float *, FINT, const float *, float *, FINT); + void F77_ssymm(FCHAR, FCHAR, FINT, FINT, const float *, const float *, FINT, const float *, FINT, const float *, float *, FINT); + void F77_ssyrk(FCHAR, FCHAR, FINT, FINT, const float *, const float *, FINT, const float *, float *, FINT); + void F77_ssyr2k(FCHAR, FCHAR, FINT, FINT, const float *, const float *, FINT, const float *, FINT, const float *, float *, FINT); + void F77_strmm(FCHAR, FCHAR, FCHAR, FCHAR, FINT, FINT, const float *, const float *, FINT, float *, FINT); + void F77_strsm(FCHAR, FCHAR, FCHAR, FCHAR, FINT, FINT, const float *, const float *, FINT, float *, FINT); + +/* Double Precision */ + + void F77_dgemm(FCHAR, FCHAR, FINT, FINT, FINT, const double *, const double *, FINT, const double *, FINT, const double *, double *, FINT); + void F77_dsymm(FCHAR, FCHAR, FINT, FINT, const double *, const double *, FINT, const double *, FINT, const double *, double *, FINT); + void F77_dsyrk(FCHAR, FCHAR, FINT, FINT, const double *, const double *, FINT, const double *, double *, FINT); + void F77_dsyr2k(FCHAR, FCHAR, FINT, FINT, const double *, const double *, FINT, const double *, FINT, const double *, double *, FINT); + void F77_dtrmm(FCHAR, FCHAR, FCHAR, FCHAR, FINT, FINT, const double *, const double *, FINT, double *, FINT); + void F77_dtrsm(FCHAR, FCHAR, FCHAR, FCHAR, FINT, FINT, const double *, const double *, FINT, double *, FINT); + +/* Single Complex Precision */ + + void F77_cgemm(FCHAR, FCHAR, FINT, FINT, FINT, const float *, const float *, FINT, const float *, FINT, const float *, float *, FINT); + void F77_csymm(FCHAR, FCHAR, FINT, FINT, const float *, const float *, FINT, const float *, FINT, const float *, float *, FINT); + void F77_chemm(FCHAR, FCHAR, FINT, FINT, const float *, const float *, FINT, const float *, FINT, const float *, float *, FINT); + void F77_csyrk(FCHAR, FCHAR, FINT, FINT, const float *, const float *, FINT, const float *, float *, FINT); + void F77_cherk(FCHAR, FCHAR, FINT, FINT, const float *, const float *, FINT, const float *, float *, FINT); + void F77_csyr2k(FCHAR, FCHAR, FINT, FINT, const float *, const float *, FINT, const float *, FINT, const float *, float *, FINT); + void F77_cher2k(FCHAR, FCHAR, FINT, FINT, const float *, const float *, FINT, const float *, FINT, const float *, float *, FINT); + void F77_ctrmm(FCHAR, FCHAR, FCHAR, FCHAR, FINT, FINT, const float *, const float *, FINT, float *, FINT); + void F77_ctrsm(FCHAR, FCHAR, FCHAR, FCHAR, FINT, FINT, const float *, const float *, FINT, float *, FINT); + +/* Double Complex Precision */ + + void F77_zgemm(FCHAR, FCHAR, FINT, FINT, FINT, const double *, const double *, FINT, const double *, FINT, const double *, double *, FINT); + void F77_zsymm(FCHAR, FCHAR, FINT, FINT, const double *, const double *, FINT, const double *, FINT, const double *, double *, FINT); + void F77_zhemm(FCHAR, FCHAR, FINT, FINT, const double *, const double *, FINT, const double *, FINT, const double *, double *, FINT); + void F77_zsyrk(FCHAR, FCHAR, FINT, FINT, const double *, const double *, FINT, const double *, double *, FINT); + void F77_zherk(FCHAR, FCHAR, FINT, FINT, const double *, const double *, FINT, const double *, double *, FINT); + void F77_zsyr2k(FCHAR, FCHAR, FINT, FINT, const double *, const double *, FINT, const double *, FINT, const double *, double *, FINT); + void F77_zher2k(FCHAR, FCHAR, FINT, FINT, const double *, const double *, FINT, const double *, FINT, const double *, double *, FINT); + void F77_ztrmm(FCHAR, FCHAR, FCHAR, FCHAR, FINT, FINT, const double *, const double *, FINT, double *, FINT); + void F77_ztrsm(FCHAR, FCHAR, FCHAR, FCHAR, FINT, FINT, const double *, const double *, FINT, double *, FINT); + +#ifdef __cplusplus +} +#endif + +#endif /* CBLAS_F77_H */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/cblas/src/cblas_ddot.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,17 @@ +#include "cblas.h" +#include "cblas_f77.h" + +extern double ddot_(const int *n, const double *dx, const int *incx, const double *dy, const int *incy); + +double cblas_ddot( const int N, const double *X, + const int incX, const double *Y, const int incY) +{ +#ifdef F77_INT + F77_INT F77_N=N, F77_incX=incX, F77_incY=incY; +#else + #define F77_N N + #define F77_incX incX + #define F77_incY incY +#endif + return ddot_( &F77_N, X, &F77_incX, Y, &F77_incY); +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/cblas/src/cblas_dgemm.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,109 @@ +/* + * + * cblas_dgemm.c + * This program is a C interface to dgemm. + * Written by Keita Teranishi + * 4/8/1998 + * + */ + +#include "cblas.h" +#include "cblas_f77.h" +void cblas_dgemm(const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_TRANSPOSE TransB, const int M, const int N, + const int K, const double alpha, const double *A, + const int lda, const double *B, const int ldb, + const double beta, double *C, const int ldc) +{ + char TA, TB; +#ifdef F77_CHAR + F77_CHAR F77_TA, F77_TB; +#else + #define F77_TA &TA + #define F77_TB &TB +#endif + +#ifdef F77_INT + F77_INT F77_M=M, F77_N=N, F77_K=K, F77_lda=lda, F77_ldb=ldb; + F77_INT F77_ldc=ldc; +#else + #define F77_M M + #define F77_N N + #define F77_K K + #define F77_lda lda + #define F77_ldb ldb + #define F77_ldc ldc +#endif + + extern int CBLAS_CallFromC; + extern int RowMajorStrg; + RowMajorStrg = 0; + CBLAS_CallFromC = 1; + + if( Order == CblasColMajor ) + { + if(TransA == CblasTrans) TA='T'; + else if ( TransA == CblasConjTrans ) TA='C'; + else if ( TransA == CblasNoTrans ) TA='N'; + else + { + cblas_xerbla(2, "cblas_dgemm","Illegal TransA setting, %d\n", TransA); + CBLAS_CallFromC = 0; + RowMajorStrg = 0; + return; + } + + if(TransB == CblasTrans) TB='T'; + else if ( TransB == CblasConjTrans ) TB='C'; + else if ( TransB == CblasNoTrans ) TB='N'; + else + { + cblas_xerbla(3, "cblas_dgemm","Illegal TransB setting, %d\n", TransB); + CBLAS_CallFromC = 0; + RowMajorStrg = 0; + return; + } + + #ifdef F77_CHAR + F77_TA = C2F_CHAR(&TA); + F77_TB = C2F_CHAR(&TB); + #endif + + F77_dgemm(F77_TA, F77_TB, &F77_M, &F77_N, &F77_K, &alpha, A, + &F77_lda, B, &F77_ldb, &beta, C, &F77_ldc); + } else if (Order == CblasRowMajor) + { + RowMajorStrg = 1; + if(TransA == CblasTrans) TB='T'; + else if ( TransA == CblasConjTrans ) TB='C'; + else if ( TransA == CblasNoTrans ) TB='N'; + else + { + cblas_xerbla(2, "cblas_dgemm","Illegal TransA setting, %d\n", TransA); + CBLAS_CallFromC = 0; + RowMajorStrg = 0; + return; + } + if(TransB == CblasTrans) TA='T'; + else if ( TransB == CblasConjTrans ) TA='C'; + else if ( TransB == CblasNoTrans ) TA='N'; + else + { + cblas_xerbla(2, "cblas_dgemm","Illegal TransB setting, %d\n", TransB); + CBLAS_CallFromC = 0; + RowMajorStrg = 0; + return; + } + #ifdef F77_CHAR + F77_TA = C2F_CHAR(&TA); + F77_TB = C2F_CHAR(&TB); + #endif + + F77_dgemm(F77_TA, F77_TB, &F77_N, &F77_M, &F77_K, &alpha, B, + &F77_ldb, A, &F77_lda, &beta, C, &F77_ldc); + } + else cblas_xerbla(1, "cblas_dgemm", "Illegal Order setting, %d\n", Order); + CBLAS_CallFromC = 0; + RowMajorStrg = 0; + return; +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/cblas/src/cblas_globals.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,2 @@ +int CBLAS_CallFromC=0; +int RowMajorStrg=0;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/cblas/src/cblas_xerbla.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,68 @@ +#include <stdio.h> +#include <stdlib.h> +#include <string.h> +#include <stdarg.h> +#include "cblas.h" +#include "cblas_f77.h" + +void cblas_xerbla(int info, const char *rout, const char *form, ...) +{ + extern int RowMajorStrg; + char empty[1] = ""; + va_list argptr; + + va_start(argptr, form); + + if (RowMajorStrg) + { + if (strstr(rout,"gemm") != 0) + { + if (info == 5 ) info = 4; + else if (info == 4 ) info = 5; + else if (info == 11) info = 9; + else if (info == 9 ) info = 11; + } + else if (strstr(rout,"symm") != 0 || strstr(rout,"hemm") != 0) + { + if (info == 5 ) info = 4; + else if (info == 4 ) info = 5; + } + else if (strstr(rout,"trmm") != 0 || strstr(rout,"trsm") != 0) + { + if (info == 7 ) info = 6; + else if (info == 6 ) info = 7; + } + else if (strstr(rout,"gemv") != 0) + { + if (info == 4) info = 3; + else if (info == 3) info = 4; + } + else if (strstr(rout,"gbmv") != 0) + { + if (info == 4) info = 3; + else if (info == 3) info = 4; + else if (info == 6) info = 5; + else if (info == 5) info = 6; + } + else if (strstr(rout,"ger") != 0) + { + if (info == 3) info = 2; + else if (info == 2) info = 3; + else if (info == 8) info = 6; + else if (info == 6) info = 8; + } + else if ( (strstr(rout,"her2") != 0 || strstr(rout,"hpr2") != 0) + && strstr(rout,"her2k") == 0 ) + { + if (info == 8) info = 6; + else if (info == 6) info = 8; + } + } + if (info) + fprintf(stderr, "Parameter %d to routine %s was incorrect\n", info, rout); + vfprintf(stderr, form, argptr); + va_end(argptr); + if (info && !info) + F77_xerbla(empty, &info); /* Force link of our F77 error handler */ + exit(-1); +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/cblas/src/ddot.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,110 @@ +/* ddot.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +doublereal ddot_(integer *n, doublereal *dx, integer *incx, doublereal *dy, + integer *incy) +{ + /* System generated locals */ + integer i__1; + doublereal ret_val; + + /* Local variables */ + integer i__, m, ix, iy, mp1; + doublereal dtemp; + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* forms the dot product of two vectors. */ +/* uses unrolled loops for increments equal to one. */ +/* jack dongarra, linpack, 3/11/78. */ +/* modified 12/3/93, array(1) declarations changed to array(*) */ + + +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + /* Parameter adjustments */ + --dy; + --dx; + + /* Function Body */ + ret_val = 0.; + dtemp = 0.; + if (*n <= 0) { + return ret_val; + } + if (*incx == 1 && *incy == 1) { + goto L20; + } + +/* code for unequal increments or equal increments */ +/* not equal to 1 */ + + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp += dx[ix] * dy[iy]; + ix += *incx; + iy += *incy; +/* L10: */ + } + ret_val = dtemp; + return ret_val; + +/* code for both increments equal to 1 */ + + +/* clean-up loop */ + +L20: + m = *n % 5; + if (m == 0) { + goto L40; + } + i__1 = m; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp += dx[i__] * dy[i__]; +/* L30: */ + } + if (*n < 5) { + goto L60; + } +L40: + mp1 = m + 1; + i__1 = *n; + for (i__ = mp1; i__ <= i__1; i__ += 5) { + dtemp = dtemp + dx[i__] * dy[i__] + dx[i__ + 1] * dy[i__ + 1] + dx[ + i__ + 2] * dy[i__ + 2] + dx[i__ + 3] * dy[i__ + 3] + dx[i__ + + 4] * dy[i__ + 4]; +/* L50: */ + } +L60: + ret_val = dtemp; + return ret_val; +} /* ddot_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/cblas/src/dgemm.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,389 @@ +/* dgemm.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +/* Subroutine */ int dgemm_(char *transa, char *transb, integer *m, integer * + n, integer *k, doublereal *alpha, doublereal *a, integer *lda, + doublereal *b, integer *ldb, doublereal *beta, doublereal *c__, + integer *ldc) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, + i__3; + + /* Local variables */ + integer i__, j, l, info; + logical nota, notb; + doublereal temp; + integer ncola; + extern logical lsame_(char *, char *); + integer nrowa, nrowb; + extern /* Subroutine */ int xerbla_(char *, integer *); + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* DGEMM performs one of the matrix-matrix operations */ + +/* C := alpha*op( A )*op( B ) + beta*C, */ + +/* where op( X ) is one of */ + +/* op( X ) = X or op( X ) = X', */ + +/* alpha and beta are scalars, and A, B and C are matrices, with op( A ) */ +/* an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. */ + +/* Arguments */ +/* ========== */ + +/* TRANSA - CHARACTER*1. */ +/* On entry, TRANSA specifies the form of op( A ) to be used in */ +/* the matrix multiplication as follows: */ + +/* TRANSA = 'N' or 'n', op( A ) = A. */ + +/* TRANSA = 'T' or 't', op( A ) = A'. */ + +/* TRANSA = 'C' or 'c', op( A ) = A'. */ + +/* Unchanged on exit. */ + +/* TRANSB - CHARACTER*1. */ +/* On entry, TRANSB specifies the form of op( B ) to be used in */ +/* the matrix multiplication as follows: */ + +/* TRANSB = 'N' or 'n', op( B ) = B. */ + +/* TRANSB = 'T' or 't', op( B ) = B'. */ + +/* TRANSB = 'C' or 'c', op( B ) = B'. */ + +/* Unchanged on exit. */ + +/* M - INTEGER. */ +/* On entry, M specifies the number of rows of the matrix */ +/* op( A ) and of the matrix C. M must be at least zero. */ +/* Unchanged on exit. */ + +/* N - INTEGER. */ +/* On entry, N specifies the number of columns of the matrix */ +/* op( B ) and the number of columns of the matrix C. N must be */ +/* at least zero. */ +/* Unchanged on exit. */ + +/* K - INTEGER. */ +/* On entry, K specifies the number of columns of the matrix */ +/* op( A ) and the number of rows of the matrix op( B ). K must */ +/* be at least zero. */ +/* Unchanged on exit. */ + +/* ALPHA - DOUBLE PRECISION. */ +/* On entry, ALPHA specifies the scalar alpha. */ +/* Unchanged on exit. */ + +/* A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is */ +/* k when TRANSA = 'N' or 'n', and is m otherwise. */ +/* Before entry with TRANSA = 'N' or 'n', the leading m by k */ +/* part of the array A must contain the matrix A, otherwise */ +/* the leading k by m part of the array A must contain the */ +/* matrix A. */ +/* Unchanged on exit. */ + +/* LDA - INTEGER. */ +/* On entry, LDA specifies the first dimension of A as declared */ +/* in the calling (sub) program. When TRANSA = 'N' or 'n' then */ +/* LDA must be at least max( 1, m ), otherwise LDA must be at */ +/* least max( 1, k ). */ +/* Unchanged on exit. */ + +/* B - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is */ +/* n when TRANSB = 'N' or 'n', and is k otherwise. */ +/* Before entry with TRANSB = 'N' or 'n', the leading k by n */ +/* part of the array B must contain the matrix B, otherwise */ +/* the leading n by k part of the array B must contain the */ +/* matrix B. */ +/* Unchanged on exit. */ + +/* LDB - INTEGER. */ +/* On entry, LDB specifies the first dimension of B as declared */ +/* in the calling (sub) program. When TRANSB = 'N' or 'n' then */ +/* LDB must be at least max( 1, k ), otherwise LDB must be at */ +/* least max( 1, n ). */ +/* Unchanged on exit. */ + +/* BETA - DOUBLE PRECISION. */ +/* On entry, BETA specifies the scalar beta. When BETA is */ +/* supplied as zero then C need not be set on input. */ +/* Unchanged on exit. */ + +/* C - DOUBLE PRECISION array of DIMENSION ( LDC, n ). */ +/* Before entry, the leading m by n part of the array C must */ +/* contain the matrix C, except when beta is zero, in which */ +/* case C need not be set on entry. */ +/* On exit, the array C is overwritten by the m by n matrix */ +/* ( alpha*op( A )*op( B ) + beta*C ). */ + +/* LDC - INTEGER. */ +/* On entry, LDC specifies the first dimension of C as declared */ +/* in the calling (sub) program. LDC must be at least */ +/* max( 1, m ). */ +/* Unchanged on exit. */ + + +/* Level 3 Blas routine. */ + +/* -- Written on 8-February-1989. */ +/* Jack Dongarra, Argonne National Laboratory. */ +/* Iain Duff, AERE Harwell. */ +/* Jeremy Du Croz, Numerical Algorithms Group Ltd. */ +/* Sven Hammarling, Numerical Algorithms Group Ltd. */ + + +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Parameters .. */ +/* .. */ + +/* Set NOTA and NOTB as true if A and B respectively are not */ +/* transposed and set NROWA, NCOLA and NROWB as the number of rows */ +/* and columns of A and the number of rows of B respectively. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + + /* Function Body */ + nota = lsame_(transa, "N"); + notb = lsame_(transb, "N"); + if (nota) { + nrowa = *m; + ncola = *k; + } else { + nrowa = *k; + ncola = *m; + } + if (notb) { + nrowb = *k; + } else { + nrowb = *n; + } + +/* Test the input parameters. */ + + info = 0; + if (! nota && ! lsame_(transa, "C") && ! lsame_( + transa, "T")) { + info = 1; + } else if (! notb && ! lsame_(transb, "C") && ! + lsame_(transb, "T")) { + info = 2; + } else if (*m < 0) { + info = 3; + } else if (*n < 0) { + info = 4; + } else if (*k < 0) { + info = 5; + } else if (*lda < max(1,nrowa)) { + info = 8; + } else if (*ldb < max(1,nrowb)) { + info = 10; + } else if (*ldc < max(1,*m)) { + info = 13; + } + if (info != 0) { + xerbla_("DGEMM ", &info); + return 0; + } + +/* Quick return if possible. */ + + if (*m == 0 || *n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) { + return 0; + } + +/* And if alpha.eq.zero. */ + + if (*alpha == 0.) { + if (*beta == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; +/* L10: */ + } +/* L20: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; +/* L30: */ + } +/* L40: */ + } + } + return 0; + } + +/* Start the operations. */ + + if (notb) { + if (nota) { + +/* Form C := alpha*A*B + beta*C. */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*beta == 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; +/* L50: */ + } + } else if (*beta != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; +/* L60: */ + } + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + if (b[l + j * b_dim1] != 0.) { + temp = *alpha * b[l + j * b_dim1]; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + c__[i__ + j * c_dim1] += temp * a[i__ + l * + a_dim1]; +/* L70: */ + } + } +/* L80: */ + } +/* L90: */ + } + } else { + +/* Form C := alpha*A'*B + beta*C */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + temp += a[l + i__ * a_dim1] * b[l + j * b_dim1]; +/* L100: */ + } + if (*beta == 0.) { + c__[i__ + j * c_dim1] = *alpha * temp; + } else { + c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[ + i__ + j * c_dim1]; + } +/* L110: */ + } +/* L120: */ + } + } + } else { + if (nota) { + +/* Form C := alpha*A*B' + beta*C */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*beta == 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; +/* L130: */ + } + } else if (*beta != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; +/* L140: */ + } + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + if (b[j + l * b_dim1] != 0.) { + temp = *alpha * b[j + l * b_dim1]; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + c__[i__ + j * c_dim1] += temp * a[i__ + l * + a_dim1]; +/* L150: */ + } + } +/* L160: */ + } +/* L170: */ + } + } else { + +/* Form C := alpha*A'*B' + beta*C */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + temp += a[l + i__ * a_dim1] * b[j + l * b_dim1]; +/* L180: */ + } + if (*beta == 0.) { + c__[i__ + j * c_dim1] = *alpha * temp; + } else { + c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[ + i__ + j * c_dim1]; + } +/* L190: */ + } +/* L200: */ + } + } + } + + return 0; + +/* End of DGEMM . */ + +} /* dgemm_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/cblas/src/dgemv.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,312 @@ +/* dgemv.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +/* Subroutine */ int dgemv_(char *trans, integer *m, integer *n, doublereal * + alpha, doublereal *a, integer *lda, doublereal *x, integer *incx, + doublereal *beta, doublereal *y, integer *incy) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + + /* Local variables */ + integer i__, j, ix, iy, jx, jy, kx, ky, info; + doublereal temp; + integer lenx, leny; + extern logical lsame_(char *, char *); + extern /* Subroutine */ int xerbla_(char *, integer *); + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* DGEMV performs one of the matrix-vector operations */ + +/* y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, */ + +/* where alpha and beta are scalars, x and y are vectors and A is an */ +/* m by n matrix. */ + +/* Arguments */ +/* ========== */ + +/* TRANS - CHARACTER*1. */ +/* On entry, TRANS specifies the operation to be performed as */ +/* follows: */ + +/* TRANS = 'N' or 'n' y := alpha*A*x + beta*y. */ + +/* TRANS = 'T' or 't' y := alpha*A'*x + beta*y. */ + +/* TRANS = 'C' or 'c' y := alpha*A'*x + beta*y. */ + +/* Unchanged on exit. */ + +/* M - INTEGER. */ +/* On entry, M specifies the number of rows of the matrix A. */ +/* M must be at least zero. */ +/* Unchanged on exit. */ + +/* N - INTEGER. */ +/* On entry, N specifies the number of columns of the matrix A. */ +/* N must be at least zero. */ +/* Unchanged on exit. */ + +/* ALPHA - DOUBLE PRECISION. */ +/* On entry, ALPHA specifies the scalar alpha. */ +/* Unchanged on exit. */ + +/* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). */ +/* Before entry, the leading m by n part of the array A must */ +/* contain the matrix of coefficients. */ +/* Unchanged on exit. */ + +/* LDA - INTEGER. */ +/* On entry, LDA specifies the first dimension of A as declared */ +/* in the calling (sub) program. LDA must be at least */ +/* max( 1, m ). */ +/* Unchanged on exit. */ + +/* X - DOUBLE PRECISION array of DIMENSION at least */ +/* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' */ +/* and at least */ +/* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. */ +/* Before entry, the incremented array X must contain the */ +/* vector x. */ +/* Unchanged on exit. */ + +/* INCX - INTEGER. */ +/* On entry, INCX specifies the increment for the elements of */ +/* X. INCX must not be zero. */ +/* Unchanged on exit. */ + +/* BETA - DOUBLE PRECISION. */ +/* On entry, BETA specifies the scalar beta. When BETA is */ +/* supplied as zero then Y need not be set on input. */ +/* Unchanged on exit. */ + +/* Y - DOUBLE PRECISION array of DIMENSION at least */ +/* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' */ +/* and at least */ +/* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. */ +/* Before entry with BETA non-zero, the incremented array Y */ +/* must contain the vector y. On exit, Y is overwritten by the */ +/* updated vector y. */ + +/* INCY - INTEGER. */ +/* On entry, INCY specifies the increment for the elements of */ +/* Y. INCY must not be zero. */ +/* Unchanged on exit. */ + + +/* Level 2 Blas routine. */ + +/* -- Written on 22-October-1986. */ +/* Jack Dongarra, Argonne National Lab. */ +/* Jeremy Du Croz, Nag Central Office. */ +/* Sven Hammarling, Nag Central Office. */ +/* Richard Hanson, Sandia National Labs. */ + + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --x; + --y; + + /* Function Body */ + info = 0; + if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C") + ) { + info = 1; + } else if (*m < 0) { + info = 2; + } else if (*n < 0) { + info = 3; + } else if (*lda < max(1,*m)) { + info = 6; + } else if (*incx == 0) { + info = 8; + } else if (*incy == 0) { + info = 11; + } + if (info != 0) { + xerbla_("DGEMV ", &info); + return 0; + } + +/* Quick return if possible. */ + + if (*m == 0 || *n == 0 || *alpha == 0. && *beta == 1.) { + return 0; + } + +/* Set LENX and LENY, the lengths of the vectors x and y, and set */ +/* up the start points in X and Y. */ + + if (lsame_(trans, "N")) { + lenx = *n; + leny = *m; + } else { + lenx = *m; + leny = *n; + } + if (*incx > 0) { + kx = 1; + } else { + kx = 1 - (lenx - 1) * *incx; + } + if (*incy > 0) { + ky = 1; + } else { + ky = 1 - (leny - 1) * *incy; + } + +/* Start the operations. In this version the elements of A are */ +/* accessed sequentially with one pass through A. */ + +/* First form y := beta*y. */ + + if (*beta != 1.) { + if (*incy == 1) { + if (*beta == 0.) { + i__1 = leny; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] = 0.; +/* L10: */ + } + } else { + i__1 = leny; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] = *beta * y[i__]; +/* L20: */ + } + } + } else { + iy = ky; + if (*beta == 0.) { + i__1 = leny; + for (i__ = 1; i__ <= i__1; ++i__) { + y[iy] = 0.; + iy += *incy; +/* L30: */ + } + } else { + i__1 = leny; + for (i__ = 1; i__ <= i__1; ++i__) { + y[iy] = *beta * y[iy]; + iy += *incy; +/* L40: */ + } + } + } + } + if (*alpha == 0.) { + return 0; + } + if (lsame_(trans, "N")) { + +/* Form y := alpha*A*x + y. */ + + jx = kx; + if (*incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (x[jx] != 0.) { + temp = *alpha * x[jx]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + y[i__] += temp * a[i__ + j * a_dim1]; +/* L50: */ + } + } + jx += *incx; +/* L60: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (x[jx] != 0.) { + temp = *alpha * x[jx]; + iy = ky; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + y[iy] += temp * a[i__ + j * a_dim1]; + iy += *incy; +/* L70: */ + } + } + jx += *incx; +/* L80: */ + } + } + } else { + +/* Form y := alpha*A'*x + y. */ + + jy = ky; + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = 0.; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp += a[i__ + j * a_dim1] * x[i__]; +/* L90: */ + } + y[jy] += *alpha * temp; + jy += *incy; +/* L100: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = 0.; + ix = kx; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp += a[i__ + j * a_dim1] * x[ix]; + ix += *incx; +/* L110: */ + } + y[jy] += *alpha * temp; + jy += *incy; +/* L120: */ + } + } + } + + return 0; + +/* End of DGEMV . */ + +} /* dgemv_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/cblas/src/dger.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,194 @@ +/* dger.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +/* Subroutine */ int dger_(integer *m, integer *n, doublereal *alpha, + doublereal *x, integer *incx, doublereal *y, integer *incy, + doublereal *a, integer *lda) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + + /* Local variables */ + integer i__, j, ix, jy, kx, info; + doublereal temp; + extern /* Subroutine */ int xerbla_(char *, integer *); + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* DGER performs the rank 1 operation */ + +/* A := alpha*x*y' + A, */ + +/* where alpha is a scalar, x is an m element vector, y is an n element */ +/* vector and A is an m by n matrix. */ + +/* Arguments */ +/* ========== */ + +/* M - INTEGER. */ +/* On entry, M specifies the number of rows of the matrix A. */ +/* M must be at least zero. */ +/* Unchanged on exit. */ + +/* N - INTEGER. */ +/* On entry, N specifies the number of columns of the matrix A. */ +/* N must be at least zero. */ +/* Unchanged on exit. */ + +/* ALPHA - DOUBLE PRECISION. */ +/* On entry, ALPHA specifies the scalar alpha. */ +/* Unchanged on exit. */ + +/* X - DOUBLE PRECISION array of dimension at least */ +/* ( 1 + ( m - 1 )*abs( INCX ) ). */ +/* Before entry, the incremented array X must contain the m */ +/* element vector x. */ +/* Unchanged on exit. */ + +/* INCX - INTEGER. */ +/* On entry, INCX specifies the increment for the elements of */ +/* X. INCX must not be zero. */ +/* Unchanged on exit. */ + +/* Y - DOUBLE PRECISION array of dimension at least */ +/* ( 1 + ( n - 1 )*abs( INCY ) ). */ +/* Before entry, the incremented array Y must contain the n */ +/* element vector y. */ +/* Unchanged on exit. */ + +/* INCY - INTEGER. */ +/* On entry, INCY specifies the increment for the elements of */ +/* Y. INCY must not be zero. */ +/* Unchanged on exit. */ + +/* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). */ +/* Before entry, the leading m by n part of the array A must */ +/* contain the matrix of coefficients. On exit, A is */ +/* overwritten by the updated matrix. */ + +/* LDA - INTEGER. */ +/* On entry, LDA specifies the first dimension of A as declared */ +/* in the calling (sub) program. LDA must be at least */ +/* max( 1, m ). */ +/* Unchanged on exit. */ + + +/* Level 2 Blas routine. */ + +/* -- Written on 22-October-1986. */ +/* Jack Dongarra, Argonne National Lab. */ +/* Jeremy Du Croz, Nag Central Office. */ +/* Sven Hammarling, Nag Central Office. */ +/* Richard Hanson, Sandia National Labs. */ + + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --x; + --y; + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + info = 0; + if (*m < 0) { + info = 1; + } else if (*n < 0) { + info = 2; + } else if (*incx == 0) { + info = 5; + } else if (*incy == 0) { + info = 7; + } else if (*lda < max(1,*m)) { + info = 9; + } + if (info != 0) { + xerbla_("DGER ", &info); + return 0; + } + +/* Quick return if possible. */ + + if (*m == 0 || *n == 0 || *alpha == 0.) { + return 0; + } + +/* Start the operations. In this version the elements of A are */ +/* accessed sequentially with one pass through A. */ + + if (*incy > 0) { + jy = 1; + } else { + jy = 1 - (*n - 1) * *incy; + } + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (y[jy] != 0.) { + temp = *alpha * y[jy]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] += x[i__] * temp; +/* L10: */ + } + } + jy += *incy; +/* L20: */ + } + } else { + if (*incx > 0) { + kx = 1; + } else { + kx = 1 - (*m - 1) * *incx; + } + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (y[jy] != 0.) { + temp = *alpha * y[jy]; + ix = kx; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] += x[ix] * temp; + ix += *incx; +/* L30: */ + } + } + jy += *incy; +/* L40: */ + } + } + + return 0; + +/* End of DGER . */ + +} /* dger_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/cblas/src/dlamch.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,1001 @@ +/* dlamch.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static doublereal c_b32 = 0.; + +doublereal dlamch_(char *cmach) +{ + /* Initialized data */ + + static logical first = TRUE_; + + /* System generated locals */ + integer i__1; + doublereal ret_val; + + /* Builtin functions */ + double pow_di(doublereal *, integer *); + + /* Local variables */ + static doublereal t; + integer it; + static doublereal rnd, eps, base; + integer beta; + static doublereal emin, prec, emax; + integer imin, imax; + logical lrnd; + static doublereal rmin, rmax; + doublereal rmach; + extern logical lsame_(char *, char *); + doublereal small; + static doublereal sfmin; + extern /* Subroutine */ int dlamc2_(integer *, integer *, logical *, + doublereal *, integer *, doublereal *, integer *, doublereal *); + + +/* -- LAPACK auxiliary routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* DLAMCH determines double precision machine parameters. */ + +/* Arguments */ +/* ========= */ + +/* CMACH (input) CHARACTER*1 */ +/* Specifies the value to be returned by DLAMCH: */ +/* = 'E' or 'e', DLAMCH := eps */ +/* = 'S' or 's , DLAMCH := sfmin */ +/* = 'B' or 'b', DLAMCH := base */ +/* = 'P' or 'p', DLAMCH := eps*base */ +/* = 'N' or 'n', DLAMCH := t */ +/* = 'R' or 'r', DLAMCH := rnd */ +/* = 'M' or 'm', DLAMCH := emin */ +/* = 'U' or 'u', DLAMCH := rmin */ +/* = 'L' or 'l', DLAMCH := emax */ +/* = 'O' or 'o', DLAMCH := rmax */ + +/* where */ + +/* eps = relative machine precision */ +/* sfmin = safe minimum, such that 1/sfmin does not overflow */ +/* base = base of the machine */ +/* prec = eps*base */ +/* t = number of (base) digits in the mantissa */ +/* rnd = 1.0 when rounding occurs in addition, 0.0 otherwise */ +/* emin = minimum exponent before (gradual) underflow */ +/* rmin = underflow threshold - base**(emin-1) */ +/* emax = largest exponent before overflow */ +/* rmax = overflow threshold - (base**emax)*(1-eps) */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Save statement .. */ +/* .. */ +/* .. Data statements .. */ +/* .. */ +/* .. Executable Statements .. */ + + if (first) { + dlamc2_(&beta, &it, &lrnd, &eps, &imin, &rmin, &imax, &rmax); + base = (doublereal) beta; + t = (doublereal) it; + if (lrnd) { + rnd = 1.; + i__1 = 1 - it; + eps = pow_di(&base, &i__1) / 2; + } else { + rnd = 0.; + i__1 = 1 - it; + eps = pow_di(&base, &i__1); + } + prec = eps * base; + emin = (doublereal) imin; + emax = (doublereal) imax; + sfmin = rmin; + small = 1. / rmax; + if (small >= sfmin) { + +/* Use SMALL plus a bit, to avoid the possibility of rounding */ +/* causing overflow when computing 1/sfmin. */ + + sfmin = small * (eps + 1.); + } + } + + if (lsame_(cmach, "E")) { + rmach = eps; + } else if (lsame_(cmach, "S")) { + rmach = sfmin; + } else if (lsame_(cmach, "B")) { + rmach = base; + } else if (lsame_(cmach, "P")) { + rmach = prec; + } else if (lsame_(cmach, "N")) { + rmach = t; + } else if (lsame_(cmach, "R")) { + rmach = rnd; + } else if (lsame_(cmach, "M")) { + rmach = emin; + } else if (lsame_(cmach, "U")) { + rmach = rmin; + } else if (lsame_(cmach, "L")) { + rmach = emax; + } else if (lsame_(cmach, "O")) { + rmach = rmax; + } + + ret_val = rmach; + first = FALSE_; + return ret_val; + +/* End of DLAMCH */ + +} /* dlamch_ */ + + +/* *********************************************************************** */ + +/* Subroutine */ int dlamc1_(integer *beta, integer *t, logical *rnd, logical + *ieee1) +{ + /* Initialized data */ + + static logical first = TRUE_; + + /* System generated locals */ + doublereal d__1, d__2; + + /* Local variables */ + doublereal a, b, c__, f, t1, t2; + static integer lt; + doublereal one, qtr; + static logical lrnd; + static integer lbeta; + doublereal savec; + extern doublereal dlamc3_(doublereal *, doublereal *); + static logical lieee1; + + +/* -- LAPACK auxiliary routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* DLAMC1 determines the machine parameters given by BETA, T, RND, and */ +/* IEEE1. */ + +/* Arguments */ +/* ========= */ + +/* BETA (output) INTEGER */ +/* The base of the machine. */ + +/* T (output) INTEGER */ +/* The number of ( BETA ) digits in the mantissa. */ + +/* RND (output) LOGICAL */ +/* Specifies whether proper rounding ( RND = .TRUE. ) or */ +/* chopping ( RND = .FALSE. ) occurs in addition. This may not */ +/* be a reliable guide to the way in which the machine performs */ +/* its arithmetic. */ + +/* IEEE1 (output) LOGICAL */ +/* Specifies whether rounding appears to be done in the IEEE */ +/* 'round to nearest' style. */ + +/* Further Details */ +/* =============== */ + +/* The routine is based on the routine ENVRON by Malcolm and */ +/* incorporates suggestions by Gentleman and Marovich. See */ + +/* Malcolm M. A. (1972) Algorithms to reveal properties of */ +/* floating-point arithmetic. Comms. of the ACM, 15, 949-951. */ + +/* Gentleman W. M. and Marovich S. B. (1974) More on algorithms */ +/* that reveal properties of floating point arithmetic units. */ +/* Comms. of the ACM, 17, 276-277. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Save statement .. */ +/* .. */ +/* .. Data statements .. */ +/* .. */ +/* .. Executable Statements .. */ + + if (first) { + one = 1.; + +/* LBETA, LIEEE1, LT and LRND are the local values of BETA, */ +/* IEEE1, T and RND. */ + +/* Throughout this routine we use the function DLAMC3 to ensure */ +/* that relevant values are stored and not held in registers, or */ +/* are not affected by optimizers. */ + +/* Compute a = 2.0**m with the smallest positive integer m such */ +/* that */ + +/* fl( a + 1.0 ) = a. */ + + a = 1.; + c__ = 1.; + +/* + WHILE( C.EQ.ONE )LOOP */ +L10: + if (c__ == one) { + a *= 2; + c__ = dlamc3_(&a, &one); + d__1 = -a; + c__ = dlamc3_(&c__, &d__1); + goto L10; + } +/* + END WHILE */ + +/* Now compute b = 2.0**m with the smallest positive integer m */ +/* such that */ + +/* fl( a + b ) .gt. a. */ + + b = 1.; + c__ = dlamc3_(&a, &b); + +/* + WHILE( C.EQ.A )LOOP */ +L20: + if (c__ == a) { + b *= 2; + c__ = dlamc3_(&a, &b); + goto L20; + } +/* + END WHILE */ + +/* Now compute the base. a and c are neighbouring floating point */ +/* numbers in the interval ( beta**t, beta**( t + 1 ) ) and so */ +/* their difference is beta. Adding 0.25 to c is to ensure that it */ +/* is truncated to beta and not ( beta - 1 ). */ + + qtr = one / 4; + savec = c__; + d__1 = -a; + c__ = dlamc3_(&c__, &d__1); + lbeta = (integer) (c__ + qtr); + +/* Now determine whether rounding or chopping occurs, by adding a */ +/* bit less than beta/2 and a bit more than beta/2 to a. */ + + b = (doublereal) lbeta; + d__1 = b / 2; + d__2 = -b / 100; + f = dlamc3_(&d__1, &d__2); + c__ = dlamc3_(&f, &a); + if (c__ == a) { + lrnd = TRUE_; + } else { + lrnd = FALSE_; + } + d__1 = b / 2; + d__2 = b / 100; + f = dlamc3_(&d__1, &d__2); + c__ = dlamc3_(&f, &a); + if (lrnd && c__ == a) { + lrnd = FALSE_; + } + +/* Try and decide whether rounding is done in the IEEE 'round to */ +/* nearest' style. B/2 is half a unit in the last place of the two */ +/* numbers A and SAVEC. Furthermore, A is even, i.e. has last bit */ +/* zero, and SAVEC is odd. Thus adding B/2 to A should not change */ +/* A, but adding B/2 to SAVEC should change SAVEC. */ + + d__1 = b / 2; + t1 = dlamc3_(&d__1, &a); + d__1 = b / 2; + t2 = dlamc3_(&d__1, &savec); + lieee1 = t1 == a && t2 > savec && lrnd; + +/* Now find the mantissa, t. It should be the integer part of */ +/* log to the base beta of a, however it is safer to determine t */ +/* by powering. So we find t as the smallest positive integer for */ +/* which */ + +/* fl( beta**t + 1.0 ) = 1.0. */ + + lt = 0; + a = 1.; + c__ = 1.; + +/* + WHILE( C.EQ.ONE )LOOP */ +L30: + if (c__ == one) { + ++lt; + a *= lbeta; + c__ = dlamc3_(&a, &one); + d__1 = -a; + c__ = dlamc3_(&c__, &d__1); + goto L30; + } +/* + END WHILE */ + + } + + *beta = lbeta; + *t = lt; + *rnd = lrnd; + *ieee1 = lieee1; + first = FALSE_; + return 0; + +/* End of DLAMC1 */ + +} /* dlamc1_ */ + + +/* *********************************************************************** */ + +/* Subroutine */ int dlamc2_(integer *beta, integer *t, logical *rnd, + doublereal *eps, integer *emin, doublereal *rmin, integer *emax, + doublereal *rmax) +{ + /* Initialized data */ + + static logical first = TRUE_; + static logical iwarn = FALSE_; + + /* Format strings */ + static char fmt_9999[] = "(//\002 WARNING. The value EMIN may be incorre" + "ct:-\002,\002 EMIN = \002,i8,/\002 If, after inspection, the va" + "lue EMIN looks\002,\002 acceptable please comment out \002,/\002" + " the IF block as marked within the code of routine\002,\002 DLAM" + "C2,\002,/\002 otherwise supply EMIN explicitly.\002,/)"; + + /* System generated locals */ + integer i__1; + doublereal d__1, d__2, d__3, d__4, d__5; + + /* Builtin functions */ + double pow_di(doublereal *, integer *); + integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void); + + /* Local variables */ + doublereal a, b, c__; + integer i__; + static integer lt; + doublereal one, two; + logical ieee; + doublereal half; + logical lrnd; + static doublereal leps; + doublereal zero; + static integer lbeta; + doublereal rbase; + static integer lemin, lemax; + integer gnmin; + doublereal small; + integer gpmin; + doublereal third; + static doublereal lrmin, lrmax; + doublereal sixth; + extern /* Subroutine */ int dlamc1_(integer *, integer *, logical *, + logical *); + extern doublereal dlamc3_(doublereal *, doublereal *); + logical lieee1; + extern /* Subroutine */ int dlamc4_(integer *, doublereal *, integer *), + dlamc5_(integer *, integer *, integer *, logical *, integer *, + doublereal *); + integer ngnmin, ngpmin; + + /* Fortran I/O blocks */ + static cilist io___58 = { 0, 6, 0, fmt_9999, 0 }; + + + +/* -- LAPACK auxiliary routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* DLAMC2 determines the machine parameters specified in its argument */ +/* list. */ + +/* Arguments */ +/* ========= */ + +/* BETA (output) INTEGER */ +/* The base of the machine. */ + +/* T (output) INTEGER */ +/* The number of ( BETA ) digits in the mantissa. */ + +/* RND (output) LOGICAL */ +/* Specifies whether proper rounding ( RND = .TRUE. ) or */ +/* chopping ( RND = .FALSE. ) occurs in addition. This may not */ +/* be a reliable guide to the way in which the machine performs */ +/* its arithmetic. */ + +/* EPS (output) DOUBLE PRECISION */ +/* The smallest positive number such that */ + +/* fl( 1.0 - EPS ) .LT. 1.0, */ + +/* where fl denotes the computed value. */ + +/* EMIN (output) INTEGER */ +/* The minimum exponent before (gradual) underflow occurs. */ + +/* RMIN (output) DOUBLE PRECISION */ +/* The smallest normalized number for the machine, given by */ +/* BASE**( EMIN - 1 ), where BASE is the floating point value */ +/* of BETA. */ + +/* EMAX (output) INTEGER */ +/* The maximum exponent before overflow occurs. */ + +/* RMAX (output) DOUBLE PRECISION */ +/* The largest positive number for the machine, given by */ +/* BASE**EMAX * ( 1 - EPS ), where BASE is the floating point */ +/* value of BETA. */ + +/* Further Details */ +/* =============== */ + +/* The computation of EPS is based on a routine PARANOIA by */ +/* W. Kahan of the University of California at Berkeley. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Save statement .. */ +/* .. */ +/* .. Data statements .. */ +/* .. */ +/* .. Executable Statements .. */ + + if (first) { + zero = 0.; + one = 1.; + two = 2.; + +/* LBETA, LT, LRND, LEPS, LEMIN and LRMIN are the local values of */ +/* BETA, T, RND, EPS, EMIN and RMIN. */ + +/* Throughout this routine we use the function DLAMC3 to ensure */ +/* that relevant values are stored and not held in registers, or */ +/* are not affected by optimizers. */ + +/* DLAMC1 returns the parameters LBETA, LT, LRND and LIEEE1. */ + + dlamc1_(&lbeta, <, &lrnd, &lieee1); + +/* Start to find EPS. */ + + b = (doublereal) lbeta; + i__1 = -lt; + a = pow_di(&b, &i__1); + leps = a; + +/* Try some tricks to see whether or not this is the correct EPS. */ + + b = two / 3; + half = one / 2; + d__1 = -half; + sixth = dlamc3_(&b, &d__1); + third = dlamc3_(&sixth, &sixth); + d__1 = -half; + b = dlamc3_(&third, &d__1); + b = dlamc3_(&b, &sixth); + b = abs(b); + if (b < leps) { + b = leps; + } + + leps = 1.; + +/* + WHILE( ( LEPS.GT.B ).AND.( B.GT.ZERO ) )LOOP */ +L10: + if (leps > b && b > zero) { + leps = b; + d__1 = half * leps; +/* Computing 5th power */ + d__3 = two, d__4 = d__3, d__3 *= d__3; +/* Computing 2nd power */ + d__5 = leps; + d__2 = d__4 * (d__3 * d__3) * (d__5 * d__5); + c__ = dlamc3_(&d__1, &d__2); + d__1 = -c__; + c__ = dlamc3_(&half, &d__1); + b = dlamc3_(&half, &c__); + d__1 = -b; + c__ = dlamc3_(&half, &d__1); + b = dlamc3_(&half, &c__); + goto L10; + } +/* + END WHILE */ + + if (a < leps) { + leps = a; + } + +/* Computation of EPS complete. */ + +/* Now find EMIN. Let A = + or - 1, and + or - (1 + BASE**(-3)). */ +/* Keep dividing A by BETA until (gradual) underflow occurs. This */ +/* is detected when we cannot recover the previous A. */ + + rbase = one / lbeta; + small = one; + for (i__ = 1; i__ <= 3; ++i__) { + d__1 = small * rbase; + small = dlamc3_(&d__1, &zero); +/* L20: */ + } + a = dlamc3_(&one, &small); + dlamc4_(&ngpmin, &one, &lbeta); + d__1 = -one; + dlamc4_(&ngnmin, &d__1, &lbeta); + dlamc4_(&gpmin, &a, &lbeta); + d__1 = -a; + dlamc4_(&gnmin, &d__1, &lbeta); + ieee = FALSE_; + + if (ngpmin == ngnmin && gpmin == gnmin) { + if (ngpmin == gpmin) { + lemin = ngpmin; +/* ( Non twos-complement machines, no gradual underflow; */ +/* e.g., VAX ) */ + } else if (gpmin - ngpmin == 3) { + lemin = ngpmin - 1 + lt; + ieee = TRUE_; +/* ( Non twos-complement machines, with gradual underflow; */ +/* e.g., IEEE standard followers ) */ + } else { + lemin = min(ngpmin,gpmin); +/* ( A guess; no known machine ) */ + iwarn = TRUE_; + } + + } else if (ngpmin == gpmin && ngnmin == gnmin) { + if ((i__1 = ngpmin - ngnmin, abs(i__1)) == 1) { + lemin = max(ngpmin,ngnmin); +/* ( Twos-complement machines, no gradual underflow; */ +/* e.g., CYBER 205 ) */ + } else { + lemin = min(ngpmin,ngnmin); +/* ( A guess; no known machine ) */ + iwarn = TRUE_; + } + + } else if ((i__1 = ngpmin - ngnmin, abs(i__1)) == 1 && gpmin == gnmin) + { + if (gpmin - min(ngpmin,ngnmin) == 3) { + lemin = max(ngpmin,ngnmin) - 1 + lt; +/* ( Twos-complement machines with gradual underflow; */ +/* no known machine ) */ + } else { + lemin = min(ngpmin,ngnmin); +/* ( A guess; no known machine ) */ + iwarn = TRUE_; + } + + } else { +/* Computing MIN */ + i__1 = min(ngpmin,ngnmin), i__1 = min(i__1,gpmin); + lemin = min(i__1,gnmin); +/* ( A guess; no known machine ) */ + iwarn = TRUE_; + } + first = FALSE_; +/* ** */ +/* Comment out this if block if EMIN is ok */ + if (iwarn) { + first = TRUE_; + s_wsfe(&io___58); + do_fio(&c__1, (char *)&lemin, (ftnlen)sizeof(integer)); + e_wsfe(); + } +/* ** */ + +/* Assume IEEE arithmetic if we found denormalised numbers above, */ +/* or if arithmetic seems to round in the IEEE style, determined */ +/* in routine DLAMC1. A true IEEE machine should have both things */ +/* true; however, faulty machines may have one or the other. */ + + ieee = ieee || lieee1; + +/* Compute RMIN by successive division by BETA. We could compute */ +/* RMIN as BASE**( EMIN - 1 ), but some machines underflow during */ +/* this computation. */ + + lrmin = 1.; + i__1 = 1 - lemin; + for (i__ = 1; i__ <= i__1; ++i__) { + d__1 = lrmin * rbase; + lrmin = dlamc3_(&d__1, &zero); +/* L30: */ + } + +/* Finally, call DLAMC5 to compute EMAX and RMAX. */ + + dlamc5_(&lbeta, <, &lemin, &ieee, &lemax, &lrmax); + } + + *beta = lbeta; + *t = lt; + *rnd = lrnd; + *eps = leps; + *emin = lemin; + *rmin = lrmin; + *emax = lemax; + *rmax = lrmax; + + return 0; + + +/* End of DLAMC2 */ + +} /* dlamc2_ */ + + +/* *********************************************************************** */ + +doublereal dlamc3_(doublereal *a, doublereal *b) +{ + /* System generated locals */ + doublereal ret_val; + + +/* -- LAPACK auxiliary routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* DLAMC3 is intended to force A and B to be stored prior to doing */ +/* the addition of A and B , for use in situations where optimizers */ +/* might hold one of these in a register. */ + +/* Arguments */ +/* ========= */ + +/* A (input) DOUBLE PRECISION */ +/* B (input) DOUBLE PRECISION */ +/* The values A and B. */ + +/* ===================================================================== */ + +/* .. Executable Statements .. */ + + ret_val = *a + *b; + + return ret_val; + +/* End of DLAMC3 */ + +} /* dlamc3_ */ + + +/* *********************************************************************** */ + +/* Subroutine */ int dlamc4_(integer *emin, doublereal *start, integer *base) +{ + /* System generated locals */ + integer i__1; + doublereal d__1; + + /* Local variables */ + doublereal a; + integer i__; + doublereal b1, b2, c1, c2, d1, d2, one, zero, rbase; + extern doublereal dlamc3_(doublereal *, doublereal *); + + +/* -- LAPACK auxiliary routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* DLAMC4 is a service routine for DLAMC2. */ + +/* Arguments */ +/* ========= */ + +/* EMIN (output) INTEGER */ +/* The minimum exponent before (gradual) underflow, computed by */ +/* setting A = START and dividing by BASE until the previous A */ +/* can not be recovered. */ + +/* START (input) DOUBLE PRECISION */ +/* The starting point for determining EMIN. */ + +/* BASE (input) INTEGER */ +/* The base of the machine. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + a = *start; + one = 1.; + rbase = one / *base; + zero = 0.; + *emin = 1; + d__1 = a * rbase; + b1 = dlamc3_(&d__1, &zero); + c1 = a; + c2 = a; + d1 = a; + d2 = a; +/* + WHILE( ( C1.EQ.A ).AND.( C2.EQ.A ).AND. */ +/* $ ( D1.EQ.A ).AND.( D2.EQ.A ) )LOOP */ +L10: + if (c1 == a && c2 == a && d1 == a && d2 == a) { + --(*emin); + a = b1; + d__1 = a / *base; + b1 = dlamc3_(&d__1, &zero); + d__1 = b1 * *base; + c1 = dlamc3_(&d__1, &zero); + d1 = zero; + i__1 = *base; + for (i__ = 1; i__ <= i__1; ++i__) { + d1 += b1; +/* L20: */ + } + d__1 = a * rbase; + b2 = dlamc3_(&d__1, &zero); + d__1 = b2 / rbase; + c2 = dlamc3_(&d__1, &zero); + d2 = zero; + i__1 = *base; + for (i__ = 1; i__ <= i__1; ++i__) { + d2 += b2; +/* L30: */ + } + goto L10; + } +/* + END WHILE */ + + return 0; + +/* End of DLAMC4 */ + +} /* dlamc4_ */ + + +/* *********************************************************************** */ + +/* Subroutine */ int dlamc5_(integer *beta, integer *p, integer *emin, + logical *ieee, integer *emax, doublereal *rmax) +{ + /* System generated locals */ + integer i__1; + doublereal d__1; + + /* Local variables */ + integer i__; + doublereal y, z__; + integer try__, lexp; + doublereal oldy; + integer uexp, nbits; + extern doublereal dlamc3_(doublereal *, doublereal *); + doublereal recbas; + integer exbits, expsum; + + +/* -- LAPACK auxiliary routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* DLAMC5 attempts to compute RMAX, the largest machine floating-point */ +/* number, without overflow. It assumes that EMAX + abs(EMIN) sum */ +/* approximately to a power of 2. It will fail on machines where this */ +/* assumption does not hold, for example, the Cyber 205 (EMIN = -28625, */ +/* EMAX = 28718). It will also fail if the value supplied for EMIN is */ +/* too large (i.e. too close to zero), probably with overflow. */ + +/* Arguments */ +/* ========= */ + +/* BETA (input) INTEGER */ +/* The base of floating-point arithmetic. */ + +/* P (input) INTEGER */ +/* The number of base BETA digits in the mantissa of a */ +/* floating-point value. */ + +/* EMIN (input) INTEGER */ +/* The minimum exponent before (gradual) underflow. */ + +/* IEEE (input) LOGICAL */ +/* A logical flag specifying whether or not the arithmetic */ +/* system is thought to comply with the IEEE standard. */ + +/* EMAX (output) INTEGER */ +/* The largest exponent before overflow */ + +/* RMAX (output) DOUBLE PRECISION */ +/* The largest machine floating-point number. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* First compute LEXP and UEXP, two powers of 2 that bound */ +/* abs(EMIN). We then assume that EMAX + abs(EMIN) will sum */ +/* approximately to the bound that is closest to abs(EMIN). */ +/* (EMAX is the exponent of the required number RMAX). */ + + lexp = 1; + exbits = 1; +L10: + try__ = lexp << 1; + if (try__ <= -(*emin)) { + lexp = try__; + ++exbits; + goto L10; + } + if (lexp == -(*emin)) { + uexp = lexp; + } else { + uexp = try__; + ++exbits; + } + +/* Now -LEXP is less than or equal to EMIN, and -UEXP is greater */ +/* than or equal to EMIN. EXBITS is the number of bits needed to */ +/* store the exponent. */ + + if (uexp + *emin > -lexp - *emin) { + expsum = lexp << 1; + } else { + expsum = uexp << 1; + } + +/* EXPSUM is the exponent range, approximately equal to */ +/* EMAX - EMIN + 1 . */ + + *emax = expsum + *emin - 1; + nbits = exbits + 1 + *p; + +/* NBITS is the total number of bits needed to store a */ +/* floating-point number. */ + + if (nbits % 2 == 1 && *beta == 2) { + +/* Either there are an odd number of bits used to store a */ +/* floating-point number, which is unlikely, or some bits are */ +/* not used in the representation of numbers, which is possible, */ +/* (e.g. Cray machines) or the mantissa has an implicit bit, */ +/* (e.g. IEEE machines, Dec Vax machines), which is perhaps the */ +/* most likely. We have to assume the last alternative. */ +/* If this is true, then we need to reduce EMAX by one because */ +/* there must be some way of representing zero in an implicit-bit */ +/* system. On machines like Cray, we are reducing EMAX by one */ +/* unnecessarily. */ + + --(*emax); + } + + if (*ieee) { + +/* Assume we are on an IEEE machine which reserves one exponent */ +/* for infinity and NaN. */ + + --(*emax); + } + +/* Now create RMAX, the largest machine number, which should */ +/* be equal to (1.0 - BETA**(-P)) * BETA**EMAX . */ + +/* First compute 1.0 - BETA**(-P), being careful that the */ +/* result is less than 1.0 . */ + + recbas = 1. / *beta; + z__ = *beta - 1.; + y = 0.; + i__1 = *p; + for (i__ = 1; i__ <= i__1; ++i__) { + z__ *= recbas; + if (y < 1.) { + oldy = y; + } + y = dlamc3_(&y, &z__); +/* L20: */ + } + if (y >= 1.) { + y = oldy; + } + +/* Now multiply by BETA**EMAX to get RMAX. */ + + i__1 = *emax; + for (i__ = 1; i__ <= i__1; ++i__) { + d__1 = y * *beta; + y = dlamc3_(&d__1, &c_b32); +/* L30: */ + } + + *rmax = y; + return 0; + +/* End of DLAMC5 */ + +} /* dlamc5_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/cblas/src/dscal.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,96 @@ +/* dscal.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +/* Subroutine */ int dscal_(integer *n, doublereal *da, doublereal *dx, + integer *incx) +{ + /* System generated locals */ + integer i__1, i__2; + + /* Local variables */ + integer i__, m, mp1, nincx; + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ +/* * */ +/* scales a vector by a constant. */ +/* uses unrolled loops for increment equal to one. */ +/* jack dongarra, linpack, 3/11/78. */ +/* modified 3/93 to return if incx .le. 0. */ +/* modified 12/3/93, array(1) declarations changed to array(*) */ + + +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + /* Parameter adjustments */ + --dx; + + /* Function Body */ + if (*n <= 0 || *incx <= 0) { + return 0; + } + if (*incx == 1) { + goto L20; + } + +/* code for increment not equal to 1 */ + + nincx = *n * *incx; + i__1 = nincx; + i__2 = *incx; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + dx[i__] = *da * dx[i__]; +/* L10: */ + } + return 0; + +/* code for increment equal to 1 */ + + +/* clean-up loop */ + +L20: + m = *n % 5; + if (m == 0) { + goto L40; + } + i__2 = m; + for (i__ = 1; i__ <= i__2; ++i__) { + dx[i__] = *da * dx[i__]; +/* L30: */ + } + if (*n < 5) { + return 0; + } +L40: + mp1 = m + 1; + i__2 = *n; + for (i__ = mp1; i__ <= i__2; i__ += 5) { + dx[i__] = *da * dx[i__]; + dx[i__ + 1] = *da * dx[i__ + 1]; + dx[i__ + 2] = *da * dx[i__ + 2]; + dx[i__ + 3] = *da * dx[i__ + 3]; + dx[i__ + 4] = *da * dx[i__ + 4]; +/* L50: */ + } + return 0; +} /* dscal_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/cblas/src/dswap.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,114 @@ +/* dswap.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +/* Subroutine */ int dswap_(integer *n, doublereal *dx, integer *incx, + doublereal *dy, integer *incy) +{ + /* System generated locals */ + integer i__1; + + /* Local variables */ + integer i__, m, ix, iy, mp1; + doublereal dtemp; + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* interchanges two vectors. */ +/* uses unrolled loops for increments equal one. */ +/* jack dongarra, linpack, 3/11/78. */ +/* modified 12/3/93, array(1) declarations changed to array(*) */ + + +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + /* Parameter adjustments */ + --dy; + --dx; + + /* Function Body */ + if (*n <= 0) { + return 0; + } + if (*incx == 1 && *incy == 1) { + goto L20; + } + +/* code for unequal increments or equal increments not equal */ +/* to 1 */ + + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp = dx[ix]; + dx[ix] = dy[iy]; + dy[iy] = dtemp; + ix += *incx; + iy += *incy; +/* L10: */ + } + return 0; + +/* code for both increments equal to 1 */ + + +/* clean-up loop */ + +L20: + m = *n % 3; + if (m == 0) { + goto L40; + } + i__1 = m; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp = dx[i__]; + dx[i__] = dy[i__]; + dy[i__] = dtemp; +/* L30: */ + } + if (*n < 3) { + return 0; + } +L40: + mp1 = m + 1; + i__1 = *n; + for (i__ = mp1; i__ <= i__1; i__ += 3) { + dtemp = dx[i__]; + dx[i__] = dy[i__]; + dy[i__] = dtemp; + dtemp = dx[i__ + 1]; + dx[i__ + 1] = dy[i__ + 1]; + dy[i__ + 1] = dtemp; + dtemp = dx[i__ + 2]; + dx[i__ + 2] = dy[i__ + 2]; + dy[i__ + 2] = dtemp; +/* L50: */ + } + return 0; +} /* dswap_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/cblas/src/dtrmm.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,453 @@ +/* dtrmm.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +/* Subroutine */ int dtrmm_(char *side, char *uplo, char *transa, char *diag, + integer *m, integer *n, doublereal *alpha, doublereal *a, integer * + lda, doublereal *b, integer *ldb) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3; + + /* Local variables */ + integer i__, j, k, info; + doublereal temp; + logical lside; + extern logical lsame_(char *, char *); + integer nrowa; + logical upper; + extern /* Subroutine */ int xerbla_(char *, integer *); + logical nounit; + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* DTRMM performs one of the matrix-matrix operations */ + +/* B := alpha*op( A )*B, or B := alpha*B*op( A ), */ + +/* where alpha is a scalar, B is an m by n matrix, A is a unit, or */ +/* non-unit, upper or lower triangular matrix and op( A ) is one of */ + +/* op( A ) = A or op( A ) = A'. */ + +/* Arguments */ +/* ========== */ + +/* SIDE - CHARACTER*1. */ +/* On entry, SIDE specifies whether op( A ) multiplies B from */ +/* the left or right as follows: */ + +/* SIDE = 'L' or 'l' B := alpha*op( A )*B. */ + +/* SIDE = 'R' or 'r' B := alpha*B*op( A ). */ + +/* Unchanged on exit. */ + +/* UPLO - CHARACTER*1. */ +/* On entry, UPLO specifies whether the matrix A is an upper or */ +/* lower triangular matrix as follows: */ + +/* UPLO = 'U' or 'u' A is an upper triangular matrix. */ + +/* UPLO = 'L' or 'l' A is a lower triangular matrix. */ + +/* Unchanged on exit. */ + +/* TRANSA - CHARACTER*1. */ +/* On entry, TRANSA specifies the form of op( A ) to be used in */ +/* the matrix multiplication as follows: */ + +/* TRANSA = 'N' or 'n' op( A ) = A. */ + +/* TRANSA = 'T' or 't' op( A ) = A'. */ + +/* TRANSA = 'C' or 'c' op( A ) = A'. */ + +/* Unchanged on exit. */ + +/* DIAG - CHARACTER*1. */ +/* On entry, DIAG specifies whether or not A is unit triangular */ +/* as follows: */ + +/* DIAG = 'U' or 'u' A is assumed to be unit triangular. */ + +/* DIAG = 'N' or 'n' A is not assumed to be unit */ +/* triangular. */ + +/* Unchanged on exit. */ + +/* M - INTEGER. */ +/* On entry, M specifies the number of rows of B. M must be at */ +/* least zero. */ +/* Unchanged on exit. */ + +/* N - INTEGER. */ +/* On entry, N specifies the number of columns of B. N must be */ +/* at least zero. */ +/* Unchanged on exit. */ + +/* ALPHA - DOUBLE PRECISION. */ +/* On entry, ALPHA specifies the scalar alpha. When alpha is */ +/* zero then A is not referenced and B need not be set before */ +/* entry. */ +/* Unchanged on exit. */ + +/* A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m */ +/* when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. */ +/* Before entry with UPLO = 'U' or 'u', the leading k by k */ +/* upper triangular part of the array A must contain the upper */ +/* triangular matrix and the strictly lower triangular part of */ +/* A is not referenced. */ +/* Before entry with UPLO = 'L' or 'l', the leading k by k */ +/* lower triangular part of the array A must contain the lower */ +/* triangular matrix and the strictly upper triangular part of */ +/* A is not referenced. */ +/* Note that when DIAG = 'U' or 'u', the diagonal elements of */ +/* A are not referenced either, but are assumed to be unity. */ +/* Unchanged on exit. */ + +/* LDA - INTEGER. */ +/* On entry, LDA specifies the first dimension of A as declared */ +/* in the calling (sub) program. When SIDE = 'L' or 'l' then */ +/* LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' */ +/* then LDA must be at least max( 1, n ). */ +/* Unchanged on exit. */ + +/* B - DOUBLE PRECISION array of DIMENSION ( LDB, n ). */ +/* Before entry, the leading m by n part of the array B must */ +/* contain the matrix B, and on exit is overwritten by the */ +/* transformed matrix. */ + +/* LDB - INTEGER. */ +/* On entry, LDB specifies the first dimension of B as declared */ +/* in the calling (sub) program. LDB must be at least */ +/* max( 1, m ). */ +/* Unchanged on exit. */ + + +/* Level 3 Blas routine. */ + +/* -- Written on 8-February-1989. */ +/* Jack Dongarra, Argonne National Laboratory. */ +/* Iain Duff, AERE Harwell. */ +/* Jeremy Du Croz, Numerical Algorithms Group Ltd. */ +/* Sven Hammarling, Numerical Algorithms Group Ltd. */ + + +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Parameters .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + + /* Function Body */ + lside = lsame_(side, "L"); + if (lside) { + nrowa = *m; + } else { + nrowa = *n; + } + nounit = lsame_(diag, "N"); + upper = lsame_(uplo, "U"); + + info = 0; + if (! lside && ! lsame_(side, "R")) { + info = 1; + } else if (! upper && ! lsame_(uplo, "L")) { + info = 2; + } else if (! lsame_(transa, "N") && ! lsame_(transa, + "T") && ! lsame_(transa, "C")) { + info = 3; + } else if (! lsame_(diag, "U") && ! lsame_(diag, + "N")) { + info = 4; + } else if (*m < 0) { + info = 5; + } else if (*n < 0) { + info = 6; + } else if (*lda < max(1,nrowa)) { + info = 9; + } else if (*ldb < max(1,*m)) { + info = 11; + } + if (info != 0) { + xerbla_("DTRMM ", &info); + return 0; + } + +/* Quick return if possible. */ + + if (*m == 0 || *n == 0) { + return 0; + } + +/* And when alpha.eq.zero. */ + + if (*alpha == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = 0.; +/* L10: */ + } +/* L20: */ + } + return 0; + } + +/* Start the operations. */ + + if (lside) { + if (lsame_(transa, "N")) { + +/* Form B := alpha*A*B. */ + + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (k = 1; k <= i__2; ++k) { + if (b[k + j * b_dim1] != 0.) { + temp = *alpha * b[k + j * b_dim1]; + i__3 = k - 1; + for (i__ = 1; i__ <= i__3; ++i__) { + b[i__ + j * b_dim1] += temp * a[i__ + k * + a_dim1]; +/* L30: */ + } + if (nounit) { + temp *= a[k + k * a_dim1]; + } + b[k + j * b_dim1] = temp; + } +/* L40: */ + } +/* L50: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + for (k = *m; k >= 1; --k) { + if (b[k + j * b_dim1] != 0.) { + temp = *alpha * b[k + j * b_dim1]; + b[k + j * b_dim1] = temp; + if (nounit) { + b[k + j * b_dim1] *= a[k + k * a_dim1]; + } + i__2 = *m; + for (i__ = k + 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] += temp * a[i__ + k * + a_dim1]; +/* L60: */ + } + } +/* L70: */ + } +/* L80: */ + } + } + } else { + +/* Form B := alpha*A'*B. */ + + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + for (i__ = *m; i__ >= 1; --i__) { + temp = b[i__ + j * b_dim1]; + if (nounit) { + temp *= a[i__ + i__ * a_dim1]; + } + i__2 = i__ - 1; + for (k = 1; k <= i__2; ++k) { + temp += a[k + i__ * a_dim1] * b[k + j * b_dim1]; +/* L90: */ + } + b[i__ + j * b_dim1] = *alpha * temp; +/* L100: */ + } +/* L110: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = b[i__ + j * b_dim1]; + if (nounit) { + temp *= a[i__ + i__ * a_dim1]; + } + i__3 = *m; + for (k = i__ + 1; k <= i__3; ++k) { + temp += a[k + i__ * a_dim1] * b[k + j * b_dim1]; +/* L120: */ + } + b[i__ + j * b_dim1] = *alpha * temp; +/* L130: */ + } +/* L140: */ + } + } + } + } else { + if (lsame_(transa, "N")) { + +/* Form B := alpha*B*A. */ + + if (upper) { + for (j = *n; j >= 1; --j) { + temp = *alpha; + if (nounit) { + temp *= a[j + j * a_dim1]; + } + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1]; +/* L150: */ + } + i__1 = j - 1; + for (k = 1; k <= i__1; ++k) { + if (a[k + j * a_dim1] != 0.) { + temp = *alpha * a[k + j * a_dim1]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] += temp * b[i__ + k * + b_dim1]; +/* L160: */ + } + } +/* L170: */ + } +/* L180: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = *alpha; + if (nounit) { + temp *= a[j + j * a_dim1]; + } + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1]; +/* L190: */ + } + i__2 = *n; + for (k = j + 1; k <= i__2; ++k) { + if (a[k + j * a_dim1] != 0.) { + temp = *alpha * a[k + j * a_dim1]; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + b[i__ + j * b_dim1] += temp * b[i__ + k * + b_dim1]; +/* L200: */ + } + } +/* L210: */ + } +/* L220: */ + } + } + } else { + +/* Form B := alpha*B*A'. */ + + if (upper) { + i__1 = *n; + for (k = 1; k <= i__1; ++k) { + i__2 = k - 1; + for (j = 1; j <= i__2; ++j) { + if (a[j + k * a_dim1] != 0.) { + temp = *alpha * a[j + k * a_dim1]; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + b[i__ + j * b_dim1] += temp * b[i__ + k * + b_dim1]; +/* L230: */ + } + } +/* L240: */ + } + temp = *alpha; + if (nounit) { + temp *= a[k + k * a_dim1]; + } + if (temp != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1]; +/* L250: */ + } + } +/* L260: */ + } + } else { + for (k = *n; k >= 1; --k) { + i__1 = *n; + for (j = k + 1; j <= i__1; ++j) { + if (a[j + k * a_dim1] != 0.) { + temp = *alpha * a[j + k * a_dim1]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] += temp * b[i__ + k * + b_dim1]; +/* L270: */ + } + } +/* L280: */ + } + temp = *alpha; + if (nounit) { + temp *= a[k + k * a_dim1]; + } + if (temp != 1.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1]; +/* L290: */ + } + } +/* L300: */ + } + } + } + } + + return 0; + +/* End of DTRMM . */ + +} /* dtrmm_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/cblas/src/dtrmv.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,345 @@ +/* dtrmv.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +/* Subroutine */ int dtrmv_(char *uplo, char *trans, char *diag, integer *n, + doublereal *a, integer *lda, doublereal *x, integer *incx) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + + /* Local variables */ + integer i__, j, ix, jx, kx, info; + doublereal temp; + extern logical lsame_(char *, char *); + extern /* Subroutine */ int xerbla_(char *, integer *); + logical nounit; + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* DTRMV performs one of the matrix-vector operations */ + +/* x := A*x, or x := A'*x, */ + +/* where x is an n element vector and A is an n by n unit, or non-unit, */ +/* upper or lower triangular matrix. */ + +/* Arguments */ +/* ========== */ + +/* UPLO - CHARACTER*1. */ +/* On entry, UPLO specifies whether the matrix is an upper or */ +/* lower triangular matrix as follows: */ + +/* UPLO = 'U' or 'u' A is an upper triangular matrix. */ + +/* UPLO = 'L' or 'l' A is a lower triangular matrix. */ + +/* Unchanged on exit. */ + +/* TRANS - CHARACTER*1. */ +/* On entry, TRANS specifies the operation to be performed as */ +/* follows: */ + +/* TRANS = 'N' or 'n' x := A*x. */ + +/* TRANS = 'T' or 't' x := A'*x. */ + +/* TRANS = 'C' or 'c' x := A'*x. */ + +/* Unchanged on exit. */ + +/* DIAG - CHARACTER*1. */ +/* On entry, DIAG specifies whether or not A is unit */ +/* triangular as follows: */ + +/* DIAG = 'U' or 'u' A is assumed to be unit triangular. */ + +/* DIAG = 'N' or 'n' A is not assumed to be unit */ +/* triangular. */ + +/* Unchanged on exit. */ + +/* N - INTEGER. */ +/* On entry, N specifies the order of the matrix A. */ +/* N must be at least zero. */ +/* Unchanged on exit. */ + +/* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). */ +/* Before entry with UPLO = 'U' or 'u', the leading n by n */ +/* upper triangular part of the array A must contain the upper */ +/* triangular matrix and the strictly lower triangular part of */ +/* A is not referenced. */ +/* Before entry with UPLO = 'L' or 'l', the leading n by n */ +/* lower triangular part of the array A must contain the lower */ +/* triangular matrix and the strictly upper triangular part of */ +/* A is not referenced. */ +/* Note that when DIAG = 'U' or 'u', the diagonal elements of */ +/* A are not referenced either, but are assumed to be unity. */ +/* Unchanged on exit. */ + +/* LDA - INTEGER. */ +/* On entry, LDA specifies the first dimension of A as declared */ +/* in the calling (sub) program. LDA must be at least */ +/* max( 1, n ). */ +/* Unchanged on exit. */ + +/* X - DOUBLE PRECISION array of dimension at least */ +/* ( 1 + ( n - 1 )*abs( INCX ) ). */ +/* Before entry, the incremented array X must contain the n */ +/* element vector x. On exit, X is overwritten with the */ +/* tranformed vector x. */ + +/* INCX - INTEGER. */ +/* On entry, INCX specifies the increment for the elements of */ +/* X. INCX must not be zero. */ +/* Unchanged on exit. */ + + +/* Level 2 Blas routine. */ + +/* -- Written on 22-October-1986. */ +/* Jack Dongarra, Argonne National Lab. */ +/* Jeremy Du Croz, Nag Central Office. */ +/* Sven Hammarling, Nag Central Office. */ +/* Richard Hanson, Sandia National Labs. */ + + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --x; + + /* Function Body */ + info = 0; + if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { + info = 1; + } else if (! lsame_(trans, "N") && ! lsame_(trans, + "T") && ! lsame_(trans, "C")) { + info = 2; + } else if (! lsame_(diag, "U") && ! lsame_(diag, + "N")) { + info = 3; + } else if (*n < 0) { + info = 4; + } else if (*lda < max(1,*n)) { + info = 6; + } else if (*incx == 0) { + info = 8; + } + if (info != 0) { + xerbla_("DTRMV ", &info); + return 0; + } + +/* Quick return if possible. */ + + if (*n == 0) { + return 0; + } + + nounit = lsame_(diag, "N"); + +/* Set up the start point in X if the increment is not unity. This */ +/* will be ( N - 1 )*INCX too small for descending loops. */ + + if (*incx <= 0) { + kx = 1 - (*n - 1) * *incx; + } else if (*incx != 1) { + kx = 1; + } + +/* Start the operations. In this version the elements of A are */ +/* accessed sequentially with one pass through A. */ + + if (lsame_(trans, "N")) { + +/* Form x := A*x. */ + + if (lsame_(uplo, "U")) { + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (x[j] != 0.) { + temp = x[j]; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + x[i__] += temp * a[i__ + j * a_dim1]; +/* L10: */ + } + if (nounit) { + x[j] *= a[j + j * a_dim1]; + } + } +/* L20: */ + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (x[jx] != 0.) { + temp = x[jx]; + ix = kx; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + x[ix] += temp * a[i__ + j * a_dim1]; + ix += *incx; +/* L30: */ + } + if (nounit) { + x[jx] *= a[j + j * a_dim1]; + } + } + jx += *incx; +/* L40: */ + } + } + } else { + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + if (x[j] != 0.) { + temp = x[j]; + i__1 = j + 1; + for (i__ = *n; i__ >= i__1; --i__) { + x[i__] += temp * a[i__ + j * a_dim1]; +/* L50: */ + } + if (nounit) { + x[j] *= a[j + j * a_dim1]; + } + } +/* L60: */ + } + } else { + kx += (*n - 1) * *incx; + jx = kx; + for (j = *n; j >= 1; --j) { + if (x[jx] != 0.) { + temp = x[jx]; + ix = kx; + i__1 = j + 1; + for (i__ = *n; i__ >= i__1; --i__) { + x[ix] += temp * a[i__ + j * a_dim1]; + ix -= *incx; +/* L70: */ + } + if (nounit) { + x[jx] *= a[j + j * a_dim1]; + } + } + jx -= *incx; +/* L80: */ + } + } + } + } else { + +/* Form x := A'*x. */ + + if (lsame_(uplo, "U")) { + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + temp = x[j]; + if (nounit) { + temp *= a[j + j * a_dim1]; + } + for (i__ = j - 1; i__ >= 1; --i__) { + temp += a[i__ + j * a_dim1] * x[i__]; +/* L90: */ + } + x[j] = temp; +/* L100: */ + } + } else { + jx = kx + (*n - 1) * *incx; + for (j = *n; j >= 1; --j) { + temp = x[jx]; + ix = jx; + if (nounit) { + temp *= a[j + j * a_dim1]; + } + for (i__ = j - 1; i__ >= 1; --i__) { + ix -= *incx; + temp += a[i__ + j * a_dim1] * x[ix]; +/* L110: */ + } + x[jx] = temp; + jx -= *incx; +/* L120: */ + } + } + } else { + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = x[j]; + if (nounit) { + temp *= a[j + j * a_dim1]; + } + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + temp += a[i__ + j * a_dim1] * x[i__]; +/* L130: */ + } + x[j] = temp; +/* L140: */ + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = x[jx]; + ix = jx; + if (nounit) { + temp *= a[j + j * a_dim1]; + } + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + ix += *incx; + temp += a[i__ + j * a_dim1] * x[ix]; +/* L150: */ + } + x[jx] = temp; + jx += *incx; +/* L160: */ + } + } + } + } + + return 0; + +/* End of DTRMV . */ + +} /* dtrmv_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/cblas/src/dtrsm.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,490 @@ +/* dtrsm.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +/* Subroutine */ int dtrsm_(char *side, char *uplo, char *transa, char *diag, + integer *m, integer *n, doublereal *alpha, doublereal *a, integer * + lda, doublereal *b, integer *ldb) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3; + + /* Local variables */ + integer i__, j, k, info; + doublereal temp; + logical lside; + extern logical lsame_(char *, char *); + integer nrowa; + logical upper; + extern /* Subroutine */ int xerbla_(char *, integer *); + logical nounit; + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* DTRSM solves one of the matrix equations */ + +/* op( A )*X = alpha*B, or X*op( A ) = alpha*B, */ + +/* where alpha is a scalar, X and B are m by n matrices, A is a unit, or */ +/* non-unit, upper or lower triangular matrix and op( A ) is one of */ + +/* op( A ) = A or op( A ) = A'. */ + +/* The matrix X is overwritten on B. */ + +/* Arguments */ +/* ========== */ + +/* SIDE - CHARACTER*1. */ +/* On entry, SIDE specifies whether op( A ) appears on the left */ +/* or right of X as follows: */ + +/* SIDE = 'L' or 'l' op( A )*X = alpha*B. */ + +/* SIDE = 'R' or 'r' X*op( A ) = alpha*B. */ + +/* Unchanged on exit. */ + +/* UPLO - CHARACTER*1. */ +/* On entry, UPLO specifies whether the matrix A is an upper or */ +/* lower triangular matrix as follows: */ + +/* UPLO = 'U' or 'u' A is an upper triangular matrix. */ + +/* UPLO = 'L' or 'l' A is a lower triangular matrix. */ + +/* Unchanged on exit. */ + +/* TRANSA - CHARACTER*1. */ +/* On entry, TRANSA specifies the form of op( A ) to be used in */ +/* the matrix multiplication as follows: */ + +/* TRANSA = 'N' or 'n' op( A ) = A. */ + +/* TRANSA = 'T' or 't' op( A ) = A'. */ + +/* TRANSA = 'C' or 'c' op( A ) = A'. */ + +/* Unchanged on exit. */ + +/* DIAG - CHARACTER*1. */ +/* On entry, DIAG specifies whether or not A is unit triangular */ +/* as follows: */ + +/* DIAG = 'U' or 'u' A is assumed to be unit triangular. */ + +/* DIAG = 'N' or 'n' A is not assumed to be unit */ +/* triangular. */ + +/* Unchanged on exit. */ + +/* M - INTEGER. */ +/* On entry, M specifies the number of rows of B. M must be at */ +/* least zero. */ +/* Unchanged on exit. */ + +/* N - INTEGER. */ +/* On entry, N specifies the number of columns of B. N must be */ +/* at least zero. */ +/* Unchanged on exit. */ + +/* ALPHA - DOUBLE PRECISION. */ +/* On entry, ALPHA specifies the scalar alpha. When alpha is */ +/* zero then A is not referenced and B need not be set before */ +/* entry. */ +/* Unchanged on exit. */ + +/* A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m */ +/* when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. */ +/* Before entry with UPLO = 'U' or 'u', the leading k by k */ +/* upper triangular part of the array A must contain the upper */ +/* triangular matrix and the strictly lower triangular part of */ +/* A is not referenced. */ +/* Before entry with UPLO = 'L' or 'l', the leading k by k */ +/* lower triangular part of the array A must contain the lower */ +/* triangular matrix and the strictly upper triangular part of */ +/* A is not referenced. */ +/* Note that when DIAG = 'U' or 'u', the diagonal elements of */ +/* A are not referenced either, but are assumed to be unity. */ +/* Unchanged on exit. */ + +/* LDA - INTEGER. */ +/* On entry, LDA specifies the first dimension of A as declared */ +/* in the calling (sub) program. When SIDE = 'L' or 'l' then */ +/* LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' */ +/* then LDA must be at least max( 1, n ). */ +/* Unchanged on exit. */ + +/* B - DOUBLE PRECISION array of DIMENSION ( LDB, n ). */ +/* Before entry, the leading m by n part of the array B must */ +/* contain the right-hand side matrix B, and on exit is */ +/* overwritten by the solution matrix X. */ + +/* LDB - INTEGER. */ +/* On entry, LDB specifies the first dimension of B as declared */ +/* in the calling (sub) program. LDB must be at least */ +/* max( 1, m ). */ +/* Unchanged on exit. */ + + +/* Level 3 Blas routine. */ + + +/* -- Written on 8-February-1989. */ +/* Jack Dongarra, Argonne National Laboratory. */ +/* Iain Duff, AERE Harwell. */ +/* Jeremy Du Croz, Numerical Algorithms Group Ltd. */ +/* Sven Hammarling, Numerical Algorithms Group Ltd. */ + + +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Parameters .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + + /* Function Body */ + lside = lsame_(side, "L"); + if (lside) { + nrowa = *m; + } else { + nrowa = *n; + } + nounit = lsame_(diag, "N"); + upper = lsame_(uplo, "U"); + + info = 0; + if (! lside && ! lsame_(side, "R")) { + info = 1; + } else if (! upper && ! lsame_(uplo, "L")) { + info = 2; + } else if (! lsame_(transa, "N") && ! lsame_(transa, + "T") && ! lsame_(transa, "C")) { + info = 3; + } else if (! lsame_(diag, "U") && ! lsame_(diag, + "N")) { + info = 4; + } else if (*m < 0) { + info = 5; + } else if (*n < 0) { + info = 6; + } else if (*lda < max(1,nrowa)) { + info = 9; + } else if (*ldb < max(1,*m)) { + info = 11; + } + if (info != 0) { + xerbla_("DTRSM ", &info); + return 0; + } + +/* Quick return if possible. */ + + if (*m == 0 || *n == 0) { + return 0; + } + +/* And when alpha.eq.zero. */ + + if (*alpha == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = 0.; +/* L10: */ + } +/* L20: */ + } + return 0; + } + +/* Start the operations. */ + + if (lside) { + if (lsame_(transa, "N")) { + +/* Form B := alpha*inv( A )*B. */ + + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*alpha != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1] + ; +/* L30: */ + } + } + for (k = *m; k >= 1; --k) { + if (b[k + j * b_dim1] != 0.) { + if (nounit) { + b[k + j * b_dim1] /= a[k + k * a_dim1]; + } + i__2 = k - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[ + i__ + k * a_dim1]; +/* L40: */ + } + } +/* L50: */ + } +/* L60: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*alpha != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1] + ; +/* L70: */ + } + } + i__2 = *m; + for (k = 1; k <= i__2; ++k) { + if (b[k + j * b_dim1] != 0.) { + if (nounit) { + b[k + j * b_dim1] /= a[k + k * a_dim1]; + } + i__3 = *m; + for (i__ = k + 1; i__ <= i__3; ++i__) { + b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[ + i__ + k * a_dim1]; +/* L80: */ + } + } +/* L90: */ + } +/* L100: */ + } + } + } else { + +/* Form B := alpha*inv( A' )*B. */ + + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = *alpha * b[i__ + j * b_dim1]; + i__3 = i__ - 1; + for (k = 1; k <= i__3; ++k) { + temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1]; +/* L110: */ + } + if (nounit) { + temp /= a[i__ + i__ * a_dim1]; + } + b[i__ + j * b_dim1] = temp; +/* L120: */ + } +/* L130: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + for (i__ = *m; i__ >= 1; --i__) { + temp = *alpha * b[i__ + j * b_dim1]; + i__2 = *m; + for (k = i__ + 1; k <= i__2; ++k) { + temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1]; +/* L140: */ + } + if (nounit) { + temp /= a[i__ + i__ * a_dim1]; + } + b[i__ + j * b_dim1] = temp; +/* L150: */ + } +/* L160: */ + } + } + } + } else { + if (lsame_(transa, "N")) { + +/* Form B := alpha*B*inv( A ). */ + + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*alpha != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1] + ; +/* L170: */ + } + } + i__2 = j - 1; + for (k = 1; k <= i__2; ++k) { + if (a[k + j * a_dim1] != 0.) { + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[ + i__ + k * b_dim1]; +/* L180: */ + } + } +/* L190: */ + } + if (nounit) { + temp = 1. / a[j + j * a_dim1]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1]; +/* L200: */ + } + } +/* L210: */ + } + } else { + for (j = *n; j >= 1; --j) { + if (*alpha != 1.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1] + ; +/* L220: */ + } + } + i__1 = *n; + for (k = j + 1; k <= i__1; ++k) { + if (a[k + j * a_dim1] != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[ + i__ + k * b_dim1]; +/* L230: */ + } + } +/* L240: */ + } + if (nounit) { + temp = 1. / a[j + j * a_dim1]; + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1]; +/* L250: */ + } + } +/* L260: */ + } + } + } else { + +/* Form B := alpha*B*inv( A' ). */ + + if (upper) { + for (k = *n; k >= 1; --k) { + if (nounit) { + temp = 1. / a[k + k * a_dim1]; + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1]; +/* L270: */ + } + } + i__1 = k - 1; + for (j = 1; j <= i__1; ++j) { + if (a[j + k * a_dim1] != 0.) { + temp = a[j + k * a_dim1]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] -= temp * b[i__ + k * + b_dim1]; +/* L280: */ + } + } +/* L290: */ + } + if (*alpha != 1.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1] + ; +/* L300: */ + } + } +/* L310: */ + } + } else { + i__1 = *n; + for (k = 1; k <= i__1; ++k) { + if (nounit) { + temp = 1. / a[k + k * a_dim1]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1]; +/* L320: */ + } + } + i__2 = *n; + for (j = k + 1; j <= i__2; ++j) { + if (a[j + k * a_dim1] != 0.) { + temp = a[j + k * a_dim1]; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + b[i__ + j * b_dim1] -= temp * b[i__ + k * + b_dim1]; +/* L330: */ + } + } +/* L340: */ + } + if (*alpha != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1] + ; +/* L350: */ + } + } +/* L360: */ + } + } + } + } + + return 0; + +/* End of DTRSM . */ + +} /* dtrsm_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/cblas/src/idamax.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,93 @@ +/* idamax.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +integer idamax_(integer *n, doublereal *dx, integer *incx) +{ + /* System generated locals */ + integer ret_val, i__1; + doublereal d__1; + + /* Local variables */ + integer i__, ix; + doublereal dmax__; + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* finds the index of element having max. absolute value. */ +/* jack dongarra, linpack, 3/11/78. */ +/* modified 3/93 to return if incx .le. 0. */ +/* modified 12/3/93, array(1) declarations changed to array(*) */ + + +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + /* Parameter adjustments */ + --dx; + + /* Function Body */ + ret_val = 0; + if (*n < 1 || *incx <= 0) { + return ret_val; + } + ret_val = 1; + if (*n == 1) { + return ret_val; + } + if (*incx == 1) { + goto L20; + } + +/* code for increment not equal to 1 */ + + ix = 1; + dmax__ = abs(dx[1]); + ix += *incx; + i__1 = *n; + for (i__ = 2; i__ <= i__1; ++i__) { + if ((d__1 = dx[ix], abs(d__1)) <= dmax__) { + goto L5; + } + ret_val = i__; + dmax__ = (d__1 = dx[ix], abs(d__1)); +L5: + ix += *incx; +/* L10: */ + } + return ret_val; + +/* code for increment equal to 1 */ + +L20: + dmax__ = abs(dx[1]); + i__1 = *n; + for (i__ = 2; i__ <= i__1; ++i__) { + if ((d__1 = dx[i__], abs(d__1)) <= dmax__) { + goto L30; + } + ret_val = i__; + dmax__ = (d__1 = dx[i__], abs(d__1)); +L30: + ; + } + return ret_val; +} /* idamax_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/cblas/src/lsame.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,117 @@ +/* lsame.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +logical lsame_(char *ca, char *cb) +{ + /* System generated locals */ + logical ret_val; + + /* Local variables */ + integer inta, intb, zcode; + + +/* -- LAPACK auxiliary routine (version 3.1) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* LSAME returns .TRUE. if CA is the same letter as CB regardless of */ +/* case. */ + +/* Arguments */ +/* ========= */ + +/* CA (input) CHARACTER*1 */ + +/* CB (input) CHARACTER*1 */ +/* CA and CB specify the single characters to be compared. */ + +/* ===================================================================== */ + +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ + +/* Test if the characters are equal */ + + ret_val = *(unsigned char *)ca == *(unsigned char *)cb; + if (ret_val) { + return ret_val; + } + +/* Now test for equivalence if both characters are alphabetic. */ + + zcode = 'Z'; + +/* Use 'Z' rather than 'A' so that ASCII can be detected on Prime */ +/* machines, on which ICHAR returns a value with bit 8 set. */ +/* ICHAR('A') on Prime machines returns 193 which is the same as */ +/* ICHAR('A') on an EBCDIC machine. */ + + inta = *(unsigned char *)ca; + intb = *(unsigned char *)cb; + + if (zcode == 90 || zcode == 122) { + +/* ASCII is assumed - ZCODE is the ASCII code of either lower or */ +/* upper case 'Z'. */ + + if (inta >= 97 && inta <= 122) { + inta += -32; + } + if (intb >= 97 && intb <= 122) { + intb += -32; + } + + } else if (zcode == 233 || zcode == 169) { + +/* EBCDIC is assumed - ZCODE is the EBCDIC code of either lower or */ +/* upper case 'Z'. */ + + if (inta >= 129 && inta <= 137 || inta >= 145 && inta <= 153 || inta + >= 162 && inta <= 169) { + inta += 64; + } + if (intb >= 129 && intb <= 137 || intb >= 145 && intb <= 153 || intb + >= 162 && intb <= 169) { + intb += 64; + } + + } else if (zcode == 218 || zcode == 250) { + +/* ASCII is assumed, on Prime machines - ZCODE is the ASCII code */ +/* plus 128 of either lower or upper case 'Z'. */ + + if (inta >= 225 && inta <= 250) { + inta += -32; + } + if (intb >= 225 && intb <= 250) { + intb += -32; + } + } + ret_val = inta == intb; + +/* RETURN */ + +/* End of LSAME */ + + return ret_val; +} /* lsame_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/clapack/include/blaswrap.h Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,160 @@ +/* CLAPACK 3.0 BLAS wrapper macros + * Feb 5, 2000 + */ + +#ifndef __BLASWRAP_H +#define __BLASWRAP_H + +#ifndef NO_BLAS_WRAP + +/* BLAS1 routines */ +#define srotg_ f2c_srotg +#define crotg_ f2c_crotg +#define drotg_ f2c_drotg +#define zrotg_ f2c_zrotg +#define srotmg_ f2c_srotmg +#define drotmg_ f2c_drotmg +#define srot_ f2c_srot +#define drot_ f2c_drot +#define srotm_ f2c_srotm +#define drotm_ f2c_drotm +#define sswap_ f2c_sswap +#define dswap_ f2c_dswap +#define cswap_ f2c_cswap +#define zswap_ f2c_zswap +#define sscal_ f2c_sscal +#define dscal_ f2c_dscal +#define cscal_ f2c_cscal +#define zscal_ f2c_zscal +#define csscal_ f2c_csscal +#define zdscal_ f2c_zdscal +#define scopy_ f2c_scopy +#define dcopy_ f2c_dcopy +#define ccopy_ f2c_ccopy +#define zcopy_ f2c_zcopy +#define saxpy_ f2c_saxpy +#define daxpy_ f2c_daxpy +#define caxpy_ f2c_caxpy +#define zaxpy_ f2c_zaxpy +#define sdot_ f2c_sdot +#define ddot_ f2c_ddot +#define cdotu_ f2c_cdotu +#define zdotu_ f2c_zdotu +#define cdotc_ f2c_cdotc +#define zdotc_ f2c_zdotc +#define snrm2_ f2c_snrm2 +#define dnrm2_ f2c_dnrm2 +#define scnrm2_ f2c_scnrm2 +#define dznrm2_ f2c_dznrm2 +#define sasum_ f2c_sasum +#define dasum_ f2c_dasum +#define scasum_ f2c_scasum +#define dzasum_ f2c_dzasum +#define isamax_ f2c_isamax +#define idamax_ f2c_idamax +#define icamax_ f2c_icamax +#define izamax_ f2c_izamax + +/* BLAS2 routines */ +#define sgemv_ f2c_sgemv +#define dgemv_ f2c_dgemv +#define cgemv_ f2c_cgemv +#define zgemv_ f2c_zgemv +#define sgbmv_ f2c_sgbmv +#define dgbmv_ f2c_dgbmv +#define cgbmv_ f2c_cgbmv +#define zgbmv_ f2c_zgbmv +#define chemv_ f2c_chemv +#define zhemv_ f2c_zhemv +#define chbmv_ f2c_chbmv +#define zhbmv_ f2c_zhbmv +#define chpmv_ f2c_chpmv +#define zhpmv_ f2c_zhpmv +#define ssymv_ f2c_ssymv +#define dsymv_ f2c_dsymv +#define ssbmv_ f2c_ssbmv +#define dsbmv_ f2c_dsbmv +#define sspmv_ f2c_sspmv +#define dspmv_ f2c_dspmv +#define strmv_ f2c_strmv +#define dtrmv_ f2c_dtrmv +#define ctrmv_ f2c_ctrmv +#define ztrmv_ f2c_ztrmv +#define stbmv_ f2c_stbmv +#define dtbmv_ f2c_dtbmv +#define ctbmv_ f2c_ctbmv +#define ztbmv_ f2c_ztbmv +#define stpmv_ f2c_stpmv +#define dtpmv_ f2c_dtpmv +#define ctpmv_ f2c_ctpmv +#define ztpmv_ f2c_ztpmv +#define strsv_ f2c_strsv +#define dtrsv_ f2c_dtrsv +#define ctrsv_ f2c_ctrsv +#define ztrsv_ f2c_ztrsv +#define stbsv_ f2c_stbsv +#define dtbsv_ f2c_dtbsv +#define ctbsv_ f2c_ctbsv +#define ztbsv_ f2c_ztbsv +#define stpsv_ f2c_stpsv +#define dtpsv_ f2c_dtpsv +#define ctpsv_ f2c_ctpsv +#define ztpsv_ f2c_ztpsv +#define sger_ f2c_sger +#define dger_ f2c_dger +#define cgeru_ f2c_cgeru +#define zgeru_ f2c_zgeru +#define cgerc_ f2c_cgerc +#define zgerc_ f2c_zgerc +#define cher_ f2c_cher +#define zher_ f2c_zher +#define chpr_ f2c_chpr +#define zhpr_ f2c_zhpr +#define cher2_ f2c_cher2 +#define zher2_ f2c_zher2 +#define chpr2_ f2c_chpr2 +#define zhpr2_ f2c_zhpr2 +#define ssyr_ f2c_ssyr +#define dsyr_ f2c_dsyr +#define sspr_ f2c_sspr +#define dspr_ f2c_dspr +#define ssyr2_ f2c_ssyr2 +#define dsyr2_ f2c_dsyr2 +#define sspr2_ f2c_sspr2 +#define dspr2_ f2c_dspr2 + +/* BLAS3 routines */ +#define sgemm_ f2c_sgemm +#define dgemm_ f2c_dgemm +#define cgemm_ f2c_cgemm +#define zgemm_ f2c_zgemm +#define ssymm_ f2c_ssymm +#define dsymm_ f2c_dsymm +#define csymm_ f2c_csymm +#define zsymm_ f2c_zsymm +#define chemm_ f2c_chemm +#define zhemm_ f2c_zhemm +#define ssyrk_ f2c_ssyrk +#define dsyrk_ f2c_dsyrk +#define csyrk_ f2c_csyrk +#define zsyrk_ f2c_zsyrk +#define cherk_ f2c_cherk +#define zherk_ f2c_zherk +#define ssyr2k_ f2c_ssyr2k +#define dsyr2k_ f2c_dsyr2k +#define csyr2k_ f2c_csyr2k +#define zsyr2k_ f2c_zsyr2k +#define cher2k_ f2c_cher2k +#define zher2k_ f2c_zher2k +#define strmm_ f2c_strmm +#define dtrmm_ f2c_dtrmm +#define ctrmm_ f2c_ctrmm +#define ztrmm_ f2c_ztrmm +#define strsm_ f2c_strsm +#define dtrsm_ f2c_dtrsm +#define ctrsm_ f2c_ctrsm +#define ztrsm_ f2c_ztrsm + +#endif /* NO_BLAS_WRAP */ + +#endif /* __BLASWRAP_H */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/clapack/include/clapack.h Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,7264 @@ +/* header file for clapack 3.2.1 */ + +#ifndef __CLAPACK_H +#define __CLAPACK_H + +#include "f2c.h" + +#ifdef __cplusplus +extern "C" { +#endif + +/* Subroutine */ int caxpy_(integer *n, complex *ca, complex *cx, integer * + incx, complex *cy, integer *incy); + +/* Subroutine */ int ccopy_(integer *n, complex *cx, integer *incx, complex * + cy, integer *incy); + +/* Complex */ VOID cdotc_(complex * ret_val, integer *n, complex *cx, integer + *incx, complex *cy, integer *incy); + +/* Complex */ VOID cdotu_(complex * ret_val, integer *n, complex *cx, integer + *incx, complex *cy, integer *incy); + +/* Subroutine */ int cgbmv_(char *trans, integer *m, integer *n, integer *kl, + integer *ku, complex *alpha, complex *a, integer *lda, complex *x, + integer *incx, complex *beta, complex *y, integer *incy); + +/* Subroutine */ int cgemm_(char *transa, char *transb, integer *m, integer * + n, integer *k, complex *alpha, complex *a, integer *lda, complex *b, + integer *ldb, complex *beta, complex *c__, integer *ldc); + +/* Subroutine */ int cgemv_(char *trans, integer *m, integer *n, complex * + alpha, complex *a, integer *lda, complex *x, integer *incx, complex * + beta, complex *y, integer *incy); + +/* Subroutine */ int cgerc_(integer *m, integer *n, complex *alpha, complex * + x, integer *incx, complex *y, integer *incy, complex *a, integer *lda); + +/* Subroutine */ int cgeru_(integer *m, integer *n, complex *alpha, complex * + x, integer *incx, complex *y, integer *incy, complex *a, integer *lda); + +/* Subroutine */ int chbmv_(char *uplo, integer *n, integer *k, complex * + alpha, complex *a, integer *lda, complex *x, integer *incx, complex * + beta, complex *y, integer *incy); + +/* Subroutine */ int chemm_(char *side, char *uplo, integer *m, integer *n, + complex *alpha, complex *a, integer *lda, complex *b, integer *ldb, + complex *beta, complex *c__, integer *ldc); + +/* Subroutine */ int chemv_(char *uplo, integer *n, complex *alpha, complex * + a, integer *lda, complex *x, integer *incx, complex *beta, complex *y, + integer *incy); + +/* Subroutine */ int cher_(char *uplo, integer *n, real *alpha, complex *x, + integer *incx, complex *a, integer *lda); + +/* Subroutine */ int cher2_(char *uplo, integer *n, complex *alpha, complex * + x, integer *incx, complex *y, integer *incy, complex *a, integer *lda); + +/* Subroutine */ int cher2k_(char *uplo, char *trans, integer *n, integer *k, + complex *alpha, complex *a, integer *lda, complex *b, integer *ldb, + real *beta, complex *c__, integer *ldc); + +/* Subroutine */ int cherk_(char *uplo, char *trans, integer *n, integer *k, + real *alpha, complex *a, integer *lda, real *beta, complex *c__, + integer *ldc); + +/* Subroutine */ int chpmv_(char *uplo, integer *n, complex *alpha, complex * + ap, complex *x, integer *incx, complex *beta, complex *y, integer * + incy); + +/* Subroutine */ int chpr_(char *uplo, integer *n, real *alpha, complex *x, + integer *incx, complex *ap); + +/* Subroutine */ int chpr2_(char *uplo, integer *n, complex *alpha, complex * + x, integer *incx, complex *y, integer *incy, complex *ap); + +/* Subroutine */ int crotg_(complex *ca, complex *cb, real *c__, complex *s); + +/* Subroutine */ int cscal_(integer *n, complex *ca, complex *cx, integer * + incx); + +/* Subroutine */ int csrot_(integer *n, complex *cx, integer *incx, complex * + cy, integer *incy, real *c__, real *s); + +/* Subroutine */ int csscal_(integer *n, real *sa, complex *cx, integer *incx); + +/* Subroutine */ int cswap_(integer *n, complex *cx, integer *incx, complex * + cy, integer *incy); + +/* Subroutine */ int csymm_(char *side, char *uplo, integer *m, integer *n, + complex *alpha, complex *a, integer *lda, complex *b, integer *ldb, + complex *beta, complex *c__, integer *ldc); + +/* Subroutine */ int csyr2k_(char *uplo, char *trans, integer *n, integer *k, + complex *alpha, complex *a, integer *lda, complex *b, integer *ldb, + complex *beta, complex *c__, integer *ldc); + +/* Subroutine */ int csyrk_(char *uplo, char *trans, integer *n, integer *k, + complex *alpha, complex *a, integer *lda, complex *beta, complex *c__, + integer *ldc); + +/* Subroutine */ int ctbmv_(char *uplo, char *trans, char *diag, integer *n, + integer *k, complex *a, integer *lda, complex *x, integer *incx); + +/* Subroutine */ int ctbsv_(char *uplo, char *trans, char *diag, integer *n, + integer *k, complex *a, integer *lda, complex *x, integer *incx); + +/* Subroutine */ int ctpmv_(char *uplo, char *trans, char *diag, integer *n, + complex *ap, complex *x, integer *incx); + +/* Subroutine */ int ctpsv_(char *uplo, char *trans, char *diag, integer *n, + complex *ap, complex *x, integer *incx); + +/* Subroutine */ int ctrmm_(char *side, char *uplo, char *transa, char *diag, + integer *m, integer *n, complex *alpha, complex *a, integer *lda, + complex *b, integer *ldb); + +/* Subroutine */ int ctrmv_(char *uplo, char *trans, char *diag, integer *n, + complex *a, integer *lda, complex *x, integer *incx); + +/* Subroutine */ int ctrsm_(char *side, char *uplo, char *transa, char *diag, + integer *m, integer *n, complex *alpha, complex *a, integer *lda, + complex *b, integer *ldb); + +/* Subroutine */ int ctrsv_(char *uplo, char *trans, char *diag, integer *n, + complex *a, integer *lda, complex *x, integer *incx); + +doublereal dasum_(integer *n, doublereal *dx, integer *incx); + +/* Subroutine */ int daxpy_(integer *n, doublereal *da, doublereal *dx, + integer *incx, doublereal *dy, integer *incy); + +doublereal dcabs1_(doublecomplex *z__); + +/* Subroutine */ int dcopy_(integer *n, doublereal *dx, integer *incx, + doublereal *dy, integer *incy); + +doublereal ddot_(integer *n, doublereal *dx, integer *incx, doublereal *dy, + integer *incy); + +/* Subroutine */ int dgbmv_(char *trans, integer *m, integer *n, integer *kl, + integer *ku, doublereal *alpha, doublereal *a, integer *lda, + doublereal *x, integer *incx, doublereal *beta, doublereal *y, + integer *incy); + +/* Subroutine */ int dgemm_(char *transa, char *transb, integer *m, integer * + n, integer *k, doublereal *alpha, doublereal *a, integer *lda, + doublereal *b, integer *ldb, doublereal *beta, doublereal *c__, + integer *ldc); + +/* Subroutine */ int dgemv_(char *trans, integer *m, integer *n, doublereal * + alpha, doublereal *a, integer *lda, doublereal *x, integer *incx, + doublereal *beta, doublereal *y, integer *incy); + +/* Subroutine */ int dger_(integer *m, integer *n, doublereal *alpha, + doublereal *x, integer *incx, doublereal *y, integer *incy, + doublereal *a, integer *lda); + +doublereal dnrm2_(integer *n, doublereal *x, integer *incx); + +/* Subroutine */ int drot_(integer *n, doublereal *dx, integer *incx, + doublereal *dy, integer *incy, doublereal *c__, doublereal *s); + +/* Subroutine */ int drotg_(doublereal *da, doublereal *db, doublereal *c__, + doublereal *s); + +/* Subroutine */ int drotm_(integer *n, doublereal *dx, integer *incx, + doublereal *dy, integer *incy, doublereal *dparam); + +/* Subroutine */ int drotmg_(doublereal *dd1, doublereal *dd2, doublereal * + dx1, doublereal *dy1, doublereal *dparam); + +/* Subroutine */ int dsbmv_(char *uplo, integer *n, integer *k, doublereal * + alpha, doublereal *a, integer *lda, doublereal *x, integer *incx, + doublereal *beta, doublereal *y, integer *incy); + +/* Subroutine */ int dscal_(integer *n, doublereal *da, doublereal *dx, + integer *incx); + +doublereal dsdot_(integer *n, real *sx, integer *incx, real *sy, integer * + incy); + +/* Subroutine */ int dspmv_(char *uplo, integer *n, doublereal *alpha, + doublereal *ap, doublereal *x, integer *incx, doublereal *beta, + doublereal *y, integer *incy); + +/* Subroutine */ int dspr_(char *uplo, integer *n, doublereal *alpha, + doublereal *x, integer *incx, doublereal *ap); + +/* Subroutine */ int dspr2_(char *uplo, integer *n, doublereal *alpha, + doublereal *x, integer *incx, doublereal *y, integer *incy, + doublereal *ap); + +/* Subroutine */ int dswap_(integer *n, doublereal *dx, integer *incx, + doublereal *dy, integer *incy); + +/* Subroutine */ int dsymm_(char *side, char *uplo, integer *m, integer *n, + doublereal *alpha, doublereal *a, integer *lda, doublereal *b, + integer *ldb, doublereal *beta, doublereal *c__, integer *ldc); + +/* Subroutine */ int dsymv_(char *uplo, integer *n, doublereal *alpha, + doublereal *a, integer *lda, doublereal *x, integer *incx, doublereal + *beta, doublereal *y, integer *incy); + +/* Subroutine */ int dsyr_(char *uplo, integer *n, doublereal *alpha, + doublereal *x, integer *incx, doublereal *a, integer *lda); + +/* Subroutine */ int dsyr2_(char *uplo, integer *n, doublereal *alpha, + doublereal *x, integer *incx, doublereal *y, integer *incy, + doublereal *a, integer *lda); + +/* Subroutine */ int dsyr2k_(char *uplo, char *trans, integer *n, integer *k, + doublereal *alpha, doublereal *a, integer *lda, doublereal *b, + integer *ldb, doublereal *beta, doublereal *c__, integer *ldc); + +/* Subroutine */ int dsyrk_(char *uplo, char *trans, integer *n, integer *k, + doublereal *alpha, doublereal *a, integer *lda, doublereal *beta, + doublereal *c__, integer *ldc); + +/* Subroutine */ int dtbmv_(char *uplo, char *trans, char *diag, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *x, integer *incx); + +/* Subroutine */ int dtbsv_(char *uplo, char *trans, char *diag, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *x, integer *incx); + +/* Subroutine */ int dtpmv_(char *uplo, char *trans, char *diag, integer *n, + doublereal *ap, doublereal *x, integer *incx); + +/* Subroutine */ int dtpsv_(char *uplo, char *trans, char *diag, integer *n, + doublereal *ap, doublereal *x, integer *incx); + +/* Subroutine */ int dtrmm_(char *side, char *uplo, char *transa, char *diag, + integer *m, integer *n, doublereal *alpha, doublereal *a, integer * + lda, doublereal *b, integer *ldb); + +/* Subroutine */ int dtrmv_(char *uplo, char *trans, char *diag, integer *n, + doublereal *a, integer *lda, doublereal *x, integer *incx); + +/* Subroutine */ int dtrsm_(char *side, char *uplo, char *transa, char *diag, + integer *m, integer *n, doublereal *alpha, doublereal *a, integer * + lda, doublereal *b, integer *ldb); + +/* Subroutine */ int dtrsv_(char *uplo, char *trans, char *diag, integer *n, + doublereal *a, integer *lda, doublereal *x, integer *incx); + +doublereal dzasum_(integer *n, doublecomplex *zx, integer *incx); + +doublereal dznrm2_(integer *n, doublecomplex *x, integer *incx); + +integer icamax_(integer *n, complex *cx, integer *incx); + +integer idamax_(integer *n, doublereal *dx, integer *incx); + +integer isamax_(integer *n, real *sx, integer *incx); + +integer izamax_(integer *n, doublecomplex *zx, integer *incx); + +logical lsame_(char *ca, char *cb); + +doublereal sasum_(integer *n, real *sx, integer *incx); + +/* Subroutine */ int saxpy_(integer *n, real *sa, real *sx, integer *incx, + real *sy, integer *incy); + +doublereal scabs1_(complex *z__); + +doublereal scasum_(integer *n, complex *cx, integer *incx); + +doublereal scnrm2_(integer *n, complex *x, integer *incx); + +/* Subroutine */ int scopy_(integer *n, real *sx, integer *incx, real *sy, + integer *incy); + +doublereal sdot_(integer *n, real *sx, integer *incx, real *sy, integer *incy); + +doublereal sdsdot_(integer *n, real *sb, real *sx, integer *incx, real *sy, + integer *incy); + +/* Subroutine */ int sgbmv_(char *trans, integer *m, integer *n, integer *kl, + integer *ku, real *alpha, real *a, integer *lda, real *x, integer * + incx, real *beta, real *y, integer *incy); + +/* Subroutine */ int sgemm_(char *transa, char *transb, integer *m, integer * + n, integer *k, real *alpha, real *a, integer *lda, real *b, integer * + ldb, real *beta, real *c__, integer *ldc); + +/* Subroutine */ int sgemv_(char *trans, integer *m, integer *n, real *alpha, + real *a, integer *lda, real *x, integer *incx, real *beta, real *y, + integer *incy); + +/* Subroutine */ int sger_(integer *m, integer *n, real *alpha, real *x, + integer *incx, real *y, integer *incy, real *a, integer *lda); + +doublereal snrm2_(integer *n, real *x, integer *incx); + +/* Subroutine */ int srot_(integer *n, real *sx, integer *incx, real *sy, + integer *incy, real *c__, real *s); + +/* Subroutine */ int srotg_(real *sa, real *sb, real *c__, real *s); + +/* Subroutine */ int srotm_(integer *n, real *sx, integer *incx, real *sy, + integer *incy, real *sparam); + +/* Subroutine */ int srotmg_(real *sd1, real *sd2, real *sx1, real *sy1, real + *sparam); + +/* Subroutine */ int ssbmv_(char *uplo, integer *n, integer *k, real *alpha, + real *a, integer *lda, real *x, integer *incx, real *beta, real *y, + integer *incy); + +/* Subroutine */ int sscal_(integer *n, real *sa, real *sx, integer *incx); + +/* Subroutine */ int sspmv_(char *uplo, integer *n, real *alpha, real *ap, + real *x, integer *incx, real *beta, real *y, integer *incy); + +/* Subroutine */ int sspr_(char *uplo, integer *n, real *alpha, real *x, + integer *incx, real *ap); + +/* Subroutine */ int sspr2_(char *uplo, integer *n, real *alpha, real *x, + integer *incx, real *y, integer *incy, real *ap); + +/* Subroutine */ int sswap_(integer *n, real *sx, integer *incx, real *sy, + integer *incy); + +/* Subroutine */ int ssymm_(char *side, char *uplo, integer *m, integer *n, + real *alpha, real *a, integer *lda, real *b, integer *ldb, real *beta, + real *c__, integer *ldc); + +/* Subroutine */ int ssymv_(char *uplo, integer *n, real *alpha, real *a, + integer *lda, real *x, integer *incx, real *beta, real *y, integer * + incy); + +/* Subroutine */ int ssyr_(char *uplo, integer *n, real *alpha, real *x, + integer *incx, real *a, integer *lda); + +/* Subroutine */ int ssyr2_(char *uplo, integer *n, real *alpha, real *x, + integer *incx, real *y, integer *incy, real *a, integer *lda); + +/* Subroutine */ int ssyr2k_(char *uplo, char *trans, integer *n, integer *k, + real *alpha, real *a, integer *lda, real *b, integer *ldb, real *beta, + real *c__, integer *ldc); + +/* Subroutine */ int ssyrk_(char *uplo, char *trans, integer *n, integer *k, + real *alpha, real *a, integer *lda, real *beta, real *c__, integer * + ldc); + +/* Subroutine */ int stbmv_(char *uplo, char *trans, char *diag, integer *n, + integer *k, real *a, integer *lda, real *x, integer *incx); + +/* Subroutine */ int stbsv_(char *uplo, char *trans, char *diag, integer *n, + integer *k, real *a, integer *lda, real *x, integer *incx); + +/* Subroutine */ int stpmv_(char *uplo, char *trans, char *diag, integer *n, + real *ap, real *x, integer *incx); + +/* Subroutine */ int stpsv_(char *uplo, char *trans, char *diag, integer *n, + real *ap, real *x, integer *incx); + +/* Subroutine */ int strmm_(char *side, char *uplo, char *transa, char *diag, + integer *m, integer *n, real *alpha, real *a, integer *lda, real *b, + integer *ldb); + +/* Subroutine */ int strmv_(char *uplo, char *trans, char *diag, integer *n, + real *a, integer *lda, real *x, integer *incx); + +/* Subroutine */ int strsm_(char *side, char *uplo, char *transa, char *diag, + integer *m, integer *n, real *alpha, real *a, integer *lda, real *b, + integer *ldb); + +/* Subroutine */ int strsv_(char *uplo, char *trans, char *diag, integer *n, + real *a, integer *lda, real *x, integer *incx); + +/* Subroutine */ int xerbla_(char *srname, integer *info); + +/* Subroutine */ int xerbla_array__(char *srname_array__, integer * + srname_len__, integer *info, ftnlen srname_array_len); + +/* Subroutine */ int zaxpy_(integer *n, doublecomplex *za, doublecomplex *zx, + integer *incx, doublecomplex *zy, integer *incy); + +/* Subroutine */ int zcopy_(integer *n, doublecomplex *zx, integer *incx, + doublecomplex *zy, integer *incy); + +/* Double Complex */ VOID zdotc_(doublecomplex * ret_val, integer *n, + doublecomplex *zx, integer *incx, doublecomplex *zy, integer *incy); + +/* Double Complex */ VOID zdotu_(doublecomplex * ret_val, integer *n, + doublecomplex *zx, integer *incx, doublecomplex *zy, integer *incy); + +/* Subroutine */ int zdrot_(integer *n, doublecomplex *cx, integer *incx, + doublecomplex *cy, integer *incy, doublereal *c__, doublereal *s); + +/* Subroutine */ int zdscal_(integer *n, doublereal *da, doublecomplex *zx, + integer *incx); + +/* Subroutine */ int zgbmv_(char *trans, integer *m, integer *n, integer *kl, + integer *ku, doublecomplex *alpha, doublecomplex *a, integer *lda, + doublecomplex *x, integer *incx, doublecomplex *beta, doublecomplex * + y, integer *incy); + +/* Subroutine */ int zgemm_(char *transa, char *transb, integer *m, integer * + n, integer *k, doublecomplex *alpha, doublecomplex *a, integer *lda, + doublecomplex *b, integer *ldb, doublecomplex *beta, doublecomplex * + c__, integer *ldc); + +/* Subroutine */ int zgemv_(char *trans, integer *m, integer *n, + doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex * + x, integer *incx, doublecomplex *beta, doublecomplex *y, integer * + incy); + +/* Subroutine */ int zgerc_(integer *m, integer *n, doublecomplex *alpha, + doublecomplex *x, integer *incx, doublecomplex *y, integer *incy, + doublecomplex *a, integer *lda); + +/* Subroutine */ int zgeru_(integer *m, integer *n, doublecomplex *alpha, + doublecomplex *x, integer *incx, doublecomplex *y, integer *incy, + doublecomplex *a, integer *lda); + +/* Subroutine */ int zhbmv_(char *uplo, integer *n, integer *k, doublecomplex + *alpha, doublecomplex *a, integer *lda, doublecomplex *x, integer * + incx, doublecomplex *beta, doublecomplex *y, integer *incy); + +/* Subroutine */ int zhemm_(char *side, char *uplo, integer *m, integer *n, + doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex * + b, integer *ldb, doublecomplex *beta, doublecomplex *c__, integer * + ldc); + +/* Subroutine */ int zhemv_(char *uplo, integer *n, doublecomplex *alpha, + doublecomplex *a, integer *lda, doublecomplex *x, integer *incx, + doublecomplex *beta, doublecomplex *y, integer *incy); + +/* Subroutine */ int zher_(char *uplo, integer *n, doublereal *alpha, + doublecomplex *x, integer *incx, doublecomplex *a, integer *lda); + +/* Subroutine */ int zher2_(char *uplo, integer *n, doublecomplex *alpha, + doublecomplex *x, integer *incx, doublecomplex *y, integer *incy, + doublecomplex *a, integer *lda); + +/* Subroutine */ int zher2k_(char *uplo, char *trans, integer *n, integer *k, + doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex * + b, integer *ldb, doublereal *beta, doublecomplex *c__, integer *ldc); + +/* Subroutine */ int zherk_(char *uplo, char *trans, integer *n, integer *k, + doublereal *alpha, doublecomplex *a, integer *lda, doublereal *beta, + doublecomplex *c__, integer *ldc); + +/* Subroutine */ int zhpmv_(char *uplo, integer *n, doublecomplex *alpha, + doublecomplex *ap, doublecomplex *x, integer *incx, doublecomplex * + beta, doublecomplex *y, integer *incy); + +/* Subroutine */ int zhpr_(char *uplo, integer *n, doublereal *alpha, + doublecomplex *x, integer *incx, doublecomplex *ap); + +/* Subroutine */ int zhpr2_(char *uplo, integer *n, doublecomplex *alpha, + doublecomplex *x, integer *incx, doublecomplex *y, integer *incy, + doublecomplex *ap); + +/* Subroutine */ int zrotg_(doublecomplex *ca, doublecomplex *cb, doublereal * + c__, doublecomplex *s); + +/* Subroutine */ int zscal_(integer *n, doublecomplex *za, doublecomplex *zx, + integer *incx); + +/* Subroutine */ int zswap_(integer *n, doublecomplex *zx, integer *incx, + doublecomplex *zy, integer *incy); + +/* Subroutine */ int zsymm_(char *side, char *uplo, integer *m, integer *n, + doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex * + b, integer *ldb, doublecomplex *beta, doublecomplex *c__, integer * + ldc); + +/* Subroutine */ int zsyr2k_(char *uplo, char *trans, integer *n, integer *k, + doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex * + b, integer *ldb, doublecomplex *beta, doublecomplex *c__, integer * + ldc); + +/* Subroutine */ int zsyrk_(char *uplo, char *trans, integer *n, integer *k, + doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex * + beta, doublecomplex *c__, integer *ldc); + +/* Subroutine */ int ztbmv_(char *uplo, char *trans, char *diag, integer *n, + integer *k, doublecomplex *a, integer *lda, doublecomplex *x, integer + *incx); + +/* Subroutine */ int ztbsv_(char *uplo, char *trans, char *diag, integer *n, + integer *k, doublecomplex *a, integer *lda, doublecomplex *x, integer + *incx); + +/* Subroutine */ int ztpmv_(char *uplo, char *trans, char *diag, integer *n, + doublecomplex *ap, doublecomplex *x, integer *incx); + +/* Subroutine */ int ztpsv_(char *uplo, char *trans, char *diag, integer *n, + doublecomplex *ap, doublecomplex *x, integer *incx); + +/* Subroutine */ int ztrmm_(char *side, char *uplo, char *transa, char *diag, + integer *m, integer *n, doublecomplex *alpha, doublecomplex *a, + integer *lda, doublecomplex *b, integer *ldb); + +/* Subroutine */ int ztrmv_(char *uplo, char *trans, char *diag, integer *n, + doublecomplex *a, integer *lda, doublecomplex *x, integer *incx); + +/* Subroutine */ int ztrsm_(char *side, char *uplo, char *transa, char *diag, + integer *m, integer *n, doublecomplex *alpha, doublecomplex *a, + integer *lda, doublecomplex *b, integer *ldb); + +/* Subroutine */ int ztrsv_(char *uplo, char *trans, char *diag, integer *n, + doublecomplex *a, integer *lda, doublecomplex *x, integer *incx); + +/* Subroutine */ int cbdsqr_(char *uplo, integer *n, integer *ncvt, integer * + nru, integer *ncc, real *d__, real *e, complex *vt, integer *ldvt, + complex *u, integer *ldu, complex *c__, integer *ldc, real *rwork, + integer *info); + +/* Subroutine */ int cgbbrd_(char *vect, integer *m, integer *n, integer *ncc, + integer *kl, integer *ku, complex *ab, integer *ldab, real *d__, + real *e, complex *q, integer *ldq, complex *pt, integer *ldpt, + complex *c__, integer *ldc, complex *work, real *rwork, integer *info); + +/* Subroutine */ int cgbcon_(char *norm, integer *n, integer *kl, integer *ku, + complex *ab, integer *ldab, integer *ipiv, real *anorm, real *rcond, + complex *work, real *rwork, integer *info); + +/* Subroutine */ int cgbequ_(integer *m, integer *n, integer *kl, integer *ku, + complex *ab, integer *ldab, real *r__, real *c__, real *rowcnd, real + *colcnd, real *amax, integer *info); + +/* Subroutine */ int cgbequb_(integer *m, integer *n, integer *kl, integer * + ku, complex *ab, integer *ldab, real *r__, real *c__, real *rowcnd, + real *colcnd, real *amax, integer *info); + +/* Subroutine */ int cgbrfs_(char *trans, integer *n, integer *kl, integer * + ku, integer *nrhs, complex *ab, integer *ldab, complex *afb, integer * + ldafb, integer *ipiv, complex *b, integer *ldb, complex *x, integer * + ldx, real *ferr, real *berr, complex *work, real *rwork, integer * + info); + +/* Subroutine */ int cgbrfsx_(char *trans, char *equed, integer *n, integer * + kl, integer *ku, integer *nrhs, complex *ab, integer *ldab, complex * + afb, integer *ldafb, integer *ipiv, real *r__, real *c__, complex *b, + integer *ldb, complex *x, integer *ldx, real *rcond, real *berr, + integer *n_err_bnds__, real *err_bnds_norm__, real *err_bnds_comp__, + integer *nparams, real *params, complex *work, real *rwork, integer * + info); + +/* Subroutine */ int cgbsv_(integer *n, integer *kl, integer *ku, integer * + nrhs, complex *ab, integer *ldab, integer *ipiv, complex *b, integer * + ldb, integer *info); + +/* Subroutine */ int cgbsvx_(char *fact, char *trans, integer *n, integer *kl, + integer *ku, integer *nrhs, complex *ab, integer *ldab, complex *afb, + integer *ldafb, integer *ipiv, char *equed, real *r__, real *c__, + complex *b, integer *ldb, complex *x, integer *ldx, real *rcond, real + *ferr, real *berr, complex *work, real *rwork, integer *info); + +/* Subroutine */ int cgbsvxx_(char *fact, char *trans, integer *n, integer * + kl, integer *ku, integer *nrhs, complex *ab, integer *ldab, complex * + afb, integer *ldafb, integer *ipiv, char *equed, real *r__, real *c__, + complex *b, integer *ldb, complex *x, integer *ldx, real *rcond, + real *rpvgrw, real *berr, integer *n_err_bnds__, real * + err_bnds_norm__, real *err_bnds_comp__, integer *nparams, real * + params, complex *work, real *rwork, integer *info); + +/* Subroutine */ int cgbtf2_(integer *m, integer *n, integer *kl, integer *ku, + complex *ab, integer *ldab, integer *ipiv, integer *info); + +/* Subroutine */ int cgbtrf_(integer *m, integer *n, integer *kl, integer *ku, + complex *ab, integer *ldab, integer *ipiv, integer *info); + +/* Subroutine */ int cgbtrs_(char *trans, integer *n, integer *kl, integer * + ku, integer *nrhs, complex *ab, integer *ldab, integer *ipiv, complex + *b, integer *ldb, integer *info); + +/* Subroutine */ int cgebak_(char *job, char *side, integer *n, integer *ilo, + integer *ihi, real *scale, integer *m, complex *v, integer *ldv, + integer *info); + +/* Subroutine */ int cgebal_(char *job, integer *n, complex *a, integer *lda, + integer *ilo, integer *ihi, real *scale, integer *info); + +/* Subroutine */ int cgebd2_(integer *m, integer *n, complex *a, integer *lda, + real *d__, real *e, complex *tauq, complex *taup, complex *work, + integer *info); + +/* Subroutine */ int cgebrd_(integer *m, integer *n, complex *a, integer *lda, + real *d__, real *e, complex *tauq, complex *taup, complex *work, + integer *lwork, integer *info); + +/* Subroutine */ int cgecon_(char *norm, integer *n, complex *a, integer *lda, + real *anorm, real *rcond, complex *work, real *rwork, integer *info); + +/* Subroutine */ int cgeequ_(integer *m, integer *n, complex *a, integer *lda, + real *r__, real *c__, real *rowcnd, real *colcnd, real *amax, + integer *info); + +/* Subroutine */ int cgeequb_(integer *m, integer *n, complex *a, integer * + lda, real *r__, real *c__, real *rowcnd, real *colcnd, real *amax, + integer *info); + +/* Subroutine */ int cgees_(char *jobvs, char *sort, L_fp select, integer *n, + complex *a, integer *lda, integer *sdim, complex *w, complex *vs, + integer *ldvs, complex *work, integer *lwork, real *rwork, logical * + bwork, integer *info); + +/* Subroutine */ int cgeesx_(char *jobvs, char *sort, L_fp select, char * + sense, integer *n, complex *a, integer *lda, integer *sdim, complex * + w, complex *vs, integer *ldvs, real *rconde, real *rcondv, complex * + work, integer *lwork, real *rwork, logical *bwork, integer *info); + +/* Subroutine */ int cgeev_(char *jobvl, char *jobvr, integer *n, complex *a, + integer *lda, complex *w, complex *vl, integer *ldvl, complex *vr, + integer *ldvr, complex *work, integer *lwork, real *rwork, integer * + info); + +/* Subroutine */ int cgeevx_(char *balanc, char *jobvl, char *jobvr, char * + sense, integer *n, complex *a, integer *lda, complex *w, complex *vl, + integer *ldvl, complex *vr, integer *ldvr, integer *ilo, integer *ihi, + real *scale, real *abnrm, real *rconde, real *rcondv, complex *work, + integer *lwork, real *rwork, integer *info); + +/* Subroutine */ int cgegs_(char *jobvsl, char *jobvsr, integer *n, complex * + a, integer *lda, complex *b, integer *ldb, complex *alpha, complex * + beta, complex *vsl, integer *ldvsl, complex *vsr, integer *ldvsr, + complex *work, integer *lwork, real *rwork, integer *info); + +/* Subroutine */ int cgegv_(char *jobvl, char *jobvr, integer *n, complex *a, + integer *lda, complex *b, integer *ldb, complex *alpha, complex *beta, + complex *vl, integer *ldvl, complex *vr, integer *ldvr, complex * + work, integer *lwork, real *rwork, integer *info); + +/* Subroutine */ int cgehd2_(integer *n, integer *ilo, integer *ihi, complex * + a, integer *lda, complex *tau, complex *work, integer *info); + +/* Subroutine */ int cgehrd_(integer *n, integer *ilo, integer *ihi, complex * + a, integer *lda, complex *tau, complex *work, integer *lwork, integer + *info); + +/* Subroutine */ int cgelq2_(integer *m, integer *n, complex *a, integer *lda, + complex *tau, complex *work, integer *info); + +/* Subroutine */ int cgelqf_(integer *m, integer *n, complex *a, integer *lda, + complex *tau, complex *work, integer *lwork, integer *info); + +/* Subroutine */ int cgels_(char *trans, integer *m, integer *n, integer * + nrhs, complex *a, integer *lda, complex *b, integer *ldb, complex * + work, integer *lwork, integer *info); + +/* Subroutine */ int cgelsd_(integer *m, integer *n, integer *nrhs, complex * + a, integer *lda, complex *b, integer *ldb, real *s, real *rcond, + integer *rank, complex *work, integer *lwork, real *rwork, integer * + iwork, integer *info); + +/* Subroutine */ int cgelss_(integer *m, integer *n, integer *nrhs, complex * + a, integer *lda, complex *b, integer *ldb, real *s, real *rcond, + integer *rank, complex *work, integer *lwork, real *rwork, integer * + info); + +/* Subroutine */ int cgelsx_(integer *m, integer *n, integer *nrhs, complex * + a, integer *lda, complex *b, integer *ldb, integer *jpvt, real *rcond, + integer *rank, complex *work, real *rwork, integer *info); + +/* Subroutine */ int cgelsy_(integer *m, integer *n, integer *nrhs, complex * + a, integer *lda, complex *b, integer *ldb, integer *jpvt, real *rcond, + integer *rank, complex *work, integer *lwork, real *rwork, integer * + info); + +/* Subroutine */ int cgeql2_(integer *m, integer *n, complex *a, integer *lda, + complex *tau, complex *work, integer *info); + +/* Subroutine */ int cgeqlf_(integer *m, integer *n, complex *a, integer *lda, + complex *tau, complex *work, integer *lwork, integer *info); + +/* Subroutine */ int cgeqp3_(integer *m, integer *n, complex *a, integer *lda, + integer *jpvt, complex *tau, complex *work, integer *lwork, real * + rwork, integer *info); + +/* Subroutine */ int cgeqpf_(integer *m, integer *n, complex *a, integer *lda, + integer *jpvt, complex *tau, complex *work, real *rwork, integer * + info); + +/* Subroutine */ int cgeqr2_(integer *m, integer *n, complex *a, integer *lda, + complex *tau, complex *work, integer *info); + +/* Subroutine */ int cgeqrf_(integer *m, integer *n, complex *a, integer *lda, + complex *tau, complex *work, integer *lwork, integer *info); + +/* Subroutine */ int cgerfs_(char *trans, integer *n, integer *nrhs, complex * + a, integer *lda, complex *af, integer *ldaf, integer *ipiv, complex * + b, integer *ldb, complex *x, integer *ldx, real *ferr, real *berr, + complex *work, real *rwork, integer *info); + +/* Subroutine */ int cgerfsx_(char *trans, char *equed, integer *n, integer * + nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer * + ipiv, real *r__, real *c__, complex *b, integer *ldb, complex *x, + integer *ldx, real *rcond, real *berr, integer *n_err_bnds__, real * + err_bnds_norm__, real *err_bnds_comp__, integer *nparams, real * + params, complex *work, real *rwork, integer *info); + +/* Subroutine */ int cgerq2_(integer *m, integer *n, complex *a, integer *lda, + complex *tau, complex *work, integer *info); + +/* Subroutine */ int cgerqf_(integer *m, integer *n, complex *a, integer *lda, + complex *tau, complex *work, integer *lwork, integer *info); + +/* Subroutine */ int cgesc2_(integer *n, complex *a, integer *lda, complex * + rhs, integer *ipiv, integer *jpiv, real *scale); + +/* Subroutine */ int cgesdd_(char *jobz, integer *m, integer *n, complex *a, + integer *lda, real *s, complex *u, integer *ldu, complex *vt, integer + *ldvt, complex *work, integer *lwork, real *rwork, integer *iwork, + integer *info); + +/* Subroutine */ int cgesv_(integer *n, integer *nrhs, complex *a, integer * + lda, integer *ipiv, complex *b, integer *ldb, integer *info); + +/* Subroutine */ int cgesvd_(char *jobu, char *jobvt, integer *m, integer *n, + complex *a, integer *lda, real *s, complex *u, integer *ldu, complex * + vt, integer *ldvt, complex *work, integer *lwork, real *rwork, + integer *info); + +/* Subroutine */ int cgesvx_(char *fact, char *trans, integer *n, integer * + nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer * + ipiv, char *equed, real *r__, real *c__, complex *b, integer *ldb, + complex *x, integer *ldx, real *rcond, real *ferr, real *berr, + complex *work, real *rwork, integer *info); + +/* Subroutine */ int cgesvxx_(char *fact, char *trans, integer *n, integer * + nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer * + ipiv, char *equed, real *r__, real *c__, complex *b, integer *ldb, + complex *x, integer *ldx, real *rcond, real *rpvgrw, real *berr, + integer *n_err_bnds__, real *err_bnds_norm__, real *err_bnds_comp__, + integer *nparams, real *params, complex *work, real *rwork, integer * + info); + +/* Subroutine */ int cgetc2_(integer *n, complex *a, integer *lda, integer * + ipiv, integer *jpiv, integer *info); + +/* Subroutine */ int cgetf2_(integer *m, integer *n, complex *a, integer *lda, + integer *ipiv, integer *info); + +/* Subroutine */ int cgetrf_(integer *m, integer *n, complex *a, integer *lda, + integer *ipiv, integer *info); + +/* Subroutine */ int cgetri_(integer *n, complex *a, integer *lda, integer * + ipiv, complex *work, integer *lwork, integer *info); + +/* Subroutine */ int cgetrs_(char *trans, integer *n, integer *nrhs, complex * + a, integer *lda, integer *ipiv, complex *b, integer *ldb, integer * + info); + +/* Subroutine */ int cggbak_(char *job, char *side, integer *n, integer *ilo, + integer *ihi, real *lscale, real *rscale, integer *m, complex *v, + integer *ldv, integer *info); + +/* Subroutine */ int cggbal_(char *job, integer *n, complex *a, integer *lda, + complex *b, integer *ldb, integer *ilo, integer *ihi, real *lscale, + real *rscale, real *work, integer *info); + +/* Subroutine */ int cgges_(char *jobvsl, char *jobvsr, char *sort, L_fp + selctg, integer *n, complex *a, integer *lda, complex *b, integer * + ldb, integer *sdim, complex *alpha, complex *beta, complex *vsl, + integer *ldvsl, complex *vsr, integer *ldvsr, complex *work, integer * + lwork, real *rwork, logical *bwork, integer *info); + +/* Subroutine */ int cggesx_(char *jobvsl, char *jobvsr, char *sort, L_fp + selctg, char *sense, integer *n, complex *a, integer *lda, complex *b, + integer *ldb, integer *sdim, complex *alpha, complex *beta, complex * + vsl, integer *ldvsl, complex *vsr, integer *ldvsr, real *rconde, real + *rcondv, complex *work, integer *lwork, real *rwork, integer *iwork, + integer *liwork, logical *bwork, integer *info); + +/* Subroutine */ int cggev_(char *jobvl, char *jobvr, integer *n, complex *a, + integer *lda, complex *b, integer *ldb, complex *alpha, complex *beta, + complex *vl, integer *ldvl, complex *vr, integer *ldvr, complex * + work, integer *lwork, real *rwork, integer *info); + +/* Subroutine */ int cggevx_(char *balanc, char *jobvl, char *jobvr, char * + sense, integer *n, complex *a, integer *lda, complex *b, integer *ldb, + complex *alpha, complex *beta, complex *vl, integer *ldvl, complex * + vr, integer *ldvr, integer *ilo, integer *ihi, real *lscale, real * + rscale, real *abnrm, real *bbnrm, real *rconde, real *rcondv, complex + *work, integer *lwork, real *rwork, integer *iwork, logical *bwork, + integer *info); + +/* Subroutine */ int cggglm_(integer *n, integer *m, integer *p, complex *a, + integer *lda, complex *b, integer *ldb, complex *d__, complex *x, + complex *y, complex *work, integer *lwork, integer *info); + +/* Subroutine */ int cgghrd_(char *compq, char *compz, integer *n, integer * + ilo, integer *ihi, complex *a, integer *lda, complex *b, integer *ldb, + complex *q, integer *ldq, complex *z__, integer *ldz, integer *info); + +/* Subroutine */ int cgglse_(integer *m, integer *n, integer *p, complex *a, + integer *lda, complex *b, integer *ldb, complex *c__, complex *d__, + complex *x, complex *work, integer *lwork, integer *info); + +/* Subroutine */ int cggqrf_(integer *n, integer *m, integer *p, complex *a, + integer *lda, complex *taua, complex *b, integer *ldb, complex *taub, + complex *work, integer *lwork, integer *info); + +/* Subroutine */ int cggrqf_(integer *m, integer *p, integer *n, complex *a, + integer *lda, complex *taua, complex *b, integer *ldb, complex *taub, + complex *work, integer *lwork, integer *info); + +/* Subroutine */ int cggsvd_(char *jobu, char *jobv, char *jobq, integer *m, + integer *n, integer *p, integer *k, integer *l, complex *a, integer * + lda, complex *b, integer *ldb, real *alpha, real *beta, complex *u, + integer *ldu, complex *v, integer *ldv, complex *q, integer *ldq, + complex *work, real *rwork, integer *iwork, integer *info); + +/* Subroutine */ int cggsvp_(char *jobu, char *jobv, char *jobq, integer *m, + integer *p, integer *n, complex *a, integer *lda, complex *b, integer + *ldb, real *tola, real *tolb, integer *k, integer *l, complex *u, + integer *ldu, complex *v, integer *ldv, complex *q, integer *ldq, + integer *iwork, real *rwork, complex *tau, complex *work, integer * + info); + +/* Subroutine */ int cgtcon_(char *norm, integer *n, complex *dl, complex * + d__, complex *du, complex *du2, integer *ipiv, real *anorm, real * + rcond, complex *work, integer *info); + +/* Subroutine */ int cgtrfs_(char *trans, integer *n, integer *nrhs, complex * + dl, complex *d__, complex *du, complex *dlf, complex *df, complex * + duf, complex *du2, integer *ipiv, complex *b, integer *ldb, complex * + x, integer *ldx, real *ferr, real *berr, complex *work, real *rwork, + integer *info); + +/* Subroutine */ int cgtsv_(integer *n, integer *nrhs, complex *dl, complex * + d__, complex *du, complex *b, integer *ldb, integer *info); + +/* Subroutine */ int cgtsvx_(char *fact, char *trans, integer *n, integer * + nrhs, complex *dl, complex *d__, complex *du, complex *dlf, complex * + df, complex *duf, complex *du2, integer *ipiv, complex *b, integer * + ldb, complex *x, integer *ldx, real *rcond, real *ferr, real *berr, + complex *work, real *rwork, integer *info); + +/* Subroutine */ int cgttrf_(integer *n, complex *dl, complex *d__, complex * + du, complex *du2, integer *ipiv, integer *info); + +/* Subroutine */ int cgttrs_(char *trans, integer *n, integer *nrhs, complex * + dl, complex *d__, complex *du, complex *du2, integer *ipiv, complex * + b, integer *ldb, integer *info); + +/* Subroutine */ int cgtts2_(integer *itrans, integer *n, integer *nrhs, + complex *dl, complex *d__, complex *du, complex *du2, integer *ipiv, + complex *b, integer *ldb); + +/* Subroutine */ int chbev_(char *jobz, char *uplo, integer *n, integer *kd, + complex *ab, integer *ldab, real *w, complex *z__, integer *ldz, + complex *work, real *rwork, integer *info); + +/* Subroutine */ int chbevd_(char *jobz, char *uplo, integer *n, integer *kd, + complex *ab, integer *ldab, real *w, complex *z__, integer *ldz, + complex *work, integer *lwork, real *rwork, integer *lrwork, integer * + iwork, integer *liwork, integer *info); + +/* Subroutine */ int chbevx_(char *jobz, char *range, char *uplo, integer *n, + integer *kd, complex *ab, integer *ldab, complex *q, integer *ldq, + real *vl, real *vu, integer *il, integer *iu, real *abstol, integer * + m, real *w, complex *z__, integer *ldz, complex *work, real *rwork, + integer *iwork, integer *ifail, integer *info); + +/* Subroutine */ int chbgst_(char *vect, char *uplo, integer *n, integer *ka, + integer *kb, complex *ab, integer *ldab, complex *bb, integer *ldbb, + complex *x, integer *ldx, complex *work, real *rwork, integer *info); + +/* Subroutine */ int chbgv_(char *jobz, char *uplo, integer *n, integer *ka, + integer *kb, complex *ab, integer *ldab, complex *bb, integer *ldbb, + real *w, complex *z__, integer *ldz, complex *work, real *rwork, + integer *info); + +/* Subroutine */ int chbgvd_(char *jobz, char *uplo, integer *n, integer *ka, + integer *kb, complex *ab, integer *ldab, complex *bb, integer *ldbb, + real *w, complex *z__, integer *ldz, complex *work, integer *lwork, + real *rwork, integer *lrwork, integer *iwork, integer *liwork, + integer *info); + +/* Subroutine */ int chbgvx_(char *jobz, char *range, char *uplo, integer *n, + integer *ka, integer *kb, complex *ab, integer *ldab, complex *bb, + integer *ldbb, complex *q, integer *ldq, real *vl, real *vu, integer * + il, integer *iu, real *abstol, integer *m, real *w, complex *z__, + integer *ldz, complex *work, real *rwork, integer *iwork, integer * + ifail, integer *info); + +/* Subroutine */ int chbtrd_(char *vect, char *uplo, integer *n, integer *kd, + complex *ab, integer *ldab, real *d__, real *e, complex *q, integer * + ldq, complex *work, integer *info); + +/* Subroutine */ int checon_(char *uplo, integer *n, complex *a, integer *lda, + integer *ipiv, real *anorm, real *rcond, complex *work, integer * + info); + +/* Subroutine */ int cheequb_(char *uplo, integer *n, complex *a, integer * + lda, real *s, real *scond, real *amax, complex *work, integer *info); + +/* Subroutine */ int cheev_(char *jobz, char *uplo, integer *n, complex *a, + integer *lda, real *w, complex *work, integer *lwork, real *rwork, + integer *info); + +/* Subroutine */ int cheevd_(char *jobz, char *uplo, integer *n, complex *a, + integer *lda, real *w, complex *work, integer *lwork, real *rwork, + integer *lrwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int cheevr_(char *jobz, char *range, char *uplo, integer *n, + complex *a, integer *lda, real *vl, real *vu, integer *il, integer * + iu, real *abstol, integer *m, real *w, complex *z__, integer *ldz, + integer *isuppz, complex *work, integer *lwork, real *rwork, integer * + lrwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int cheevx_(char *jobz, char *range, char *uplo, integer *n, + complex *a, integer *lda, real *vl, real *vu, integer *il, integer * + iu, real *abstol, integer *m, real *w, complex *z__, integer *ldz, + complex *work, integer *lwork, real *rwork, integer *iwork, integer * + ifail, integer *info); + +/* Subroutine */ int chegs2_(integer *itype, char *uplo, integer *n, complex * + a, integer *lda, complex *b, integer *ldb, integer *info); + +/* Subroutine */ int chegst_(integer *itype, char *uplo, integer *n, complex * + a, integer *lda, complex *b, integer *ldb, integer *info); + +/* Subroutine */ int chegv_(integer *itype, char *jobz, char *uplo, integer * + n, complex *a, integer *lda, complex *b, integer *ldb, real *w, + complex *work, integer *lwork, real *rwork, integer *info); + +/* Subroutine */ int chegvd_(integer *itype, char *jobz, char *uplo, integer * + n, complex *a, integer *lda, complex *b, integer *ldb, real *w, + complex *work, integer *lwork, real *rwork, integer *lrwork, integer * + iwork, integer *liwork, integer *info); + +/* Subroutine */ int chegvx_(integer *itype, char *jobz, char *range, char * + uplo, integer *n, complex *a, integer *lda, complex *b, integer *ldb, + real *vl, real *vu, integer *il, integer *iu, real *abstol, integer * + m, real *w, complex *z__, integer *ldz, complex *work, integer *lwork, + real *rwork, integer *iwork, integer *ifail, integer *info); + +/* Subroutine */ int cherfs_(char *uplo, integer *n, integer *nrhs, complex * + a, integer *lda, complex *af, integer *ldaf, integer *ipiv, complex * + b, integer *ldb, complex *x, integer *ldx, real *ferr, real *berr, + complex *work, real *rwork, integer *info); + +/* Subroutine */ int cherfsx_(char *uplo, char *equed, integer *n, integer * + nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer * + ipiv, real *s, complex *b, integer *ldb, complex *x, integer *ldx, + real *rcond, real *berr, integer *n_err_bnds__, real *err_bnds_norm__, + real *err_bnds_comp__, integer *nparams, real *params, complex *work, + real *rwork, integer *info); + +/* Subroutine */ int chesv_(char *uplo, integer *n, integer *nrhs, complex *a, + integer *lda, integer *ipiv, complex *b, integer *ldb, complex *work, + integer *lwork, integer *info); + +/* Subroutine */ int chesvx_(char *fact, char *uplo, integer *n, integer * + nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer * + ipiv, complex *b, integer *ldb, complex *x, integer *ldx, real *rcond, + real *ferr, real *berr, complex *work, integer *lwork, real *rwork, + integer *info); + +/* Subroutine */ int chesvxx_(char *fact, char *uplo, integer *n, integer * + nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer * + ipiv, char *equed, real *s, complex *b, integer *ldb, complex *x, + integer *ldx, real *rcond, real *rpvgrw, real *berr, integer * + n_err_bnds__, real *err_bnds_norm__, real *err_bnds_comp__, integer * + nparams, real *params, complex *work, real *rwork, integer *info); + +/* Subroutine */ int chetd2_(char *uplo, integer *n, complex *a, integer *lda, + real *d__, real *e, complex *tau, integer *info); + +/* Subroutine */ int chetf2_(char *uplo, integer *n, complex *a, integer *lda, + integer *ipiv, integer *info); + +/* Subroutine */ int chetrd_(char *uplo, integer *n, complex *a, integer *lda, + real *d__, real *e, complex *tau, complex *work, integer *lwork, + integer *info); + +/* Subroutine */ int chetrf_(char *uplo, integer *n, complex *a, integer *lda, + integer *ipiv, complex *work, integer *lwork, integer *info); + +/* Subroutine */ int chetri_(char *uplo, integer *n, complex *a, integer *lda, + integer *ipiv, complex *work, integer *info); + +/* Subroutine */ int chetrs_(char *uplo, integer *n, integer *nrhs, complex * + a, integer *lda, integer *ipiv, complex *b, integer *ldb, integer * + info); + +/* Subroutine */ int chfrk_(char *transr, char *uplo, char *trans, integer *n, + integer *k, real *alpha, complex *a, integer *lda, real *beta, + complex *c__); + +/* Subroutine */ int chgeqz_(char *job, char *compq, char *compz, integer *n, + integer *ilo, integer *ihi, complex *h__, integer *ldh, complex *t, + integer *ldt, complex *alpha, complex *beta, complex *q, integer *ldq, + complex *z__, integer *ldz, complex *work, integer *lwork, real * + rwork, integer *info); + +/* Character */ VOID chla_transtype__(char *ret_val, ftnlen ret_val_len, + integer *trans); + +/* Subroutine */ int chpcon_(char *uplo, integer *n, complex *ap, integer * + ipiv, real *anorm, real *rcond, complex *work, integer *info); + +/* Subroutine */ int chpev_(char *jobz, char *uplo, integer *n, complex *ap, + real *w, complex *z__, integer *ldz, complex *work, real *rwork, + integer *info); + +/* Subroutine */ int chpevd_(char *jobz, char *uplo, integer *n, complex *ap, + real *w, complex *z__, integer *ldz, complex *work, integer *lwork, + real *rwork, integer *lrwork, integer *iwork, integer *liwork, + integer *info); + +/* Subroutine */ int chpevx_(char *jobz, char *range, char *uplo, integer *n, + complex *ap, real *vl, real *vu, integer *il, integer *iu, real * + abstol, integer *m, real *w, complex *z__, integer *ldz, complex * + work, real *rwork, integer *iwork, integer *ifail, integer *info); + +/* Subroutine */ int chpgst_(integer *itype, char *uplo, integer *n, complex * + ap, complex *bp, integer *info); + +/* Subroutine */ int chpgv_(integer *itype, char *jobz, char *uplo, integer * + n, complex *ap, complex *bp, real *w, complex *z__, integer *ldz, + complex *work, real *rwork, integer *info); + +/* Subroutine */ int chpgvd_(integer *itype, char *jobz, char *uplo, integer * + n, complex *ap, complex *bp, real *w, complex *z__, integer *ldz, + complex *work, integer *lwork, real *rwork, integer *lrwork, integer * + iwork, integer *liwork, integer *info); + +/* Subroutine */ int chpgvx_(integer *itype, char *jobz, char *range, char * + uplo, integer *n, complex *ap, complex *bp, real *vl, real *vu, + integer *il, integer *iu, real *abstol, integer *m, real *w, complex * + z__, integer *ldz, complex *work, real *rwork, integer *iwork, + integer *ifail, integer *info); + +/* Subroutine */ int chprfs_(char *uplo, integer *n, integer *nrhs, complex * + ap, complex *afp, integer *ipiv, complex *b, integer *ldb, complex *x, + integer *ldx, real *ferr, real *berr, complex *work, real *rwork, + integer *info); + +/* Subroutine */ int chpsv_(char *uplo, integer *n, integer *nrhs, complex * + ap, integer *ipiv, complex *b, integer *ldb, integer *info); + +/* Subroutine */ int chpsvx_(char *fact, char *uplo, integer *n, integer * + nrhs, complex *ap, complex *afp, integer *ipiv, complex *b, integer * + ldb, complex *x, integer *ldx, real *rcond, real *ferr, real *berr, + complex *work, real *rwork, integer *info); + +/* Subroutine */ int chptrd_(char *uplo, integer *n, complex *ap, real *d__, + real *e, complex *tau, integer *info); + +/* Subroutine */ int chptrf_(char *uplo, integer *n, complex *ap, integer * + ipiv, integer *info); + +/* Subroutine */ int chptri_(char *uplo, integer *n, complex *ap, integer * + ipiv, complex *work, integer *info); + +/* Subroutine */ int chptrs_(char *uplo, integer *n, integer *nrhs, complex * + ap, integer *ipiv, complex *b, integer *ldb, integer *info); + +/* Subroutine */ int chsein_(char *side, char *eigsrc, char *initv, logical * + select, integer *n, complex *h__, integer *ldh, complex *w, complex * + vl, integer *ldvl, complex *vr, integer *ldvr, integer *mm, integer * + m, complex *work, real *rwork, integer *ifaill, integer *ifailr, + integer *info); + +/* Subroutine */ int chseqr_(char *job, char *compz, integer *n, integer *ilo, + integer *ihi, complex *h__, integer *ldh, complex *w, complex *z__, + integer *ldz, complex *work, integer *lwork, integer *info); + +/* Subroutine */ int cla_gbamv__(integer *trans, integer *m, integer *n, + integer *kl, integer *ku, real *alpha, complex *ab, integer *ldab, + complex *x, integer *incx, real *beta, real *y, integer *incy); + +doublereal cla_gbrcond_c__(char *trans, integer *n, integer *kl, integer *ku, + complex *ab, integer *ldab, complex *afb, integer *ldafb, integer * + ipiv, real *c__, logical *capply, integer *info, complex *work, real * + rwork, ftnlen trans_len); + +doublereal cla_gbrcond_x__(char *trans, integer *n, integer *kl, integer *ku, + complex *ab, integer *ldab, complex *afb, integer *ldafb, integer * + ipiv, complex *x, integer *info, complex *work, real *rwork, ftnlen + trans_len); + +/* Subroutine */ int cla_gbrfsx_extended__(integer *prec_type__, integer * + trans_type__, integer *n, integer *kl, integer *ku, integer *nrhs, + complex *ab, integer *ldab, complex *afb, integer *ldafb, integer * + ipiv, logical *colequ, real *c__, complex *b, integer *ldb, complex * + y, integer *ldy, real *berr_out__, integer *n_norms__, real *errs_n__, + real *errs_c__, complex *res, real *ayb, complex *dy, complex * + y_tail__, real *rcond, integer *ithresh, real *rthresh, real *dz_ub__, + logical *ignore_cwise__, integer *info); + +doublereal cla_gbrpvgrw__(integer *n, integer *kl, integer *ku, integer * + ncols, complex *ab, integer *ldab, complex *afb, integer *ldafb); + +/* Subroutine */ int cla_geamv__(integer *trans, integer *m, integer *n, real + *alpha, complex *a, integer *lda, complex *x, integer *incx, real * + beta, real *y, integer *incy); + +doublereal cla_gercond_c__(char *trans, integer *n, complex *a, integer *lda, + complex *af, integer *ldaf, integer *ipiv, real *c__, logical *capply, + integer *info, complex *work, real *rwork, ftnlen trans_len); + +doublereal cla_gercond_x__(char *trans, integer *n, complex *a, integer *lda, + complex *af, integer *ldaf, integer *ipiv, complex *x, integer *info, + complex *work, real *rwork, ftnlen trans_len); + +/* Subroutine */ int cla_gerfsx_extended__(integer *prec_type__, integer * + trans_type__, integer *n, integer *nrhs, complex *a, integer *lda, + complex *af, integer *ldaf, integer *ipiv, logical *colequ, real *c__, + complex *b, integer *ldb, complex *y, integer *ldy, real *berr_out__, + integer *n_norms__, real *errs_n__, real *errs_c__, complex *res, + real *ayb, complex *dy, complex *y_tail__, real *rcond, integer * + ithresh, real *rthresh, real *dz_ub__, logical *ignore_cwise__, + integer *info); + +/* Subroutine */ int cla_heamv__(integer *uplo, integer *n, real *alpha, + complex *a, integer *lda, complex *x, integer *incx, real *beta, real + *y, integer *incy); + +doublereal cla_hercond_c__(char *uplo, integer *n, complex *a, integer *lda, + complex *af, integer *ldaf, integer *ipiv, real *c__, logical *capply, + integer *info, complex *work, real *rwork, ftnlen uplo_len); + +doublereal cla_hercond_x__(char *uplo, integer *n, complex *a, integer *lda, + complex *af, integer *ldaf, integer *ipiv, complex *x, integer *info, + complex *work, real *rwork, ftnlen uplo_len); + +/* Subroutine */ int cla_herfsx_extended__(integer *prec_type__, char *uplo, + integer *n, integer *nrhs, complex *a, integer *lda, complex *af, + integer *ldaf, integer *ipiv, logical *colequ, real *c__, complex *b, + integer *ldb, complex *y, integer *ldy, real *berr_out__, integer * + n_norms__, real *errs_n__, real *errs_c__, complex *res, real *ayb, + complex *dy, complex *y_tail__, real *rcond, integer *ithresh, real * + rthresh, real *dz_ub__, logical *ignore_cwise__, integer *info, + ftnlen uplo_len); + +doublereal cla_herpvgrw__(char *uplo, integer *n, integer *info, complex *a, + integer *lda, complex *af, integer *ldaf, integer *ipiv, real *work, + ftnlen uplo_len); + +/* Subroutine */ int cla_lin_berr__(integer *n, integer *nz, integer *nrhs, + complex *res, real *ayb, real *berr); + +doublereal cla_porcond_c__(char *uplo, integer *n, complex *a, integer *lda, + complex *af, integer *ldaf, real *c__, logical *capply, integer *info, + complex *work, real *rwork, ftnlen uplo_len); + +doublereal cla_porcond_x__(char *uplo, integer *n, complex *a, integer *lda, + complex *af, integer *ldaf, complex *x, integer *info, complex *work, + real *rwork, ftnlen uplo_len); + +/* Subroutine */ int cla_porfsx_extended__(integer *prec_type__, char *uplo, + integer *n, integer *nrhs, complex *a, integer *lda, complex *af, + integer *ldaf, logical *colequ, real *c__, complex *b, integer *ldb, + complex *y, integer *ldy, real *berr_out__, integer *n_norms__, real * + errs_n__, real *errs_c__, complex *res, real *ayb, complex *dy, + complex *y_tail__, real *rcond, integer *ithresh, real *rthresh, real + *dz_ub__, logical *ignore_cwise__, integer *info, ftnlen uplo_len); + +doublereal cla_porpvgrw__(char *uplo, integer *ncols, complex *a, integer * + lda, complex *af, integer *ldaf, real *work, ftnlen uplo_len); + +doublereal cla_rpvgrw__(integer *n, integer *ncols, complex *a, integer *lda, + complex *af, integer *ldaf); + +/* Subroutine */ int cla_syamv__(integer *uplo, integer *n, real *alpha, + complex *a, integer *lda, complex *x, integer *incx, real *beta, real + *y, integer *incy); + +doublereal cla_syrcond_c__(char *uplo, integer *n, complex *a, integer *lda, + complex *af, integer *ldaf, integer *ipiv, real *c__, logical *capply, + integer *info, complex *work, real *rwork, ftnlen uplo_len); + +doublereal cla_syrcond_x__(char *uplo, integer *n, complex *a, integer *lda, + complex *af, integer *ldaf, integer *ipiv, complex *x, integer *info, + complex *work, real *rwork, ftnlen uplo_len); + +/* Subroutine */ int cla_syrfsx_extended__(integer *prec_type__, char *uplo, + integer *n, integer *nrhs, complex *a, integer *lda, complex *af, + integer *ldaf, integer *ipiv, logical *colequ, real *c__, complex *b, + integer *ldb, complex *y, integer *ldy, real *berr_out__, integer * + n_norms__, real *errs_n__, real *errs_c__, complex *res, real *ayb, + complex *dy, complex *y_tail__, real *rcond, integer *ithresh, real * + rthresh, real *dz_ub__, logical *ignore_cwise__, integer *info, + ftnlen uplo_len); + +doublereal cla_syrpvgrw__(char *uplo, integer *n, integer *info, complex *a, + integer *lda, complex *af, integer *ldaf, integer *ipiv, real *work, + ftnlen uplo_len); + +/* Subroutine */ int cla_wwaddw__(integer *n, complex *x, complex *y, complex + *w); + +/* Subroutine */ int clabrd_(integer *m, integer *n, integer *nb, complex *a, + integer *lda, real *d__, real *e, complex *tauq, complex *taup, + complex *x, integer *ldx, complex *y, integer *ldy); + +/* Subroutine */ int clacgv_(integer *n, complex *x, integer *incx); + +/* Subroutine */ int clacn2_(integer *n, complex *v, complex *x, real *est, + integer *kase, integer *isave); + +/* Subroutine */ int clacon_(integer *n, complex *v, complex *x, real *est, + integer *kase); + +/* Subroutine */ int clacp2_(char *uplo, integer *m, integer *n, real *a, + integer *lda, complex *b, integer *ldb); + +/* Subroutine */ int clacpy_(char *uplo, integer *m, integer *n, complex *a, + integer *lda, complex *b, integer *ldb); + +/* Subroutine */ int clacrm_(integer *m, integer *n, complex *a, integer *lda, + real *b, integer *ldb, complex *c__, integer *ldc, real *rwork); + +/* Subroutine */ int clacrt_(integer *n, complex *cx, integer *incx, complex * + cy, integer *incy, complex *c__, complex *s); + +/* Complex */ VOID cladiv_(complex * ret_val, complex *x, complex *y); + +/* Subroutine */ int claed0_(integer *qsiz, integer *n, real *d__, real *e, + complex *q, integer *ldq, complex *qstore, integer *ldqs, real *rwork, + integer *iwork, integer *info); + +/* Subroutine */ int claed7_(integer *n, integer *cutpnt, integer *qsiz, + integer *tlvls, integer *curlvl, integer *curpbm, real *d__, complex * + q, integer *ldq, real *rho, integer *indxq, real *qstore, integer * + qptr, integer *prmptr, integer *perm, integer *givptr, integer * + givcol, real *givnum, complex *work, real *rwork, integer *iwork, + integer *info); + +/* Subroutine */ int claed8_(integer *k, integer *n, integer *qsiz, complex * + q, integer *ldq, real *d__, real *rho, integer *cutpnt, real *z__, + real *dlamda, complex *q2, integer *ldq2, real *w, integer *indxp, + integer *indx, integer *indxq, integer *perm, integer *givptr, + integer *givcol, real *givnum, integer *info); + +/* Subroutine */ int claein_(logical *rightv, logical *noinit, integer *n, + complex *h__, integer *ldh, complex *w, complex *v, complex *b, + integer *ldb, real *rwork, real *eps3, real *smlnum, integer *info); + +/* Subroutine */ int claesy_(complex *a, complex *b, complex *c__, complex * + rt1, complex *rt2, complex *evscal, complex *cs1, complex *sn1); + +/* Subroutine */ int claev2_(complex *a, complex *b, complex *c__, real *rt1, + real *rt2, real *cs1, complex *sn1); + +/* Subroutine */ int clag2z_(integer *m, integer *n, complex *sa, integer * + ldsa, doublecomplex *a, integer *lda, integer *info); + +/* Subroutine */ int clags2_(logical *upper, real *a1, complex *a2, real *a3, + real *b1, complex *b2, real *b3, real *csu, complex *snu, real *csv, + complex *snv, real *csq, complex *snq); + +/* Subroutine */ int clagtm_(char *trans, integer *n, integer *nrhs, real * + alpha, complex *dl, complex *d__, complex *du, complex *x, integer * + ldx, real *beta, complex *b, integer *ldb); + +/* Subroutine */ int clahef_(char *uplo, integer *n, integer *nb, integer *kb, + complex *a, integer *lda, integer *ipiv, complex *w, integer *ldw, + integer *info); + +/* Subroutine */ int clahqr_(logical *wantt, logical *wantz, integer *n, + integer *ilo, integer *ihi, complex *h__, integer *ldh, complex *w, + integer *iloz, integer *ihiz, complex *z__, integer *ldz, integer * + info); + +/* Subroutine */ int clahr2_(integer *n, integer *k, integer *nb, complex *a, + integer *lda, complex *tau, complex *t, integer *ldt, complex *y, + integer *ldy); + +/* Subroutine */ int clahrd_(integer *n, integer *k, integer *nb, complex *a, + integer *lda, complex *tau, complex *t, integer *ldt, complex *y, + integer *ldy); + +/* Subroutine */ int claic1_(integer *job, integer *j, complex *x, real *sest, + complex *w, complex *gamma, real *sestpr, complex *s, complex *c__); + +/* Subroutine */ int clals0_(integer *icompq, integer *nl, integer *nr, + integer *sqre, integer *nrhs, complex *b, integer *ldb, complex *bx, + integer *ldbx, integer *perm, integer *givptr, integer *givcol, + integer *ldgcol, real *givnum, integer *ldgnum, real *poles, real * + difl, real *difr, real *z__, integer *k, real *c__, real *s, real * + rwork, integer *info); + +/* Subroutine */ int clalsa_(integer *icompq, integer *smlsiz, integer *n, + integer *nrhs, complex *b, integer *ldb, complex *bx, integer *ldbx, + real *u, integer *ldu, real *vt, integer *k, real *difl, real *difr, + real *z__, real *poles, integer *givptr, integer *givcol, integer * + ldgcol, integer *perm, real *givnum, real *c__, real *s, real *rwork, + integer *iwork, integer *info); + +/* Subroutine */ int clalsd_(char *uplo, integer *smlsiz, integer *n, integer + *nrhs, real *d__, real *e, complex *b, integer *ldb, real *rcond, + integer *rank, complex *work, real *rwork, integer *iwork, integer * + info); + +doublereal clangb_(char *norm, integer *n, integer *kl, integer *ku, complex * + ab, integer *ldab, real *work); + +doublereal clange_(char *norm, integer *m, integer *n, complex *a, integer * + lda, real *work); + +doublereal clangt_(char *norm, integer *n, complex *dl, complex *d__, complex + *du); + +doublereal clanhb_(char *norm, char *uplo, integer *n, integer *k, complex * + ab, integer *ldab, real *work); + +doublereal clanhe_(char *norm, char *uplo, integer *n, complex *a, integer * + lda, real *work); + +doublereal clanhf_(char *norm, char *transr, char *uplo, integer *n, complex * + a, real *work); + +doublereal clanhp_(char *norm, char *uplo, integer *n, complex *ap, real * + work); + +doublereal clanhs_(char *norm, integer *n, complex *a, integer *lda, real * + work); + +doublereal clanht_(char *norm, integer *n, real *d__, complex *e); + +doublereal clansb_(char *norm, char *uplo, integer *n, integer *k, complex * + ab, integer *ldab, real *work); + +doublereal clansp_(char *norm, char *uplo, integer *n, complex *ap, real * + work); + +doublereal clansy_(char *norm, char *uplo, integer *n, complex *a, integer * + lda, real *work); + +doublereal clantb_(char *norm, char *uplo, char *diag, integer *n, integer *k, + complex *ab, integer *ldab, real *work); + +doublereal clantp_(char *norm, char *uplo, char *diag, integer *n, complex * + ap, real *work); + +doublereal clantr_(char *norm, char *uplo, char *diag, integer *m, integer *n, + complex *a, integer *lda, real *work); + +/* Subroutine */ int clapll_(integer *n, complex *x, integer *incx, complex * + y, integer *incy, real *ssmin); + +/* Subroutine */ int clapmt_(logical *forwrd, integer *m, integer *n, complex + *x, integer *ldx, integer *k); + +/* Subroutine */ int claqgb_(integer *m, integer *n, integer *kl, integer *ku, + complex *ab, integer *ldab, real *r__, real *c__, real *rowcnd, real + *colcnd, real *amax, char *equed); + +/* Subroutine */ int claqge_(integer *m, integer *n, complex *a, integer *lda, + real *r__, real *c__, real *rowcnd, real *colcnd, real *amax, char * + equed); + +/* Subroutine */ int claqhb_(char *uplo, integer *n, integer *kd, complex *ab, + integer *ldab, real *s, real *scond, real *amax, char *equed); + +/* Subroutine */ int claqhe_(char *uplo, integer *n, complex *a, integer *lda, + real *s, real *scond, real *amax, char *equed); + +/* Subroutine */ int claqhp_(char *uplo, integer *n, complex *ap, real *s, + real *scond, real *amax, char *equed); + +/* Subroutine */ int claqp2_(integer *m, integer *n, integer *offset, complex + *a, integer *lda, integer *jpvt, complex *tau, real *vn1, real *vn2, + complex *work); + +/* Subroutine */ int claqps_(integer *m, integer *n, integer *offset, integer + *nb, integer *kb, complex *a, integer *lda, integer *jpvt, complex * + tau, real *vn1, real *vn2, complex *auxv, complex *f, integer *ldf); + +/* Subroutine */ int claqr0_(logical *wantt, logical *wantz, integer *n, + integer *ilo, integer *ihi, complex *h__, integer *ldh, complex *w, + integer *iloz, integer *ihiz, complex *z__, integer *ldz, complex * + work, integer *lwork, integer *info); + +/* Subroutine */ int claqr1_(integer *n, complex *h__, integer *ldh, complex * + s1, complex *s2, complex *v); + +/* Subroutine */ int claqr2_(logical *wantt, logical *wantz, integer *n, + integer *ktop, integer *kbot, integer *nw, complex *h__, integer *ldh, + integer *iloz, integer *ihiz, complex *z__, integer *ldz, integer * + ns, integer *nd, complex *sh, complex *v, integer *ldv, integer *nh, + complex *t, integer *ldt, integer *nv, complex *wv, integer *ldwv, + complex *work, integer *lwork); + +/* Subroutine */ int claqr3_(logical *wantt, logical *wantz, integer *n, + integer *ktop, integer *kbot, integer *nw, complex *h__, integer *ldh, + integer *iloz, integer *ihiz, complex *z__, integer *ldz, integer * + ns, integer *nd, complex *sh, complex *v, integer *ldv, integer *nh, + complex *t, integer *ldt, integer *nv, complex *wv, integer *ldwv, + complex *work, integer *lwork); + +/* Subroutine */ int claqr4_(logical *wantt, logical *wantz, integer *n, + integer *ilo, integer *ihi, complex *h__, integer *ldh, complex *w, + integer *iloz, integer *ihiz, complex *z__, integer *ldz, complex * + work, integer *lwork, integer *info); + +/* Subroutine */ int claqr5_(logical *wantt, logical *wantz, integer *kacc22, + integer *n, integer *ktop, integer *kbot, integer *nshfts, complex *s, + complex *h__, integer *ldh, integer *iloz, integer *ihiz, complex * + z__, integer *ldz, complex *v, integer *ldv, complex *u, integer *ldu, + integer *nv, complex *wv, integer *ldwv, integer *nh, complex *wh, + integer *ldwh); + +/* Subroutine */ int claqsb_(char *uplo, integer *n, integer *kd, complex *ab, + integer *ldab, real *s, real *scond, real *amax, char *equed); + +/* Subroutine */ int claqsp_(char *uplo, integer *n, complex *ap, real *s, + real *scond, real *amax, char *equed); + +/* Subroutine */ int claqsy_(char *uplo, integer *n, complex *a, integer *lda, + real *s, real *scond, real *amax, char *equed); + +/* Subroutine */ int clar1v_(integer *n, integer *b1, integer *bn, real * + lambda, real *d__, real *l, real *ld, real *lld, real *pivmin, real * + gaptol, complex *z__, logical *wantnc, integer *negcnt, real *ztz, + real *mingma, integer *r__, integer *isuppz, real *nrminv, real * + resid, real *rqcorr, real *work); + +/* Subroutine */ int clar2v_(integer *n, complex *x, complex *y, complex *z__, + integer *incx, real *c__, complex *s, integer *incc); + +/* Subroutine */ int clarcm_(integer *m, integer *n, real *a, integer *lda, + complex *b, integer *ldb, complex *c__, integer *ldc, real *rwork); + +/* Subroutine */ int clarf_(char *side, integer *m, integer *n, complex *v, + integer *incv, complex *tau, complex *c__, integer *ldc, complex * + work); + +/* Subroutine */ int clarfb_(char *side, char *trans, char *direct, char * + storev, integer *m, integer *n, integer *k, complex *v, integer *ldv, + complex *t, integer *ldt, complex *c__, integer *ldc, complex *work, + integer *ldwork); + +/* Subroutine */ int clarfg_(integer *n, complex *alpha, complex *x, integer * + incx, complex *tau); + +/* Subroutine */ int clarfp_(integer *n, complex *alpha, complex *x, integer * + incx, complex *tau); + +/* Subroutine */ int clarft_(char *direct, char *storev, integer *n, integer * + k, complex *v, integer *ldv, complex *tau, complex *t, integer *ldt); + +/* Subroutine */ int clarfx_(char *side, integer *m, integer *n, complex *v, + complex *tau, complex *c__, integer *ldc, complex *work); + +/* Subroutine */ int clargv_(integer *n, complex *x, integer *incx, complex * + y, integer *incy, real *c__, integer *incc); + +/* Subroutine */ int clarnv_(integer *idist, integer *iseed, integer *n, + complex *x); + +/* Subroutine */ int clarrv_(integer *n, real *vl, real *vu, real *d__, real * + l, real *pivmin, integer *isplit, integer *m, integer *dol, integer * + dou, real *minrgp, real *rtol1, real *rtol2, real *w, real *werr, + real *wgap, integer *iblock, integer *indexw, real *gers, complex * + z__, integer *ldz, integer *isuppz, real *work, integer *iwork, + integer *info); + +/* Subroutine */ int clarscl2_(integer *m, integer *n, real *d__, complex *x, + integer *ldx); + +/* Subroutine */ int clartg_(complex *f, complex *g, real *cs, complex *sn, + complex *r__); + +/* Subroutine */ int clartv_(integer *n, complex *x, integer *incx, complex * + y, integer *incy, real *c__, complex *s, integer *incc); + +/* Subroutine */ int clarz_(char *side, integer *m, integer *n, integer *l, + complex *v, integer *incv, complex *tau, complex *c__, integer *ldc, + complex *work); + +/* Subroutine */ int clarzb_(char *side, char *trans, char *direct, char * + storev, integer *m, integer *n, integer *k, integer *l, complex *v, + integer *ldv, complex *t, integer *ldt, complex *c__, integer *ldc, + complex *work, integer *ldwork); + +/* Subroutine */ int clarzt_(char *direct, char *storev, integer *n, integer * + k, complex *v, integer *ldv, complex *tau, complex *t, integer *ldt); + +/* Subroutine */ int clascl_(char *type__, integer *kl, integer *ku, real * + cfrom, real *cto, integer *m, integer *n, complex *a, integer *lda, + integer *info); + +/* Subroutine */ int clascl2_(integer *m, integer *n, real *d__, complex *x, + integer *ldx); + +/* Subroutine */ int claset_(char *uplo, integer *m, integer *n, complex * + alpha, complex *beta, complex *a, integer *lda); + +/* Subroutine */ int clasr_(char *side, char *pivot, char *direct, integer *m, + integer *n, real *c__, real *s, complex *a, integer *lda); + +/* Subroutine */ int classq_(integer *n, complex *x, integer *incx, real * + scale, real *sumsq); + +/* Subroutine */ int claswp_(integer *n, complex *a, integer *lda, integer * + k1, integer *k2, integer *ipiv, integer *incx); + +/* Subroutine */ int clasyf_(char *uplo, integer *n, integer *nb, integer *kb, + complex *a, integer *lda, integer *ipiv, complex *w, integer *ldw, + integer *info); + +/* Subroutine */ int clatbs_(char *uplo, char *trans, char *diag, char * + normin, integer *n, integer *kd, complex *ab, integer *ldab, complex * + x, real *scale, real *cnorm, integer *info); + +/* Subroutine */ int clatdf_(integer *ijob, integer *n, complex *z__, integer + *ldz, complex *rhs, real *rdsum, real *rdscal, integer *ipiv, integer + *jpiv); + +/* Subroutine */ int clatps_(char *uplo, char *trans, char *diag, char * + normin, integer *n, complex *ap, complex *x, real *scale, real *cnorm, + integer *info); + +/* Subroutine */ int clatrd_(char *uplo, integer *n, integer *nb, complex *a, + integer *lda, real *e, complex *tau, complex *w, integer *ldw); + +/* Subroutine */ int clatrs_(char *uplo, char *trans, char *diag, char * + normin, integer *n, complex *a, integer *lda, complex *x, real *scale, + real *cnorm, integer *info); + +/* Subroutine */ int clatrz_(integer *m, integer *n, integer *l, complex *a, + integer *lda, complex *tau, complex *work); + +/* Subroutine */ int clatzm_(char *side, integer *m, integer *n, complex *v, + integer *incv, complex *tau, complex *c1, complex *c2, integer *ldc, + complex *work); + +/* Subroutine */ int clauu2_(char *uplo, integer *n, complex *a, integer *lda, + integer *info); + +/* Subroutine */ int clauum_(char *uplo, integer *n, complex *a, integer *lda, + integer *info); + +/* Subroutine */ int cpbcon_(char *uplo, integer *n, integer *kd, complex *ab, + integer *ldab, real *anorm, real *rcond, complex *work, real *rwork, + integer *info); + +/* Subroutine */ int cpbequ_(char *uplo, integer *n, integer *kd, complex *ab, + integer *ldab, real *s, real *scond, real *amax, integer *info); + +/* Subroutine */ int cpbrfs_(char *uplo, integer *n, integer *kd, integer * + nrhs, complex *ab, integer *ldab, complex *afb, integer *ldafb, + complex *b, integer *ldb, complex *x, integer *ldx, real *ferr, real * + berr, complex *work, real *rwork, integer *info); + +/* Subroutine */ int cpbstf_(char *uplo, integer *n, integer *kd, complex *ab, + integer *ldab, integer *info); + +/* Subroutine */ int cpbsv_(char *uplo, integer *n, integer *kd, integer * + nrhs, complex *ab, integer *ldab, complex *b, integer *ldb, integer * + info); + +/* Subroutine */ int cpbsvx_(char *fact, char *uplo, integer *n, integer *kd, + integer *nrhs, complex *ab, integer *ldab, complex *afb, integer * + ldafb, char *equed, real *s, complex *b, integer *ldb, complex *x, + integer *ldx, real *rcond, real *ferr, real *berr, complex *work, + real *rwork, integer *info); + +/* Subroutine */ int cpbtf2_(char *uplo, integer *n, integer *kd, complex *ab, + integer *ldab, integer *info); + +/* Subroutine */ int cpbtrf_(char *uplo, integer *n, integer *kd, complex *ab, + integer *ldab, integer *info); + +/* Subroutine */ int cpbtrs_(char *uplo, integer *n, integer *kd, integer * + nrhs, complex *ab, integer *ldab, complex *b, integer *ldb, integer * + info); + +/* Subroutine */ int cpftrf_(char *transr, char *uplo, integer *n, complex *a, + integer *info); + +/* Subroutine */ int cpftri_(char *transr, char *uplo, integer *n, complex *a, + integer *info); + +/* Subroutine */ int cpftrs_(char *transr, char *uplo, integer *n, integer * + nrhs, complex *a, complex *b, integer *ldb, integer *info); + +/* Subroutine */ int cpocon_(char *uplo, integer *n, complex *a, integer *lda, + real *anorm, real *rcond, complex *work, real *rwork, integer *info); + +/* Subroutine */ int cpoequ_(integer *n, complex *a, integer *lda, real *s, + real *scond, real *amax, integer *info); + +/* Subroutine */ int cpoequb_(integer *n, complex *a, integer *lda, real *s, + real *scond, real *amax, integer *info); + +/* Subroutine */ int cporfs_(char *uplo, integer *n, integer *nrhs, complex * + a, integer *lda, complex *af, integer *ldaf, complex *b, integer *ldb, + complex *x, integer *ldx, real *ferr, real *berr, complex *work, + real *rwork, integer *info); + +/* Subroutine */ int cporfsx_(char *uplo, char *equed, integer *n, integer * + nrhs, complex *a, integer *lda, complex *af, integer *ldaf, real *s, + complex *b, integer *ldb, complex *x, integer *ldx, real *rcond, real + *berr, integer *n_err_bnds__, real *err_bnds_norm__, real * + err_bnds_comp__, integer *nparams, real *params, complex *work, real * + rwork, integer *info); + +/* Subroutine */ int cposv_(char *uplo, integer *n, integer *nrhs, complex *a, + integer *lda, complex *b, integer *ldb, integer *info); + +/* Subroutine */ int cposvx_(char *fact, char *uplo, integer *n, integer * + nrhs, complex *a, integer *lda, complex *af, integer *ldaf, char * + equed, real *s, complex *b, integer *ldb, complex *x, integer *ldx, + real *rcond, real *ferr, real *berr, complex *work, real *rwork, + integer *info); + +/* Subroutine */ int cposvxx_(char *fact, char *uplo, integer *n, integer * + nrhs, complex *a, integer *lda, complex *af, integer *ldaf, char * + equed, real *s, complex *b, integer *ldb, complex *x, integer *ldx, + real *rcond, real *rpvgrw, real *berr, integer *n_err_bnds__, real * + err_bnds_norm__, real *err_bnds_comp__, integer *nparams, real * + params, complex *work, real *rwork, integer *info); + +/* Subroutine */ int cpotf2_(char *uplo, integer *n, complex *a, integer *lda, + integer *info); + +/* Subroutine */ int cpotrf_(char *uplo, integer *n, complex *a, integer *lda, + integer *info); + +/* Subroutine */ int cpotri_(char *uplo, integer *n, complex *a, integer *lda, + integer *info); + +/* Subroutine */ int cpotrs_(char *uplo, integer *n, integer *nrhs, complex * + a, integer *lda, complex *b, integer *ldb, integer *info); + +/* Subroutine */ int cppcon_(char *uplo, integer *n, complex *ap, real *anorm, + real *rcond, complex *work, real *rwork, integer *info); + +/* Subroutine */ int cppequ_(char *uplo, integer *n, complex *ap, real *s, + real *scond, real *amax, integer *info); + +/* Subroutine */ int cpprfs_(char *uplo, integer *n, integer *nrhs, complex * + ap, complex *afp, complex *b, integer *ldb, complex *x, integer *ldx, + real *ferr, real *berr, complex *work, real *rwork, integer *info); + +/* Subroutine */ int cppsv_(char *uplo, integer *n, integer *nrhs, complex * + ap, complex *b, integer *ldb, integer *info); + +/* Subroutine */ int cppsvx_(char *fact, char *uplo, integer *n, integer * + nrhs, complex *ap, complex *afp, char *equed, real *s, complex *b, + integer *ldb, complex *x, integer *ldx, real *rcond, real *ferr, real + *berr, complex *work, real *rwork, integer *info); + +/* Subroutine */ int cpptrf_(char *uplo, integer *n, complex *ap, integer * + info); + +/* Subroutine */ int cpptri_(char *uplo, integer *n, complex *ap, integer * + info); + +/* Subroutine */ int cpptrs_(char *uplo, integer *n, integer *nrhs, complex * + ap, complex *b, integer *ldb, integer *info); + +/* Subroutine */ int cpstf2_(char *uplo, integer *n, complex *a, integer *lda, + integer *piv, integer *rank, real *tol, real *work, integer *info); + +/* Subroutine */ int cpstrf_(char *uplo, integer *n, complex *a, integer *lda, + integer *piv, integer *rank, real *tol, real *work, integer *info); + +/* Subroutine */ int cptcon_(integer *n, real *d__, complex *e, real *anorm, + real *rcond, real *rwork, integer *info); + +/* Subroutine */ int cpteqr_(char *compz, integer *n, real *d__, real *e, + complex *z__, integer *ldz, real *work, integer *info); + +/* Subroutine */ int cptrfs_(char *uplo, integer *n, integer *nrhs, real *d__, + complex *e, real *df, complex *ef, complex *b, integer *ldb, complex + *x, integer *ldx, real *ferr, real *berr, complex *work, real *rwork, + integer *info); + +/* Subroutine */ int cptsv_(integer *n, integer *nrhs, real *d__, complex *e, + complex *b, integer *ldb, integer *info); + +/* Subroutine */ int cptsvx_(char *fact, integer *n, integer *nrhs, real *d__, + complex *e, real *df, complex *ef, complex *b, integer *ldb, complex + *x, integer *ldx, real *rcond, real *ferr, real *berr, complex *work, + real *rwork, integer *info); + +/* Subroutine */ int cpttrf_(integer *n, real *d__, complex *e, integer *info); + +/* Subroutine */ int cpttrs_(char *uplo, integer *n, integer *nrhs, real *d__, + complex *e, complex *b, integer *ldb, integer *info); + +/* Subroutine */ int cptts2_(integer *iuplo, integer *n, integer *nrhs, real * + d__, complex *e, complex *b, integer *ldb); + +/* Subroutine */ int crot_(integer *n, complex *cx, integer *incx, complex * + cy, integer *incy, real *c__, complex *s); + +/* Subroutine */ int cspcon_(char *uplo, integer *n, complex *ap, integer * + ipiv, real *anorm, real *rcond, complex *work, integer *info); + +/* Subroutine */ int cspmv_(char *uplo, integer *n, complex *alpha, complex * + ap, complex *x, integer *incx, complex *beta, complex *y, integer * + incy); + +/* Subroutine */ int cspr_(char *uplo, integer *n, complex *alpha, complex *x, + integer *incx, complex *ap); + +/* Subroutine */ int csprfs_(char *uplo, integer *n, integer *nrhs, complex * + ap, complex *afp, integer *ipiv, complex *b, integer *ldb, complex *x, + integer *ldx, real *ferr, real *berr, complex *work, real *rwork, + integer *info); + +/* Subroutine */ int cspsv_(char *uplo, integer *n, integer *nrhs, complex * + ap, integer *ipiv, complex *b, integer *ldb, integer *info); + +/* Subroutine */ int cspsvx_(char *fact, char *uplo, integer *n, integer * + nrhs, complex *ap, complex *afp, integer *ipiv, complex *b, integer * + ldb, complex *x, integer *ldx, real *rcond, real *ferr, real *berr, + complex *work, real *rwork, integer *info); + +/* Subroutine */ int csptrf_(char *uplo, integer *n, complex *ap, integer * + ipiv, integer *info); + +/* Subroutine */ int csptri_(char *uplo, integer *n, complex *ap, integer * + ipiv, complex *work, integer *info); + +/* Subroutine */ int csptrs_(char *uplo, integer *n, integer *nrhs, complex * + ap, integer *ipiv, complex *b, integer *ldb, integer *info); + +/* Subroutine */ int csrscl_(integer *n, real *sa, complex *sx, integer *incx); + +/* Subroutine */ int cstedc_(char *compz, integer *n, real *d__, real *e, + complex *z__, integer *ldz, complex *work, integer *lwork, real * + rwork, integer *lrwork, integer *iwork, integer *liwork, integer * + info); + +/* Subroutine */ int cstegr_(char *jobz, char *range, integer *n, real *d__, + real *e, real *vl, real *vu, integer *il, integer *iu, real *abstol, + integer *m, real *w, complex *z__, integer *ldz, integer *isuppz, + real *work, integer *lwork, integer *iwork, integer *liwork, integer * + info); + +/* Subroutine */ int cstein_(integer *n, real *d__, real *e, integer *m, real + *w, integer *iblock, integer *isplit, complex *z__, integer *ldz, + real *work, integer *iwork, integer *ifail, integer *info); + +/* Subroutine */ int cstemr_(char *jobz, char *range, integer *n, real *d__, + real *e, real *vl, real *vu, integer *il, integer *iu, integer *m, + real *w, complex *z__, integer *ldz, integer *nzc, integer *isuppz, + logical *tryrac, real *work, integer *lwork, integer *iwork, integer * + liwork, integer *info); + +/* Subroutine */ int csteqr_(char *compz, integer *n, real *d__, real *e, + complex *z__, integer *ldz, real *work, integer *info); + +/* Subroutine */ int csycon_(char *uplo, integer *n, complex *a, integer *lda, + integer *ipiv, real *anorm, real *rcond, complex *work, integer * + info); + +/* Subroutine */ int csyequb_(char *uplo, integer *n, complex *a, integer * + lda, real *s, real *scond, real *amax, complex *work, integer *info); + +/* Subroutine */ int csymv_(char *uplo, integer *n, complex *alpha, complex * + a, integer *lda, complex *x, integer *incx, complex *beta, complex *y, + integer *incy); + +/* Subroutine */ int csyr_(char *uplo, integer *n, complex *alpha, complex *x, + integer *incx, complex *a, integer *lda); + +/* Subroutine */ int csyrfs_(char *uplo, integer *n, integer *nrhs, complex * + a, integer *lda, complex *af, integer *ldaf, integer *ipiv, complex * + b, integer *ldb, complex *x, integer *ldx, real *ferr, real *berr, + complex *work, real *rwork, integer *info); + +/* Subroutine */ int csyrfsx_(char *uplo, char *equed, integer *n, integer * + nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer * + ipiv, real *s, complex *b, integer *ldb, complex *x, integer *ldx, + real *rcond, real *berr, integer *n_err_bnds__, real *err_bnds_norm__, + real *err_bnds_comp__, integer *nparams, real *params, complex *work, + real *rwork, integer *info); + +/* Subroutine */ int csysv_(char *uplo, integer *n, integer *nrhs, complex *a, + integer *lda, integer *ipiv, complex *b, integer *ldb, complex *work, + integer *lwork, integer *info); + +/* Subroutine */ int csysvx_(char *fact, char *uplo, integer *n, integer * + nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer * + ipiv, complex *b, integer *ldb, complex *x, integer *ldx, real *rcond, + real *ferr, real *berr, complex *work, integer *lwork, real *rwork, + integer *info); + +/* Subroutine */ int csysvxx_(char *fact, char *uplo, integer *n, integer * + nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer * + ipiv, char *equed, real *s, complex *b, integer *ldb, complex *x, + integer *ldx, real *rcond, real *rpvgrw, real *berr, integer * + n_err_bnds__, real *err_bnds_norm__, real *err_bnds_comp__, integer * + nparams, real *params, complex *work, real *rwork, integer *info); + +/* Subroutine */ int csytf2_(char *uplo, integer *n, complex *a, integer *lda, + integer *ipiv, integer *info); + +/* Subroutine */ int csytrf_(char *uplo, integer *n, complex *a, integer *lda, + integer *ipiv, complex *work, integer *lwork, integer *info); + +/* Subroutine */ int csytri_(char *uplo, integer *n, complex *a, integer *lda, + integer *ipiv, complex *work, integer *info); + +/* Subroutine */ int csytrs_(char *uplo, integer *n, integer *nrhs, complex * + a, integer *lda, integer *ipiv, complex *b, integer *ldb, integer * + info); + +/* Subroutine */ int ctbcon_(char *norm, char *uplo, char *diag, integer *n, + integer *kd, complex *ab, integer *ldab, real *rcond, complex *work, + real *rwork, integer *info); + +/* Subroutine */ int ctbrfs_(char *uplo, char *trans, char *diag, integer *n, + integer *kd, integer *nrhs, complex *ab, integer *ldab, complex *b, + integer *ldb, complex *x, integer *ldx, real *ferr, real *berr, + complex *work, real *rwork, integer *info); + +/* Subroutine */ int ctbtrs_(char *uplo, char *trans, char *diag, integer *n, + integer *kd, integer *nrhs, complex *ab, integer *ldab, complex *b, + integer *ldb, integer *info); + +/* Subroutine */ int ctfsm_(char *transr, char *side, char *uplo, char *trans, + char *diag, integer *m, integer *n, complex *alpha, complex *a, + complex *b, integer *ldb); + +/* Subroutine */ int ctftri_(char *transr, char *uplo, char *diag, integer *n, + complex *a, integer *info); + +/* Subroutine */ int ctfttp_(char *transr, char *uplo, integer *n, complex * + arf, complex *ap, integer *info); + +/* Subroutine */ int ctfttr_(char *transr, char *uplo, integer *n, complex * + arf, complex *a, integer *lda, integer *info); + +/* Subroutine */ int ctgevc_(char *side, char *howmny, logical *select, + integer *n, complex *s, integer *lds, complex *p, integer *ldp, + complex *vl, integer *ldvl, complex *vr, integer *ldvr, integer *mm, + integer *m, complex *work, real *rwork, integer *info); + +/* Subroutine */ int ctgex2_(logical *wantq, logical *wantz, integer *n, + complex *a, integer *lda, complex *b, integer *ldb, complex *q, + integer *ldq, complex *z__, integer *ldz, integer *j1, integer *info); + +/* Subroutine */ int ctgexc_(logical *wantq, logical *wantz, integer *n, + complex *a, integer *lda, complex *b, integer *ldb, complex *q, + integer *ldq, complex *z__, integer *ldz, integer *ifst, integer * + ilst, integer *info); + +/* Subroutine */ int ctgsen_(integer *ijob, logical *wantq, logical *wantz, + logical *select, integer *n, complex *a, integer *lda, complex *b, + integer *ldb, complex *alpha, complex *beta, complex *q, integer *ldq, + complex *z__, integer *ldz, integer *m, real *pl, real *pr, real * + dif, complex *work, integer *lwork, integer *iwork, integer *liwork, + integer *info); + +/* Subroutine */ int ctgsja_(char *jobu, char *jobv, char *jobq, integer *m, + integer *p, integer *n, integer *k, integer *l, complex *a, integer * + lda, complex *b, integer *ldb, real *tola, real *tolb, real *alpha, + real *beta, complex *u, integer *ldu, complex *v, integer *ldv, + complex *q, integer *ldq, complex *work, integer *ncycle, integer * + info); + +/* Subroutine */ int ctgsna_(char *job, char *howmny, logical *select, + integer *n, complex *a, integer *lda, complex *b, integer *ldb, + complex *vl, integer *ldvl, complex *vr, integer *ldvr, real *s, real + *dif, integer *mm, integer *m, complex *work, integer *lwork, integer + *iwork, integer *info); + +/* Subroutine */ int ctgsy2_(char *trans, integer *ijob, integer *m, integer * + n, complex *a, integer *lda, complex *b, integer *ldb, complex *c__, + integer *ldc, complex *d__, integer *ldd, complex *e, integer *lde, + complex *f, integer *ldf, real *scale, real *rdsum, real *rdscal, + integer *info); + +/* Subroutine */ int ctgsyl_(char *trans, integer *ijob, integer *m, integer * + n, complex *a, integer *lda, complex *b, integer *ldb, complex *c__, + integer *ldc, complex *d__, integer *ldd, complex *e, integer *lde, + complex *f, integer *ldf, real *scale, real *dif, complex *work, + integer *lwork, integer *iwork, integer *info); + +/* Subroutine */ int ctpcon_(char *norm, char *uplo, char *diag, integer *n, + complex *ap, real *rcond, complex *work, real *rwork, integer *info); + +/* Subroutine */ int ctprfs_(char *uplo, char *trans, char *diag, integer *n, + integer *nrhs, complex *ap, complex *b, integer *ldb, complex *x, + integer *ldx, real *ferr, real *berr, complex *work, real *rwork, + integer *info); + +/* Subroutine */ int ctptri_(char *uplo, char *diag, integer *n, complex *ap, + integer *info); + +/* Subroutine */ int ctptrs_(char *uplo, char *trans, char *diag, integer *n, + integer *nrhs, complex *ap, complex *b, integer *ldb, integer *info); + +/* Subroutine */ int ctpttf_(char *transr, char *uplo, integer *n, complex * + ap, complex *arf, integer *info); + +/* Subroutine */ int ctpttr_(char *uplo, integer *n, complex *ap, complex *a, + integer *lda, integer *info); + +/* Subroutine */ int ctrcon_(char *norm, char *uplo, char *diag, integer *n, + complex *a, integer *lda, real *rcond, complex *work, real *rwork, + integer *info); + +/* Subroutine */ int ctrevc_(char *side, char *howmny, logical *select, + integer *n, complex *t, integer *ldt, complex *vl, integer *ldvl, + complex *vr, integer *ldvr, integer *mm, integer *m, complex *work, + real *rwork, integer *info); + +/* Subroutine */ int ctrexc_(char *compq, integer *n, complex *t, integer * + ldt, complex *q, integer *ldq, integer *ifst, integer *ilst, integer * + info); + +/* Subroutine */ int ctrrfs_(char *uplo, char *trans, char *diag, integer *n, + integer *nrhs, complex *a, integer *lda, complex *b, integer *ldb, + complex *x, integer *ldx, real *ferr, real *berr, complex *work, real + *rwork, integer *info); + +/* Subroutine */ int ctrsen_(char *job, char *compq, logical *select, integer + *n, complex *t, integer *ldt, complex *q, integer *ldq, complex *w, + integer *m, real *s, real *sep, complex *work, integer *lwork, + integer *info); + +/* Subroutine */ int ctrsna_(char *job, char *howmny, logical *select, + integer *n, complex *t, integer *ldt, complex *vl, integer *ldvl, + complex *vr, integer *ldvr, real *s, real *sep, integer *mm, integer * + m, complex *work, integer *ldwork, real *rwork, integer *info); + +/* Subroutine */ int ctrsyl_(char *trana, char *tranb, integer *isgn, integer + *m, integer *n, complex *a, integer *lda, complex *b, integer *ldb, + complex *c__, integer *ldc, real *scale, integer *info); + +/* Subroutine */ int ctrti2_(char *uplo, char *diag, integer *n, complex *a, + integer *lda, integer *info); + +/* Subroutine */ int ctrtri_(char *uplo, char *diag, integer *n, complex *a, + integer *lda, integer *info); + +/* Subroutine */ int ctrtrs_(char *uplo, char *trans, char *diag, integer *n, + integer *nrhs, complex *a, integer *lda, complex *b, integer *ldb, + integer *info); + +/* Subroutine */ int ctrttf_(char *transr, char *uplo, integer *n, complex *a, + integer *lda, complex *arf, integer *info); + +/* Subroutine */ int ctrttp_(char *uplo, integer *n, complex *a, integer *lda, + complex *ap, integer *info); + +/* Subroutine */ int ctzrqf_(integer *m, integer *n, complex *a, integer *lda, + complex *tau, integer *info); + +/* Subroutine */ int ctzrzf_(integer *m, integer *n, complex *a, integer *lda, + complex *tau, complex *work, integer *lwork, integer *info); + +/* Subroutine */ int cung2l_(integer *m, integer *n, integer *k, complex *a, + integer *lda, complex *tau, complex *work, integer *info); + +/* Subroutine */ int cung2r_(integer *m, integer *n, integer *k, complex *a, + integer *lda, complex *tau, complex *work, integer *info); + +/* Subroutine */ int cungbr_(char *vect, integer *m, integer *n, integer *k, + complex *a, integer *lda, complex *tau, complex *work, integer *lwork, + integer *info); + +/* Subroutine */ int cunghr_(integer *n, integer *ilo, integer *ihi, complex * + a, integer *lda, complex *tau, complex *work, integer *lwork, integer + *info); + +/* Subroutine */ int cungl2_(integer *m, integer *n, integer *k, complex *a, + integer *lda, complex *tau, complex *work, integer *info); + +/* Subroutine */ int cunglq_(integer *m, integer *n, integer *k, complex *a, + integer *lda, complex *tau, complex *work, integer *lwork, integer * + info); + +/* Subroutine */ int cungql_(integer *m, integer *n, integer *k, complex *a, + integer *lda, complex *tau, complex *work, integer *lwork, integer * + info); + +/* Subroutine */ int cungqr_(integer *m, integer *n, integer *k, complex *a, + integer *lda, complex *tau, complex *work, integer *lwork, integer * + info); + +/* Subroutine */ int cungr2_(integer *m, integer *n, integer *k, complex *a, + integer *lda, complex *tau, complex *work, integer *info); + +/* Subroutine */ int cungrq_(integer *m, integer *n, integer *k, complex *a, + integer *lda, complex *tau, complex *work, integer *lwork, integer * + info); + +/* Subroutine */ int cungtr_(char *uplo, integer *n, complex *a, integer *lda, + complex *tau, complex *work, integer *lwork, integer *info); + +/* Subroutine */ int cunm2l_(char *side, char *trans, integer *m, integer *n, + integer *k, complex *a, integer *lda, complex *tau, complex *c__, + integer *ldc, complex *work, integer *info); + +/* Subroutine */ int cunm2r_(char *side, char *trans, integer *m, integer *n, + integer *k, complex *a, integer *lda, complex *tau, complex *c__, + integer *ldc, complex *work, integer *info); + +/* Subroutine */ int cunmbr_(char *vect, char *side, char *trans, integer *m, + integer *n, integer *k, complex *a, integer *lda, complex *tau, + complex *c__, integer *ldc, complex *work, integer *lwork, integer * + info); + +/* Subroutine */ int cunmhr_(char *side, char *trans, integer *m, integer *n, + integer *ilo, integer *ihi, complex *a, integer *lda, complex *tau, + complex *c__, integer *ldc, complex *work, integer *lwork, integer * + info); + +/* Subroutine */ int cunml2_(char *side, char *trans, integer *m, integer *n, + integer *k, complex *a, integer *lda, complex *tau, complex *c__, + integer *ldc, complex *work, integer *info); + +/* Subroutine */ int cunmlq_(char *side, char *trans, integer *m, integer *n, + integer *k, complex *a, integer *lda, complex *tau, complex *c__, + integer *ldc, complex *work, integer *lwork, integer *info); + +/* Subroutine */ int cunmql_(char *side, char *trans, integer *m, integer *n, + integer *k, complex *a, integer *lda, complex *tau, complex *c__, + integer *ldc, complex *work, integer *lwork, integer *info); + +/* Subroutine */ int cunmqr_(char *side, char *trans, integer *m, integer *n, + integer *k, complex *a, integer *lda, complex *tau, complex *c__, + integer *ldc, complex *work, integer *lwork, integer *info); + +/* Subroutine */ int cunmr2_(char *side, char *trans, integer *m, integer *n, + integer *k, complex *a, integer *lda, complex *tau, complex *c__, + integer *ldc, complex *work, integer *info); + +/* Subroutine */ int cunmr3_(char *side, char *trans, integer *m, integer *n, + integer *k, integer *l, complex *a, integer *lda, complex *tau, + complex *c__, integer *ldc, complex *work, integer *info); + +/* Subroutine */ int cunmrq_(char *side, char *trans, integer *m, integer *n, + integer *k, complex *a, integer *lda, complex *tau, complex *c__, + integer *ldc, complex *work, integer *lwork, integer *info); + +/* Subroutine */ int cunmrz_(char *side, char *trans, integer *m, integer *n, + integer *k, integer *l, complex *a, integer *lda, complex *tau, + complex *c__, integer *ldc, complex *work, integer *lwork, integer * + info); + +/* Subroutine */ int cunmtr_(char *side, char *uplo, char *trans, integer *m, + integer *n, complex *a, integer *lda, complex *tau, complex *c__, + integer *ldc, complex *work, integer *lwork, integer *info); + +/* Subroutine */ int cupgtr_(char *uplo, integer *n, complex *ap, complex * + tau, complex *q, integer *ldq, complex *work, integer *info); + +/* Subroutine */ int cupmtr_(char *side, char *uplo, char *trans, integer *m, + integer *n, complex *ap, complex *tau, complex *c__, integer *ldc, + complex *work, integer *info); + +/* Subroutine */ int dbdsdc_(char *uplo, char *compq, integer *n, doublereal * + d__, doublereal *e, doublereal *u, integer *ldu, doublereal *vt, + integer *ldvt, doublereal *q, integer *iq, doublereal *work, integer * + iwork, integer *info); + +/* Subroutine */ int dbdsqr_(char *uplo, integer *n, integer *ncvt, integer * + nru, integer *ncc, doublereal *d__, doublereal *e, doublereal *vt, + integer *ldvt, doublereal *u, integer *ldu, doublereal *c__, integer * + ldc, doublereal *work, integer *info); + +/* Subroutine */ int ddisna_(char *job, integer *m, integer *n, doublereal * + d__, doublereal *sep, integer *info); + +/* Subroutine */ int dgbbrd_(char *vect, integer *m, integer *n, integer *ncc, + integer *kl, integer *ku, doublereal *ab, integer *ldab, doublereal * + d__, doublereal *e, doublereal *q, integer *ldq, doublereal *pt, + integer *ldpt, doublereal *c__, integer *ldc, doublereal *work, + integer *info); + +/* Subroutine */ int dgbcon_(char *norm, integer *n, integer *kl, integer *ku, + doublereal *ab, integer *ldab, integer *ipiv, doublereal *anorm, + doublereal *rcond, doublereal *work, integer *iwork, integer *info); + +/* Subroutine */ int dgbequ_(integer *m, integer *n, integer *kl, integer *ku, + doublereal *ab, integer *ldab, doublereal *r__, doublereal *c__, + doublereal *rowcnd, doublereal *colcnd, doublereal *amax, integer * + info); + +/* Subroutine */ int dgbequb_(integer *m, integer *n, integer *kl, integer * + ku, doublereal *ab, integer *ldab, doublereal *r__, doublereal *c__, + doublereal *rowcnd, doublereal *colcnd, doublereal *amax, integer * + info); + +/* Subroutine */ int dgbrfs_(char *trans, integer *n, integer *kl, integer * + ku, integer *nrhs, doublereal *ab, integer *ldab, doublereal *afb, + integer *ldafb, integer *ipiv, doublereal *b, integer *ldb, + doublereal *x, integer *ldx, doublereal *ferr, doublereal *berr, + doublereal *work, integer *iwork, integer *info); + +/* Subroutine */ int dgbrfsx_(char *trans, char *equed, integer *n, integer * + kl, integer *ku, integer *nrhs, doublereal *ab, integer *ldab, + doublereal *afb, integer *ldafb, integer *ipiv, doublereal *r__, + doublereal *c__, doublereal *b, integer *ldb, doublereal *x, integer * + ldx, doublereal *rcond, doublereal *berr, integer *n_err_bnds__, + doublereal *err_bnds_norm__, doublereal *err_bnds_comp__, integer * + nparams, doublereal *params, doublereal *work, integer *iwork, + integer *info); + +/* Subroutine */ int dgbsv_(integer *n, integer *kl, integer *ku, integer * + nrhs, doublereal *ab, integer *ldab, integer *ipiv, doublereal *b, + integer *ldb, integer *info); + +/* Subroutine */ int dgbsvx_(char *fact, char *trans, integer *n, integer *kl, + integer *ku, integer *nrhs, doublereal *ab, integer *ldab, + doublereal *afb, integer *ldafb, integer *ipiv, char *equed, + doublereal *r__, doublereal *c__, doublereal *b, integer *ldb, + doublereal *x, integer *ldx, doublereal *rcond, doublereal *ferr, + doublereal *berr, doublereal *work, integer *iwork, integer *info); + +/* Subroutine */ int dgbsvxx_(char *fact, char *trans, integer *n, integer * + kl, integer *ku, integer *nrhs, doublereal *ab, integer *ldab, + doublereal *afb, integer *ldafb, integer *ipiv, char *equed, + doublereal *r__, doublereal *c__, doublereal *b, integer *ldb, + doublereal *x, integer *ldx, doublereal *rcond, doublereal *rpvgrw, + doublereal *berr, integer *n_err_bnds__, doublereal *err_bnds_norm__, + doublereal *err_bnds_comp__, integer *nparams, doublereal *params, + doublereal *work, integer *iwork, integer *info); + +/* Subroutine */ int dgbtf2_(integer *m, integer *n, integer *kl, integer *ku, + doublereal *ab, integer *ldab, integer *ipiv, integer *info); + +/* Subroutine */ int dgbtrf_(integer *m, integer *n, integer *kl, integer *ku, + doublereal *ab, integer *ldab, integer *ipiv, integer *info); + +/* Subroutine */ int dgbtrs_(char *trans, integer *n, integer *kl, integer * + ku, integer *nrhs, doublereal *ab, integer *ldab, integer *ipiv, + doublereal *b, integer *ldb, integer *info); + +/* Subroutine */ int dgebak_(char *job, char *side, integer *n, integer *ilo, + integer *ihi, doublereal *scale, integer *m, doublereal *v, integer * + ldv, integer *info); + +/* Subroutine */ int dgebal_(char *job, integer *n, doublereal *a, integer * + lda, integer *ilo, integer *ihi, doublereal *scale, integer *info); + +/* Subroutine */ int dgebd2_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *d__, doublereal *e, doublereal *tauq, doublereal * + taup, doublereal *work, integer *info); + +/* Subroutine */ int dgebrd_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *d__, doublereal *e, doublereal *tauq, doublereal * + taup, doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dgecon_(char *norm, integer *n, doublereal *a, integer * + lda, doublereal *anorm, doublereal *rcond, doublereal *work, integer * + iwork, integer *info); + +/* Subroutine */ int dgeequ_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *r__, doublereal *c__, doublereal *rowcnd, doublereal + *colcnd, doublereal *amax, integer *info); + +/* Subroutine */ int dgeequb_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *r__, doublereal *c__, doublereal *rowcnd, doublereal + *colcnd, doublereal *amax, integer *info); + +/* Subroutine */ int dgees_(char *jobvs, char *sort, L_fp select, integer *n, + doublereal *a, integer *lda, integer *sdim, doublereal *wr, + doublereal *wi, doublereal *vs, integer *ldvs, doublereal *work, + integer *lwork, logical *bwork, integer *info); + +/* Subroutine */ int dgeesx_(char *jobvs, char *sort, L_fp select, char * + sense, integer *n, doublereal *a, integer *lda, integer *sdim, + doublereal *wr, doublereal *wi, doublereal *vs, integer *ldvs, + doublereal *rconde, doublereal *rcondv, doublereal *work, integer * + lwork, integer *iwork, integer *liwork, logical *bwork, integer *info); + +/* Subroutine */ int dgeev_(char *jobvl, char *jobvr, integer *n, doublereal * + a, integer *lda, doublereal *wr, doublereal *wi, doublereal *vl, + integer *ldvl, doublereal *vr, integer *ldvr, doublereal *work, + integer *lwork, integer *info); + +/* Subroutine */ int dgeevx_(char *balanc, char *jobvl, char *jobvr, char * + sense, integer *n, doublereal *a, integer *lda, doublereal *wr, + doublereal *wi, doublereal *vl, integer *ldvl, doublereal *vr, + integer *ldvr, integer *ilo, integer *ihi, doublereal *scale, + doublereal *abnrm, doublereal *rconde, doublereal *rcondv, doublereal + *work, integer *lwork, integer *iwork, integer *info); + +/* Subroutine */ int dgegs_(char *jobvsl, char *jobvsr, integer *n, + doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal * + alphar, doublereal *alphai, doublereal *beta, doublereal *vsl, + integer *ldvsl, doublereal *vsr, integer *ldvsr, doublereal *work, + integer *lwork, integer *info); + +/* Subroutine */ int dgegv_(char *jobvl, char *jobvr, integer *n, doublereal * + a, integer *lda, doublereal *b, integer *ldb, doublereal *alphar, + doublereal *alphai, doublereal *beta, doublereal *vl, integer *ldvl, + doublereal *vr, integer *ldvr, doublereal *work, integer *lwork, + integer *info); + +/* Subroutine */ int dgehd2_(integer *n, integer *ilo, integer *ihi, + doublereal *a, integer *lda, doublereal *tau, doublereal *work, + integer *info); + +/* Subroutine */ int dgehrd_(integer *n, integer *ilo, integer *ihi, + doublereal *a, integer *lda, doublereal *tau, doublereal *work, + integer *lwork, integer *info); + +/* Subroutine */ int dgejsv_(char *joba, char *jobu, char *jobv, char *jobr, + char *jobt, char *jobp, integer *m, integer *n, doublereal *a, + integer *lda, doublereal *sva, doublereal *u, integer *ldu, + doublereal *v, integer *ldv, doublereal *work, integer *lwork, + integer *iwork, integer *info); + +/* Subroutine */ int dgelq2_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *tau, doublereal *work, integer *info); + +/* Subroutine */ int dgelqf_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *tau, doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dgels_(char *trans, integer *m, integer *n, integer * + nrhs, doublereal *a, integer *lda, doublereal *b, integer *ldb, + doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dgelsd_(integer *m, integer *n, integer *nrhs, + doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal * + s, doublereal *rcond, integer *rank, doublereal *work, integer *lwork, + integer *iwork, integer *info); + +/* Subroutine */ int dgelss_(integer *m, integer *n, integer *nrhs, + doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal * + s, doublereal *rcond, integer *rank, doublereal *work, integer *lwork, + integer *info); + +/* Subroutine */ int dgelsx_(integer *m, integer *n, integer *nrhs, + doublereal *a, integer *lda, doublereal *b, integer *ldb, integer * + jpvt, doublereal *rcond, integer *rank, doublereal *work, integer * + info); + +/* Subroutine */ int dgelsy_(integer *m, integer *n, integer *nrhs, + doublereal *a, integer *lda, doublereal *b, integer *ldb, integer * + jpvt, doublereal *rcond, integer *rank, doublereal *work, integer * + lwork, integer *info); + +/* Subroutine */ int dgeql2_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *tau, doublereal *work, integer *info); + +/* Subroutine */ int dgeqlf_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *tau, doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dgeqp3_(integer *m, integer *n, doublereal *a, integer * + lda, integer *jpvt, doublereal *tau, doublereal *work, integer *lwork, + integer *info); + +/* Subroutine */ int dgeqpf_(integer *m, integer *n, doublereal *a, integer * + lda, integer *jpvt, doublereal *tau, doublereal *work, integer *info); + +/* Subroutine */ int dgeqr2_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *tau, doublereal *work, integer *info); + +/* Subroutine */ int dgeqrf_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *tau, doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dgerfs_(char *trans, integer *n, integer *nrhs, + doublereal *a, integer *lda, doublereal *af, integer *ldaf, integer * + ipiv, doublereal *b, integer *ldb, doublereal *x, integer *ldx, + doublereal *ferr, doublereal *berr, doublereal *work, integer *iwork, + integer *info); + +/* Subroutine */ int dgerfsx_(char *trans, char *equed, integer *n, integer * + nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf, + integer *ipiv, doublereal *r__, doublereal *c__, doublereal *b, + integer *ldb, doublereal *x, integer *ldx, doublereal *rcond, + doublereal *berr, integer *n_err_bnds__, doublereal *err_bnds_norm__, + doublereal *err_bnds_comp__, integer *nparams, doublereal *params, + doublereal *work, integer *iwork, integer *info); + +/* Subroutine */ int dgerq2_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *tau, doublereal *work, integer *info); + +/* Subroutine */ int dgerqf_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *tau, doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dgesc2_(integer *n, doublereal *a, integer *lda, + doublereal *rhs, integer *ipiv, integer *jpiv, doublereal *scale); + +/* Subroutine */ int dgesdd_(char *jobz, integer *m, integer *n, doublereal * + a, integer *lda, doublereal *s, doublereal *u, integer *ldu, + doublereal *vt, integer *ldvt, doublereal *work, integer *lwork, + integer *iwork, integer *info); + +/* Subroutine */ int dgesv_(integer *n, integer *nrhs, doublereal *a, integer + *lda, integer *ipiv, doublereal *b, integer *ldb, integer *info); + +/* Subroutine */ int dgesvd_(char *jobu, char *jobvt, integer *m, integer *n, + doublereal *a, integer *lda, doublereal *s, doublereal *u, integer * + ldu, doublereal *vt, integer *ldvt, doublereal *work, integer *lwork, + integer *info); + +/* Subroutine */ int dgesvj_(char *joba, char *jobu, char *jobv, integer *m, + integer *n, doublereal *a, integer *lda, doublereal *sva, integer *mv, + doublereal *v, integer *ldv, doublereal *work, integer *lwork, + integer *info); + +/* Subroutine */ int dgesvx_(char *fact, char *trans, integer *n, integer * + nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf, + integer *ipiv, char *equed, doublereal *r__, doublereal *c__, + doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal * + rcond, doublereal *ferr, doublereal *berr, doublereal *work, integer * + iwork, integer *info); + +/* Subroutine */ int dgesvxx_(char *fact, char *trans, integer *n, integer * + nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf, + integer *ipiv, char *equed, doublereal *r__, doublereal *c__, + doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal * + rcond, doublereal *rpvgrw, doublereal *berr, integer *n_err_bnds__, + doublereal *err_bnds_norm__, doublereal *err_bnds_comp__, integer * + nparams, doublereal *params, doublereal *work, integer *iwork, + integer *info); + +/* Subroutine */ int dgetc2_(integer *n, doublereal *a, integer *lda, integer + *ipiv, integer *jpiv, integer *info); + +/* Subroutine */ int dgetf2_(integer *m, integer *n, doublereal *a, integer * + lda, integer *ipiv, integer *info); + +/* Subroutine */ int dgetrf_(integer *m, integer *n, doublereal *a, integer * + lda, integer *ipiv, integer *info); + +/* Subroutine */ int dgetri_(integer *n, doublereal *a, integer *lda, integer + *ipiv, doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dgetrs_(char *trans, integer *n, integer *nrhs, + doublereal *a, integer *lda, integer *ipiv, doublereal *b, integer * + ldb, integer *info); + +/* Subroutine */ int dggbak_(char *job, char *side, integer *n, integer *ilo, + integer *ihi, doublereal *lscale, doublereal *rscale, integer *m, + doublereal *v, integer *ldv, integer *info); + +/* Subroutine */ int dggbal_(char *job, integer *n, doublereal *a, integer * + lda, doublereal *b, integer *ldb, integer *ilo, integer *ihi, + doublereal *lscale, doublereal *rscale, doublereal *work, integer * + info); + +/* Subroutine */ int dgges_(char *jobvsl, char *jobvsr, char *sort, L_fp + selctg, integer *n, doublereal *a, integer *lda, doublereal *b, + integer *ldb, integer *sdim, doublereal *alphar, doublereal *alphai, + doublereal *beta, doublereal *vsl, integer *ldvsl, doublereal *vsr, + integer *ldvsr, doublereal *work, integer *lwork, logical *bwork, + integer *info); + +/* Subroutine */ int dggesx_(char *jobvsl, char *jobvsr, char *sort, L_fp + selctg, char *sense, integer *n, doublereal *a, integer *lda, + doublereal *b, integer *ldb, integer *sdim, doublereal *alphar, + doublereal *alphai, doublereal *beta, doublereal *vsl, integer *ldvsl, + doublereal *vsr, integer *ldvsr, doublereal *rconde, doublereal * + rcondv, doublereal *work, integer *lwork, integer *iwork, integer * + liwork, logical *bwork, integer *info); + +/* Subroutine */ int dggev_(char *jobvl, char *jobvr, integer *n, doublereal * + a, integer *lda, doublereal *b, integer *ldb, doublereal *alphar, + doublereal *alphai, doublereal *beta, doublereal *vl, integer *ldvl, + doublereal *vr, integer *ldvr, doublereal *work, integer *lwork, + integer *info); + +/* Subroutine */ int dggevx_(char *balanc, char *jobvl, char *jobvr, char * + sense, integer *n, doublereal *a, integer *lda, doublereal *b, + integer *ldb, doublereal *alphar, doublereal *alphai, doublereal * + beta, doublereal *vl, integer *ldvl, doublereal *vr, integer *ldvr, + integer *ilo, integer *ihi, doublereal *lscale, doublereal *rscale, + doublereal *abnrm, doublereal *bbnrm, doublereal *rconde, doublereal * + rcondv, doublereal *work, integer *lwork, integer *iwork, logical * + bwork, integer *info); + +/* Subroutine */ int dggglm_(integer *n, integer *m, integer *p, doublereal * + a, integer *lda, doublereal *b, integer *ldb, doublereal *d__, + doublereal *x, doublereal *y, doublereal *work, integer *lwork, + integer *info); + +/* Subroutine */ int dgghrd_(char *compq, char *compz, integer *n, integer * + ilo, integer *ihi, doublereal *a, integer *lda, doublereal *b, + integer *ldb, doublereal *q, integer *ldq, doublereal *z__, integer * + ldz, integer *info); + +/* Subroutine */ int dgglse_(integer *m, integer *n, integer *p, doublereal * + a, integer *lda, doublereal *b, integer *ldb, doublereal *c__, + doublereal *d__, doublereal *x, doublereal *work, integer *lwork, + integer *info); + +/* Subroutine */ int dggqrf_(integer *n, integer *m, integer *p, doublereal * + a, integer *lda, doublereal *taua, doublereal *b, integer *ldb, + doublereal *taub, doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dggrqf_(integer *m, integer *p, integer *n, doublereal * + a, integer *lda, doublereal *taua, doublereal *b, integer *ldb, + doublereal *taub, doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dggsvd_(char *jobu, char *jobv, char *jobq, integer *m, + integer *n, integer *p, integer *k, integer *l, doublereal *a, + integer *lda, doublereal *b, integer *ldb, doublereal *alpha, + doublereal *beta, doublereal *u, integer *ldu, doublereal *v, integer + *ldv, doublereal *q, integer *ldq, doublereal *work, integer *iwork, + integer *info); + +/* Subroutine */ int dggsvp_(char *jobu, char *jobv, char *jobq, integer *m, + integer *p, integer *n, doublereal *a, integer *lda, doublereal *b, + integer *ldb, doublereal *tola, doublereal *tolb, integer *k, integer + *l, doublereal *u, integer *ldu, doublereal *v, integer *ldv, + doublereal *q, integer *ldq, integer *iwork, doublereal *tau, + doublereal *work, integer *info); + +/* Subroutine */ int dgsvj0_(char *jobv, integer *m, integer *n, doublereal * + a, integer *lda, doublereal *d__, doublereal *sva, integer *mv, + doublereal *v, integer *ldv, doublereal *eps, doublereal *sfmin, + doublereal *tol, integer *nsweep, doublereal *work, integer *lwork, + integer *info); + +/* Subroutine */ int dgsvj1_(char *jobv, integer *m, integer *n, integer *n1, + doublereal *a, integer *lda, doublereal *d__, doublereal *sva, + integer *mv, doublereal *v, integer *ldv, doublereal *eps, doublereal + *sfmin, doublereal *tol, integer *nsweep, doublereal *work, integer * + lwork, integer *info); + +/* Subroutine */ int dgtcon_(char *norm, integer *n, doublereal *dl, + doublereal *d__, doublereal *du, doublereal *du2, integer *ipiv, + doublereal *anorm, doublereal *rcond, doublereal *work, integer * + iwork, integer *info); + +/* Subroutine */ int dgtrfs_(char *trans, integer *n, integer *nrhs, + doublereal *dl, doublereal *d__, doublereal *du, doublereal *dlf, + doublereal *df, doublereal *duf, doublereal *du2, integer *ipiv, + doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal * + ferr, doublereal *berr, doublereal *work, integer *iwork, integer * + info); + +/* Subroutine */ int dgtsv_(integer *n, integer *nrhs, doublereal *dl, + doublereal *d__, doublereal *du, doublereal *b, integer *ldb, integer + *info); + +/* Subroutine */ int dgtsvx_(char *fact, char *trans, integer *n, integer * + nrhs, doublereal *dl, doublereal *d__, doublereal *du, doublereal * + dlf, doublereal *df, doublereal *duf, doublereal *du2, integer *ipiv, + doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal * + rcond, doublereal *ferr, doublereal *berr, doublereal *work, integer * + iwork, integer *info); + +/* Subroutine */ int dgttrf_(integer *n, doublereal *dl, doublereal *d__, + doublereal *du, doublereal *du2, integer *ipiv, integer *info); + +/* Subroutine */ int dgttrs_(char *trans, integer *n, integer *nrhs, + doublereal *dl, doublereal *d__, doublereal *du, doublereal *du2, + integer *ipiv, doublereal *b, integer *ldb, integer *info); + +/* Subroutine */ int dgtts2_(integer *itrans, integer *n, integer *nrhs, + doublereal *dl, doublereal *d__, doublereal *du, doublereal *du2, + integer *ipiv, doublereal *b, integer *ldb); + +/* Subroutine */ int dhgeqz_(char *job, char *compq, char *compz, integer *n, + integer *ilo, integer *ihi, doublereal *h__, integer *ldh, doublereal + *t, integer *ldt, doublereal *alphar, doublereal *alphai, doublereal * + beta, doublereal *q, integer *ldq, doublereal *z__, integer *ldz, + doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dhsein_(char *side, char *eigsrc, char *initv, logical * + select, integer *n, doublereal *h__, integer *ldh, doublereal *wr, + doublereal *wi, doublereal *vl, integer *ldvl, doublereal *vr, + integer *ldvr, integer *mm, integer *m, doublereal *work, integer * + ifaill, integer *ifailr, integer *info); + +/* Subroutine */ int dhseqr_(char *job, char *compz, integer *n, integer *ilo, + integer *ihi, doublereal *h__, integer *ldh, doublereal *wr, + doublereal *wi, doublereal *z__, integer *ldz, doublereal *work, + integer *lwork, integer *info); + +logical disnan_(doublereal *din); + +/* Subroutine */ int dla_gbamv__(integer *trans, integer *m, integer *n, + integer *kl, integer *ku, doublereal *alpha, doublereal *ab, integer * + ldab, doublereal *x, integer *incx, doublereal *beta, doublereal *y, + integer *incy); + +doublereal dla_gbrcond__(char *trans, integer *n, integer *kl, integer *ku, + doublereal *ab, integer *ldab, doublereal *afb, integer *ldafb, + integer *ipiv, integer *cmode, doublereal *c__, integer *info, + doublereal *work, integer *iwork, ftnlen trans_len); + +/* Subroutine */ int dla_gbrfsx_extended__(integer *prec_type__, integer * + trans_type__, integer *n, integer *kl, integer *ku, integer *nrhs, + doublereal *ab, integer *ldab, doublereal *afb, integer *ldafb, + integer *ipiv, logical *colequ, doublereal *c__, doublereal *b, + integer *ldb, doublereal *y, integer *ldy, doublereal *berr_out__, + integer *n_norms__, doublereal *errs_n__, doublereal *errs_c__, + doublereal *res, doublereal *ayb, doublereal *dy, doublereal * + y_tail__, doublereal *rcond, integer *ithresh, doublereal *rthresh, + doublereal *dz_ub__, logical *ignore_cwise__, integer *info); + +doublereal dla_gbrpvgrw__(integer *n, integer *kl, integer *ku, integer * + ncols, doublereal *ab, integer *ldab, doublereal *afb, integer *ldafb); + +/* Subroutine */ int dla_geamv__(integer *trans, integer *m, integer *n, + doublereal *alpha, doublereal *a, integer *lda, doublereal *x, + integer *incx, doublereal *beta, doublereal *y, integer *incy); + +doublereal dla_gercond__(char *trans, integer *n, doublereal *a, integer *lda, + doublereal *af, integer *ldaf, integer *ipiv, integer *cmode, + doublereal *c__, integer *info, doublereal *work, integer *iwork, + ftnlen trans_len); + +/* Subroutine */ int dla_gerfsx_extended__(integer *prec_type__, integer * + trans_type__, integer *n, integer *nrhs, doublereal *a, integer *lda, + doublereal *af, integer *ldaf, integer *ipiv, logical *colequ, + doublereal *c__, doublereal *b, integer *ldb, doublereal *y, integer * + ldy, doublereal *berr_out__, integer *n_norms__, doublereal *errs_n__, + doublereal *errs_c__, doublereal *res, doublereal *ayb, doublereal * + dy, doublereal *y_tail__, doublereal *rcond, integer *ithresh, + doublereal *rthresh, doublereal *dz_ub__, logical *ignore_cwise__, + integer *info); + +/* Subroutine */ int dla_lin_berr__(integer *n, integer *nz, integer *nrhs, + doublereal *res, doublereal *ayb, doublereal *berr); + +doublereal dla_porcond__(char *uplo, integer *n, doublereal *a, integer *lda, + doublereal *af, integer *ldaf, integer *cmode, doublereal *c__, + integer *info, doublereal *work, integer *iwork, ftnlen uplo_len); + +/* Subroutine */ int dla_porfsx_extended__(integer *prec_type__, char *uplo, + integer *n, integer *nrhs, doublereal *a, integer *lda, doublereal * + af, integer *ldaf, logical *colequ, doublereal *c__, doublereal *b, + integer *ldb, doublereal *y, integer *ldy, doublereal *berr_out__, + integer *n_norms__, doublereal *errs_n__, doublereal *errs_c__, + doublereal *res, doublereal *ayb, doublereal *dy, doublereal * + y_tail__, doublereal *rcond, integer *ithresh, doublereal *rthresh, + doublereal *dz_ub__, logical *ignore_cwise__, integer *info, ftnlen + uplo_len); + +doublereal dla_porpvgrw__(char *uplo, integer *ncols, doublereal *a, integer * + lda, doublereal *af, integer *ldaf, doublereal *work, ftnlen uplo_len); + +doublereal dla_rpvgrw__(integer *n, integer *ncols, doublereal *a, integer * + lda, doublereal *af, integer *ldaf); + +/* Subroutine */ int dla_syamv__(integer *uplo, integer *n, doublereal *alpha, + doublereal *a, integer *lda, doublereal *x, integer *incx, + doublereal *beta, doublereal *y, integer *incy); + +doublereal dla_syrcond__(char *uplo, integer *n, doublereal *a, integer *lda, + doublereal *af, integer *ldaf, integer *ipiv, integer *cmode, + doublereal *c__, integer *info, doublereal *work, integer *iwork, + ftnlen uplo_len); + +/* Subroutine */ int dla_syrfsx_extended__(integer *prec_type__, char *uplo, + integer *n, integer *nrhs, doublereal *a, integer *lda, doublereal * + af, integer *ldaf, integer *ipiv, logical *colequ, doublereal *c__, + doublereal *b, integer *ldb, doublereal *y, integer *ldy, doublereal * + berr_out__, integer *n_norms__, doublereal *errs_n__, doublereal * + errs_c__, doublereal *res, doublereal *ayb, doublereal *dy, + doublereal *y_tail__, doublereal *rcond, integer *ithresh, doublereal + *rthresh, doublereal *dz_ub__, logical *ignore_cwise__, integer *info, + ftnlen uplo_len); + +doublereal dla_syrpvgrw__(char *uplo, integer *n, integer *info, doublereal * + a, integer *lda, doublereal *af, integer *ldaf, integer *ipiv, + doublereal *work, ftnlen uplo_len); + +/* Subroutine */ int dla_wwaddw__(integer *n, doublereal *x, doublereal *y, + doublereal *w); + +/* Subroutine */ int dlabad_(doublereal *small, doublereal *large); + +/* Subroutine */ int dlabrd_(integer *m, integer *n, integer *nb, doublereal * + a, integer *lda, doublereal *d__, doublereal *e, doublereal *tauq, + doublereal *taup, doublereal *x, integer *ldx, doublereal *y, integer + *ldy); + +/* Subroutine */ int dlacn2_(integer *n, doublereal *v, doublereal *x, + integer *isgn, doublereal *est, integer *kase, integer *isave); + +/* Subroutine */ int dlacon_(integer *n, doublereal *v, doublereal *x, + integer *isgn, doublereal *est, integer *kase); + +/* Subroutine */ int dlacpy_(char *uplo, integer *m, integer *n, doublereal * + a, integer *lda, doublereal *b, integer *ldb); + +/* Subroutine */ int dladiv_(doublereal *a, doublereal *b, doublereal *c__, + doublereal *d__, doublereal *p, doublereal *q); + +/* Subroutine */ int dlae2_(doublereal *a, doublereal *b, doublereal *c__, + doublereal *rt1, doublereal *rt2); + +/* Subroutine */ int dlaebz_(integer *ijob, integer *nitmax, integer *n, + integer *mmax, integer *minp, integer *nbmin, doublereal *abstol, + doublereal *reltol, doublereal *pivmin, doublereal *d__, doublereal * + e, doublereal *e2, integer *nval, doublereal *ab, doublereal *c__, + integer *mout, integer *nab, doublereal *work, integer *iwork, + integer *info); + +/* Subroutine */ int dlaed0_(integer *icompq, integer *qsiz, integer *n, + doublereal *d__, doublereal *e, doublereal *q, integer *ldq, + doublereal *qstore, integer *ldqs, doublereal *work, integer *iwork, + integer *info); + +/* Subroutine */ int dlaed1_(integer *n, doublereal *d__, doublereal *q, + integer *ldq, integer *indxq, doublereal *rho, integer *cutpnt, + doublereal *work, integer *iwork, integer *info); + +/* Subroutine */ int dlaed2_(integer *k, integer *n, integer *n1, doublereal * + d__, doublereal *q, integer *ldq, integer *indxq, doublereal *rho, + doublereal *z__, doublereal *dlamda, doublereal *w, doublereal *q2, + integer *indx, integer *indxc, integer *indxp, integer *coltyp, + integer *info); + +/* Subroutine */ int dlaed3_(integer *k, integer *n, integer *n1, doublereal * + d__, doublereal *q, integer *ldq, doublereal *rho, doublereal *dlamda, + doublereal *q2, integer *indx, integer *ctot, doublereal *w, + doublereal *s, integer *info); + +/* Subroutine */ int dlaed4_(integer *n, integer *i__, doublereal *d__, + doublereal *z__, doublereal *delta, doublereal *rho, doublereal *dlam, + integer *info); + +/* Subroutine */ int dlaed5_(integer *i__, doublereal *d__, doublereal *z__, + doublereal *delta, doublereal *rho, doublereal *dlam); + +/* Subroutine */ int dlaed6_(integer *kniter, logical *orgati, doublereal * + rho, doublereal *d__, doublereal *z__, doublereal *finit, doublereal * + tau, integer *info); + +/* Subroutine */ int dlaed7_(integer *icompq, integer *n, integer *qsiz, + integer *tlvls, integer *curlvl, integer *curpbm, doublereal *d__, + doublereal *q, integer *ldq, integer *indxq, doublereal *rho, integer + *cutpnt, doublereal *qstore, integer *qptr, integer *prmptr, integer * + perm, integer *givptr, integer *givcol, doublereal *givnum, + doublereal *work, integer *iwork, integer *info); + +/* Subroutine */ int dlaed8_(integer *icompq, integer *k, integer *n, integer + *qsiz, doublereal *d__, doublereal *q, integer *ldq, integer *indxq, + doublereal *rho, integer *cutpnt, doublereal *z__, doublereal *dlamda, + doublereal *q2, integer *ldq2, doublereal *w, integer *perm, integer + *givptr, integer *givcol, doublereal *givnum, integer *indxp, integer + *indx, integer *info); + +/* Subroutine */ int dlaed9_(integer *k, integer *kstart, integer *kstop, + integer *n, doublereal *d__, doublereal *q, integer *ldq, doublereal * + rho, doublereal *dlamda, doublereal *w, doublereal *s, integer *lds, + integer *info); + +/* Subroutine */ int dlaeda_(integer *n, integer *tlvls, integer *curlvl, + integer *curpbm, integer *prmptr, integer *perm, integer *givptr, + integer *givcol, doublereal *givnum, doublereal *q, integer *qptr, + doublereal *z__, doublereal *ztemp, integer *info); + +/* Subroutine */ int dlaein_(logical *rightv, logical *noinit, integer *n, + doublereal *h__, integer *ldh, doublereal *wr, doublereal *wi, + doublereal *vr, doublereal *vi, doublereal *b, integer *ldb, + doublereal *work, doublereal *eps3, doublereal *smlnum, doublereal * + bignum, integer *info); + +/* Subroutine */ int dlaev2_(doublereal *a, doublereal *b, doublereal *c__, + doublereal *rt1, doublereal *rt2, doublereal *cs1, doublereal *sn1); + +/* Subroutine */ int dlaexc_(logical *wantq, integer *n, doublereal *t, + integer *ldt, doublereal *q, integer *ldq, integer *j1, integer *n1, + integer *n2, doublereal *work, integer *info); + +/* Subroutine */ int dlag2_(doublereal *a, integer *lda, doublereal *b, + integer *ldb, doublereal *safmin, doublereal *scale1, doublereal * + scale2, doublereal *wr1, doublereal *wr2, doublereal *wi); + +/* Subroutine */ int dlag2s_(integer *m, integer *n, doublereal *a, integer * + lda, real *sa, integer *ldsa, integer *info); + +/* Subroutine */ int dlags2_(logical *upper, doublereal *a1, doublereal *a2, + doublereal *a3, doublereal *b1, doublereal *b2, doublereal *b3, + doublereal *csu, doublereal *snu, doublereal *csv, doublereal *snv, + doublereal *csq, doublereal *snq); + +/* Subroutine */ int dlagtf_(integer *n, doublereal *a, doublereal *lambda, + doublereal *b, doublereal *c__, doublereal *tol, doublereal *d__, + integer *in, integer *info); + +/* Subroutine */ int dlagtm_(char *trans, integer *n, integer *nrhs, + doublereal *alpha, doublereal *dl, doublereal *d__, doublereal *du, + doublereal *x, integer *ldx, doublereal *beta, doublereal *b, integer + *ldb); + +/* Subroutine */ int dlagts_(integer *job, integer *n, doublereal *a, + doublereal *b, doublereal *c__, doublereal *d__, integer *in, + doublereal *y, doublereal *tol, integer *info); + +/* Subroutine */ int dlagv2_(doublereal *a, integer *lda, doublereal *b, + integer *ldb, doublereal *alphar, doublereal *alphai, doublereal * + beta, doublereal *csl, doublereal *snl, doublereal *csr, doublereal * + snr); + +/* Subroutine */ int dlahqr_(logical *wantt, logical *wantz, integer *n, + integer *ilo, integer *ihi, doublereal *h__, integer *ldh, doublereal + *wr, doublereal *wi, integer *iloz, integer *ihiz, doublereal *z__, + integer *ldz, integer *info); + +/* Subroutine */ int dlahr2_(integer *n, integer *k, integer *nb, doublereal * + a, integer *lda, doublereal *tau, doublereal *t, integer *ldt, + doublereal *y, integer *ldy); + +/* Subroutine */ int dlahrd_(integer *n, integer *k, integer *nb, doublereal * + a, integer *lda, doublereal *tau, doublereal *t, integer *ldt, + doublereal *y, integer *ldy); + +/* Subroutine */ int dlaic1_(integer *job, integer *j, doublereal *x, + doublereal *sest, doublereal *w, doublereal *gamma, doublereal * + sestpr, doublereal *s, doublereal *c__); + +logical dlaisnan_(doublereal *din1, doublereal *din2); + +/* Subroutine */ int dlaln2_(logical *ltrans, integer *na, integer *nw, + doublereal *smin, doublereal *ca, doublereal *a, integer *lda, + doublereal *d1, doublereal *d2, doublereal *b, integer *ldb, + doublereal *wr, doublereal *wi, doublereal *x, integer *ldx, + doublereal *scale, doublereal *xnorm, integer *info); + +/* Subroutine */ int dlals0_(integer *icompq, integer *nl, integer *nr, + integer *sqre, integer *nrhs, doublereal *b, integer *ldb, doublereal + *bx, integer *ldbx, integer *perm, integer *givptr, integer *givcol, + integer *ldgcol, doublereal *givnum, integer *ldgnum, doublereal * + poles, doublereal *difl, doublereal *difr, doublereal *z__, integer * + k, doublereal *c__, doublereal *s, doublereal *work, integer *info); + +/* Subroutine */ int dlalsa_(integer *icompq, integer *smlsiz, integer *n, + integer *nrhs, doublereal *b, integer *ldb, doublereal *bx, integer * + ldbx, doublereal *u, integer *ldu, doublereal *vt, integer *k, + doublereal *difl, doublereal *difr, doublereal *z__, doublereal * + poles, integer *givptr, integer *givcol, integer *ldgcol, integer * + perm, doublereal *givnum, doublereal *c__, doublereal *s, doublereal * + work, integer *iwork, integer *info); + +/* Subroutine */ int dlalsd_(char *uplo, integer *smlsiz, integer *n, integer + *nrhs, doublereal *d__, doublereal *e, doublereal *b, integer *ldb, + doublereal *rcond, integer *rank, doublereal *work, integer *iwork, + integer *info); + +/* Subroutine */ int dlamrg_(integer *n1, integer *n2, doublereal *a, integer + *dtrd1, integer *dtrd2, integer *index); + +integer dlaneg_(integer *n, doublereal *d__, doublereal *lld, doublereal * + sigma, doublereal *pivmin, integer *r__); + +doublereal dlangb_(char *norm, integer *n, integer *kl, integer *ku, + doublereal *ab, integer *ldab, doublereal *work); + +doublereal dlange_(char *norm, integer *m, integer *n, doublereal *a, integer + *lda, doublereal *work); + +doublereal dlangt_(char *norm, integer *n, doublereal *dl, doublereal *d__, + doublereal *du); + +doublereal dlanhs_(char *norm, integer *n, doublereal *a, integer *lda, + doublereal *work); + +doublereal dlansb_(char *norm, char *uplo, integer *n, integer *k, doublereal + *ab, integer *ldab, doublereal *work); + +doublereal dlansf_(char *norm, char *transr, char *uplo, integer *n, + doublereal *a, doublereal *work); + +doublereal dlansp_(char *norm, char *uplo, integer *n, doublereal *ap, + doublereal *work); + +doublereal dlanst_(char *norm, integer *n, doublereal *d__, doublereal *e); + +doublereal dlansy_(char *norm, char *uplo, integer *n, doublereal *a, integer + *lda, doublereal *work); + +doublereal dlantb_(char *norm, char *uplo, char *diag, integer *n, integer *k, + doublereal *ab, integer *ldab, doublereal *work); + +doublereal dlantp_(char *norm, char *uplo, char *diag, integer *n, doublereal + *ap, doublereal *work); + +doublereal dlantr_(char *norm, char *uplo, char *diag, integer *m, integer *n, + doublereal *a, integer *lda, doublereal *work); + +/* Subroutine */ int dlanv2_(doublereal *a, doublereal *b, doublereal *c__, + doublereal *d__, doublereal *rt1r, doublereal *rt1i, doublereal *rt2r, + doublereal *rt2i, doublereal *cs, doublereal *sn); + +/* Subroutine */ int dlapll_(integer *n, doublereal *x, integer *incx, + doublereal *y, integer *incy, doublereal *ssmin); + +/* Subroutine */ int dlapmt_(logical *forwrd, integer *m, integer *n, + doublereal *x, integer *ldx, integer *k); + +doublereal dlapy2_(doublereal *x, doublereal *y); + +doublereal dlapy3_(doublereal *x, doublereal *y, doublereal *z__); + +/* Subroutine */ int dlaqgb_(integer *m, integer *n, integer *kl, integer *ku, + doublereal *ab, integer *ldab, doublereal *r__, doublereal *c__, + doublereal *rowcnd, doublereal *colcnd, doublereal *amax, char *equed); + +/* Subroutine */ int dlaqge_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *r__, doublereal *c__, doublereal *rowcnd, doublereal + *colcnd, doublereal *amax, char *equed); + +/* Subroutine */ int dlaqp2_(integer *m, integer *n, integer *offset, + doublereal *a, integer *lda, integer *jpvt, doublereal *tau, + doublereal *vn1, doublereal *vn2, doublereal *work); + +/* Subroutine */ int dlaqps_(integer *m, integer *n, integer *offset, integer + *nb, integer *kb, doublereal *a, integer *lda, integer *jpvt, + doublereal *tau, doublereal *vn1, doublereal *vn2, doublereal *auxv, + doublereal *f, integer *ldf); + +/* Subroutine */ int dlaqr0_(logical *wantt, logical *wantz, integer *n, + integer *ilo, integer *ihi, doublereal *h__, integer *ldh, doublereal + *wr, doublereal *wi, integer *iloz, integer *ihiz, doublereal *z__, + integer *ldz, doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dlaqr1_(integer *n, doublereal *h__, integer *ldh, + doublereal *sr1, doublereal *si1, doublereal *sr2, doublereal *si2, + doublereal *v); + +/* Subroutine */ int dlaqr2_(logical *wantt, logical *wantz, integer *n, + integer *ktop, integer *kbot, integer *nw, doublereal *h__, integer * + ldh, integer *iloz, integer *ihiz, doublereal *z__, integer *ldz, + integer *ns, integer *nd, doublereal *sr, doublereal *si, doublereal * + v, integer *ldv, integer *nh, doublereal *t, integer *ldt, integer * + nv, doublereal *wv, integer *ldwv, doublereal *work, integer *lwork); + +/* Subroutine */ int dlaqr3_(logical *wantt, logical *wantz, integer *n, + integer *ktop, integer *kbot, integer *nw, doublereal *h__, integer * + ldh, integer *iloz, integer *ihiz, doublereal *z__, integer *ldz, + integer *ns, integer *nd, doublereal *sr, doublereal *si, doublereal * + v, integer *ldv, integer *nh, doublereal *t, integer *ldt, integer * + nv, doublereal *wv, integer *ldwv, doublereal *work, integer *lwork); + +/* Subroutine */ int dlaqr4_(logical *wantt, logical *wantz, integer *n, + integer *ilo, integer *ihi, doublereal *h__, integer *ldh, doublereal + *wr, doublereal *wi, integer *iloz, integer *ihiz, doublereal *z__, + integer *ldz, doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dlaqr5_(logical *wantt, logical *wantz, integer *kacc22, + integer *n, integer *ktop, integer *kbot, integer *nshfts, doublereal + *sr, doublereal *si, doublereal *h__, integer *ldh, integer *iloz, + integer *ihiz, doublereal *z__, integer *ldz, doublereal *v, integer * + ldv, doublereal *u, integer *ldu, integer *nv, doublereal *wv, + integer *ldwv, integer *nh, doublereal *wh, integer *ldwh); + +/* Subroutine */ int dlaqsb_(char *uplo, integer *n, integer *kd, doublereal * + ab, integer *ldab, doublereal *s, doublereal *scond, doublereal *amax, + char *equed); + +/* Subroutine */ int dlaqsp_(char *uplo, integer *n, doublereal *ap, + doublereal *s, doublereal *scond, doublereal *amax, char *equed); + +/* Subroutine */ int dlaqsy_(char *uplo, integer *n, doublereal *a, integer * + lda, doublereal *s, doublereal *scond, doublereal *amax, char *equed); + +/* Subroutine */ int dlaqtr_(logical *ltran, logical *lreal, integer *n, + doublereal *t, integer *ldt, doublereal *b, doublereal *w, doublereal + *scale, doublereal *x, doublereal *work, integer *info); + +/* Subroutine */ int dlar1v_(integer *n, integer *b1, integer *bn, doublereal + *lambda, doublereal *d__, doublereal *l, doublereal *ld, doublereal * + lld, doublereal *pivmin, doublereal *gaptol, doublereal *z__, logical + *wantnc, integer *negcnt, doublereal *ztz, doublereal *mingma, + integer *r__, integer *isuppz, doublereal *nrminv, doublereal *resid, + doublereal *rqcorr, doublereal *work); + +/* Subroutine */ int dlar2v_(integer *n, doublereal *x, doublereal *y, + doublereal *z__, integer *incx, doublereal *c__, doublereal *s, + integer *incc); + +/* Subroutine */ int dlarf_(char *side, integer *m, integer *n, doublereal *v, + integer *incv, doublereal *tau, doublereal *c__, integer *ldc, + doublereal *work); + +/* Subroutine */ int dlarfb_(char *side, char *trans, char *direct, char * + storev, integer *m, integer *n, integer *k, doublereal *v, integer * + ldv, doublereal *t, integer *ldt, doublereal *c__, integer *ldc, + doublereal *work, integer *ldwork); + +/* Subroutine */ int dlarfg_(integer *n, doublereal *alpha, doublereal *x, + integer *incx, doublereal *tau); + +/* Subroutine */ int dlarfp_(integer *n, doublereal *alpha, doublereal *x, + integer *incx, doublereal *tau); + +/* Subroutine */ int dlarft_(char *direct, char *storev, integer *n, integer * + k, doublereal *v, integer *ldv, doublereal *tau, doublereal *t, + integer *ldt); + +/* Subroutine */ int dlarfx_(char *side, integer *m, integer *n, doublereal * + v, doublereal *tau, doublereal *c__, integer *ldc, doublereal *work); + +/* Subroutine */ int dlargv_(integer *n, doublereal *x, integer *incx, + doublereal *y, integer *incy, doublereal *c__, integer *incc); + +/* Subroutine */ int dlarnv_(integer *idist, integer *iseed, integer *n, + doublereal *x); + +/* Subroutine */ int dlarra_(integer *n, doublereal *d__, doublereal *e, + doublereal *e2, doublereal *spltol, doublereal *tnrm, integer *nsplit, + integer *isplit, integer *info); + +/* Subroutine */ int dlarrb_(integer *n, doublereal *d__, doublereal *lld, + integer *ifirst, integer *ilast, doublereal *rtol1, doublereal *rtol2, + integer *offset, doublereal *w, doublereal *wgap, doublereal *werr, + doublereal *work, integer *iwork, doublereal *pivmin, doublereal * + spdiam, integer *twist, integer *info); + +/* Subroutine */ int dlarrc_(char *jobt, integer *n, doublereal *vl, + doublereal *vu, doublereal *d__, doublereal *e, doublereal *pivmin, + integer *eigcnt, integer *lcnt, integer *rcnt, integer *info); + +/* Subroutine */ int dlarrd_(char *range, char *order, integer *n, doublereal + *vl, doublereal *vu, integer *il, integer *iu, doublereal *gers, + doublereal *reltol, doublereal *d__, doublereal *e, doublereal *e2, + doublereal *pivmin, integer *nsplit, integer *isplit, integer *m, + doublereal *w, doublereal *werr, doublereal *wl, doublereal *wu, + integer *iblock, integer *indexw, doublereal *work, integer *iwork, + integer *info); + +/* Subroutine */ int dlarre_(char *range, integer *n, doublereal *vl, + doublereal *vu, integer *il, integer *iu, doublereal *d__, doublereal + *e, doublereal *e2, doublereal *rtol1, doublereal *rtol2, doublereal * + spltol, integer *nsplit, integer *isplit, integer *m, doublereal *w, + doublereal *werr, doublereal *wgap, integer *iblock, integer *indexw, + doublereal *gers, doublereal *pivmin, doublereal *work, integer * + iwork, integer *info); + +/* Subroutine */ int dlarrf_(integer *n, doublereal *d__, doublereal *l, + doublereal *ld, integer *clstrt, integer *clend, doublereal *w, + doublereal *wgap, doublereal *werr, doublereal *spdiam, doublereal * + clgapl, doublereal *clgapr, doublereal *pivmin, doublereal *sigma, + doublereal *dplus, doublereal *lplus, doublereal *work, integer *info); + +/* Subroutine */ int dlarrj_(integer *n, doublereal *d__, doublereal *e2, + integer *ifirst, integer *ilast, doublereal *rtol, integer *offset, + doublereal *w, doublereal *werr, doublereal *work, integer *iwork, + doublereal *pivmin, doublereal *spdiam, integer *info); + +/* Subroutine */ int dlarrk_(integer *n, integer *iw, doublereal *gl, + doublereal *gu, doublereal *d__, doublereal *e2, doublereal *pivmin, + doublereal *reltol, doublereal *w, doublereal *werr, integer *info); + +/* Subroutine */ int dlarrr_(integer *n, doublereal *d__, doublereal *e, + integer *info); + +/* Subroutine */ int dlarrv_(integer *n, doublereal *vl, doublereal *vu, + doublereal *d__, doublereal *l, doublereal *pivmin, integer *isplit, + integer *m, integer *dol, integer *dou, doublereal *minrgp, + doublereal *rtol1, doublereal *rtol2, doublereal *w, doublereal *werr, + doublereal *wgap, integer *iblock, integer *indexw, doublereal *gers, + doublereal *z__, integer *ldz, integer *isuppz, doublereal *work, + integer *iwork, integer *info); + +/* Subroutine */ int dlarscl2_(integer *m, integer *n, doublereal *d__, + doublereal *x, integer *ldx); + +/* Subroutine */ int dlartg_(doublereal *f, doublereal *g, doublereal *cs, + doublereal *sn, doublereal *r__); + +/* Subroutine */ int dlartv_(integer *n, doublereal *x, integer *incx, + doublereal *y, integer *incy, doublereal *c__, doublereal *s, integer + *incc); + +/* Subroutine */ int dlaruv_(integer *iseed, integer *n, doublereal *x); + +/* Subroutine */ int dlarz_(char *side, integer *m, integer *n, integer *l, + doublereal *v, integer *incv, doublereal *tau, doublereal *c__, + integer *ldc, doublereal *work); + +/* Subroutine */ int dlarzb_(char *side, char *trans, char *direct, char * + storev, integer *m, integer *n, integer *k, integer *l, doublereal *v, + integer *ldv, doublereal *t, integer *ldt, doublereal *c__, integer * + ldc, doublereal *work, integer *ldwork); + +/* Subroutine */ int dlarzt_(char *direct, char *storev, integer *n, integer * + k, doublereal *v, integer *ldv, doublereal *tau, doublereal *t, + integer *ldt); + +/* Subroutine */ int dlas2_(doublereal *f, doublereal *g, doublereal *h__, + doublereal *ssmin, doublereal *ssmax); + +/* Subroutine */ int dlascl_(char *type__, integer *kl, integer *ku, + doublereal *cfrom, doublereal *cto, integer *m, integer *n, + doublereal *a, integer *lda, integer *info); + +/* Subroutine */ int dlascl2_(integer *m, integer *n, doublereal *d__, + doublereal *x, integer *ldx); + +/* Subroutine */ int dlasd0_(integer *n, integer *sqre, doublereal *d__, + doublereal *e, doublereal *u, integer *ldu, doublereal *vt, integer * + ldvt, integer *smlsiz, integer *iwork, doublereal *work, integer * + info); + +/* Subroutine */ int dlasd1_(integer *nl, integer *nr, integer *sqre, + doublereal *d__, doublereal *alpha, doublereal *beta, doublereal *u, + integer *ldu, doublereal *vt, integer *ldvt, integer *idxq, integer * + iwork, doublereal *work, integer *info); + +/* Subroutine */ int dlasd2_(integer *nl, integer *nr, integer *sqre, integer + *k, doublereal *d__, doublereal *z__, doublereal *alpha, doublereal * + beta, doublereal *u, integer *ldu, doublereal *vt, integer *ldvt, + doublereal *dsigma, doublereal *u2, integer *ldu2, doublereal *vt2, + integer *ldvt2, integer *idxp, integer *idx, integer *idxc, integer * + idxq, integer *coltyp, integer *info); + +/* Subroutine */ int dlasd3_(integer *nl, integer *nr, integer *sqre, integer + *k, doublereal *d__, doublereal *q, integer *ldq, doublereal *dsigma, + doublereal *u, integer *ldu, doublereal *u2, integer *ldu2, + doublereal *vt, integer *ldvt, doublereal *vt2, integer *ldvt2, + integer *idxc, integer *ctot, doublereal *z__, integer *info); + +/* Subroutine */ int dlasd4_(integer *n, integer *i__, doublereal *d__, + doublereal *z__, doublereal *delta, doublereal *rho, doublereal * + sigma, doublereal *work, integer *info); + +/* Subroutine */ int dlasd5_(integer *i__, doublereal *d__, doublereal *z__, + doublereal *delta, doublereal *rho, doublereal *dsigma, doublereal * + work); + +/* Subroutine */ int dlasd6_(integer *icompq, integer *nl, integer *nr, + integer *sqre, doublereal *d__, doublereal *vf, doublereal *vl, + doublereal *alpha, doublereal *beta, integer *idxq, integer *perm, + integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum, + integer *ldgnum, doublereal *poles, doublereal *difl, doublereal * + difr, doublereal *z__, integer *k, doublereal *c__, doublereal *s, + doublereal *work, integer *iwork, integer *info); + +/* Subroutine */ int dlasd7_(integer *icompq, integer *nl, integer *nr, + integer *sqre, integer *k, doublereal *d__, doublereal *z__, + doublereal *zw, doublereal *vf, doublereal *vfw, doublereal *vl, + doublereal *vlw, doublereal *alpha, doublereal *beta, doublereal * + dsigma, integer *idx, integer *idxp, integer *idxq, integer *perm, + integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum, + integer *ldgnum, doublereal *c__, doublereal *s, integer *info); + +/* Subroutine */ int dlasd8_(integer *icompq, integer *k, doublereal *d__, + doublereal *z__, doublereal *vf, doublereal *vl, doublereal *difl, + doublereal *difr, integer *lddifr, doublereal *dsigma, doublereal * + work, integer *info); + +/* Subroutine */ int dlasda_(integer *icompq, integer *smlsiz, integer *n, + integer *sqre, doublereal *d__, doublereal *e, doublereal *u, integer + *ldu, doublereal *vt, integer *k, doublereal *difl, doublereal *difr, + doublereal *z__, doublereal *poles, integer *givptr, integer *givcol, + integer *ldgcol, integer *perm, doublereal *givnum, doublereal *c__, + doublereal *s, doublereal *work, integer *iwork, integer *info); + +/* Subroutine */ int dlasdq_(char *uplo, integer *sqre, integer *n, integer * + ncvt, integer *nru, integer *ncc, doublereal *d__, doublereal *e, + doublereal *vt, integer *ldvt, doublereal *u, integer *ldu, + doublereal *c__, integer *ldc, doublereal *work, integer *info); + +/* Subroutine */ int dlasdt_(integer *n, integer *lvl, integer *nd, integer * + inode, integer *ndiml, integer *ndimr, integer *msub); + +/* Subroutine */ int dlaset_(char *uplo, integer *m, integer *n, doublereal * + alpha, doublereal *beta, doublereal *a, integer *lda); + +/* Subroutine */ int dlasq1_(integer *n, doublereal *d__, doublereal *e, + doublereal *work, integer *info); + +/* Subroutine */ int dlasq2_(integer *n, doublereal *z__, integer *info); + +/* Subroutine */ int dlasq3_(integer *i0, integer *n0, doublereal *z__, + integer *pp, doublereal *dmin__, doublereal *sigma, doublereal *desig, + doublereal *qmax, integer *nfail, integer *iter, integer *ndiv, + logical *ieee, integer *ttype, doublereal *dmin1, doublereal *dmin2, + doublereal *dn, doublereal *dn1, doublereal *dn2, doublereal *g, + doublereal *tau); + +/* Subroutine */ int dlasq4_(integer *i0, integer *n0, doublereal *z__, + integer *pp, integer *n0in, doublereal *dmin__, doublereal *dmin1, + doublereal *dmin2, doublereal *dn, doublereal *dn1, doublereal *dn2, + doublereal *tau, integer *ttype, doublereal *g); + +/* Subroutine */ int dlasq5_(integer *i0, integer *n0, doublereal *z__, + integer *pp, doublereal *tau, doublereal *dmin__, doublereal *dmin1, + doublereal *dmin2, doublereal *dn, doublereal *dnm1, doublereal *dnm2, + logical *ieee); + +/* Subroutine */ int dlasq6_(integer *i0, integer *n0, doublereal *z__, + integer *pp, doublereal *dmin__, doublereal *dmin1, doublereal *dmin2, + doublereal *dn, doublereal *dnm1, doublereal *dnm2); + +/* Subroutine */ int dlasr_(char *side, char *pivot, char *direct, integer *m, + integer *n, doublereal *c__, doublereal *s, doublereal *a, integer * + lda); + +/* Subroutine */ int dlasrt_(char *id, integer *n, doublereal *d__, integer * + info); + +/* Subroutine */ int dlassq_(integer *n, doublereal *x, integer *incx, + doublereal *scale, doublereal *sumsq); + +/* Subroutine */ int dlasv2_(doublereal *f, doublereal *g, doublereal *h__, + doublereal *ssmin, doublereal *ssmax, doublereal *snr, doublereal * + csr, doublereal *snl, doublereal *csl); + +/* Subroutine */ int dlaswp_(integer *n, doublereal *a, integer *lda, integer + *k1, integer *k2, integer *ipiv, integer *incx); + +/* Subroutine */ int dlasy2_(logical *ltranl, logical *ltranr, integer *isgn, + integer *n1, integer *n2, doublereal *tl, integer *ldtl, doublereal * + tr, integer *ldtr, doublereal *b, integer *ldb, doublereal *scale, + doublereal *x, integer *ldx, doublereal *xnorm, integer *info); + +/* Subroutine */ int dlasyf_(char *uplo, integer *n, integer *nb, integer *kb, + doublereal *a, integer *lda, integer *ipiv, doublereal *w, integer * + ldw, integer *info); + +/* Subroutine */ int dlat2s_(char *uplo, integer *n, doublereal *a, integer * + lda, real *sa, integer *ldsa, integer *info); + +/* Subroutine */ int dlatbs_(char *uplo, char *trans, char *diag, char * + normin, integer *n, integer *kd, doublereal *ab, integer *ldab, + doublereal *x, doublereal *scale, doublereal *cnorm, integer *info); + +/* Subroutine */ int dlatdf_(integer *ijob, integer *n, doublereal *z__, + integer *ldz, doublereal *rhs, doublereal *rdsum, doublereal *rdscal, + integer *ipiv, integer *jpiv); + +/* Subroutine */ int dlatps_(char *uplo, char *trans, char *diag, char * + normin, integer *n, doublereal *ap, doublereal *x, doublereal *scale, + doublereal *cnorm, integer *info); + +/* Subroutine */ int dlatrd_(char *uplo, integer *n, integer *nb, doublereal * + a, integer *lda, doublereal *e, doublereal *tau, doublereal *w, + integer *ldw); + +/* Subroutine */ int dlatrs_(char *uplo, char *trans, char *diag, char * + normin, integer *n, doublereal *a, integer *lda, doublereal *x, + doublereal *scale, doublereal *cnorm, integer *info); + +/* Subroutine */ int dlatrz_(integer *m, integer *n, integer *l, doublereal * + a, integer *lda, doublereal *tau, doublereal *work); + +/* Subroutine */ int dlatzm_(char *side, integer *m, integer *n, doublereal * + v, integer *incv, doublereal *tau, doublereal *c1, doublereal *c2, + integer *ldc, doublereal *work); + +/* Subroutine */ int dlauu2_(char *uplo, integer *n, doublereal *a, integer * + lda, integer *info); + +/* Subroutine */ int dlauum_(char *uplo, integer *n, doublereal *a, integer * + lda, integer *info); + +/* Subroutine */ int dopgtr_(char *uplo, integer *n, doublereal *ap, + doublereal *tau, doublereal *q, integer *ldq, doublereal *work, + integer *info); + +/* Subroutine */ int dopmtr_(char *side, char *uplo, char *trans, integer *m, + integer *n, doublereal *ap, doublereal *tau, doublereal *c__, integer + *ldc, doublereal *work, integer *info); + +/* Subroutine */ int dorg2l_(integer *m, integer *n, integer *k, doublereal * + a, integer *lda, doublereal *tau, doublereal *work, integer *info); + +/* Subroutine */ int dorg2r_(integer *m, integer *n, integer *k, doublereal * + a, integer *lda, doublereal *tau, doublereal *work, integer *info); + +/* Subroutine */ int dorgbr_(char *vect, integer *m, integer *n, integer *k, + doublereal *a, integer *lda, doublereal *tau, doublereal *work, + integer *lwork, integer *info); + +/* Subroutine */ int dorghr_(integer *n, integer *ilo, integer *ihi, + doublereal *a, integer *lda, doublereal *tau, doublereal *work, + integer *lwork, integer *info); + +/* Subroutine */ int dorgl2_(integer *m, integer *n, integer *k, doublereal * + a, integer *lda, doublereal *tau, doublereal *work, integer *info); + +/* Subroutine */ int dorglq_(integer *m, integer *n, integer *k, doublereal * + a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, + integer *info); + +/* Subroutine */ int dorgql_(integer *m, integer *n, integer *k, doublereal * + a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, + integer *info); + +/* Subroutine */ int dorgqr_(integer *m, integer *n, integer *k, doublereal * + a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, + integer *info); + +/* Subroutine */ int dorgr2_(integer *m, integer *n, integer *k, doublereal * + a, integer *lda, doublereal *tau, doublereal *work, integer *info); + +/* Subroutine */ int dorgrq_(integer *m, integer *n, integer *k, doublereal * + a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, + integer *info); + +/* Subroutine */ int dorgtr_(char *uplo, integer *n, doublereal *a, integer * + lda, doublereal *tau, doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dorm2l_(char *side, char *trans, integer *m, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *info); + +/* Subroutine */ int dorm2r_(char *side, char *trans, integer *m, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *info); + +/* Subroutine */ int dormbr_(char *vect, char *side, char *trans, integer *m, + integer *n, integer *k, doublereal *a, integer *lda, doublereal *tau, + doublereal *c__, integer *ldc, doublereal *work, integer *lwork, + integer *info); + +/* Subroutine */ int dormhr_(char *side, char *trans, integer *m, integer *n, + integer *ilo, integer *ihi, doublereal *a, integer *lda, doublereal * + tau, doublereal *c__, integer *ldc, doublereal *work, integer *lwork, + integer *info); + +/* Subroutine */ int dorml2_(char *side, char *trans, integer *m, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *info); + +/* Subroutine */ int dormlq_(char *side, char *trans, integer *m, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dormql_(char *side, char *trans, integer *m, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dormqr_(char *side, char *trans, integer *m, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dormr2_(char *side, char *trans, integer *m, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *info); + +/* Subroutine */ int dormr3_(char *side, char *trans, integer *m, integer *n, + integer *k, integer *l, doublereal *a, integer *lda, doublereal *tau, + doublereal *c__, integer *ldc, doublereal *work, integer *info); + +/* Subroutine */ int dormrq_(char *side, char *trans, integer *m, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dormrz_(char *side, char *trans, integer *m, integer *n, + integer *k, integer *l, doublereal *a, integer *lda, doublereal *tau, + doublereal *c__, integer *ldc, doublereal *work, integer *lwork, + integer *info); + +/* Subroutine */ int dormtr_(char *side, char *uplo, char *trans, integer *m, + integer *n, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dpbcon_(char *uplo, integer *n, integer *kd, doublereal * + ab, integer *ldab, doublereal *anorm, doublereal *rcond, doublereal * + work, integer *iwork, integer *info); + +/* Subroutine */ int dpbequ_(char *uplo, integer *n, integer *kd, doublereal * + ab, integer *ldab, doublereal *s, doublereal *scond, doublereal *amax, + integer *info); + +/* Subroutine */ int dpbrfs_(char *uplo, integer *n, integer *kd, integer * + nrhs, doublereal *ab, integer *ldab, doublereal *afb, integer *ldafb, + doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal * + ferr, doublereal *berr, doublereal *work, integer *iwork, integer * + info); + +/* Subroutine */ int dpbstf_(char *uplo, integer *n, integer *kd, doublereal * + ab, integer *ldab, integer *info); + +/* Subroutine */ int dpbsv_(char *uplo, integer *n, integer *kd, integer * + nrhs, doublereal *ab, integer *ldab, doublereal *b, integer *ldb, + integer *info); + +/* Subroutine */ int dpbsvx_(char *fact, char *uplo, integer *n, integer *kd, + integer *nrhs, doublereal *ab, integer *ldab, doublereal *afb, + integer *ldafb, char *equed, doublereal *s, doublereal *b, integer * + ldb, doublereal *x, integer *ldx, doublereal *rcond, doublereal *ferr, + doublereal *berr, doublereal *work, integer *iwork, integer *info); + +/* Subroutine */ int dpbtf2_(char *uplo, integer *n, integer *kd, doublereal * + ab, integer *ldab, integer *info); + +/* Subroutine */ int dpbtrf_(char *uplo, integer *n, integer *kd, doublereal * + ab, integer *ldab, integer *info); + +/* Subroutine */ int dpbtrs_(char *uplo, integer *n, integer *kd, integer * + nrhs, doublereal *ab, integer *ldab, doublereal *b, integer *ldb, + integer *info); + +/* Subroutine */ int dpftrf_(char *transr, char *uplo, integer *n, doublereal + *a, integer *info); + +/* Subroutine */ int dpftri_(char *transr, char *uplo, integer *n, doublereal + *a, integer *info); + +/* Subroutine */ int dpftrs_(char *transr, char *uplo, integer *n, integer * + nrhs, doublereal *a, doublereal *b, integer *ldb, integer *info); + +/* Subroutine */ int dpocon_(char *uplo, integer *n, doublereal *a, integer * + lda, doublereal *anorm, doublereal *rcond, doublereal *work, integer * + iwork, integer *info); + +/* Subroutine */ int dpoequ_(integer *n, doublereal *a, integer *lda, + doublereal *s, doublereal *scond, doublereal *amax, integer *info); + +/* Subroutine */ int dpoequb_(integer *n, doublereal *a, integer *lda, + doublereal *s, doublereal *scond, doublereal *amax, integer *info); + +/* Subroutine */ int dporfs_(char *uplo, integer *n, integer *nrhs, + doublereal *a, integer *lda, doublereal *af, integer *ldaf, + doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal * + ferr, doublereal *berr, doublereal *work, integer *iwork, integer * + info); + +/* Subroutine */ int dporfsx_(char *uplo, char *equed, integer *n, integer * + nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf, + doublereal *s, doublereal *b, integer *ldb, doublereal *x, integer * + ldx, doublereal *rcond, doublereal *berr, integer *n_err_bnds__, + doublereal *err_bnds_norm__, doublereal *err_bnds_comp__, integer * + nparams, doublereal *params, doublereal *work, integer *iwork, + integer *info); + +/* Subroutine */ int dposv_(char *uplo, integer *n, integer *nrhs, doublereal + *a, integer *lda, doublereal *b, integer *ldb, integer *info); + +/* Subroutine */ int dposvx_(char *fact, char *uplo, integer *n, integer * + nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf, + char *equed, doublereal *s, doublereal *b, integer *ldb, doublereal * + x, integer *ldx, doublereal *rcond, doublereal *ferr, doublereal * + berr, doublereal *work, integer *iwork, integer *info); + +/* Subroutine */ int dposvxx_(char *fact, char *uplo, integer *n, integer * + nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf, + char *equed, doublereal *s, doublereal *b, integer *ldb, doublereal * + x, integer *ldx, doublereal *rcond, doublereal *rpvgrw, doublereal * + berr, integer *n_err_bnds__, doublereal *err_bnds_norm__, doublereal * + err_bnds_comp__, integer *nparams, doublereal *params, doublereal * + work, integer *iwork, integer *info); + +/* Subroutine */ int dpotf2_(char *uplo, integer *n, doublereal *a, integer * + lda, integer *info); + +/* Subroutine */ int dpotrf_(char *uplo, integer *n, doublereal *a, integer * + lda, integer *info); + +/* Subroutine */ int dpotri_(char *uplo, integer *n, doublereal *a, integer * + lda, integer *info); + +/* Subroutine */ int dpotrs_(char *uplo, integer *n, integer *nrhs, + doublereal *a, integer *lda, doublereal *b, integer *ldb, integer * + info); + +/* Subroutine */ int dppcon_(char *uplo, integer *n, doublereal *ap, + doublereal *anorm, doublereal *rcond, doublereal *work, integer * + iwork, integer *info); + +/* Subroutine */ int dppequ_(char *uplo, integer *n, doublereal *ap, + doublereal *s, doublereal *scond, doublereal *amax, integer *info); + +/* Subroutine */ int dpprfs_(char *uplo, integer *n, integer *nrhs, + doublereal *ap, doublereal *afp, doublereal *b, integer *ldb, + doublereal *x, integer *ldx, doublereal *ferr, doublereal *berr, + doublereal *work, integer *iwork, integer *info); + +/* Subroutine */ int dppsv_(char *uplo, integer *n, integer *nrhs, doublereal + *ap, doublereal *b, integer *ldb, integer *info); + +/* Subroutine */ int dppsvx_(char *fact, char *uplo, integer *n, integer * + nrhs, doublereal *ap, doublereal *afp, char *equed, doublereal *s, + doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal * + rcond, doublereal *ferr, doublereal *berr, doublereal *work, integer * + iwork, integer *info); + +/* Subroutine */ int dpptrf_(char *uplo, integer *n, doublereal *ap, integer * + info); + +/* Subroutine */ int dpptri_(char *uplo, integer *n, doublereal *ap, integer * + info); + +/* Subroutine */ int dpptrs_(char *uplo, integer *n, integer *nrhs, + doublereal *ap, doublereal *b, integer *ldb, integer *info); + +/* Subroutine */ int dpstf2_(char *uplo, integer *n, doublereal *a, integer * + lda, integer *piv, integer *rank, doublereal *tol, doublereal *work, + integer *info); + +/* Subroutine */ int dpstrf_(char *uplo, integer *n, doublereal *a, integer * + lda, integer *piv, integer *rank, doublereal *tol, doublereal *work, + integer *info); + +/* Subroutine */ int dptcon_(integer *n, doublereal *d__, doublereal *e, + doublereal *anorm, doublereal *rcond, doublereal *work, integer *info); + +/* Subroutine */ int dpteqr_(char *compz, integer *n, doublereal *d__, + doublereal *e, doublereal *z__, integer *ldz, doublereal *work, + integer *info); + +/* Subroutine */ int dptrfs_(integer *n, integer *nrhs, doublereal *d__, + doublereal *e, doublereal *df, doublereal *ef, doublereal *b, integer + *ldb, doublereal *x, integer *ldx, doublereal *ferr, doublereal *berr, + doublereal *work, integer *info); + +/* Subroutine */ int dptsv_(integer *n, integer *nrhs, doublereal *d__, + doublereal *e, doublereal *b, integer *ldb, integer *info); + +/* Subroutine */ int dptsvx_(char *fact, integer *n, integer *nrhs, + doublereal *d__, doublereal *e, doublereal *df, doublereal *ef, + doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal * + rcond, doublereal *ferr, doublereal *berr, doublereal *work, integer * + info); + +/* Subroutine */ int dpttrf_(integer *n, doublereal *d__, doublereal *e, + integer *info); + +/* Subroutine */ int dpttrs_(integer *n, integer *nrhs, doublereal *d__, + doublereal *e, doublereal *b, integer *ldb, integer *info); + +/* Subroutine */ int dptts2_(integer *n, integer *nrhs, doublereal *d__, + doublereal *e, doublereal *b, integer *ldb); + +/* Subroutine */ int drscl_(integer *n, doublereal *sa, doublereal *sx, + integer *incx); + +/* Subroutine */ int dsbev_(char *jobz, char *uplo, integer *n, integer *kd, + doublereal *ab, integer *ldab, doublereal *w, doublereal *z__, + integer *ldz, doublereal *work, integer *info); + +/* Subroutine */ int dsbevd_(char *jobz, char *uplo, integer *n, integer *kd, + doublereal *ab, integer *ldab, doublereal *w, doublereal *z__, + integer *ldz, doublereal *work, integer *lwork, integer *iwork, + integer *liwork, integer *info); + +/* Subroutine */ int dsbevx_(char *jobz, char *range, char *uplo, integer *n, + integer *kd, doublereal *ab, integer *ldab, doublereal *q, integer * + ldq, doublereal *vl, doublereal *vu, integer *il, integer *iu, + doublereal *abstol, integer *m, doublereal *w, doublereal *z__, + integer *ldz, doublereal *work, integer *iwork, integer *ifail, + integer *info); + +/* Subroutine */ int dsbgst_(char *vect, char *uplo, integer *n, integer *ka, + integer *kb, doublereal *ab, integer *ldab, doublereal *bb, integer * + ldbb, doublereal *x, integer *ldx, doublereal *work, integer *info); + +/* Subroutine */ int dsbgv_(char *jobz, char *uplo, integer *n, integer *ka, + integer *kb, doublereal *ab, integer *ldab, doublereal *bb, integer * + ldbb, doublereal *w, doublereal *z__, integer *ldz, doublereal *work, + integer *info); + +/* Subroutine */ int dsbgvd_(char *jobz, char *uplo, integer *n, integer *ka, + integer *kb, doublereal *ab, integer *ldab, doublereal *bb, integer * + ldbb, doublereal *w, doublereal *z__, integer *ldz, doublereal *work, + integer *lwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int dsbgvx_(char *jobz, char *range, char *uplo, integer *n, + integer *ka, integer *kb, doublereal *ab, integer *ldab, doublereal * + bb, integer *ldbb, doublereal *q, integer *ldq, doublereal *vl, + doublereal *vu, integer *il, integer *iu, doublereal *abstol, integer + *m, doublereal *w, doublereal *z__, integer *ldz, doublereal *work, + integer *iwork, integer *ifail, integer *info); + +/* Subroutine */ int dsbtrd_(char *vect, char *uplo, integer *n, integer *kd, + doublereal *ab, integer *ldab, doublereal *d__, doublereal *e, + doublereal *q, integer *ldq, doublereal *work, integer *info); + +/* Subroutine */ int dsfrk_(char *transr, char *uplo, char *trans, integer *n, + integer *k, doublereal *alpha, doublereal *a, integer *lda, + doublereal *beta, doublereal *c__); + +/* Subroutine */ int dsgesv_(integer *n, integer *nrhs, doublereal *a, + integer *lda, integer *ipiv, doublereal *b, integer *ldb, doublereal * + x, integer *ldx, doublereal *work, real *swork, integer *iter, + integer *info); + +/* Subroutine */ int dspcon_(char *uplo, integer *n, doublereal *ap, integer * + ipiv, doublereal *anorm, doublereal *rcond, doublereal *work, integer + *iwork, integer *info); + +/* Subroutine */ int dspev_(char *jobz, char *uplo, integer *n, doublereal * + ap, doublereal *w, doublereal *z__, integer *ldz, doublereal *work, + integer *info); + +/* Subroutine */ int dspevd_(char *jobz, char *uplo, integer *n, doublereal * + ap, doublereal *w, doublereal *z__, integer *ldz, doublereal *work, + integer *lwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int dspevx_(char *jobz, char *range, char *uplo, integer *n, + doublereal *ap, doublereal *vl, doublereal *vu, integer *il, integer * + iu, doublereal *abstol, integer *m, doublereal *w, doublereal *z__, + integer *ldz, doublereal *work, integer *iwork, integer *ifail, + integer *info); + +/* Subroutine */ int dspgst_(integer *itype, char *uplo, integer *n, + doublereal *ap, doublereal *bp, integer *info); + +/* Subroutine */ int dspgv_(integer *itype, char *jobz, char *uplo, integer * + n, doublereal *ap, doublereal *bp, doublereal *w, doublereal *z__, + integer *ldz, doublereal *work, integer *info); + +/* Subroutine */ int dspgvd_(integer *itype, char *jobz, char *uplo, integer * + n, doublereal *ap, doublereal *bp, doublereal *w, doublereal *z__, + integer *ldz, doublereal *work, integer *lwork, integer *iwork, + integer *liwork, integer *info); + +/* Subroutine */ int dspgvx_(integer *itype, char *jobz, char *range, char * + uplo, integer *n, doublereal *ap, doublereal *bp, doublereal *vl, + doublereal *vu, integer *il, integer *iu, doublereal *abstol, integer + *m, doublereal *w, doublereal *z__, integer *ldz, doublereal *work, + integer *iwork, integer *ifail, integer *info); + +/* Subroutine */ int dsposv_(char *uplo, integer *n, integer *nrhs, + doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal * + x, integer *ldx, doublereal *work, real *swork, integer *iter, + integer *info); + +/* Subroutine */ int dsprfs_(char *uplo, integer *n, integer *nrhs, + doublereal *ap, doublereal *afp, integer *ipiv, doublereal *b, + integer *ldb, doublereal *x, integer *ldx, doublereal *ferr, + doublereal *berr, doublereal *work, integer *iwork, integer *info); + +/* Subroutine */ int dspsv_(char *uplo, integer *n, integer *nrhs, doublereal + *ap, integer *ipiv, doublereal *b, integer *ldb, integer *info); + +/* Subroutine */ int dspsvx_(char *fact, char *uplo, integer *n, integer * + nrhs, doublereal *ap, doublereal *afp, integer *ipiv, doublereal *b, + integer *ldb, doublereal *x, integer *ldx, doublereal *rcond, + doublereal *ferr, doublereal *berr, doublereal *work, integer *iwork, + integer *info); + +/* Subroutine */ int dsptrd_(char *uplo, integer *n, doublereal *ap, + doublereal *d__, doublereal *e, doublereal *tau, integer *info); + +/* Subroutine */ int dsptrf_(char *uplo, integer *n, doublereal *ap, integer * + ipiv, integer *info); + +/* Subroutine */ int dsptri_(char *uplo, integer *n, doublereal *ap, integer * + ipiv, doublereal *work, integer *info); + +/* Subroutine */ int dsptrs_(char *uplo, integer *n, integer *nrhs, + doublereal *ap, integer *ipiv, doublereal *b, integer *ldb, integer * + info); + +/* Subroutine */ int dstebz_(char *range, char *order, integer *n, doublereal + *vl, doublereal *vu, integer *il, integer *iu, doublereal *abstol, + doublereal *d__, doublereal *e, integer *m, integer *nsplit, + doublereal *w, integer *iblock, integer *isplit, doublereal *work, + integer *iwork, integer *info); + +/* Subroutine */ int dstedc_(char *compz, integer *n, doublereal *d__, + doublereal *e, doublereal *z__, integer *ldz, doublereal *work, + integer *lwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int dstegr_(char *jobz, char *range, integer *n, doublereal * + d__, doublereal *e, doublereal *vl, doublereal *vu, integer *il, + integer *iu, doublereal *abstol, integer *m, doublereal *w, + doublereal *z__, integer *ldz, integer *isuppz, doublereal *work, + integer *lwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int dstein_(integer *n, doublereal *d__, doublereal *e, + integer *m, doublereal *w, integer *iblock, integer *isplit, + doublereal *z__, integer *ldz, doublereal *work, integer *iwork, + integer *ifail, integer *info); + +/* Subroutine */ int dstemr_(char *jobz, char *range, integer *n, doublereal * + d__, doublereal *e, doublereal *vl, doublereal *vu, integer *il, + integer *iu, integer *m, doublereal *w, doublereal *z__, integer *ldz, + integer *nzc, integer *isuppz, logical *tryrac, doublereal *work, + integer *lwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int dsteqr_(char *compz, integer *n, doublereal *d__, + doublereal *e, doublereal *z__, integer *ldz, doublereal *work, + integer *info); + +/* Subroutine */ int dsterf_(integer *n, doublereal *d__, doublereal *e, + integer *info); + +/* Subroutine */ int dstev_(char *jobz, integer *n, doublereal *d__, + doublereal *e, doublereal *z__, integer *ldz, doublereal *work, + integer *info); + +/* Subroutine */ int dstevd_(char *jobz, integer *n, doublereal *d__, + doublereal *e, doublereal *z__, integer *ldz, doublereal *work, + integer *lwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int dstevr_(char *jobz, char *range, integer *n, doublereal * + d__, doublereal *e, doublereal *vl, doublereal *vu, integer *il, + integer *iu, doublereal *abstol, integer *m, doublereal *w, + doublereal *z__, integer *ldz, integer *isuppz, doublereal *work, + integer *lwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int dstevx_(char *jobz, char *range, integer *n, doublereal * + d__, doublereal *e, doublereal *vl, doublereal *vu, integer *il, + integer *iu, doublereal *abstol, integer *m, doublereal *w, + doublereal *z__, integer *ldz, doublereal *work, integer *iwork, + integer *ifail, integer *info); + +/* Subroutine */ int dsycon_(char *uplo, integer *n, doublereal *a, integer * + lda, integer *ipiv, doublereal *anorm, doublereal *rcond, doublereal * + work, integer *iwork, integer *info); + +/* Subroutine */ int dsyequb_(char *uplo, integer *n, doublereal *a, integer * + lda, doublereal *s, doublereal *scond, doublereal *amax, doublereal * + work, integer *info); + +/* Subroutine */ int dsyev_(char *jobz, char *uplo, integer *n, doublereal *a, + integer *lda, doublereal *w, doublereal *work, integer *lwork, + integer *info); + +/* Subroutine */ int dsyevd_(char *jobz, char *uplo, integer *n, doublereal * + a, integer *lda, doublereal *w, doublereal *work, integer *lwork, + integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int dsyevr_(char *jobz, char *range, char *uplo, integer *n, + doublereal *a, integer *lda, doublereal *vl, doublereal *vu, integer * + il, integer *iu, doublereal *abstol, integer *m, doublereal *w, + doublereal *z__, integer *ldz, integer *isuppz, doublereal *work, + integer *lwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int dsyevx_(char *jobz, char *range, char *uplo, integer *n, + doublereal *a, integer *lda, doublereal *vl, doublereal *vu, integer * + il, integer *iu, doublereal *abstol, integer *m, doublereal *w, + doublereal *z__, integer *ldz, doublereal *work, integer *lwork, + integer *iwork, integer *ifail, integer *info); + +/* Subroutine */ int dsygs2_(integer *itype, char *uplo, integer *n, + doublereal *a, integer *lda, doublereal *b, integer *ldb, integer * + info); + +/* Subroutine */ int dsygst_(integer *itype, char *uplo, integer *n, + doublereal *a, integer *lda, doublereal *b, integer *ldb, integer * + info); + +/* Subroutine */ int dsygv_(integer *itype, char *jobz, char *uplo, integer * + n, doublereal *a, integer *lda, doublereal *b, integer *ldb, + doublereal *w, doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dsygvd_(integer *itype, char *jobz, char *uplo, integer * + n, doublereal *a, integer *lda, doublereal *b, integer *ldb, + doublereal *w, doublereal *work, integer *lwork, integer *iwork, + integer *liwork, integer *info); + +/* Subroutine */ int dsygvx_(integer *itype, char *jobz, char *range, char * + uplo, integer *n, doublereal *a, integer *lda, doublereal *b, integer + *ldb, doublereal *vl, doublereal *vu, integer *il, integer *iu, + doublereal *abstol, integer *m, doublereal *w, doublereal *z__, + integer *ldz, doublereal *work, integer *lwork, integer *iwork, + integer *ifail, integer *info); + +/* Subroutine */ int dsyrfs_(char *uplo, integer *n, integer *nrhs, + doublereal *a, integer *lda, doublereal *af, integer *ldaf, integer * + ipiv, doublereal *b, integer *ldb, doublereal *x, integer *ldx, + doublereal *ferr, doublereal *berr, doublereal *work, integer *iwork, + integer *info); + +/* Subroutine */ int dsyrfsx_(char *uplo, char *equed, integer *n, integer * + nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf, + integer *ipiv, doublereal *s, doublereal *b, integer *ldb, doublereal + *x, integer *ldx, doublereal *rcond, doublereal *berr, integer * + n_err_bnds__, doublereal *err_bnds_norm__, doublereal * + err_bnds_comp__, integer *nparams, doublereal *params, doublereal * + work, integer *iwork, integer *info); + +/* Subroutine */ int dsysv_(char *uplo, integer *n, integer *nrhs, doublereal + *a, integer *lda, integer *ipiv, doublereal *b, integer *ldb, + doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dsysvx_(char *fact, char *uplo, integer *n, integer * + nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf, + integer *ipiv, doublereal *b, integer *ldb, doublereal *x, integer * + ldx, doublereal *rcond, doublereal *ferr, doublereal *berr, + doublereal *work, integer *lwork, integer *iwork, integer *info); + +/* Subroutine */ int dsysvxx_(char *fact, char *uplo, integer *n, integer * + nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf, + integer *ipiv, char *equed, doublereal *s, doublereal *b, integer * + ldb, doublereal *x, integer *ldx, doublereal *rcond, doublereal * + rpvgrw, doublereal *berr, integer *n_err_bnds__, doublereal * + err_bnds_norm__, doublereal *err_bnds_comp__, integer *nparams, + doublereal *params, doublereal *work, integer *iwork, integer *info); + +/* Subroutine */ int dsytd2_(char *uplo, integer *n, doublereal *a, integer * + lda, doublereal *d__, doublereal *e, doublereal *tau, integer *info); + +/* Subroutine */ int dsytf2_(char *uplo, integer *n, doublereal *a, integer * + lda, integer *ipiv, integer *info); + +/* Subroutine */ int dsytrd_(char *uplo, integer *n, doublereal *a, integer * + lda, doublereal *d__, doublereal *e, doublereal *tau, doublereal * + work, integer *lwork, integer *info); + +/* Subroutine */ int dsytrf_(char *uplo, integer *n, doublereal *a, integer * + lda, integer *ipiv, doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dsytri_(char *uplo, integer *n, doublereal *a, integer * + lda, integer *ipiv, doublereal *work, integer *info); + +/* Subroutine */ int dsytrs_(char *uplo, integer *n, integer *nrhs, + doublereal *a, integer *lda, integer *ipiv, doublereal *b, integer * + ldb, integer *info); + +/* Subroutine */ int dtbcon_(char *norm, char *uplo, char *diag, integer *n, + integer *kd, doublereal *ab, integer *ldab, doublereal *rcond, + doublereal *work, integer *iwork, integer *info); + +/* Subroutine */ int dtbrfs_(char *uplo, char *trans, char *diag, integer *n, + integer *kd, integer *nrhs, doublereal *ab, integer *ldab, doublereal + *b, integer *ldb, doublereal *x, integer *ldx, doublereal *ferr, + doublereal *berr, doublereal *work, integer *iwork, integer *info); + +/* Subroutine */ int dtbtrs_(char *uplo, char *trans, char *diag, integer *n, + integer *kd, integer *nrhs, doublereal *ab, integer *ldab, doublereal + *b, integer *ldb, integer *info); + +/* Subroutine */ int dtfsm_(char *transr, char *side, char *uplo, char *trans, + char *diag, integer *m, integer *n, doublereal *alpha, doublereal *a, + doublereal *b, integer *ldb); + +/* Subroutine */ int dtftri_(char *transr, char *uplo, char *diag, integer *n, + doublereal *a, integer *info); + +/* Subroutine */ int dtfttp_(char *transr, char *uplo, integer *n, doublereal + *arf, doublereal *ap, integer *info); + +/* Subroutine */ int dtfttr_(char *transr, char *uplo, integer *n, doublereal + *arf, doublereal *a, integer *lda, integer *info); + +/* Subroutine */ int dtgevc_(char *side, char *howmny, logical *select, + integer *n, doublereal *s, integer *lds, doublereal *p, integer *ldp, + doublereal *vl, integer *ldvl, doublereal *vr, integer *ldvr, integer + *mm, integer *m, doublereal *work, integer *info); + +/* Subroutine */ int dtgex2_(logical *wantq, logical *wantz, integer *n, + doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal * + q, integer *ldq, doublereal *z__, integer *ldz, integer *j1, integer * + n1, integer *n2, doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dtgexc_(logical *wantq, logical *wantz, integer *n, + doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal * + q, integer *ldq, doublereal *z__, integer *ldz, integer *ifst, + integer *ilst, doublereal *work, integer *lwork, integer *info); + +/* Subroutine */ int dtgsen_(integer *ijob, logical *wantq, logical *wantz, + logical *select, integer *n, doublereal *a, integer *lda, doublereal * + b, integer *ldb, doublereal *alphar, doublereal *alphai, doublereal * + beta, doublereal *q, integer *ldq, doublereal *z__, integer *ldz, + integer *m, doublereal *pl, doublereal *pr, doublereal *dif, + doublereal *work, integer *lwork, integer *iwork, integer *liwork, + integer *info); + +/* Subroutine */ int dtgsja_(char *jobu, char *jobv, char *jobq, integer *m, + integer *p, integer *n, integer *k, integer *l, doublereal *a, + integer *lda, doublereal *b, integer *ldb, doublereal *tola, + doublereal *tolb, doublereal *alpha, doublereal *beta, doublereal *u, + integer *ldu, doublereal *v, integer *ldv, doublereal *q, integer * + ldq, doublereal *work, integer *ncycle, integer *info); + +/* Subroutine */ int dtgsna_(char *job, char *howmny, logical *select, + integer *n, doublereal *a, integer *lda, doublereal *b, integer *ldb, + doublereal *vl, integer *ldvl, doublereal *vr, integer *ldvr, + doublereal *s, doublereal *dif, integer *mm, integer *m, doublereal * + work, integer *lwork, integer *iwork, integer *info); + +/* Subroutine */ int dtgsy2_(char *trans, integer *ijob, integer *m, integer * + n, doublereal *a, integer *lda, doublereal *b, integer *ldb, + doublereal *c__, integer *ldc, doublereal *d__, integer *ldd, + doublereal *e, integer *lde, doublereal *f, integer *ldf, doublereal * + scale, doublereal *rdsum, doublereal *rdscal, integer *iwork, integer + *pq, integer *info); + +/* Subroutine */ int dtgsyl_(char *trans, integer *ijob, integer *m, integer * + n, doublereal *a, integer *lda, doublereal *b, integer *ldb, + doublereal *c__, integer *ldc, doublereal *d__, integer *ldd, + doublereal *e, integer *lde, doublereal *f, integer *ldf, doublereal * + scale, doublereal *dif, doublereal *work, integer *lwork, integer * + iwork, integer *info); + +/* Subroutine */ int dtpcon_(char *norm, char *uplo, char *diag, integer *n, + doublereal *ap, doublereal *rcond, doublereal *work, integer *iwork, + integer *info); + +/* Subroutine */ int dtprfs_(char *uplo, char *trans, char *diag, integer *n, + integer *nrhs, doublereal *ap, doublereal *b, integer *ldb, + doublereal *x, integer *ldx, doublereal *ferr, doublereal *berr, + doublereal *work, integer *iwork, integer *info); + +/* Subroutine */ int dtptri_(char *uplo, char *diag, integer *n, doublereal * + ap, integer *info); + +/* Subroutine */ int dtptrs_(char *uplo, char *trans, char *diag, integer *n, + integer *nrhs, doublereal *ap, doublereal *b, integer *ldb, integer * + info); + +/* Subroutine */ int dtpttf_(char *transr, char *uplo, integer *n, doublereal + *ap, doublereal *arf, integer *info); + +/* Subroutine */ int dtpttr_(char *uplo, integer *n, doublereal *ap, + doublereal *a, integer *lda, integer *info); + +/* Subroutine */ int dtrcon_(char *norm, char *uplo, char *diag, integer *n, + doublereal *a, integer *lda, doublereal *rcond, doublereal *work, + integer *iwork, integer *info); + +/* Subroutine */ int dtrevc_(char *side, char *howmny, logical *select, + integer *n, doublereal *t, integer *ldt, doublereal *vl, integer * + ldvl, doublereal *vr, integer *ldvr, integer *mm, integer *m, + doublereal *work, integer *info); + +/* Subroutine */ int dtrexc_(char *compq, integer *n, doublereal *t, integer * + ldt, doublereal *q, integer *ldq, integer *ifst, integer *ilst, + doublereal *work, integer *info); + +/* Subroutine */ int dtrrfs_(char *uplo, char *trans, char *diag, integer *n, + integer *nrhs, doublereal *a, integer *lda, doublereal *b, integer * + ldb, doublereal *x, integer *ldx, doublereal *ferr, doublereal *berr, + doublereal *work, integer *iwork, integer *info); + +/* Subroutine */ int dtrsen_(char *job, char *compq, logical *select, integer + *n, doublereal *t, integer *ldt, doublereal *q, integer *ldq, + doublereal *wr, doublereal *wi, integer *m, doublereal *s, doublereal + *sep, doublereal *work, integer *lwork, integer *iwork, integer * + liwork, integer *info); + +/* Subroutine */ int dtrsna_(char *job, char *howmny, logical *select, + integer *n, doublereal *t, integer *ldt, doublereal *vl, integer * + ldvl, doublereal *vr, integer *ldvr, doublereal *s, doublereal *sep, + integer *mm, integer *m, doublereal *work, integer *ldwork, integer * + iwork, integer *info); + +/* Subroutine */ int dtrsyl_(char *trana, char *tranb, integer *isgn, integer + *m, integer *n, doublereal *a, integer *lda, doublereal *b, integer * + ldb, doublereal *c__, integer *ldc, doublereal *scale, integer *info); + +/* Subroutine */ int dtrti2_(char *uplo, char *diag, integer *n, doublereal * + a, integer *lda, integer *info); + +/* Subroutine */ int dtrtri_(char *uplo, char *diag, integer *n, doublereal * + a, integer *lda, integer *info); + +/* Subroutine */ int dtrtrs_(char *uplo, char *trans, char *diag, integer *n, + integer *nrhs, doublereal *a, integer *lda, doublereal *b, integer * + ldb, integer *info); + +/* Subroutine */ int dtrttf_(char *transr, char *uplo, integer *n, doublereal + *a, integer *lda, doublereal *arf, integer *info); + +/* Subroutine */ int dtrttp_(char *uplo, integer *n, doublereal *a, integer * + lda, doublereal *ap, integer *info); + +/* Subroutine */ int dtzrqf_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *tau, integer *info); + +/* Subroutine */ int dtzrzf_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *tau, doublereal *work, integer *lwork, integer *info); + +doublereal dzsum1_(integer *n, doublecomplex *cx, integer *incx); + +integer icmax1_(integer *n, complex *cx, integer *incx); + +integer ieeeck_(integer *ispec, real *zero, real *one); + +integer ilaclc_(integer *m, integer *n, complex *a, integer *lda); + +integer ilaclr_(integer *m, integer *n, complex *a, integer *lda); + +integer iladiag_(char *diag); + +integer iladlc_(integer *m, integer *n, doublereal *a, integer *lda); + +integer iladlr_(integer *m, integer *n, doublereal *a, integer *lda); + +integer ilaenv_(integer *ispec, char *name__, char *opts, integer *n1, + integer *n2, integer *n3, integer *n4); + +integer ilaprec_(char *prec); + +integer ilaslc_(integer *m, integer *n, real *a, integer *lda); + +integer ilaslr_(integer *m, integer *n, real *a, integer *lda); + +integer ilatrans_(char *trans); + +integer ilauplo_(char *uplo); + +/* Subroutine */ int ilaver_(integer *vers_major__, integer *vers_minor__, + integer *vers_patch__); + +integer ilazlc_(integer *m, integer *n, doublecomplex *a, integer *lda); + +integer ilazlr_(integer *m, integer *n, doublecomplex *a, integer *lda); + +integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer + *ilo, integer *ihi, integer *lwork); + +integer izmax1_(integer *n, doublecomplex *cx, integer *incx); + +logical lsamen_(integer *n, char *ca, char *cb); + +integer smaxloc_(real *a, integer *dimm); + +/* Subroutine */ int sbdsdc_(char *uplo, char *compq, integer *n, real *d__, + real *e, real *u, integer *ldu, real *vt, integer *ldvt, real *q, + integer *iq, real *work, integer *iwork, integer *info); + +/* Subroutine */ int sbdsqr_(char *uplo, integer *n, integer *ncvt, integer * + nru, integer *ncc, real *d__, real *e, real *vt, integer *ldvt, real * + u, integer *ldu, real *c__, integer *ldc, real *work, integer *info); + +doublereal scsum1_(integer *n, complex *cx, integer *incx); + +/* Subroutine */ int sdisna_(char *job, integer *m, integer *n, real *d__, + real *sep, integer *info); + +/* Subroutine */ int sgbbrd_(char *vect, integer *m, integer *n, integer *ncc, + integer *kl, integer *ku, real *ab, integer *ldab, real *d__, real * + e, real *q, integer *ldq, real *pt, integer *ldpt, real *c__, integer + *ldc, real *work, integer *info); + +/* Subroutine */ int sgbcon_(char *norm, integer *n, integer *kl, integer *ku, + real *ab, integer *ldab, integer *ipiv, real *anorm, real *rcond, + real *work, integer *iwork, integer *info); + +/* Subroutine */ int sgbequ_(integer *m, integer *n, integer *kl, integer *ku, + real *ab, integer *ldab, real *r__, real *c__, real *rowcnd, real * + colcnd, real *amax, integer *info); + +/* Subroutine */ int sgbequb_(integer *m, integer *n, integer *kl, integer * + ku, real *ab, integer *ldab, real *r__, real *c__, real *rowcnd, real + *colcnd, real *amax, integer *info); + +/* Subroutine */ int sgbrfs_(char *trans, integer *n, integer *kl, integer * + ku, integer *nrhs, real *ab, integer *ldab, real *afb, integer *ldafb, + integer *ipiv, real *b, integer *ldb, real *x, integer *ldx, real * + ferr, real *berr, real *work, integer *iwork, integer *info); + +/* Subroutine */ int sgbrfsx_(char *trans, char *equed, integer *n, integer * + kl, integer *ku, integer *nrhs, real *ab, integer *ldab, real *afb, + integer *ldafb, integer *ipiv, real *r__, real *c__, real *b, integer + *ldb, real *x, integer *ldx, real *rcond, real *berr, integer * + n_err_bnds__, real *err_bnds_norm__, real *err_bnds_comp__, integer * + nparams, real *params, real *work, integer *iwork, integer *info); + +/* Subroutine */ int sgbsv_(integer *n, integer *kl, integer *ku, integer * + nrhs, real *ab, integer *ldab, integer *ipiv, real *b, integer *ldb, + integer *info); + +/* Subroutine */ int sgbsvx_(char *fact, char *trans, integer *n, integer *kl, + integer *ku, integer *nrhs, real *ab, integer *ldab, real *afb, + integer *ldafb, integer *ipiv, char *equed, real *r__, real *c__, + real *b, integer *ldb, real *x, integer *ldx, real *rcond, real *ferr, + real *berr, real *work, integer *iwork, integer *info); + +/* Subroutine */ int sgbsvxx_(char *fact, char *trans, integer *n, integer * + kl, integer *ku, integer *nrhs, real *ab, integer *ldab, real *afb, + integer *ldafb, integer *ipiv, char *equed, real *r__, real *c__, + real *b, integer *ldb, real *x, integer *ldx, real *rcond, real * + rpvgrw, real *berr, integer *n_err_bnds__, real *err_bnds_norm__, + real *err_bnds_comp__, integer *nparams, real *params, real *work, + integer *iwork, integer *info); + +/* Subroutine */ int sgbtf2_(integer *m, integer *n, integer *kl, integer *ku, + real *ab, integer *ldab, integer *ipiv, integer *info); + +/* Subroutine */ int sgbtrf_(integer *m, integer *n, integer *kl, integer *ku, + real *ab, integer *ldab, integer *ipiv, integer *info); + +/* Subroutine */ int sgbtrs_(char *trans, integer *n, integer *kl, integer * + ku, integer *nrhs, real *ab, integer *ldab, integer *ipiv, real *b, + integer *ldb, integer *info); + +/* Subroutine */ int sgebak_(char *job, char *side, integer *n, integer *ilo, + integer *ihi, real *scale, integer *m, real *v, integer *ldv, integer + *info); + +/* Subroutine */ int sgebal_(char *job, integer *n, real *a, integer *lda, + integer *ilo, integer *ihi, real *scale, integer *info); + +/* Subroutine */ int sgebd2_(integer *m, integer *n, real *a, integer *lda, + real *d__, real *e, real *tauq, real *taup, real *work, integer *info); + +/* Subroutine */ int sgebrd_(integer *m, integer *n, real *a, integer *lda, + real *d__, real *e, real *tauq, real *taup, real *work, integer * + lwork, integer *info); + +/* Subroutine */ int sgecon_(char *norm, integer *n, real *a, integer *lda, + real *anorm, real *rcond, real *work, integer *iwork, integer *info); + +/* Subroutine */ int sgeequ_(integer *m, integer *n, real *a, integer *lda, + real *r__, real *c__, real *rowcnd, real *colcnd, real *amax, integer + *info); + +/* Subroutine */ int sgeequb_(integer *m, integer *n, real *a, integer *lda, + real *r__, real *c__, real *rowcnd, real *colcnd, real *amax, integer + *info); + +/* Subroutine */ int sgees_(char *jobvs, char *sort, L_fp select, integer *n, + real *a, integer *lda, integer *sdim, real *wr, real *wi, real *vs, + integer *ldvs, real *work, integer *lwork, logical *bwork, integer * + info); + +/* Subroutine */ int sgeesx_(char *jobvs, char *sort, L_fp select, char * + sense, integer *n, real *a, integer *lda, integer *sdim, real *wr, + real *wi, real *vs, integer *ldvs, real *rconde, real *rcondv, real * + work, integer *lwork, integer *iwork, integer *liwork, logical *bwork, + integer *info); + +/* Subroutine */ int sgeev_(char *jobvl, char *jobvr, integer *n, real *a, + integer *lda, real *wr, real *wi, real *vl, integer *ldvl, real *vr, + integer *ldvr, real *work, integer *lwork, integer *info); + +/* Subroutine */ int sgeevx_(char *balanc, char *jobvl, char *jobvr, char * + sense, integer *n, real *a, integer *lda, real *wr, real *wi, real * + vl, integer *ldvl, real *vr, integer *ldvr, integer *ilo, integer * + ihi, real *scale, real *abnrm, real *rconde, real *rcondv, real *work, + integer *lwork, integer *iwork, integer *info); + +/* Subroutine */ int sgegs_(char *jobvsl, char *jobvsr, integer *n, real *a, + integer *lda, real *b, integer *ldb, real *alphar, real *alphai, real + *beta, real *vsl, integer *ldvsl, real *vsr, integer *ldvsr, real * + work, integer *lwork, integer *info); + +/* Subroutine */ int sgegv_(char *jobvl, char *jobvr, integer *n, real *a, + integer *lda, real *b, integer *ldb, real *alphar, real *alphai, real + *beta, real *vl, integer *ldvl, real *vr, integer *ldvr, real *work, + integer *lwork, integer *info); + +/* Subroutine */ int sgehd2_(integer *n, integer *ilo, integer *ihi, real *a, + integer *lda, real *tau, real *work, integer *info); + +/* Subroutine */ int sgehrd_(integer *n, integer *ilo, integer *ihi, real *a, + integer *lda, real *tau, real *work, integer *lwork, integer *info); + +/* Subroutine */ int sgejsv_(char *joba, char *jobu, char *jobv, char *jobr, + char *jobt, char *jobp, integer *m, integer *n, real *a, integer *lda, + real *sva, real *u, integer *ldu, real *v, integer *ldv, real *work, + integer *lwork, integer *iwork, integer *info); + +/* Subroutine */ int sgelq2_(integer *m, integer *n, real *a, integer *lda, + real *tau, real *work, integer *info); + +/* Subroutine */ int sgelqf_(integer *m, integer *n, real *a, integer *lda, + real *tau, real *work, integer *lwork, integer *info); + +/* Subroutine */ int sgels_(char *trans, integer *m, integer *n, integer * + nrhs, real *a, integer *lda, real *b, integer *ldb, real *work, + integer *lwork, integer *info); + +/* Subroutine */ int sgelsd_(integer *m, integer *n, integer *nrhs, real *a, + integer *lda, real *b, integer *ldb, real *s, real *rcond, integer * + rank, real *work, integer *lwork, integer *iwork, integer *info); + +/* Subroutine */ int sgelss_(integer *m, integer *n, integer *nrhs, real *a, + integer *lda, real *b, integer *ldb, real *s, real *rcond, integer * + rank, real *work, integer *lwork, integer *info); + +/* Subroutine */ int sgelsx_(integer *m, integer *n, integer *nrhs, real *a, + integer *lda, real *b, integer *ldb, integer *jpvt, real *rcond, + integer *rank, real *work, integer *info); + +/* Subroutine */ int sgelsy_(integer *m, integer *n, integer *nrhs, real *a, + integer *lda, real *b, integer *ldb, integer *jpvt, real *rcond, + integer *rank, real *work, integer *lwork, integer *info); + +/* Subroutine */ int sgeql2_(integer *m, integer *n, real *a, integer *lda, + real *tau, real *work, integer *info); + +/* Subroutine */ int sgeqlf_(integer *m, integer *n, real *a, integer *lda, + real *tau, real *work, integer *lwork, integer *info); + +/* Subroutine */ int sgeqp3_(integer *m, integer *n, real *a, integer *lda, + integer *jpvt, real *tau, real *work, integer *lwork, integer *info); + +/* Subroutine */ int sgeqpf_(integer *m, integer *n, real *a, integer *lda, + integer *jpvt, real *tau, real *work, integer *info); + +/* Subroutine */ int sgeqr2_(integer *m, integer *n, real *a, integer *lda, + real *tau, real *work, integer *info); + +/* Subroutine */ int sgeqrf_(integer *m, integer *n, real *a, integer *lda, + real *tau, real *work, integer *lwork, integer *info); + +/* Subroutine */ int sgerfs_(char *trans, integer *n, integer *nrhs, real *a, + integer *lda, real *af, integer *ldaf, integer *ipiv, real *b, + integer *ldb, real *x, integer *ldx, real *ferr, real *berr, real * + work, integer *iwork, integer *info); + +/* Subroutine */ int sgerfsx_(char *trans, char *equed, integer *n, integer * + nrhs, real *a, integer *lda, real *af, integer *ldaf, integer *ipiv, + real *r__, real *c__, real *b, integer *ldb, real *x, integer *ldx, + real *rcond, real *berr, integer *n_err_bnds__, real *err_bnds_norm__, + real *err_bnds_comp__, integer *nparams, real *params, real *work, + integer *iwork, integer *info); + +/* Subroutine */ int sgerq2_(integer *m, integer *n, real *a, integer *lda, + real *tau, real *work, integer *info); + +/* Subroutine */ int sgerqf_(integer *m, integer *n, real *a, integer *lda, + real *tau, real *work, integer *lwork, integer *info); + +/* Subroutine */ int sgesc2_(integer *n, real *a, integer *lda, real *rhs, + integer *ipiv, integer *jpiv, real *scale); + +/* Subroutine */ int sgesdd_(char *jobz, integer *m, integer *n, real *a, + integer *lda, real *s, real *u, integer *ldu, real *vt, integer *ldvt, + real *work, integer *lwork, integer *iwork, integer *info); + +/* Subroutine */ int sgesv_(integer *n, integer *nrhs, real *a, integer *lda, + integer *ipiv, real *b, integer *ldb, integer *info); + +/* Subroutine */ int sgesvd_(char *jobu, char *jobvt, integer *m, integer *n, + real *a, integer *lda, real *s, real *u, integer *ldu, real *vt, + integer *ldvt, real *work, integer *lwork, integer *info); + +/* Subroutine */ int sgesvj_(char *joba, char *jobu, char *jobv, integer *m, + integer *n, real *a, integer *lda, real *sva, integer *mv, real *v, + integer *ldv, real *work, integer *lwork, integer *info); + +/* Subroutine */ int sgesvx_(char *fact, char *trans, integer *n, integer * + nrhs, real *a, integer *lda, real *af, integer *ldaf, integer *ipiv, + char *equed, real *r__, real *c__, real *b, integer *ldb, real *x, + integer *ldx, real *rcond, real *ferr, real *berr, real *work, + integer *iwork, integer *info); + +/* Subroutine */ int sgesvxx_(char *fact, char *trans, integer *n, integer * + nrhs, real *a, integer *lda, real *af, integer *ldaf, integer *ipiv, + char *equed, real *r__, real *c__, real *b, integer *ldb, real *x, + integer *ldx, real *rcond, real *rpvgrw, real *berr, integer * + n_err_bnds__, real *err_bnds_norm__, real *err_bnds_comp__, integer * + nparams, real *params, real *work, integer *iwork, integer *info); + +/* Subroutine */ int sgetc2_(integer *n, real *a, integer *lda, integer *ipiv, + integer *jpiv, integer *info); + +/* Subroutine */ int sgetf2_(integer *m, integer *n, real *a, integer *lda, + integer *ipiv, integer *info); + +/* Subroutine */ int sgetrf_(integer *m, integer *n, real *a, integer *lda, + integer *ipiv, integer *info); + +/* Subroutine */ int sgetri_(integer *n, real *a, integer *lda, integer *ipiv, + real *work, integer *lwork, integer *info); + +/* Subroutine */ int sgetrs_(char *trans, integer *n, integer *nrhs, real *a, + integer *lda, integer *ipiv, real *b, integer *ldb, integer *info); + +/* Subroutine */ int sggbak_(char *job, char *side, integer *n, integer *ilo, + integer *ihi, real *lscale, real *rscale, integer *m, real *v, + integer *ldv, integer *info); + +/* Subroutine */ int sggbal_(char *job, integer *n, real *a, integer *lda, + real *b, integer *ldb, integer *ilo, integer *ihi, real *lscale, real + *rscale, real *work, integer *info); + +/* Subroutine */ int sgges_(char *jobvsl, char *jobvsr, char *sort, L_fp + selctg, integer *n, real *a, integer *lda, real *b, integer *ldb, + integer *sdim, real *alphar, real *alphai, real *beta, real *vsl, + integer *ldvsl, real *vsr, integer *ldvsr, real *work, integer *lwork, + logical *bwork, integer *info); + +/* Subroutine */ int sggesx_(char *jobvsl, char *jobvsr, char *sort, L_fp + selctg, char *sense, integer *n, real *a, integer *lda, real *b, + integer *ldb, integer *sdim, real *alphar, real *alphai, real *beta, + real *vsl, integer *ldvsl, real *vsr, integer *ldvsr, real *rconde, + real *rcondv, real *work, integer *lwork, integer *iwork, integer * + liwork, logical *bwork, integer *info); + +/* Subroutine */ int sggev_(char *jobvl, char *jobvr, integer *n, real *a, + integer *lda, real *b, integer *ldb, real *alphar, real *alphai, real + *beta, real *vl, integer *ldvl, real *vr, integer *ldvr, real *work, + integer *lwork, integer *info); + +/* Subroutine */ int sggevx_(char *balanc, char *jobvl, char *jobvr, char * + sense, integer *n, real *a, integer *lda, real *b, integer *ldb, real + *alphar, real *alphai, real *beta, real *vl, integer *ldvl, real *vr, + integer *ldvr, integer *ilo, integer *ihi, real *lscale, real *rscale, + real *abnrm, real *bbnrm, real *rconde, real *rcondv, real *work, + integer *lwork, integer *iwork, logical *bwork, integer *info); + +/* Subroutine */ int sggglm_(integer *n, integer *m, integer *p, real *a, + integer *lda, real *b, integer *ldb, real *d__, real *x, real *y, + real *work, integer *lwork, integer *info); + +/* Subroutine */ int sgghrd_(char *compq, char *compz, integer *n, integer * + ilo, integer *ihi, real *a, integer *lda, real *b, integer *ldb, real + *q, integer *ldq, real *z__, integer *ldz, integer *info); + +/* Subroutine */ int sgglse_(integer *m, integer *n, integer *p, real *a, + integer *lda, real *b, integer *ldb, real *c__, real *d__, real *x, + real *work, integer *lwork, integer *info); + +/* Subroutine */ int sggqrf_(integer *n, integer *m, integer *p, real *a, + integer *lda, real *taua, real *b, integer *ldb, real *taub, real * + work, integer *lwork, integer *info); + +/* Subroutine */ int sggrqf_(integer *m, integer *p, integer *n, real *a, + integer *lda, real *taua, real *b, integer *ldb, real *taub, real * + work, integer *lwork, integer *info); + +/* Subroutine */ int sggsvd_(char *jobu, char *jobv, char *jobq, integer *m, + integer *n, integer *p, integer *k, integer *l, real *a, integer *lda, + real *b, integer *ldb, real *alpha, real *beta, real *u, integer * + ldu, real *v, integer *ldv, real *q, integer *ldq, real *work, + integer *iwork, integer *info); + +/* Subroutine */ int sggsvp_(char *jobu, char *jobv, char *jobq, integer *m, + integer *p, integer *n, real *a, integer *lda, real *b, integer *ldb, + real *tola, real *tolb, integer *k, integer *l, real *u, integer *ldu, + real *v, integer *ldv, real *q, integer *ldq, integer *iwork, real * + tau, real *work, integer *info); + +/* Subroutine */ int sgsvj0_(char *jobv, integer *m, integer *n, real *a, + integer *lda, real *d__, real *sva, integer *mv, real *v, integer * + ldv, real *eps, real *sfmin, real *tol, integer *nsweep, real *work, + integer *lwork, integer *info); + +/* Subroutine */ int sgsvj1_(char *jobv, integer *m, integer *n, integer *n1, + real *a, integer *lda, real *d__, real *sva, integer *mv, real *v, + integer *ldv, real *eps, real *sfmin, real *tol, integer *nsweep, + real *work, integer *lwork, integer *info); + +/* Subroutine */ int sgtcon_(char *norm, integer *n, real *dl, real *d__, + real *du, real *du2, integer *ipiv, real *anorm, real *rcond, real * + work, integer *iwork, integer *info); + +/* Subroutine */ int sgtrfs_(char *trans, integer *n, integer *nrhs, real *dl, + real *d__, real *du, real *dlf, real *df, real *duf, real *du2, + integer *ipiv, real *b, integer *ldb, real *x, integer *ldx, real * + ferr, real *berr, real *work, integer *iwork, integer *info); + +/* Subroutine */ int sgtsv_(integer *n, integer *nrhs, real *dl, real *d__, + real *du, real *b, integer *ldb, integer *info); + +/* Subroutine */ int sgtsvx_(char *fact, char *trans, integer *n, integer * + nrhs, real *dl, real *d__, real *du, real *dlf, real *df, real *duf, + real *du2, integer *ipiv, real *b, integer *ldb, real *x, integer * + ldx, real *rcond, real *ferr, real *berr, real *work, integer *iwork, + integer *info); + +/* Subroutine */ int sgttrf_(integer *n, real *dl, real *d__, real *du, real * + du2, integer *ipiv, integer *info); + +/* Subroutine */ int sgttrs_(char *trans, integer *n, integer *nrhs, real *dl, + real *d__, real *du, real *du2, integer *ipiv, real *b, integer *ldb, + integer *info); + +/* Subroutine */ int sgtts2_(integer *itrans, integer *n, integer *nrhs, real + *dl, real *d__, real *du, real *du2, integer *ipiv, real *b, integer * + ldb); + +/* Subroutine */ int shgeqz_(char *job, char *compq, char *compz, integer *n, + integer *ilo, integer *ihi, real *h__, integer *ldh, real *t, integer + *ldt, real *alphar, real *alphai, real *beta, real *q, integer *ldq, + real *z__, integer *ldz, real *work, integer *lwork, integer *info); + +/* Subroutine */ int shsein_(char *side, char *eigsrc, char *initv, logical * + select, integer *n, real *h__, integer *ldh, real *wr, real *wi, real + *vl, integer *ldvl, real *vr, integer *ldvr, integer *mm, integer *m, + real *work, integer *ifaill, integer *ifailr, integer *info); + +/* Subroutine */ int shseqr_(char *job, char *compz, integer *n, integer *ilo, + integer *ihi, real *h__, integer *ldh, real *wr, real *wi, real *z__, + integer *ldz, real *work, integer *lwork, integer *info); + +logical sisnan_(real *sin__); + +/* Subroutine */ int sla_gbamv__(integer *trans, integer *m, integer *n, + integer *kl, integer *ku, real *alpha, real *ab, integer *ldab, real * + x, integer *incx, real *beta, real *y, integer *incy); + +doublereal sla_gbrcond__(char *trans, integer *n, integer *kl, integer *ku, + real *ab, integer *ldab, real *afb, integer *ldafb, integer *ipiv, + integer *cmode, real *c__, integer *info, real *work, integer *iwork, + ftnlen trans_len); + +/* Subroutine */ int sla_gbrfsx_extended__(integer *prec_type__, integer * + trans_type__, integer *n, integer *kl, integer *ku, integer *nrhs, + real *ab, integer *ldab, real *afb, integer *ldafb, integer *ipiv, + logical *colequ, real *c__, real *b, integer *ldb, real *y, integer * + ldy, real *berr_out__, integer *n_norms__, real *errs_n__, real * + errs_c__, real *res, real *ayb, real *dy, real *y_tail__, real *rcond, + integer *ithresh, real *rthresh, real *dz_ub__, logical * + ignore_cwise__, integer *info); + +doublereal sla_gbrpvgrw__(integer *n, integer *kl, integer *ku, integer * + ncols, real *ab, integer *ldab, real *afb, integer *ldafb); + +/* Subroutine */ int sla_geamv__(integer *trans, integer *m, integer *n, real + *alpha, real *a, integer *lda, real *x, integer *incx, real *beta, + real *y, integer *incy); + +doublereal sla_gercond__(char *trans, integer *n, real *a, integer *lda, real + *af, integer *ldaf, integer *ipiv, integer *cmode, real *c__, integer + *info, real *work, integer *iwork, ftnlen trans_len); + +/* Subroutine */ int sla_gerfsx_extended__(integer *prec_type__, integer * + trans_type__, integer *n, integer *nrhs, real *a, integer *lda, real * + af, integer *ldaf, integer *ipiv, logical *colequ, real *c__, real *b, + integer *ldb, real *y, integer *ldy, real *berr_out__, integer * + n_norms__, real *errs_n__, real *errs_c__, real *res, real *ayb, real + *dy, real *y_tail__, real *rcond, integer *ithresh, real *rthresh, + real *dz_ub__, logical *ignore_cwise__, integer *info); + +/* Subroutine */ int sla_lin_berr__(integer *n, integer *nz, integer *nrhs, + real *res, real *ayb, real *berr); + +doublereal sla_porcond__(char *uplo, integer *n, real *a, integer *lda, real * + af, integer *ldaf, integer *cmode, real *c__, integer *info, real * + work, integer *iwork, ftnlen uplo_len); + +/* Subroutine */ int sla_porfsx_extended__(integer *prec_type__, char *uplo, + integer *n, integer *nrhs, real *a, integer *lda, real *af, integer * + ldaf, logical *colequ, real *c__, real *b, integer *ldb, real *y, + integer *ldy, real *berr_out__, integer *n_norms__, real *errs_n__, + real *errs_c__, real *res, real *ayb, real *dy, real *y_tail__, real * + rcond, integer *ithresh, real *rthresh, real *dz_ub__, logical * + ignore_cwise__, integer *info, ftnlen uplo_len); + +doublereal sla_porpvgrw__(char *uplo, integer *ncols, real *a, integer *lda, + real *af, integer *ldaf, real *work, ftnlen uplo_len); + +doublereal sla_rpvgrw__(integer *n, integer *ncols, real *a, integer *lda, + real *af, integer *ldaf); + +/* Subroutine */ int sla_syamv__(integer *uplo, integer *n, real *alpha, real + *a, integer *lda, real *x, integer *incx, real *beta, real *y, + integer *incy); + +doublereal sla_syrcond__(char *uplo, integer *n, real *a, integer *lda, real * + af, integer *ldaf, integer *ipiv, integer *cmode, real *c__, integer * + info, real *work, integer *iwork, ftnlen uplo_len); + +/* Subroutine */ int sla_syrfsx_extended__(integer *prec_type__, char *uplo, + integer *n, integer *nrhs, real *a, integer *lda, real *af, integer * + ldaf, integer *ipiv, logical *colequ, real *c__, real *b, integer * + ldb, real *y, integer *ldy, real *berr_out__, integer *n_norms__, + real *errs_n__, real *errs_c__, real *res, real *ayb, real *dy, real * + y_tail__, real *rcond, integer *ithresh, real *rthresh, real *dz_ub__, + logical *ignore_cwise__, integer *info, ftnlen uplo_len); + +doublereal sla_syrpvgrw__(char *uplo, integer *n, integer *info, real *a, + integer *lda, real *af, integer *ldaf, integer *ipiv, real *work, + ftnlen uplo_len); + +/* Subroutine */ int sla_wwaddw__(integer *n, real *x, real *y, real *w); + +/* Subroutine */ int slabad_(real *small, real *large); + +/* Subroutine */ int slabrd_(integer *m, integer *n, integer *nb, real *a, + integer *lda, real *d__, real *e, real *tauq, real *taup, real *x, + integer *ldx, real *y, integer *ldy); + +/* Subroutine */ int slacn2_(integer *n, real *v, real *x, integer *isgn, + real *est, integer *kase, integer *isave); + +/* Subroutine */ int slacon_(integer *n, real *v, real *x, integer *isgn, + real *est, integer *kase); + +/* Subroutine */ int slacpy_(char *uplo, integer *m, integer *n, real *a, + integer *lda, real *b, integer *ldb); + +/* Subroutine */ int sladiv_(real *a, real *b, real *c__, real *d__, real *p, + real *q); + +/* Subroutine */ int slae2_(real *a, real *b, real *c__, real *rt1, real *rt2); + +/* Subroutine */ int slaebz_(integer *ijob, integer *nitmax, integer *n, + integer *mmax, integer *minp, integer *nbmin, real *abstol, real * + reltol, real *pivmin, real *d__, real *e, real *e2, integer *nval, + real *ab, real *c__, integer *mout, integer *nab, real *work, integer + *iwork, integer *info); + +/* Subroutine */ int slaed0_(integer *icompq, integer *qsiz, integer *n, real + *d__, real *e, real *q, integer *ldq, real *qstore, integer *ldqs, + real *work, integer *iwork, integer *info); + +/* Subroutine */ int slaed1_(integer *n, real *d__, real *q, integer *ldq, + integer *indxq, real *rho, integer *cutpnt, real *work, integer * + iwork, integer *info); + +/* Subroutine */ int slaed2_(integer *k, integer *n, integer *n1, real *d__, + real *q, integer *ldq, integer *indxq, real *rho, real *z__, real * + dlamda, real *w, real *q2, integer *indx, integer *indxc, integer * + indxp, integer *coltyp, integer *info); + +/* Subroutine */ int slaed3_(integer *k, integer *n, integer *n1, real *d__, + real *q, integer *ldq, real *rho, real *dlamda, real *q2, integer * + indx, integer *ctot, real *w, real *s, integer *info); + +/* Subroutine */ int slaed4_(integer *n, integer *i__, real *d__, real *z__, + real *delta, real *rho, real *dlam, integer *info); + +/* Subroutine */ int slaed5_(integer *i__, real *d__, real *z__, real *delta, + real *rho, real *dlam); + +/* Subroutine */ int slaed6_(integer *kniter, logical *orgati, real *rho, + real *d__, real *z__, real *finit, real *tau, integer *info); + +/* Subroutine */ int slaed7_(integer *icompq, integer *n, integer *qsiz, + integer *tlvls, integer *curlvl, integer *curpbm, real *d__, real *q, + integer *ldq, integer *indxq, real *rho, integer *cutpnt, real * + qstore, integer *qptr, integer *prmptr, integer *perm, integer * + givptr, integer *givcol, real *givnum, real *work, integer *iwork, + integer *info); + +/* Subroutine */ int slaed8_(integer *icompq, integer *k, integer *n, integer + *qsiz, real *d__, real *q, integer *ldq, integer *indxq, real *rho, + integer *cutpnt, real *z__, real *dlamda, real *q2, integer *ldq2, + real *w, integer *perm, integer *givptr, integer *givcol, real * + givnum, integer *indxp, integer *indx, integer *info); + +/* Subroutine */ int slaed9_(integer *k, integer *kstart, integer *kstop, + integer *n, real *d__, real *q, integer *ldq, real *rho, real *dlamda, + real *w, real *s, integer *lds, integer *info); + +/* Subroutine */ int slaeda_(integer *n, integer *tlvls, integer *curlvl, + integer *curpbm, integer *prmptr, integer *perm, integer *givptr, + integer *givcol, real *givnum, real *q, integer *qptr, real *z__, + real *ztemp, integer *info); + +/* Subroutine */ int slaein_(logical *rightv, logical *noinit, integer *n, + real *h__, integer *ldh, real *wr, real *wi, real *vr, real *vi, real + *b, integer *ldb, real *work, real *eps3, real *smlnum, real *bignum, + integer *info); + +/* Subroutine */ int slaev2_(real *a, real *b, real *c__, real *rt1, real * + rt2, real *cs1, real *sn1); + +/* Subroutine */ int slaexc_(logical *wantq, integer *n, real *t, integer * + ldt, real *q, integer *ldq, integer *j1, integer *n1, integer *n2, + real *work, integer *info); + +/* Subroutine */ int slag2_(real *a, integer *lda, real *b, integer *ldb, + real *safmin, real *scale1, real *scale2, real *wr1, real *wr2, real * + wi); + +/* Subroutine */ int slag2d_(integer *m, integer *n, real *sa, integer *ldsa, + doublereal *a, integer *lda, integer *info); + +/* Subroutine */ int slags2_(logical *upper, real *a1, real *a2, real *a3, + real *b1, real *b2, real *b3, real *csu, real *snu, real *csv, real * + snv, real *csq, real *snq); + +/* Subroutine */ int slagtf_(integer *n, real *a, real *lambda, real *b, real + *c__, real *tol, real *d__, integer *in, integer *info); + +/* Subroutine */ int slagtm_(char *trans, integer *n, integer *nrhs, real * + alpha, real *dl, real *d__, real *du, real *x, integer *ldx, real * + beta, real *b, integer *ldb); + +/* Subroutine */ int slagts_(integer *job, integer *n, real *a, real *b, real + *c__, real *d__, integer *in, real *y, real *tol, integer *info); + +/* Subroutine */ int slagv2_(real *a, integer *lda, real *b, integer *ldb, + real *alphar, real *alphai, real *beta, real *csl, real *snl, real * + csr, real *snr); + +/* Subroutine */ int slahqr_(logical *wantt, logical *wantz, integer *n, + integer *ilo, integer *ihi, real *h__, integer *ldh, real *wr, real * + wi, integer *iloz, integer *ihiz, real *z__, integer *ldz, integer * + info); + +/* Subroutine */ int slahr2_(integer *n, integer *k, integer *nb, real *a, + integer *lda, real *tau, real *t, integer *ldt, real *y, integer *ldy); + +/* Subroutine */ int slahrd_(integer *n, integer *k, integer *nb, real *a, + integer *lda, real *tau, real *t, integer *ldt, real *y, integer *ldy); + +/* Subroutine */ int slaic1_(integer *job, integer *j, real *x, real *sest, + real *w, real *gamma, real *sestpr, real *s, real *c__); + +logical slaisnan_(real *sin1, real *sin2); + +/* Subroutine */ int slaln2_(logical *ltrans, integer *na, integer *nw, real * + smin, real *ca, real *a, integer *lda, real *d1, real *d2, real *b, + integer *ldb, real *wr, real *wi, real *x, integer *ldx, real *scale, + real *xnorm, integer *info); + +/* Subroutine */ int slals0_(integer *icompq, integer *nl, integer *nr, + integer *sqre, integer *nrhs, real *b, integer *ldb, real *bx, + integer *ldbx, integer *perm, integer *givptr, integer *givcol, + integer *ldgcol, real *givnum, integer *ldgnum, real *poles, real * + difl, real *difr, real *z__, integer *k, real *c__, real *s, real * + work, integer *info); + +/* Subroutine */ int slalsa_(integer *icompq, integer *smlsiz, integer *n, + integer *nrhs, real *b, integer *ldb, real *bx, integer *ldbx, real * + u, integer *ldu, real *vt, integer *k, real *difl, real *difr, real * + z__, real *poles, integer *givptr, integer *givcol, integer *ldgcol, + integer *perm, real *givnum, real *c__, real *s, real *work, integer * + iwork, integer *info); + +/* Subroutine */ int slalsd_(char *uplo, integer *smlsiz, integer *n, integer + *nrhs, real *d__, real *e, real *b, integer *ldb, real *rcond, + integer *rank, real *work, integer *iwork, integer *info); + +/* Subroutine */ int slamrg_(integer *n1, integer *n2, real *a, integer * + strd1, integer *strd2, integer *index); + +integer slaneg_(integer *n, real *d__, real *lld, real *sigma, real *pivmin, + integer *r__); + +doublereal slangb_(char *norm, integer *n, integer *kl, integer *ku, real *ab, + integer *ldab, real *work); + +doublereal slange_(char *norm, integer *m, integer *n, real *a, integer *lda, + real *work); + +doublereal slangt_(char *norm, integer *n, real *dl, real *d__, real *du); + +doublereal slanhs_(char *norm, integer *n, real *a, integer *lda, real *work); + +doublereal slansb_(char *norm, char *uplo, integer *n, integer *k, real *ab, + integer *ldab, real *work); + +doublereal slansf_(char *norm, char *transr, char *uplo, integer *n, real *a, + real *work); + +doublereal slansp_(char *norm, char *uplo, integer *n, real *ap, real *work); + +doublereal slanst_(char *norm, integer *n, real *d__, real *e); + +doublereal slansy_(char *norm, char *uplo, integer *n, real *a, integer *lda, + real *work); + +doublereal slantb_(char *norm, char *uplo, char *diag, integer *n, integer *k, + real *ab, integer *ldab, real *work); + +doublereal slantp_(char *norm, char *uplo, char *diag, integer *n, real *ap, + real *work); + +doublereal slantr_(char *norm, char *uplo, char *diag, integer *m, integer *n, + real *a, integer *lda, real *work); + +/* Subroutine */ int slanv2_(real *a, real *b, real *c__, real *d__, real * + rt1r, real *rt1i, real *rt2r, real *rt2i, real *cs, real *sn); + +/* Subroutine */ int slapll_(integer *n, real *x, integer *incx, real *y, + integer *incy, real *ssmin); + +/* Subroutine */ int slapmt_(logical *forwrd, integer *m, integer *n, real *x, + integer *ldx, integer *k); + +doublereal slapy2_(real *x, real *y); + +doublereal slapy3_(real *x, real *y, real *z__); + +/* Subroutine */ int slaqgb_(integer *m, integer *n, integer *kl, integer *ku, + real *ab, integer *ldab, real *r__, real *c__, real *rowcnd, real * + colcnd, real *amax, char *equed); + +/* Subroutine */ int slaqge_(integer *m, integer *n, real *a, integer *lda, + real *r__, real *c__, real *rowcnd, real *colcnd, real *amax, char * + equed); + +/* Subroutine */ int slaqp2_(integer *m, integer *n, integer *offset, real *a, + integer *lda, integer *jpvt, real *tau, real *vn1, real *vn2, real * + work); + +/* Subroutine */ int slaqps_(integer *m, integer *n, integer *offset, integer + *nb, integer *kb, real *a, integer *lda, integer *jpvt, real *tau, + real *vn1, real *vn2, real *auxv, real *f, integer *ldf); + +/* Subroutine */ int slaqr0_(logical *wantt, logical *wantz, integer *n, + integer *ilo, integer *ihi, real *h__, integer *ldh, real *wr, real * + wi, integer *iloz, integer *ihiz, real *z__, integer *ldz, real *work, + integer *lwork, integer *info); + +/* Subroutine */ int slaqr1_(integer *n, real *h__, integer *ldh, real *sr1, + real *si1, real *sr2, real *si2, real *v); + +/* Subroutine */ int slaqr2_(logical *wantt, logical *wantz, integer *n, + integer *ktop, integer *kbot, integer *nw, real *h__, integer *ldh, + integer *iloz, integer *ihiz, real *z__, integer *ldz, integer *ns, + integer *nd, real *sr, real *si, real *v, integer *ldv, integer *nh, + real *t, integer *ldt, integer *nv, real *wv, integer *ldwv, real * + work, integer *lwork); + +/* Subroutine */ int slaqr3_(logical *wantt, logical *wantz, integer *n, + integer *ktop, integer *kbot, integer *nw, real *h__, integer *ldh, + integer *iloz, integer *ihiz, real *z__, integer *ldz, integer *ns, + integer *nd, real *sr, real *si, real *v, integer *ldv, integer *nh, + real *t, integer *ldt, integer *nv, real *wv, integer *ldwv, real * + work, integer *lwork); + +/* Subroutine */ int slaqr4_(logical *wantt, logical *wantz, integer *n, + integer *ilo, integer *ihi, real *h__, integer *ldh, real *wr, real * + wi, integer *iloz, integer *ihiz, real *z__, integer *ldz, real *work, + integer *lwork, integer *info); + +/* Subroutine */ int slaqr5_(logical *wantt, logical *wantz, integer *kacc22, + integer *n, integer *ktop, integer *kbot, integer *nshfts, real *sr, + real *si, real *h__, integer *ldh, integer *iloz, integer *ihiz, real + *z__, integer *ldz, real *v, integer *ldv, real *u, integer *ldu, + integer *nv, real *wv, integer *ldwv, integer *nh, real *wh, integer * + ldwh); + +/* Subroutine */ int slaqsb_(char *uplo, integer *n, integer *kd, real *ab, + integer *ldab, real *s, real *scond, real *amax, char *equed); + +/* Subroutine */ int slaqsp_(char *uplo, integer *n, real *ap, real *s, real * + scond, real *amax, char *equed); + +/* Subroutine */ int slaqsy_(char *uplo, integer *n, real *a, integer *lda, + real *s, real *scond, real *amax, char *equed); + +/* Subroutine */ int slaqtr_(logical *ltran, logical *lreal, integer *n, real + *t, integer *ldt, real *b, real *w, real *scale, real *x, real *work, + integer *info); + +/* Subroutine */ int slar1v_(integer *n, integer *b1, integer *bn, real * + lambda, real *d__, real *l, real *ld, real *lld, real *pivmin, real * + gaptol, real *z__, logical *wantnc, integer *negcnt, real *ztz, real * + mingma, integer *r__, integer *isuppz, real *nrminv, real *resid, + real *rqcorr, real *work); + +/* Subroutine */ int slar2v_(integer *n, real *x, real *y, real *z__, integer + *incx, real *c__, real *s, integer *incc); + +/* Subroutine */ int slarf_(char *side, integer *m, integer *n, real *v, + integer *incv, real *tau, real *c__, integer *ldc, real *work); + +/* Subroutine */ int slarfb_(char *side, char *trans, char *direct, char * + storev, integer *m, integer *n, integer *k, real *v, integer *ldv, + real *t, integer *ldt, real *c__, integer *ldc, real *work, integer * + ldwork); + +/* Subroutine */ int slarfg_(integer *n, real *alpha, real *x, integer *incx, + real *tau); + +/* Subroutine */ int slarfp_(integer *n, real *alpha, real *x, integer *incx, + real *tau); + +/* Subroutine */ int slarft_(char *direct, char *storev, integer *n, integer * + k, real *v, integer *ldv, real *tau, real *t, integer *ldt); + +/* Subroutine */ int slarfx_(char *side, integer *m, integer *n, real *v, + real *tau, real *c__, integer *ldc, real *work); + +/* Subroutine */ int slargv_(integer *n, real *x, integer *incx, real *y, + integer *incy, real *c__, integer *incc); + +/* Subroutine */ int slarnv_(integer *idist, integer *iseed, integer *n, real + *x); + +/* Subroutine */ int slarra_(integer *n, real *d__, real *e, real *e2, real * + spltol, real *tnrm, integer *nsplit, integer *isplit, integer *info); + +/* Subroutine */ int slarrb_(integer *n, real *d__, real *lld, integer * + ifirst, integer *ilast, real *rtol1, real *rtol2, integer *offset, + real *w, real *wgap, real *werr, real *work, integer *iwork, real * + pivmin, real *spdiam, integer *twist, integer *info); + +/* Subroutine */ int slarrc_(char *jobt, integer *n, real *vl, real *vu, real + *d__, real *e, real *pivmin, integer *eigcnt, integer *lcnt, integer * + rcnt, integer *info); + +/* Subroutine */ int slarrd_(char *range, char *order, integer *n, real *vl, + real *vu, integer *il, integer *iu, real *gers, real *reltol, real * + d__, real *e, real *e2, real *pivmin, integer *nsplit, integer * + isplit, integer *m, real *w, real *werr, real *wl, real *wu, integer * + iblock, integer *indexw, real *work, integer *iwork, integer *info); + +/* Subroutine */ int slarre_(char *range, integer *n, real *vl, real *vu, + integer *il, integer *iu, real *d__, real *e, real *e2, real *rtol1, + real *rtol2, real *spltol, integer *nsplit, integer *isplit, integer * + m, real *w, real *werr, real *wgap, integer *iblock, integer *indexw, + real *gers, real *pivmin, real *work, integer *iwork, integer *info); + +/* Subroutine */ int slarrf_(integer *n, real *d__, real *l, real *ld, + integer *clstrt, integer *clend, real *w, real *wgap, real *werr, + real *spdiam, real *clgapl, real *clgapr, real *pivmin, real *sigma, + real *dplus, real *lplus, real *work, integer *info); + +/* Subroutine */ int slarrj_(integer *n, real *d__, real *e2, integer *ifirst, + integer *ilast, real *rtol, integer *offset, real *w, real *werr, + real *work, integer *iwork, real *pivmin, real *spdiam, integer *info); + +/* Subroutine */ int slarrk_(integer *n, integer *iw, real *gl, real *gu, + real *d__, real *e2, real *pivmin, real *reltol, real *w, real *werr, + integer *info); + +/* Subroutine */ int slarrr_(integer *n, real *d__, real *e, integer *info); + +/* Subroutine */ int slarrv_(integer *n, real *vl, real *vu, real *d__, real * + l, real *pivmin, integer *isplit, integer *m, integer *dol, integer * + dou, real *minrgp, real *rtol1, real *rtol2, real *w, real *werr, + real *wgap, integer *iblock, integer *indexw, real *gers, real *z__, + integer *ldz, integer *isuppz, real *work, integer *iwork, integer * + info); + +/* Subroutine */ int slarscl2_(integer *m, integer *n, real *d__, real *x, + integer *ldx); + +/* Subroutine */ int slartg_(real *f, real *g, real *cs, real *sn, real *r__); + +/* Subroutine */ int slartv_(integer *n, real *x, integer *incx, real *y, + integer *incy, real *c__, real *s, integer *incc); + +/* Subroutine */ int slaruv_(integer *iseed, integer *n, real *x); + +/* Subroutine */ int slarz_(char *side, integer *m, integer *n, integer *l, + real *v, integer *incv, real *tau, real *c__, integer *ldc, real * + work); + +/* Subroutine */ int slarzb_(char *side, char *trans, char *direct, char * + storev, integer *m, integer *n, integer *k, integer *l, real *v, + integer *ldv, real *t, integer *ldt, real *c__, integer *ldc, real * + work, integer *ldwork); + +/* Subroutine */ int slarzt_(char *direct, char *storev, integer *n, integer * + k, real *v, integer *ldv, real *tau, real *t, integer *ldt); + +/* Subroutine */ int slas2_(real *f, real *g, real *h__, real *ssmin, real * + ssmax); + +/* Subroutine */ int slascl_(char *type__, integer *kl, integer *ku, real * + cfrom, real *cto, integer *m, integer *n, real *a, integer *lda, + integer *info); + +/* Subroutine */ int slascl2_(integer *m, integer *n, real *d__, real *x, + integer *ldx); + +/* Subroutine */ int slasd0_(integer *n, integer *sqre, real *d__, real *e, + real *u, integer *ldu, real *vt, integer *ldvt, integer *smlsiz, + integer *iwork, real *work, integer *info); + +/* Subroutine */ int slasd1_(integer *nl, integer *nr, integer *sqre, real * + d__, real *alpha, real *beta, real *u, integer *ldu, real *vt, + integer *ldvt, integer *idxq, integer *iwork, real *work, integer * + info); + +/* Subroutine */ int slasd2_(integer *nl, integer *nr, integer *sqre, integer + *k, real *d__, real *z__, real *alpha, real *beta, real *u, integer * + ldu, real *vt, integer *ldvt, real *dsigma, real *u2, integer *ldu2, + real *vt2, integer *ldvt2, integer *idxp, integer *idx, integer *idxc, + integer *idxq, integer *coltyp, integer *info); + +/* Subroutine */ int slasd3_(integer *nl, integer *nr, integer *sqre, integer + *k, real *d__, real *q, integer *ldq, real *dsigma, real *u, integer * + ldu, real *u2, integer *ldu2, real *vt, integer *ldvt, real *vt2, + integer *ldvt2, integer *idxc, integer *ctot, real *z__, integer * + info); + +/* Subroutine */ int slasd4_(integer *n, integer *i__, real *d__, real *z__, + real *delta, real *rho, real *sigma, real *work, integer *info); + +/* Subroutine */ int slasd5_(integer *i__, real *d__, real *z__, real *delta, + real *rho, real *dsigma, real *work); + +/* Subroutine */ int slasd6_(integer *icompq, integer *nl, integer *nr, + integer *sqre, real *d__, real *vf, real *vl, real *alpha, real *beta, + integer *idxq, integer *perm, integer *givptr, integer *givcol, + integer *ldgcol, real *givnum, integer *ldgnum, real *poles, real * + difl, real *difr, real *z__, integer *k, real *c__, real *s, real * + work, integer *iwork, integer *info); + +/* Subroutine */ int slasd7_(integer *icompq, integer *nl, integer *nr, + integer *sqre, integer *k, real *d__, real *z__, real *zw, real *vf, + real *vfw, real *vl, real *vlw, real *alpha, real *beta, real *dsigma, + integer *idx, integer *idxp, integer *idxq, integer *perm, integer * + givptr, integer *givcol, integer *ldgcol, real *givnum, integer * + ldgnum, real *c__, real *s, integer *info); + +/* Subroutine */ int slasd8_(integer *icompq, integer *k, real *d__, real * + z__, real *vf, real *vl, real *difl, real *difr, integer *lddifr, + real *dsigma, real *work, integer *info); + +/* Subroutine */ int slasda_(integer *icompq, integer *smlsiz, integer *n, + integer *sqre, real *d__, real *e, real *u, integer *ldu, real *vt, + integer *k, real *difl, real *difr, real *z__, real *poles, integer * + givptr, integer *givcol, integer *ldgcol, integer *perm, real *givnum, + real *c__, real *s, real *work, integer *iwork, integer *info); + +/* Subroutine */ int slasdq_(char *uplo, integer *sqre, integer *n, integer * + ncvt, integer *nru, integer *ncc, real *d__, real *e, real *vt, + integer *ldvt, real *u, integer *ldu, real *c__, integer *ldc, real * + work, integer *info); + +/* Subroutine */ int slasdt_(integer *n, integer *lvl, integer *nd, integer * + inode, integer *ndiml, integer *ndimr, integer *msub); + +/* Subroutine */ int slaset_(char *uplo, integer *m, integer *n, real *alpha, + real *beta, real *a, integer *lda); + +/* Subroutine */ int slasq1_(integer *n, real *d__, real *e, real *work, + integer *info); + +/* Subroutine */ int slasq2_(integer *n, real *z__, integer *info); + +/* Subroutine */ int slasq3_(integer *i0, integer *n0, real *z__, integer *pp, + real *dmin__, real *sigma, real *desig, real *qmax, integer *nfail, + integer *iter, integer *ndiv, logical *ieee, integer *ttype, real * + dmin1, real *dmin2, real *dn, real *dn1, real *dn2, real *g, real * + tau); + +/* Subroutine */ int slasq4_(integer *i0, integer *n0, real *z__, integer *pp, + integer *n0in, real *dmin__, real *dmin1, real *dmin2, real *dn, + real *dn1, real *dn2, real *tau, integer *ttype, real *g); + +/* Subroutine */ int slasq5_(integer *i0, integer *n0, real *z__, integer *pp, + real *tau, real *dmin__, real *dmin1, real *dmin2, real *dn, real * + dnm1, real *dnm2, logical *ieee); + +/* Subroutine */ int slasq6_(integer *i0, integer *n0, real *z__, integer *pp, + real *dmin__, real *dmin1, real *dmin2, real *dn, real *dnm1, real * + dnm2); + +/* Subroutine */ int slasr_(char *side, char *pivot, char *direct, integer *m, + integer *n, real *c__, real *s, real *a, integer *lda); + +/* Subroutine */ int slasrt_(char *id, integer *n, real *d__, integer *info); + +/* Subroutine */ int slassq_(integer *n, real *x, integer *incx, real *scale, + real *sumsq); + +/* Subroutine */ int slasv2_(real *f, real *g, real *h__, real *ssmin, real * + ssmax, real *snr, real *csr, real *snl, real *csl); + +/* Subroutine */ int slaswp_(integer *n, real *a, integer *lda, integer *k1, + integer *k2, integer *ipiv, integer *incx); + +/* Subroutine */ int slasy2_(logical *ltranl, logical *ltranr, integer *isgn, + integer *n1, integer *n2, real *tl, integer *ldtl, real *tr, integer * + ldtr, real *b, integer *ldb, real *scale, real *x, integer *ldx, real + *xnorm, integer *info); + +/* Subroutine */ int slasyf_(char *uplo, integer *n, integer *nb, integer *kb, + real *a, integer *lda, integer *ipiv, real *w, integer *ldw, integer + *info); + +/* Subroutine */ int slatbs_(char *uplo, char *trans, char *diag, char * + normin, integer *n, integer *kd, real *ab, integer *ldab, real *x, + real *scale, real *cnorm, integer *info); + +/* Subroutine */ int slatdf_(integer *ijob, integer *n, real *z__, integer * + ldz, real *rhs, real *rdsum, real *rdscal, integer *ipiv, integer * + jpiv); + +/* Subroutine */ int slatps_(char *uplo, char *trans, char *diag, char * + normin, integer *n, real *ap, real *x, real *scale, real *cnorm, + integer *info); + +/* Subroutine */ int slatrd_(char *uplo, integer *n, integer *nb, real *a, + integer *lda, real *e, real *tau, real *w, integer *ldw); + +/* Subroutine */ int slatrs_(char *uplo, char *trans, char *diag, char * + normin, integer *n, real *a, integer *lda, real *x, real *scale, real + *cnorm, integer *info); + +/* Subroutine */ int slatrz_(integer *m, integer *n, integer *l, real *a, + integer *lda, real *tau, real *work); + +/* Subroutine */ int slatzm_(char *side, integer *m, integer *n, real *v, + integer *incv, real *tau, real *c1, real *c2, integer *ldc, real * + work); + +/* Subroutine */ int slauu2_(char *uplo, integer *n, real *a, integer *lda, + integer *info); + +/* Subroutine */ int slauum_(char *uplo, integer *n, real *a, integer *lda, + integer *info); + +/* Subroutine */ int sopgtr_(char *uplo, integer *n, real *ap, real *tau, + real *q, integer *ldq, real *work, integer *info); + +/* Subroutine */ int sopmtr_(char *side, char *uplo, char *trans, integer *m, + integer *n, real *ap, real *tau, real *c__, integer *ldc, real *work, + integer *info); + +/* Subroutine */ int sorg2l_(integer *m, integer *n, integer *k, real *a, + integer *lda, real *tau, real *work, integer *info); + +/* Subroutine */ int sorg2r_(integer *m, integer *n, integer *k, real *a, + integer *lda, real *tau, real *work, integer *info); + +/* Subroutine */ int sorgbr_(char *vect, integer *m, integer *n, integer *k, + real *a, integer *lda, real *tau, real *work, integer *lwork, integer + *info); + +/* Subroutine */ int sorghr_(integer *n, integer *ilo, integer *ihi, real *a, + integer *lda, real *tau, real *work, integer *lwork, integer *info); + +/* Subroutine */ int sorgl2_(integer *m, integer *n, integer *k, real *a, + integer *lda, real *tau, real *work, integer *info); + +/* Subroutine */ int sorglq_(integer *m, integer *n, integer *k, real *a, + integer *lda, real *tau, real *work, integer *lwork, integer *info); + +/* Subroutine */ int sorgql_(integer *m, integer *n, integer *k, real *a, + integer *lda, real *tau, real *work, integer *lwork, integer *info); + +/* Subroutine */ int sorgqr_(integer *m, integer *n, integer *k, real *a, + integer *lda, real *tau, real *work, integer *lwork, integer *info); + +/* Subroutine */ int sorgr2_(integer *m, integer *n, integer *k, real *a, + integer *lda, real *tau, real *work, integer *info); + +/* Subroutine */ int sorgrq_(integer *m, integer *n, integer *k, real *a, + integer *lda, real *tau, real *work, integer *lwork, integer *info); + +/* Subroutine */ int sorgtr_(char *uplo, integer *n, real *a, integer *lda, + real *tau, real *work, integer *lwork, integer *info); + +/* Subroutine */ int sorm2l_(char *side, char *trans, integer *m, integer *n, + integer *k, real *a, integer *lda, real *tau, real *c__, integer *ldc, + real *work, integer *info); + +/* Subroutine */ int sorm2r_(char *side, char *trans, integer *m, integer *n, + integer *k, real *a, integer *lda, real *tau, real *c__, integer *ldc, + real *work, integer *info); + +/* Subroutine */ int sormbr_(char *vect, char *side, char *trans, integer *m, + integer *n, integer *k, real *a, integer *lda, real *tau, real *c__, + integer *ldc, real *work, integer *lwork, integer *info); + +/* Subroutine */ int sormhr_(char *side, char *trans, integer *m, integer *n, + integer *ilo, integer *ihi, real *a, integer *lda, real *tau, real * + c__, integer *ldc, real *work, integer *lwork, integer *info); + +/* Subroutine */ int sorml2_(char *side, char *trans, integer *m, integer *n, + integer *k, real *a, integer *lda, real *tau, real *c__, integer *ldc, + real *work, integer *info); + +/* Subroutine */ int sormlq_(char *side, char *trans, integer *m, integer *n, + integer *k, real *a, integer *lda, real *tau, real *c__, integer *ldc, + real *work, integer *lwork, integer *info); + +/* Subroutine */ int sormql_(char *side, char *trans, integer *m, integer *n, + integer *k, real *a, integer *lda, real *tau, real *c__, integer *ldc, + real *work, integer *lwork, integer *info); + +/* Subroutine */ int sormqr_(char *side, char *trans, integer *m, integer *n, + integer *k, real *a, integer *lda, real *tau, real *c__, integer *ldc, + real *work, integer *lwork, integer *info); + +/* Subroutine */ int sormr2_(char *side, char *trans, integer *m, integer *n, + integer *k, real *a, integer *lda, real *tau, real *c__, integer *ldc, + real *work, integer *info); + +/* Subroutine */ int sormr3_(char *side, char *trans, integer *m, integer *n, + integer *k, integer *l, real *a, integer *lda, real *tau, real *c__, + integer *ldc, real *work, integer *info); + +/* Subroutine */ int sormrq_(char *side, char *trans, integer *m, integer *n, + integer *k, real *a, integer *lda, real *tau, real *c__, integer *ldc, + real *work, integer *lwork, integer *info); + +/* Subroutine */ int sormrz_(char *side, char *trans, integer *m, integer *n, + integer *k, integer *l, real *a, integer *lda, real *tau, real *c__, + integer *ldc, real *work, integer *lwork, integer *info); + +/* Subroutine */ int sormtr_(char *side, char *uplo, char *trans, integer *m, + integer *n, real *a, integer *lda, real *tau, real *c__, integer *ldc, + real *work, integer *lwork, integer *info); + +/* Subroutine */ int spbcon_(char *uplo, integer *n, integer *kd, real *ab, + integer *ldab, real *anorm, real *rcond, real *work, integer *iwork, + integer *info); + +/* Subroutine */ int spbequ_(char *uplo, integer *n, integer *kd, real *ab, + integer *ldab, real *s, real *scond, real *amax, integer *info); + +/* Subroutine */ int spbrfs_(char *uplo, integer *n, integer *kd, integer * + nrhs, real *ab, integer *ldab, real *afb, integer *ldafb, real *b, + integer *ldb, real *x, integer *ldx, real *ferr, real *berr, real * + work, integer *iwork, integer *info); + +/* Subroutine */ int spbstf_(char *uplo, integer *n, integer *kd, real *ab, + integer *ldab, integer *info); + +/* Subroutine */ int spbsv_(char *uplo, integer *n, integer *kd, integer * + nrhs, real *ab, integer *ldab, real *b, integer *ldb, integer *info); + +/* Subroutine */ int spbsvx_(char *fact, char *uplo, integer *n, integer *kd, + integer *nrhs, real *ab, integer *ldab, real *afb, integer *ldafb, + char *equed, real *s, real *b, integer *ldb, real *x, integer *ldx, + real *rcond, real *ferr, real *berr, real *work, integer *iwork, + integer *info); + +/* Subroutine */ int spbtf2_(char *uplo, integer *n, integer *kd, real *ab, + integer *ldab, integer *info); + +/* Subroutine */ int spbtrf_(char *uplo, integer *n, integer *kd, real *ab, + integer *ldab, integer *info); + +/* Subroutine */ int spbtrs_(char *uplo, integer *n, integer *kd, integer * + nrhs, real *ab, integer *ldab, real *b, integer *ldb, integer *info); + +/* Subroutine */ int spftrf_(char *transr, char *uplo, integer *n, real *a, + integer *info); + +/* Subroutine */ int spftri_(char *transr, char *uplo, integer *n, real *a, + integer *info); + +/* Subroutine */ int spftrs_(char *transr, char *uplo, integer *n, integer * + nrhs, real *a, real *b, integer *ldb, integer *info); + +/* Subroutine */ int spocon_(char *uplo, integer *n, real *a, integer *lda, + real *anorm, real *rcond, real *work, integer *iwork, integer *info); + +/* Subroutine */ int spoequ_(integer *n, real *a, integer *lda, real *s, real + *scond, real *amax, integer *info); + +/* Subroutine */ int spoequb_(integer *n, real *a, integer *lda, real *s, + real *scond, real *amax, integer *info); + +/* Subroutine */ int sporfs_(char *uplo, integer *n, integer *nrhs, real *a, + integer *lda, real *af, integer *ldaf, real *b, integer *ldb, real *x, + integer *ldx, real *ferr, real *berr, real *work, integer *iwork, + integer *info); + +/* Subroutine */ int sporfsx_(char *uplo, char *equed, integer *n, integer * + nrhs, real *a, integer *lda, real *af, integer *ldaf, real *s, real * + b, integer *ldb, real *x, integer *ldx, real *rcond, real *berr, + integer *n_err_bnds__, real *err_bnds_norm__, real *err_bnds_comp__, + integer *nparams, real *params, real *work, integer *iwork, integer * + info); + +/* Subroutine */ int sposv_(char *uplo, integer *n, integer *nrhs, real *a, + integer *lda, real *b, integer *ldb, integer *info); + +/* Subroutine */ int sposvx_(char *fact, char *uplo, integer *n, integer * + nrhs, real *a, integer *lda, real *af, integer *ldaf, char *equed, + real *s, real *b, integer *ldb, real *x, integer *ldx, real *rcond, + real *ferr, real *berr, real *work, integer *iwork, integer *info); + +/* Subroutine */ int sposvxx_(char *fact, char *uplo, integer *n, integer * + nrhs, real *a, integer *lda, real *af, integer *ldaf, char *equed, + real *s, real *b, integer *ldb, real *x, integer *ldx, real *rcond, + real *rpvgrw, real *berr, integer *n_err_bnds__, real * + err_bnds_norm__, real *err_bnds_comp__, integer *nparams, real * + params, real *work, integer *iwork, integer *info); + +/* Subroutine */ int spotf2_(char *uplo, integer *n, real *a, integer *lda, + integer *info); + +/* Subroutine */ int spotrf_(char *uplo, integer *n, real *a, integer *lda, + integer *info); + +/* Subroutine */ int spotri_(char *uplo, integer *n, real *a, integer *lda, + integer *info); + +/* Subroutine */ int spotrs_(char *uplo, integer *n, integer *nrhs, real *a, + integer *lda, real *b, integer *ldb, integer *info); + +/* Subroutine */ int sppcon_(char *uplo, integer *n, real *ap, real *anorm, + real *rcond, real *work, integer *iwork, integer *info); + +/* Subroutine */ int sppequ_(char *uplo, integer *n, real *ap, real *s, real * + scond, real *amax, integer *info); + +/* Subroutine */ int spprfs_(char *uplo, integer *n, integer *nrhs, real *ap, + real *afp, real *b, integer *ldb, real *x, integer *ldx, real *ferr, + real *berr, real *work, integer *iwork, integer *info); + +/* Subroutine */ int sppsv_(char *uplo, integer *n, integer *nrhs, real *ap, + real *b, integer *ldb, integer *info); + +/* Subroutine */ int sppsvx_(char *fact, char *uplo, integer *n, integer * + nrhs, real *ap, real *afp, char *equed, real *s, real *b, integer * + ldb, real *x, integer *ldx, real *rcond, real *ferr, real *berr, real + *work, integer *iwork, integer *info); + +/* Subroutine */ int spptrf_(char *uplo, integer *n, real *ap, integer *info); + +/* Subroutine */ int spptri_(char *uplo, integer *n, real *ap, integer *info); + +/* Subroutine */ int spptrs_(char *uplo, integer *n, integer *nrhs, real *ap, + real *b, integer *ldb, integer *info); + +/* Subroutine */ int spstf2_(char *uplo, integer *n, real *a, integer *lda, + integer *piv, integer *rank, real *tol, real *work, integer *info); + +/* Subroutine */ int spstrf_(char *uplo, integer *n, real *a, integer *lda, + integer *piv, integer *rank, real *tol, real *work, integer *info); + +/* Subroutine */ int sptcon_(integer *n, real *d__, real *e, real *anorm, + real *rcond, real *work, integer *info); + +/* Subroutine */ int spteqr_(char *compz, integer *n, real *d__, real *e, + real *z__, integer *ldz, real *work, integer *info); + +/* Subroutine */ int sptrfs_(integer *n, integer *nrhs, real *d__, real *e, + real *df, real *ef, real *b, integer *ldb, real *x, integer *ldx, + real *ferr, real *berr, real *work, integer *info); + +/* Subroutine */ int sptsv_(integer *n, integer *nrhs, real *d__, real *e, + real *b, integer *ldb, integer *info); + +/* Subroutine */ int sptsvx_(char *fact, integer *n, integer *nrhs, real *d__, + real *e, real *df, real *ef, real *b, integer *ldb, real *x, integer + *ldx, real *rcond, real *ferr, real *berr, real *work, integer *info); + +/* Subroutine */ int spttrf_(integer *n, real *d__, real *e, integer *info); + +/* Subroutine */ int spttrs_(integer *n, integer *nrhs, real *d__, real *e, + real *b, integer *ldb, integer *info); + +/* Subroutine */ int sptts2_(integer *n, integer *nrhs, real *d__, real *e, + real *b, integer *ldb); + +/* Subroutine */ int srscl_(integer *n, real *sa, real *sx, integer *incx); + +/* Subroutine */ int ssbev_(char *jobz, char *uplo, integer *n, integer *kd, + real *ab, integer *ldab, real *w, real *z__, integer *ldz, real *work, + integer *info); + +/* Subroutine */ int ssbevd_(char *jobz, char *uplo, integer *n, integer *kd, + real *ab, integer *ldab, real *w, real *z__, integer *ldz, real *work, + integer *lwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int ssbevx_(char *jobz, char *range, char *uplo, integer *n, + integer *kd, real *ab, integer *ldab, real *q, integer *ldq, real *vl, + real *vu, integer *il, integer *iu, real *abstol, integer *m, real * + w, real *z__, integer *ldz, real *work, integer *iwork, integer * + ifail, integer *info); + +/* Subroutine */ int ssbgst_(char *vect, char *uplo, integer *n, integer *ka, + integer *kb, real *ab, integer *ldab, real *bb, integer *ldbb, real * + x, integer *ldx, real *work, integer *info); + +/* Subroutine */ int ssbgv_(char *jobz, char *uplo, integer *n, integer *ka, + integer *kb, real *ab, integer *ldab, real *bb, integer *ldbb, real * + w, real *z__, integer *ldz, real *work, integer *info); + +/* Subroutine */ int ssbgvd_(char *jobz, char *uplo, integer *n, integer *ka, + integer *kb, real *ab, integer *ldab, real *bb, integer *ldbb, real * + w, real *z__, integer *ldz, real *work, integer *lwork, integer * + iwork, integer *liwork, integer *info); + +/* Subroutine */ int ssbgvx_(char *jobz, char *range, char *uplo, integer *n, + integer *ka, integer *kb, real *ab, integer *ldab, real *bb, integer * + ldbb, real *q, integer *ldq, real *vl, real *vu, integer *il, integer + *iu, real *abstol, integer *m, real *w, real *z__, integer *ldz, real + *work, integer *iwork, integer *ifail, integer *info); + +/* Subroutine */ int ssbtrd_(char *vect, char *uplo, integer *n, integer *kd, + real *ab, integer *ldab, real *d__, real *e, real *q, integer *ldq, + real *work, integer *info); + +/* Subroutine */ int ssfrk_(char *transr, char *uplo, char *trans, integer *n, + integer *k, real *alpha, real *a, integer *lda, real *beta, real * + c__); + +/* Subroutine */ int sspcon_(char *uplo, integer *n, real *ap, integer *ipiv, + real *anorm, real *rcond, real *work, integer *iwork, integer *info); + +/* Subroutine */ int sspev_(char *jobz, char *uplo, integer *n, real *ap, + real *w, real *z__, integer *ldz, real *work, integer *info); + +/* Subroutine */ int sspevd_(char *jobz, char *uplo, integer *n, real *ap, + real *w, real *z__, integer *ldz, real *work, integer *lwork, integer + *iwork, integer *liwork, integer *info); + +/* Subroutine */ int sspevx_(char *jobz, char *range, char *uplo, integer *n, + real *ap, real *vl, real *vu, integer *il, integer *iu, real *abstol, + integer *m, real *w, real *z__, integer *ldz, real *work, integer * + iwork, integer *ifail, integer *info); + +/* Subroutine */ int sspgst_(integer *itype, char *uplo, integer *n, real *ap, + real *bp, integer *info); + +/* Subroutine */ int sspgv_(integer *itype, char *jobz, char *uplo, integer * + n, real *ap, real *bp, real *w, real *z__, integer *ldz, real *work, + integer *info); + +/* Subroutine */ int sspgvd_(integer *itype, char *jobz, char *uplo, integer * + n, real *ap, real *bp, real *w, real *z__, integer *ldz, real *work, + integer *lwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int sspgvx_(integer *itype, char *jobz, char *range, char * + uplo, integer *n, real *ap, real *bp, real *vl, real *vu, integer *il, + integer *iu, real *abstol, integer *m, real *w, real *z__, integer * + ldz, real *work, integer *iwork, integer *ifail, integer *info); + +/* Subroutine */ int ssprfs_(char *uplo, integer *n, integer *nrhs, real *ap, + real *afp, integer *ipiv, real *b, integer *ldb, real *x, integer * + ldx, real *ferr, real *berr, real *work, integer *iwork, integer * + info); + +/* Subroutine */ int sspsv_(char *uplo, integer *n, integer *nrhs, real *ap, + integer *ipiv, real *b, integer *ldb, integer *info); + +/* Subroutine */ int sspsvx_(char *fact, char *uplo, integer *n, integer * + nrhs, real *ap, real *afp, integer *ipiv, real *b, integer *ldb, real + *x, integer *ldx, real *rcond, real *ferr, real *berr, real *work, + integer *iwork, integer *info); + +/* Subroutine */ int ssptrd_(char *uplo, integer *n, real *ap, real *d__, + real *e, real *tau, integer *info); + +/* Subroutine */ int ssptrf_(char *uplo, integer *n, real *ap, integer *ipiv, + integer *info); + +/* Subroutine */ int ssptri_(char *uplo, integer *n, real *ap, integer *ipiv, + real *work, integer *info); + +/* Subroutine */ int ssptrs_(char *uplo, integer *n, integer *nrhs, real *ap, + integer *ipiv, real *b, integer *ldb, integer *info); + +/* Subroutine */ int sstebz_(char *range, char *order, integer *n, real *vl, + real *vu, integer *il, integer *iu, real *abstol, real *d__, real *e, + integer *m, integer *nsplit, real *w, integer *iblock, integer * + isplit, real *work, integer *iwork, integer *info); + +/* Subroutine */ int sstedc_(char *compz, integer *n, real *d__, real *e, + real *z__, integer *ldz, real *work, integer *lwork, integer *iwork, + integer *liwork, integer *info); + +/* Subroutine */ int sstegr_(char *jobz, char *range, integer *n, real *d__, + real *e, real *vl, real *vu, integer *il, integer *iu, real *abstol, + integer *m, real *w, real *z__, integer *ldz, integer *isuppz, real * + work, integer *lwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int sstein_(integer *n, real *d__, real *e, integer *m, real + *w, integer *iblock, integer *isplit, real *z__, integer *ldz, real * + work, integer *iwork, integer *ifail, integer *info); + +/* Subroutine */ int sstemr_(char *jobz, char *range, integer *n, real *d__, + real *e, real *vl, real *vu, integer *il, integer *iu, integer *m, + real *w, real *z__, integer *ldz, integer *nzc, integer *isuppz, + logical *tryrac, real *work, integer *lwork, integer *iwork, integer * + liwork, integer *info); + +/* Subroutine */ int ssteqr_(char *compz, integer *n, real *d__, real *e, + real *z__, integer *ldz, real *work, integer *info); + +/* Subroutine */ int ssterf_(integer *n, real *d__, real *e, integer *info); + +/* Subroutine */ int sstev_(char *jobz, integer *n, real *d__, real *e, real * + z__, integer *ldz, real *work, integer *info); + +/* Subroutine */ int sstevd_(char *jobz, integer *n, real *d__, real *e, real + *z__, integer *ldz, real *work, integer *lwork, integer *iwork, + integer *liwork, integer *info); + +/* Subroutine */ int sstevr_(char *jobz, char *range, integer *n, real *d__, + real *e, real *vl, real *vu, integer *il, integer *iu, real *abstol, + integer *m, real *w, real *z__, integer *ldz, integer *isuppz, real * + work, integer *lwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int sstevx_(char *jobz, char *range, integer *n, real *d__, + real *e, real *vl, real *vu, integer *il, integer *iu, real *abstol, + integer *m, real *w, real *z__, integer *ldz, real *work, integer * + iwork, integer *ifail, integer *info); + +/* Subroutine */ int ssycon_(char *uplo, integer *n, real *a, integer *lda, + integer *ipiv, real *anorm, real *rcond, real *work, integer *iwork, + integer *info); + +/* Subroutine */ int ssyequb_(char *uplo, integer *n, real *a, integer *lda, + real *s, real *scond, real *amax, real *work, integer *info); + +/* Subroutine */ int ssyev_(char *jobz, char *uplo, integer *n, real *a, + integer *lda, real *w, real *work, integer *lwork, integer *info); + +/* Subroutine */ int ssyevd_(char *jobz, char *uplo, integer *n, real *a, + integer *lda, real *w, real *work, integer *lwork, integer *iwork, + integer *liwork, integer *info); + +/* Subroutine */ int ssyevr_(char *jobz, char *range, char *uplo, integer *n, + real *a, integer *lda, real *vl, real *vu, integer *il, integer *iu, + real *abstol, integer *m, real *w, real *z__, integer *ldz, integer * + isuppz, real *work, integer *lwork, integer *iwork, integer *liwork, + integer *info); + +/* Subroutine */ int ssyevx_(char *jobz, char *range, char *uplo, integer *n, + real *a, integer *lda, real *vl, real *vu, integer *il, integer *iu, + real *abstol, integer *m, real *w, real *z__, integer *ldz, real * + work, integer *lwork, integer *iwork, integer *ifail, integer *info); + +/* Subroutine */ int ssygs2_(integer *itype, char *uplo, integer *n, real *a, + integer *lda, real *b, integer *ldb, integer *info); + +/* Subroutine */ int ssygst_(integer *itype, char *uplo, integer *n, real *a, + integer *lda, real *b, integer *ldb, integer *info); + +/* Subroutine */ int ssygv_(integer *itype, char *jobz, char *uplo, integer * + n, real *a, integer *lda, real *b, integer *ldb, real *w, real *work, + integer *lwork, integer *info); + +/* Subroutine */ int ssygvd_(integer *itype, char *jobz, char *uplo, integer * + n, real *a, integer *lda, real *b, integer *ldb, real *w, real *work, + integer *lwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int ssygvx_(integer *itype, char *jobz, char *range, char * + uplo, integer *n, real *a, integer *lda, real *b, integer *ldb, real * + vl, real *vu, integer *il, integer *iu, real *abstol, integer *m, + real *w, real *z__, integer *ldz, real *work, integer *lwork, integer + *iwork, integer *ifail, integer *info); + +/* Subroutine */ int ssyrfs_(char *uplo, integer *n, integer *nrhs, real *a, + integer *lda, real *af, integer *ldaf, integer *ipiv, real *b, + integer *ldb, real *x, integer *ldx, real *ferr, real *berr, real * + work, integer *iwork, integer *info); + +/* Subroutine */ int ssyrfsx_(char *uplo, char *equed, integer *n, integer * + nrhs, real *a, integer *lda, real *af, integer *ldaf, integer *ipiv, + real *s, real *b, integer *ldb, real *x, integer *ldx, real *rcond, + real *berr, integer *n_err_bnds__, real *err_bnds_norm__, real * + err_bnds_comp__, integer *nparams, real *params, real *work, integer * + iwork, integer *info); + +/* Subroutine */ int ssysv_(char *uplo, integer *n, integer *nrhs, real *a, + integer *lda, integer *ipiv, real *b, integer *ldb, real *work, + integer *lwork, integer *info); + +/* Subroutine */ int ssysvx_(char *fact, char *uplo, integer *n, integer * + nrhs, real *a, integer *lda, real *af, integer *ldaf, integer *ipiv, + real *b, integer *ldb, real *x, integer *ldx, real *rcond, real *ferr, + real *berr, real *work, integer *lwork, integer *iwork, integer * + info); + +/* Subroutine */ int ssysvxx_(char *fact, char *uplo, integer *n, integer * + nrhs, real *a, integer *lda, real *af, integer *ldaf, integer *ipiv, + char *equed, real *s, real *b, integer *ldb, real *x, integer *ldx, + real *rcond, real *rpvgrw, real *berr, integer *n_err_bnds__, real * + err_bnds_norm__, real *err_bnds_comp__, integer *nparams, real * + params, real *work, integer *iwork, integer *info); + +/* Subroutine */ int ssytd2_(char *uplo, integer *n, real *a, integer *lda, + real *d__, real *e, real *tau, integer *info); + +/* Subroutine */ int ssytf2_(char *uplo, integer *n, real *a, integer *lda, + integer *ipiv, integer *info); + +/* Subroutine */ int ssytrd_(char *uplo, integer *n, real *a, integer *lda, + real *d__, real *e, real *tau, real *work, integer *lwork, integer * + info); + +/* Subroutine */ int ssytrf_(char *uplo, integer *n, real *a, integer *lda, + integer *ipiv, real *work, integer *lwork, integer *info); + +/* Subroutine */ int ssytri_(char *uplo, integer *n, real *a, integer *lda, + integer *ipiv, real *work, integer *info); + +/* Subroutine */ int ssytrs_(char *uplo, integer *n, integer *nrhs, real *a, + integer *lda, integer *ipiv, real *b, integer *ldb, integer *info); + +/* Subroutine */ int stbcon_(char *norm, char *uplo, char *diag, integer *n, + integer *kd, real *ab, integer *ldab, real *rcond, real *work, + integer *iwork, integer *info); + +/* Subroutine */ int stbrfs_(char *uplo, char *trans, char *diag, integer *n, + integer *kd, integer *nrhs, real *ab, integer *ldab, real *b, integer + *ldb, real *x, integer *ldx, real *ferr, real *berr, real *work, + integer *iwork, integer *info); + +/* Subroutine */ int stbtrs_(char *uplo, char *trans, char *diag, integer *n, + integer *kd, integer *nrhs, real *ab, integer *ldab, real *b, integer + *ldb, integer *info); + +/* Subroutine */ int stfsm_(char *transr, char *side, char *uplo, char *trans, + char *diag, integer *m, integer *n, real *alpha, real *a, real *b, + integer *ldb); + +/* Subroutine */ int stftri_(char *transr, char *uplo, char *diag, integer *n, + real *a, integer *info); + +/* Subroutine */ int stfttp_(char *transr, char *uplo, integer *n, real *arf, + real *ap, integer *info); + +/* Subroutine */ int stfttr_(char *transr, char *uplo, integer *n, real *arf, + real *a, integer *lda, integer *info); + +/* Subroutine */ int stgevc_(char *side, char *howmny, logical *select, + integer *n, real *s, integer *lds, real *p, integer *ldp, real *vl, + integer *ldvl, real *vr, integer *ldvr, integer *mm, integer *m, real + *work, integer *info); + +/* Subroutine */ int stgex2_(logical *wantq, logical *wantz, integer *n, real + *a, integer *lda, real *b, integer *ldb, real *q, integer *ldq, real * + z__, integer *ldz, integer *j1, integer *n1, integer *n2, real *work, + integer *lwork, integer *info); + +/* Subroutine */ int stgexc_(logical *wantq, logical *wantz, integer *n, real + *a, integer *lda, real *b, integer *ldb, real *q, integer *ldq, real * + z__, integer *ldz, integer *ifst, integer *ilst, real *work, integer * + lwork, integer *info); + +/* Subroutine */ int stgsen_(integer *ijob, logical *wantq, logical *wantz, + logical *select, integer *n, real *a, integer *lda, real *b, integer * + ldb, real *alphar, real *alphai, real *beta, real *q, integer *ldq, + real *z__, integer *ldz, integer *m, real *pl, real *pr, real *dif, + real *work, integer *lwork, integer *iwork, integer *liwork, integer * + info); + +/* Subroutine */ int stgsja_(char *jobu, char *jobv, char *jobq, integer *m, + integer *p, integer *n, integer *k, integer *l, real *a, integer *lda, + real *b, integer *ldb, real *tola, real *tolb, real *alpha, real * + beta, real *u, integer *ldu, real *v, integer *ldv, real *q, integer * + ldq, real *work, integer *ncycle, integer *info); + +/* Subroutine */ int stgsna_(char *job, char *howmny, logical *select, + integer *n, real *a, integer *lda, real *b, integer *ldb, real *vl, + integer *ldvl, real *vr, integer *ldvr, real *s, real *dif, integer * + mm, integer *m, real *work, integer *lwork, integer *iwork, integer * + info); + +/* Subroutine */ int stgsy2_(char *trans, integer *ijob, integer *m, integer * + n, real *a, integer *lda, real *b, integer *ldb, real *c__, integer * + ldc, real *d__, integer *ldd, real *e, integer *lde, real *f, integer + *ldf, real *scale, real *rdsum, real *rdscal, integer *iwork, integer + *pq, integer *info); + +/* Subroutine */ int stgsyl_(char *trans, integer *ijob, integer *m, integer * + n, real *a, integer *lda, real *b, integer *ldb, real *c__, integer * + ldc, real *d__, integer *ldd, real *e, integer *lde, real *f, integer + *ldf, real *scale, real *dif, real *work, integer *lwork, integer * + iwork, integer *info); + +/* Subroutine */ int stpcon_(char *norm, char *uplo, char *diag, integer *n, + real *ap, real *rcond, real *work, integer *iwork, integer *info); + +/* Subroutine */ int stprfs_(char *uplo, char *trans, char *diag, integer *n, + integer *nrhs, real *ap, real *b, integer *ldb, real *x, integer *ldx, + real *ferr, real *berr, real *work, integer *iwork, integer *info); + +/* Subroutine */ int stptri_(char *uplo, char *diag, integer *n, real *ap, + integer *info); + +/* Subroutine */ int stptrs_(char *uplo, char *trans, char *diag, integer *n, + integer *nrhs, real *ap, real *b, integer *ldb, integer *info); + +/* Subroutine */ int stpttf_(char *transr, char *uplo, integer *n, real *ap, + real *arf, integer *info); + +/* Subroutine */ int stpttr_(char *uplo, integer *n, real *ap, real *a, + integer *lda, integer *info); + +/* Subroutine */ int strcon_(char *norm, char *uplo, char *diag, integer *n, + real *a, integer *lda, real *rcond, real *work, integer *iwork, + integer *info); + +/* Subroutine */ int strevc_(char *side, char *howmny, logical *select, + integer *n, real *t, integer *ldt, real *vl, integer *ldvl, real *vr, + integer *ldvr, integer *mm, integer *m, real *work, integer *info); + +/* Subroutine */ int strexc_(char *compq, integer *n, real *t, integer *ldt, + real *q, integer *ldq, integer *ifst, integer *ilst, real *work, + integer *info); + +/* Subroutine */ int strrfs_(char *uplo, char *trans, char *diag, integer *n, + integer *nrhs, real *a, integer *lda, real *b, integer *ldb, real *x, + integer *ldx, real *ferr, real *berr, real *work, integer *iwork, + integer *info); + +/* Subroutine */ int strsen_(char *job, char *compq, logical *select, integer + *n, real *t, integer *ldt, real *q, integer *ldq, real *wr, real *wi, + integer *m, real *s, real *sep, real *work, integer *lwork, integer * + iwork, integer *liwork, integer *info); + +/* Subroutine */ int strsna_(char *job, char *howmny, logical *select, + integer *n, real *t, integer *ldt, real *vl, integer *ldvl, real *vr, + integer *ldvr, real *s, real *sep, integer *mm, integer *m, real * + work, integer *ldwork, integer *iwork, integer *info); + +/* Subroutine */ int strsyl_(char *trana, char *tranb, integer *isgn, integer + *m, integer *n, real *a, integer *lda, real *b, integer *ldb, real * + c__, integer *ldc, real *scale, integer *info); + +/* Subroutine */ int strti2_(char *uplo, char *diag, integer *n, real *a, + integer *lda, integer *info); + +/* Subroutine */ int strtri_(char *uplo, char *diag, integer *n, real *a, + integer *lda, integer *info); + +/* Subroutine */ int strtrs_(char *uplo, char *trans, char *diag, integer *n, + integer *nrhs, real *a, integer *lda, real *b, integer *ldb, integer * + info); + +/* Subroutine */ int strttf_(char *transr, char *uplo, integer *n, real *a, + integer *lda, real *arf, integer *info); + +/* Subroutine */ int strttp_(char *uplo, integer *n, real *a, integer *lda, + real *ap, integer *info); + +/* Subroutine */ int stzrqf_(integer *m, integer *n, real *a, integer *lda, + real *tau, integer *info); + +/* Subroutine */ int stzrzf_(integer *m, integer *n, real *a, integer *lda, + real *tau, real *work, integer *lwork, integer *info); + +/* Subroutine */ int xerbla_(char *srname, integer *info); + +/* Subroutine */ int xerbla_array__(char *srname_array__, integer * + srname_len__, integer *info, ftnlen srname_array_len); + +/* Subroutine */ int zbdsqr_(char *uplo, integer *n, integer *ncvt, integer * + nru, integer *ncc, doublereal *d__, doublereal *e, doublecomplex *vt, + integer *ldvt, doublecomplex *u, integer *ldu, doublecomplex *c__, + integer *ldc, doublereal *rwork, integer *info); + +/* Subroutine */ int zcgesv_(integer *n, integer *nrhs, doublecomplex *a, + integer *lda, integer *ipiv, doublecomplex *b, integer *ldb, + doublecomplex *x, integer *ldx, doublecomplex *work, complex *swork, + doublereal *rwork, integer *iter, integer *info); + +/* Subroutine */ int zcposv_(char *uplo, integer *n, integer *nrhs, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + doublecomplex *x, integer *ldx, doublecomplex *work, complex *swork, + doublereal *rwork, integer *iter, integer *info); + +/* Subroutine */ int zdrscl_(integer *n, doublereal *sa, doublecomplex *sx, + integer *incx); + +/* Subroutine */ int zgbbrd_(char *vect, integer *m, integer *n, integer *ncc, + integer *kl, integer *ku, doublecomplex *ab, integer *ldab, + doublereal *d__, doublereal *e, doublecomplex *q, integer *ldq, + doublecomplex *pt, integer *ldpt, doublecomplex *c__, integer *ldc, + doublecomplex *work, doublereal *rwork, integer *info); + +/* Subroutine */ int zgbcon_(char *norm, integer *n, integer *kl, integer *ku, + doublecomplex *ab, integer *ldab, integer *ipiv, doublereal *anorm, + doublereal *rcond, doublecomplex *work, doublereal *rwork, integer * + info); + +/* Subroutine */ int zgbequ_(integer *m, integer *n, integer *kl, integer *ku, + doublecomplex *ab, integer *ldab, doublereal *r__, doublereal *c__, + doublereal *rowcnd, doublereal *colcnd, doublereal *amax, integer * + info); + +/* Subroutine */ int zgbequb_(integer *m, integer *n, integer *kl, integer * + ku, doublecomplex *ab, integer *ldab, doublereal *r__, doublereal * + c__, doublereal *rowcnd, doublereal *colcnd, doublereal *amax, + integer *info); + +/* Subroutine */ int zgbrfs_(char *trans, integer *n, integer *kl, integer * + ku, integer *nrhs, doublecomplex *ab, integer *ldab, doublecomplex * + afb, integer *ldafb, integer *ipiv, doublecomplex *b, integer *ldb, + doublecomplex *x, integer *ldx, doublereal *ferr, doublereal *berr, + doublecomplex *work, doublereal *rwork, integer *info); + +/* Subroutine */ int zgbrfsx_(char *trans, char *equed, integer *n, integer * + kl, integer *ku, integer *nrhs, doublecomplex *ab, integer *ldab, + doublecomplex *afb, integer *ldafb, integer *ipiv, doublereal *r__, + doublereal *c__, doublecomplex *b, integer *ldb, doublecomplex *x, + integer *ldx, doublereal *rcond, doublereal *berr, integer * + n_err_bnds__, doublereal *err_bnds_norm__, doublereal * + err_bnds_comp__, integer *nparams, doublereal *params, doublecomplex * + work, doublereal *rwork, integer *info); + +/* Subroutine */ int zgbsv_(integer *n, integer *kl, integer *ku, integer * + nrhs, doublecomplex *ab, integer *ldab, integer *ipiv, doublecomplex * + b, integer *ldb, integer *info); + +/* Subroutine */ int zgbsvx_(char *fact, char *trans, integer *n, integer *kl, + integer *ku, integer *nrhs, doublecomplex *ab, integer *ldab, + doublecomplex *afb, integer *ldafb, integer *ipiv, char *equed, + doublereal *r__, doublereal *c__, doublecomplex *b, integer *ldb, + doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *ferr, + doublereal *berr, doublecomplex *work, doublereal *rwork, integer * + info); + +/* Subroutine */ int zgbsvxx_(char *fact, char *trans, integer *n, integer * + kl, integer *ku, integer *nrhs, doublecomplex *ab, integer *ldab, + doublecomplex *afb, integer *ldafb, integer *ipiv, char *equed, + doublereal *r__, doublereal *c__, doublecomplex *b, integer *ldb, + doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *rpvgrw, + doublereal *berr, integer *n_err_bnds__, doublereal *err_bnds_norm__, + doublereal *err_bnds_comp__, integer *nparams, doublereal *params, + doublecomplex *work, doublereal *rwork, integer *info); + +/* Subroutine */ int zgbtf2_(integer *m, integer *n, integer *kl, integer *ku, + doublecomplex *ab, integer *ldab, integer *ipiv, integer *info); + +/* Subroutine */ int zgbtrf_(integer *m, integer *n, integer *kl, integer *ku, + doublecomplex *ab, integer *ldab, integer *ipiv, integer *info); + +/* Subroutine */ int zgbtrs_(char *trans, integer *n, integer *kl, integer * + ku, integer *nrhs, doublecomplex *ab, integer *ldab, integer *ipiv, + doublecomplex *b, integer *ldb, integer *info); + +/* Subroutine */ int zgebak_(char *job, char *side, integer *n, integer *ilo, + integer *ihi, doublereal *scale, integer *m, doublecomplex *v, + integer *ldv, integer *info); + +/* Subroutine */ int zgebal_(char *job, integer *n, doublecomplex *a, integer + *lda, integer *ilo, integer *ihi, doublereal *scale, integer *info); + +/* Subroutine */ int zgebd2_(integer *m, integer *n, doublecomplex *a, + integer *lda, doublereal *d__, doublereal *e, doublecomplex *tauq, + doublecomplex *taup, doublecomplex *work, integer *info); + +/* Subroutine */ int zgebrd_(integer *m, integer *n, doublecomplex *a, + integer *lda, doublereal *d__, doublereal *e, doublecomplex *tauq, + doublecomplex *taup, doublecomplex *work, integer *lwork, integer * + info); + +/* Subroutine */ int zgecon_(char *norm, integer *n, doublecomplex *a, + integer *lda, doublereal *anorm, doublereal *rcond, doublecomplex * + work, doublereal *rwork, integer *info); + +/* Subroutine */ int zgeequ_(integer *m, integer *n, doublecomplex *a, + integer *lda, doublereal *r__, doublereal *c__, doublereal *rowcnd, + doublereal *colcnd, doublereal *amax, integer *info); + +/* Subroutine */ int zgeequb_(integer *m, integer *n, doublecomplex *a, + integer *lda, doublereal *r__, doublereal *c__, doublereal *rowcnd, + doublereal *colcnd, doublereal *amax, integer *info); + +/* Subroutine */ int zgees_(char *jobvs, char *sort, L_fp select, integer *n, + doublecomplex *a, integer *lda, integer *sdim, doublecomplex *w, + doublecomplex *vs, integer *ldvs, doublecomplex *work, integer *lwork, + doublereal *rwork, logical *bwork, integer *info); + +/* Subroutine */ int zgeesx_(char *jobvs, char *sort, L_fp select, char * + sense, integer *n, doublecomplex *a, integer *lda, integer *sdim, + doublecomplex *w, doublecomplex *vs, integer *ldvs, doublereal * + rconde, doublereal *rcondv, doublecomplex *work, integer *lwork, + doublereal *rwork, logical *bwork, integer *info); + +/* Subroutine */ int zgeev_(char *jobvl, char *jobvr, integer *n, + doublecomplex *a, integer *lda, doublecomplex *w, doublecomplex *vl, + integer *ldvl, doublecomplex *vr, integer *ldvr, doublecomplex *work, + integer *lwork, doublereal *rwork, integer *info); + +/* Subroutine */ int zgeevx_(char *balanc, char *jobvl, char *jobvr, char * + sense, integer *n, doublecomplex *a, integer *lda, doublecomplex *w, + doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *ldvr, + integer *ilo, integer *ihi, doublereal *scale, doublereal *abnrm, + doublereal *rconde, doublereal *rcondv, doublecomplex *work, integer * + lwork, doublereal *rwork, integer *info); + +/* Subroutine */ int zgegs_(char *jobvsl, char *jobvsr, integer *n, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + doublecomplex *alpha, doublecomplex *beta, doublecomplex *vsl, + integer *ldvsl, doublecomplex *vsr, integer *ldvsr, doublecomplex * + work, integer *lwork, doublereal *rwork, integer *info); + +/* Subroutine */ int zgegv_(char *jobvl, char *jobvr, integer *n, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + doublecomplex *alpha, doublecomplex *beta, doublecomplex *vl, integer + *ldvl, doublecomplex *vr, integer *ldvr, doublecomplex *work, integer + *lwork, doublereal *rwork, integer *info); + +/* Subroutine */ int zgehd2_(integer *n, integer *ilo, integer *ihi, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *info); + +/* Subroutine */ int zgehrd_(integer *n, integer *ilo, integer *ihi, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *lwork, integer *info); + +/* Subroutine */ int zgelq2_(integer *m, integer *n, doublecomplex *a, + integer *lda, doublecomplex *tau, doublecomplex *work, integer *info); + +/* Subroutine */ int zgelqf_(integer *m, integer *n, doublecomplex *a, + integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork, + integer *info); + +/* Subroutine */ int zgels_(char *trans, integer *m, integer *n, integer * + nrhs, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + doublecomplex *work, integer *lwork, integer *info); + +/* Subroutine */ int zgelsd_(integer *m, integer *n, integer *nrhs, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + doublereal *s, doublereal *rcond, integer *rank, doublecomplex *work, + integer *lwork, doublereal *rwork, integer *iwork, integer *info); + +/* Subroutine */ int zgelss_(integer *m, integer *n, integer *nrhs, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + doublereal *s, doublereal *rcond, integer *rank, doublecomplex *work, + integer *lwork, doublereal *rwork, integer *info); + +/* Subroutine */ int zgelsx_(integer *m, integer *n, integer *nrhs, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + integer *jpvt, doublereal *rcond, integer *rank, doublecomplex *work, + doublereal *rwork, integer *info); + +/* Subroutine */ int zgelsy_(integer *m, integer *n, integer *nrhs, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + integer *jpvt, doublereal *rcond, integer *rank, doublecomplex *work, + integer *lwork, doublereal *rwork, integer *info); + +/* Subroutine */ int zgeql2_(integer *m, integer *n, doublecomplex *a, + integer *lda, doublecomplex *tau, doublecomplex *work, integer *info); + +/* Subroutine */ int zgeqlf_(integer *m, integer *n, doublecomplex *a, + integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork, + integer *info); + +/* Subroutine */ int zgeqp3_(integer *m, integer *n, doublecomplex *a, + integer *lda, integer *jpvt, doublecomplex *tau, doublecomplex *work, + integer *lwork, doublereal *rwork, integer *info); + +/* Subroutine */ int zgeqpf_(integer *m, integer *n, doublecomplex *a, + integer *lda, integer *jpvt, doublecomplex *tau, doublecomplex *work, + doublereal *rwork, integer *info); + +/* Subroutine */ int zgeqr2_(integer *m, integer *n, doublecomplex *a, + integer *lda, doublecomplex *tau, doublecomplex *work, integer *info); + +/* Subroutine */ int zgeqrf_(integer *m, integer *n, doublecomplex *a, + integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork, + integer *info); + +/* Subroutine */ int zgerfs_(char *trans, integer *n, integer *nrhs, + doublecomplex *a, integer *lda, doublecomplex *af, integer *ldaf, + integer *ipiv, doublecomplex *b, integer *ldb, doublecomplex *x, + integer *ldx, doublereal *ferr, doublereal *berr, doublecomplex *work, + doublereal *rwork, integer *info); + +/* Subroutine */ int zgerfsx_(char *trans, char *equed, integer *n, integer * + nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * + ldaf, integer *ipiv, doublereal *r__, doublereal *c__, doublecomplex * + b, integer *ldb, doublecomplex *x, integer *ldx, doublereal *rcond, + doublereal *berr, integer *n_err_bnds__, doublereal *err_bnds_norm__, + doublereal *err_bnds_comp__, integer *nparams, doublereal *params, + doublecomplex *work, doublereal *rwork, integer *info); + +/* Subroutine */ int zgerq2_(integer *m, integer *n, doublecomplex *a, + integer *lda, doublecomplex *tau, doublecomplex *work, integer *info); + +/* Subroutine */ int zgerqf_(integer *m, integer *n, doublecomplex *a, + integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork, + integer *info); + +/* Subroutine */ int zgesc2_(integer *n, doublecomplex *a, integer *lda, + doublecomplex *rhs, integer *ipiv, integer *jpiv, doublereal *scale); + +/* Subroutine */ int zgesdd_(char *jobz, integer *m, integer *n, + doublecomplex *a, integer *lda, doublereal *s, doublecomplex *u, + integer *ldu, doublecomplex *vt, integer *ldvt, doublecomplex *work, + integer *lwork, doublereal *rwork, integer *iwork, integer *info); + +/* Subroutine */ int zgesv_(integer *n, integer *nrhs, doublecomplex *a, + integer *lda, integer *ipiv, doublecomplex *b, integer *ldb, integer * + info); + +/* Subroutine */ int zgesvd_(char *jobu, char *jobvt, integer *m, integer *n, + doublecomplex *a, integer *lda, doublereal *s, doublecomplex *u, + integer *ldu, doublecomplex *vt, integer *ldvt, doublecomplex *work, + integer *lwork, doublereal *rwork, integer *info); + +/* Subroutine */ int zgesvx_(char *fact, char *trans, integer *n, integer * + nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * + ldaf, integer *ipiv, char *equed, doublereal *r__, doublereal *c__, + doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, + doublereal *rcond, doublereal *ferr, doublereal *berr, doublecomplex * + work, doublereal *rwork, integer *info); + +/* Subroutine */ int zgesvxx_(char *fact, char *trans, integer *n, integer * + nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * + ldaf, integer *ipiv, char *equed, doublereal *r__, doublereal *c__, + doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, + doublereal *rcond, doublereal *rpvgrw, doublereal *berr, integer * + n_err_bnds__, doublereal *err_bnds_norm__, doublereal * + err_bnds_comp__, integer *nparams, doublereal *params, doublecomplex * + work, doublereal *rwork, integer *info); + +/* Subroutine */ int zgetc2_(integer *n, doublecomplex *a, integer *lda, + integer *ipiv, integer *jpiv, integer *info); + +/* Subroutine */ int zgetf2_(integer *m, integer *n, doublecomplex *a, + integer *lda, integer *ipiv, integer *info); + +/* Subroutine */ int zgetrf_(integer *m, integer *n, doublecomplex *a, + integer *lda, integer *ipiv, integer *info); + +/* Subroutine */ int zgetri_(integer *n, doublecomplex *a, integer *lda, + integer *ipiv, doublecomplex *work, integer *lwork, integer *info); + +/* Subroutine */ int zgetrs_(char *trans, integer *n, integer *nrhs, + doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *b, + integer *ldb, integer *info); + +/* Subroutine */ int zggbak_(char *job, char *side, integer *n, integer *ilo, + integer *ihi, doublereal *lscale, doublereal *rscale, integer *m, + doublecomplex *v, integer *ldv, integer *info); + +/* Subroutine */ int zggbal_(char *job, integer *n, doublecomplex *a, integer + *lda, doublecomplex *b, integer *ldb, integer *ilo, integer *ihi, + doublereal *lscale, doublereal *rscale, doublereal *work, integer * + info); + +/* Subroutine */ int zgges_(char *jobvsl, char *jobvsr, char *sort, L_fp + selctg, integer *n, doublecomplex *a, integer *lda, doublecomplex *b, + integer *ldb, integer *sdim, doublecomplex *alpha, doublecomplex * + beta, doublecomplex *vsl, integer *ldvsl, doublecomplex *vsr, integer + *ldvsr, doublecomplex *work, integer *lwork, doublereal *rwork, + logical *bwork, integer *info); + +/* Subroutine */ int zggesx_(char *jobvsl, char *jobvsr, char *sort, L_fp + selctg, char *sense, integer *n, doublecomplex *a, integer *lda, + doublecomplex *b, integer *ldb, integer *sdim, doublecomplex *alpha, + doublecomplex *beta, doublecomplex *vsl, integer *ldvsl, + doublecomplex *vsr, integer *ldvsr, doublereal *rconde, doublereal * + rcondv, doublecomplex *work, integer *lwork, doublereal *rwork, + integer *iwork, integer *liwork, logical *bwork, integer *info); + +/* Subroutine */ int zggev_(char *jobvl, char *jobvr, integer *n, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + doublecomplex *alpha, doublecomplex *beta, doublecomplex *vl, integer + *ldvl, doublecomplex *vr, integer *ldvr, doublecomplex *work, integer + *lwork, doublereal *rwork, integer *info); + +/* Subroutine */ int zggevx_(char *balanc, char *jobvl, char *jobvr, char * + sense, integer *n, doublecomplex *a, integer *lda, doublecomplex *b, + integer *ldb, doublecomplex *alpha, doublecomplex *beta, + doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *ldvr, + integer *ilo, integer *ihi, doublereal *lscale, doublereal *rscale, + doublereal *abnrm, doublereal *bbnrm, doublereal *rconde, doublereal * + rcondv, doublecomplex *work, integer *lwork, doublereal *rwork, + integer *iwork, logical *bwork, integer *info); + +/* Subroutine */ int zggglm_(integer *n, integer *m, integer *p, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + doublecomplex *d__, doublecomplex *x, doublecomplex *y, doublecomplex + *work, integer *lwork, integer *info); + +/* Subroutine */ int zgghrd_(char *compq, char *compz, integer *n, integer * + ilo, integer *ihi, doublecomplex *a, integer *lda, doublecomplex *b, + integer *ldb, doublecomplex *q, integer *ldq, doublecomplex *z__, + integer *ldz, integer *info); + +/* Subroutine */ int zgglse_(integer *m, integer *n, integer *p, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + doublecomplex *c__, doublecomplex *d__, doublecomplex *x, + doublecomplex *work, integer *lwork, integer *info); + +/* Subroutine */ int zggqrf_(integer *n, integer *m, integer *p, + doublecomplex *a, integer *lda, doublecomplex *taua, doublecomplex *b, + integer *ldb, doublecomplex *taub, doublecomplex *work, integer * + lwork, integer *info); + +/* Subroutine */ int zggrqf_(integer *m, integer *p, integer *n, + doublecomplex *a, integer *lda, doublecomplex *taua, doublecomplex *b, + integer *ldb, doublecomplex *taub, doublecomplex *work, integer * + lwork, integer *info); + +/* Subroutine */ int zggsvd_(char *jobu, char *jobv, char *jobq, integer *m, + integer *n, integer *p, integer *k, integer *l, doublecomplex *a, + integer *lda, doublecomplex *b, integer *ldb, doublereal *alpha, + doublereal *beta, doublecomplex *u, integer *ldu, doublecomplex *v, + integer *ldv, doublecomplex *q, integer *ldq, doublecomplex *work, + doublereal *rwork, integer *iwork, integer *info); + +/* Subroutine */ int zggsvp_(char *jobu, char *jobv, char *jobq, integer *m, + integer *p, integer *n, doublecomplex *a, integer *lda, doublecomplex + *b, integer *ldb, doublereal *tola, doublereal *tolb, integer *k, + integer *l, doublecomplex *u, integer *ldu, doublecomplex *v, integer + *ldv, doublecomplex *q, integer *ldq, integer *iwork, doublereal * + rwork, doublecomplex *tau, doublecomplex *work, integer *info); + +/* Subroutine */ int zgtcon_(char *norm, integer *n, doublecomplex *dl, + doublecomplex *d__, doublecomplex *du, doublecomplex *du2, integer * + ipiv, doublereal *anorm, doublereal *rcond, doublecomplex *work, + integer *info); + +/* Subroutine */ int zgtrfs_(char *trans, integer *n, integer *nrhs, + doublecomplex *dl, doublecomplex *d__, doublecomplex *du, + doublecomplex *dlf, doublecomplex *df, doublecomplex *duf, + doublecomplex *du2, integer *ipiv, doublecomplex *b, integer *ldb, + doublecomplex *x, integer *ldx, doublereal *ferr, doublereal *berr, + doublecomplex *work, doublereal *rwork, integer *info); + +/* Subroutine */ int zgtsv_(integer *n, integer *nrhs, doublecomplex *dl, + doublecomplex *d__, doublecomplex *du, doublecomplex *b, integer *ldb, + integer *info); + +/* Subroutine */ int zgtsvx_(char *fact, char *trans, integer *n, integer * + nrhs, doublecomplex *dl, doublecomplex *d__, doublecomplex *du, + doublecomplex *dlf, doublecomplex *df, doublecomplex *duf, + doublecomplex *du2, integer *ipiv, doublecomplex *b, integer *ldb, + doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *ferr, + doublereal *berr, doublecomplex *work, doublereal *rwork, integer * + info); + +/* Subroutine */ int zgttrf_(integer *n, doublecomplex *dl, doublecomplex * + d__, doublecomplex *du, doublecomplex *du2, integer *ipiv, integer * + info); + +/* Subroutine */ int zgttrs_(char *trans, integer *n, integer *nrhs, + doublecomplex *dl, doublecomplex *d__, doublecomplex *du, + doublecomplex *du2, integer *ipiv, doublecomplex *b, integer *ldb, + integer *info); + +/* Subroutine */ int zgtts2_(integer *itrans, integer *n, integer *nrhs, + doublecomplex *dl, doublecomplex *d__, doublecomplex *du, + doublecomplex *du2, integer *ipiv, doublecomplex *b, integer *ldb); + +/* Subroutine */ int zhbev_(char *jobz, char *uplo, integer *n, integer *kd, + doublecomplex *ab, integer *ldab, doublereal *w, doublecomplex *z__, + integer *ldz, doublecomplex *work, doublereal *rwork, integer *info); + +/* Subroutine */ int zhbevd_(char *jobz, char *uplo, integer *n, integer *kd, + doublecomplex *ab, integer *ldab, doublereal *w, doublecomplex *z__, + integer *ldz, doublecomplex *work, integer *lwork, doublereal *rwork, + integer *lrwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int zhbevx_(char *jobz, char *range, char *uplo, integer *n, + integer *kd, doublecomplex *ab, integer *ldab, doublecomplex *q, + integer *ldq, doublereal *vl, doublereal *vu, integer *il, integer * + iu, doublereal *abstol, integer *m, doublereal *w, doublecomplex *z__, + integer *ldz, doublecomplex *work, doublereal *rwork, integer *iwork, + integer *ifail, integer *info); + +/* Subroutine */ int zhbgst_(char *vect, char *uplo, integer *n, integer *ka, + integer *kb, doublecomplex *ab, integer *ldab, doublecomplex *bb, + integer *ldbb, doublecomplex *x, integer *ldx, doublecomplex *work, + doublereal *rwork, integer *info); + +/* Subroutine */ int zhbgv_(char *jobz, char *uplo, integer *n, integer *ka, + integer *kb, doublecomplex *ab, integer *ldab, doublecomplex *bb, + integer *ldbb, doublereal *w, doublecomplex *z__, integer *ldz, + doublecomplex *work, doublereal *rwork, integer *info); + +/* Subroutine */ int zhbgvd_(char *jobz, char *uplo, integer *n, integer *ka, + integer *kb, doublecomplex *ab, integer *ldab, doublecomplex *bb, + integer *ldbb, doublereal *w, doublecomplex *z__, integer *ldz, + doublecomplex *work, integer *lwork, doublereal *rwork, integer * + lrwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int zhbgvx_(char *jobz, char *range, char *uplo, integer *n, + integer *ka, integer *kb, doublecomplex *ab, integer *ldab, + doublecomplex *bb, integer *ldbb, doublecomplex *q, integer *ldq, + doublereal *vl, doublereal *vu, integer *il, integer *iu, doublereal * + abstol, integer *m, doublereal *w, doublecomplex *z__, integer *ldz, + doublecomplex *work, doublereal *rwork, integer *iwork, integer * + ifail, integer *info); + +/* Subroutine */ int zhbtrd_(char *vect, char *uplo, integer *n, integer *kd, + doublecomplex *ab, integer *ldab, doublereal *d__, doublereal *e, + doublecomplex *q, integer *ldq, doublecomplex *work, integer *info); + +/* Subroutine */ int zhecon_(char *uplo, integer *n, doublecomplex *a, + integer *lda, integer *ipiv, doublereal *anorm, doublereal *rcond, + doublecomplex *work, integer *info); + +/* Subroutine */ int zheequb_(char *uplo, integer *n, doublecomplex *a, + integer *lda, doublereal *s, doublereal *scond, doublereal *amax, + doublecomplex *work, integer *info); + +/* Subroutine */ int zheev_(char *jobz, char *uplo, integer *n, doublecomplex + *a, integer *lda, doublereal *w, doublecomplex *work, integer *lwork, + doublereal *rwork, integer *info); + +/* Subroutine */ int zheevd_(char *jobz, char *uplo, integer *n, + doublecomplex *a, integer *lda, doublereal *w, doublecomplex *work, + integer *lwork, doublereal *rwork, integer *lrwork, integer *iwork, + integer *liwork, integer *info); + +/* Subroutine */ int zheevr_(char *jobz, char *range, char *uplo, integer *n, + doublecomplex *a, integer *lda, doublereal *vl, doublereal *vu, + integer *il, integer *iu, doublereal *abstol, integer *m, doublereal * + w, doublecomplex *z__, integer *ldz, integer *isuppz, doublecomplex * + work, integer *lwork, doublereal *rwork, integer *lrwork, integer * + iwork, integer *liwork, integer *info); + +/* Subroutine */ int zheevx_(char *jobz, char *range, char *uplo, integer *n, + doublecomplex *a, integer *lda, doublereal *vl, doublereal *vu, + integer *il, integer *iu, doublereal *abstol, integer *m, doublereal * + w, doublecomplex *z__, integer *ldz, doublecomplex *work, integer * + lwork, doublereal *rwork, integer *iwork, integer *ifail, integer * + info); + +/* Subroutine */ int zhegs2_(integer *itype, char *uplo, integer *n, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + integer *info); + +/* Subroutine */ int zhegst_(integer *itype, char *uplo, integer *n, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + integer *info); + +/* Subroutine */ int zhegv_(integer *itype, char *jobz, char *uplo, integer * + n, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + doublereal *w, doublecomplex *work, integer *lwork, doublereal *rwork, + integer *info); + +/* Subroutine */ int zhegvd_(integer *itype, char *jobz, char *uplo, integer * + n, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + doublereal *w, doublecomplex *work, integer *lwork, doublereal *rwork, + integer *lrwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int zhegvx_(integer *itype, char *jobz, char *range, char * + uplo, integer *n, doublecomplex *a, integer *lda, doublecomplex *b, + integer *ldb, doublereal *vl, doublereal *vu, integer *il, integer * + iu, doublereal *abstol, integer *m, doublereal *w, doublecomplex *z__, + integer *ldz, doublecomplex *work, integer *lwork, doublereal *rwork, + integer *iwork, integer *ifail, integer *info); + +/* Subroutine */ int zherfs_(char *uplo, integer *n, integer *nrhs, + doublecomplex *a, integer *lda, doublecomplex *af, integer *ldaf, + integer *ipiv, doublecomplex *b, integer *ldb, doublecomplex *x, + integer *ldx, doublereal *ferr, doublereal *berr, doublecomplex *work, + doublereal *rwork, integer *info); + +/* Subroutine */ int zherfsx_(char *uplo, char *equed, integer *n, integer * + nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * + ldaf, integer *ipiv, doublereal *s, doublecomplex *b, integer *ldb, + doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *berr, + integer *n_err_bnds__, doublereal *err_bnds_norm__, doublereal * + err_bnds_comp__, integer *nparams, doublereal *params, doublecomplex * + work, doublereal *rwork, integer *info); + +/* Subroutine */ int zhesv_(char *uplo, integer *n, integer *nrhs, + doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *b, + integer *ldb, doublecomplex *work, integer *lwork, integer *info); + +/* Subroutine */ int zhesvx_(char *fact, char *uplo, integer *n, integer * + nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * + ldaf, integer *ipiv, doublecomplex *b, integer *ldb, doublecomplex *x, + integer *ldx, doublereal *rcond, doublereal *ferr, doublereal *berr, + doublecomplex *work, integer *lwork, doublereal *rwork, integer *info); + +/* Subroutine */ int zhesvxx_(char *fact, char *uplo, integer *n, integer * + nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * + ldaf, integer *ipiv, char *equed, doublereal *s, doublecomplex *b, + integer *ldb, doublecomplex *x, integer *ldx, doublereal *rcond, + doublereal *rpvgrw, doublereal *berr, integer *n_err_bnds__, + doublereal *err_bnds_norm__, doublereal *err_bnds_comp__, integer * + nparams, doublereal *params, doublecomplex *work, doublereal *rwork, + integer *info); + +/* Subroutine */ int zhetd2_(char *uplo, integer *n, doublecomplex *a, + integer *lda, doublereal *d__, doublereal *e, doublecomplex *tau, + integer *info); + +/* Subroutine */ int zhetf2_(char *uplo, integer *n, doublecomplex *a, + integer *lda, integer *ipiv, integer *info); + +/* Subroutine */ int zhetrd_(char *uplo, integer *n, doublecomplex *a, + integer *lda, doublereal *d__, doublereal *e, doublecomplex *tau, + doublecomplex *work, integer *lwork, integer *info); + +/* Subroutine */ int zhetrf_(char *uplo, integer *n, doublecomplex *a, + integer *lda, integer *ipiv, doublecomplex *work, integer *lwork, + integer *info); + +/* Subroutine */ int zhetri_(char *uplo, integer *n, doublecomplex *a, + integer *lda, integer *ipiv, doublecomplex *work, integer *info); + +/* Subroutine */ int zhetrs_(char *uplo, integer *n, integer *nrhs, + doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *b, + integer *ldb, integer *info); + +/* Subroutine */ int zhfrk_(char *transr, char *uplo, char *trans, integer *n, + integer *k, doublereal *alpha, doublecomplex *a, integer *lda, + doublereal *beta, doublecomplex *c__); + +/* Subroutine */ int zhgeqz_(char *job, char *compq, char *compz, integer *n, + integer *ilo, integer *ihi, doublecomplex *h__, integer *ldh, + doublecomplex *t, integer *ldt, doublecomplex *alpha, doublecomplex * + beta, doublecomplex *q, integer *ldq, doublecomplex *z__, integer * + ldz, doublecomplex *work, integer *lwork, doublereal *rwork, integer * + info); + +/* Subroutine */ int zhpcon_(char *uplo, integer *n, doublecomplex *ap, + integer *ipiv, doublereal *anorm, doublereal *rcond, doublecomplex * + work, integer *info); + +/* Subroutine */ int zhpev_(char *jobz, char *uplo, integer *n, doublecomplex + *ap, doublereal *w, doublecomplex *z__, integer *ldz, doublecomplex * + work, doublereal *rwork, integer *info); + +/* Subroutine */ int zhpevd_(char *jobz, char *uplo, integer *n, + doublecomplex *ap, doublereal *w, doublecomplex *z__, integer *ldz, + doublecomplex *work, integer *lwork, doublereal *rwork, integer * + lrwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int zhpevx_(char *jobz, char *range, char *uplo, integer *n, + doublecomplex *ap, doublereal *vl, doublereal *vu, integer *il, + integer *iu, doublereal *abstol, integer *m, doublereal *w, + doublecomplex *z__, integer *ldz, doublecomplex *work, doublereal * + rwork, integer *iwork, integer *ifail, integer *info); + +/* Subroutine */ int zhpgst_(integer *itype, char *uplo, integer *n, + doublecomplex *ap, doublecomplex *bp, integer *info); + +/* Subroutine */ int zhpgv_(integer *itype, char *jobz, char *uplo, integer * + n, doublecomplex *ap, doublecomplex *bp, doublereal *w, doublecomplex + *z__, integer *ldz, doublecomplex *work, doublereal *rwork, integer * + info); + +/* Subroutine */ int zhpgvd_(integer *itype, char *jobz, char *uplo, integer * + n, doublecomplex *ap, doublecomplex *bp, doublereal *w, doublecomplex + *z__, integer *ldz, doublecomplex *work, integer *lwork, doublereal * + rwork, integer *lrwork, integer *iwork, integer *liwork, integer * + info); + +/* Subroutine */ int zhpgvx_(integer *itype, char *jobz, char *range, char * + uplo, integer *n, doublecomplex *ap, doublecomplex *bp, doublereal * + vl, doublereal *vu, integer *il, integer *iu, doublereal *abstol, + integer *m, doublereal *w, doublecomplex *z__, integer *ldz, + doublecomplex *work, doublereal *rwork, integer *iwork, integer * + ifail, integer *info); + +/* Subroutine */ int zhprfs_(char *uplo, integer *n, integer *nrhs, + doublecomplex *ap, doublecomplex *afp, integer *ipiv, doublecomplex * + b, integer *ldb, doublecomplex *x, integer *ldx, doublereal *ferr, + doublereal *berr, doublecomplex *work, doublereal *rwork, integer * + info); + +/* Subroutine */ int zhpsv_(char *uplo, integer *n, integer *nrhs, + doublecomplex *ap, integer *ipiv, doublecomplex *b, integer *ldb, + integer *info); + +/* Subroutine */ int zhpsvx_(char *fact, char *uplo, integer *n, integer * + nrhs, doublecomplex *ap, doublecomplex *afp, integer *ipiv, + doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, + doublereal *rcond, doublereal *ferr, doublereal *berr, doublecomplex * + work, doublereal *rwork, integer *info); + +/* Subroutine */ int zhptrd_(char *uplo, integer *n, doublecomplex *ap, + doublereal *d__, doublereal *e, doublecomplex *tau, integer *info); + +/* Subroutine */ int zhptrf_(char *uplo, integer *n, doublecomplex *ap, + integer *ipiv, integer *info); + +/* Subroutine */ int zhptri_(char *uplo, integer *n, doublecomplex *ap, + integer *ipiv, doublecomplex *work, integer *info); + +/* Subroutine */ int zhptrs_(char *uplo, integer *n, integer *nrhs, + doublecomplex *ap, integer *ipiv, doublecomplex *b, integer *ldb, + integer *info); + +/* Subroutine */ int zhsein_(char *side, char *eigsrc, char *initv, logical * + select, integer *n, doublecomplex *h__, integer *ldh, doublecomplex * + w, doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *ldvr, + integer *mm, integer *m, doublecomplex *work, doublereal *rwork, + integer *ifaill, integer *ifailr, integer *info); + +/* Subroutine */ int zhseqr_(char *job, char *compz, integer *n, integer *ilo, + integer *ihi, doublecomplex *h__, integer *ldh, doublecomplex *w, + doublecomplex *z__, integer *ldz, doublecomplex *work, integer *lwork, + integer *info); + +/* Subroutine */ int zla_gbamv__(integer *trans, integer *m, integer *n, + integer *kl, integer *ku, doublereal *alpha, doublecomplex *ab, + integer *ldab, doublecomplex *x, integer *incx, doublereal *beta, + doublereal *y, integer *incy); + +doublereal zla_gbrcond_c__(char *trans, integer *n, integer *kl, integer *ku, + doublecomplex *ab, integer *ldab, doublecomplex *afb, integer *ldafb, + integer *ipiv, doublereal *c__, logical *capply, integer *info, + doublecomplex *work, doublereal *rwork, ftnlen trans_len); + +doublereal zla_gbrcond_x__(char *trans, integer *n, integer *kl, integer *ku, + doublecomplex *ab, integer *ldab, doublecomplex *afb, integer *ldafb, + integer *ipiv, doublecomplex *x, integer *info, doublecomplex *work, + doublereal *rwork, ftnlen trans_len); + +/* Subroutine */ int zla_gbrfsx_extended__(integer *prec_type__, integer * + trans_type__, integer *n, integer *kl, integer *ku, integer *nrhs, + doublecomplex *ab, integer *ldab, doublecomplex *afb, integer *ldafb, + integer *ipiv, logical *colequ, doublereal *c__, doublecomplex *b, + integer *ldb, doublecomplex *y, integer *ldy, doublereal *berr_out__, + integer *n_norms__, doublereal *errs_n__, doublereal *errs_c__, + doublecomplex *res, doublereal *ayb, doublecomplex *dy, doublecomplex + *y_tail__, doublereal *rcond, integer *ithresh, doublereal *rthresh, + doublereal *dz_ub__, logical *ignore_cwise__, integer *info); + +doublereal zla_gbrpvgrw__(integer *n, integer *kl, integer *ku, integer * + ncols, doublecomplex *ab, integer *ldab, doublecomplex *afb, integer * + ldafb); + +/* Subroutine */ int zla_geamv__(integer *trans, integer *m, integer *n, + doublereal *alpha, doublecomplex *a, integer *lda, doublecomplex *x, + integer *incx, doublereal *beta, doublereal *y, integer *incy); + +doublereal zla_gercond_c__(char *trans, integer *n, doublecomplex *a, integer + *lda, doublecomplex *af, integer *ldaf, integer *ipiv, doublereal * + c__, logical *capply, integer *info, doublecomplex *work, doublereal * + rwork, ftnlen trans_len); + +doublereal zla_gercond_x__(char *trans, integer *n, doublecomplex *a, integer + *lda, doublecomplex *af, integer *ldaf, integer *ipiv, doublecomplex * + x, integer *info, doublecomplex *work, doublereal *rwork, ftnlen + trans_len); + +/* Subroutine */ int zla_gerfsx_extended__(integer *prec_type__, integer * + trans_type__, integer *n, integer *nrhs, doublecomplex *a, integer * + lda, doublecomplex *af, integer *ldaf, integer *ipiv, logical *colequ, + doublereal *c__, doublecomplex *b, integer *ldb, doublecomplex *y, + integer *ldy, doublereal *berr_out__, integer *n_norms__, doublereal * + errs_n__, doublereal *errs_c__, doublecomplex *res, doublereal *ayb, + doublecomplex *dy, doublecomplex *y_tail__, doublereal *rcond, + integer *ithresh, doublereal *rthresh, doublereal *dz_ub__, logical * + ignore_cwise__, integer *info); + +/* Subroutine */ int zla_heamv__(integer *uplo, integer *n, doublereal *alpha, + doublecomplex *a, integer *lda, doublecomplex *x, integer *incx, + doublereal *beta, doublereal *y, integer *incy); + +doublereal zla_hercond_c__(char *uplo, integer *n, doublecomplex *a, integer * + lda, doublecomplex *af, integer *ldaf, integer *ipiv, doublereal *c__, + logical *capply, integer *info, doublecomplex *work, doublereal * + rwork, ftnlen uplo_len); + +doublereal zla_hercond_x__(char *uplo, integer *n, doublecomplex *a, integer * + lda, doublecomplex *af, integer *ldaf, integer *ipiv, doublecomplex * + x, integer *info, doublecomplex *work, doublereal *rwork, ftnlen + uplo_len); + +/* Subroutine */ int zla_herfsx_extended__(integer *prec_type__, char *uplo, + integer *n, integer *nrhs, doublecomplex *a, integer *lda, + doublecomplex *af, integer *ldaf, integer *ipiv, logical *colequ, + doublereal *c__, doublecomplex *b, integer *ldb, doublecomplex *y, + integer *ldy, doublereal *berr_out__, integer *n_norms__, doublereal * + errs_n__, doublereal *errs_c__, doublecomplex *res, doublereal *ayb, + doublecomplex *dy, doublecomplex *y_tail__, doublereal *rcond, + integer *ithresh, doublereal *rthresh, doublereal *dz_ub__, logical * + ignore_cwise__, integer *info, ftnlen uplo_len); + +doublereal zla_herpvgrw__(char *uplo, integer *n, integer *info, + doublecomplex *a, integer *lda, doublecomplex *af, integer *ldaf, + integer *ipiv, doublereal *work, ftnlen uplo_len); + +/* Subroutine */ int zla_lin_berr__(integer *n, integer *nz, integer *nrhs, + doublecomplex *res, doublereal *ayb, doublereal *berr); + +doublereal zla_porcond_c__(char *uplo, integer *n, doublecomplex *a, integer * + lda, doublecomplex *af, integer *ldaf, doublereal *c__, logical * + capply, integer *info, doublecomplex *work, doublereal *rwork, ftnlen + uplo_len); + +doublereal zla_porcond_x__(char *uplo, integer *n, doublecomplex *a, integer * + lda, doublecomplex *af, integer *ldaf, doublecomplex *x, integer * + info, doublecomplex *work, doublereal *rwork, ftnlen uplo_len); + +/* Subroutine */ int zla_porfsx_extended__(integer *prec_type__, char *uplo, + integer *n, integer *nrhs, doublecomplex *a, integer *lda, + doublecomplex *af, integer *ldaf, logical *colequ, doublereal *c__, + doublecomplex *b, integer *ldb, doublecomplex *y, integer *ldy, + doublereal *berr_out__, integer *n_norms__, doublereal *errs_n__, + doublereal *errs_c__, doublecomplex *res, doublereal *ayb, + doublecomplex *dy, doublecomplex *y_tail__, doublereal *rcond, + integer *ithresh, doublereal *rthresh, doublereal *dz_ub__, logical * + ignore_cwise__, integer *info, ftnlen uplo_len); + +doublereal zla_porpvgrw__(char *uplo, integer *ncols, doublecomplex *a, + integer *lda, doublecomplex *af, integer *ldaf, doublereal *work, + ftnlen uplo_len); + +doublereal zla_rpvgrw__(integer *n, integer *ncols, doublecomplex *a, integer + *lda, doublecomplex *af, integer *ldaf); + +/* Subroutine */ int zla_syamv__(integer *uplo, integer *n, doublereal *alpha, + doublecomplex *a, integer *lda, doublecomplex *x, integer *incx, + doublereal *beta, doublereal *y, integer *incy); + +doublereal zla_syrcond_c__(char *uplo, integer *n, doublecomplex *a, integer * + lda, doublecomplex *af, integer *ldaf, integer *ipiv, doublereal *c__, + logical *capply, integer *info, doublecomplex *work, doublereal * + rwork, ftnlen uplo_len); + +doublereal zla_syrcond_x__(char *uplo, integer *n, doublecomplex *a, integer * + lda, doublecomplex *af, integer *ldaf, integer *ipiv, doublecomplex * + x, integer *info, doublecomplex *work, doublereal *rwork, ftnlen + uplo_len); + +/* Subroutine */ int zla_syrfsx_extended__(integer *prec_type__, char *uplo, + integer *n, integer *nrhs, doublecomplex *a, integer *lda, + doublecomplex *af, integer *ldaf, integer *ipiv, logical *colequ, + doublereal *c__, doublecomplex *b, integer *ldb, doublecomplex *y, + integer *ldy, doublereal *berr_out__, integer *n_norms__, doublereal * + errs_n__, doublereal *errs_c__, doublecomplex *res, doublereal *ayb, + doublecomplex *dy, doublecomplex *y_tail__, doublereal *rcond, + integer *ithresh, doublereal *rthresh, doublereal *dz_ub__, logical * + ignore_cwise__, integer *info, ftnlen uplo_len); + +doublereal zla_syrpvgrw__(char *uplo, integer *n, integer *info, + doublecomplex *a, integer *lda, doublecomplex *af, integer *ldaf, + integer *ipiv, doublereal *work, ftnlen uplo_len); + +/* Subroutine */ int zla_wwaddw__(integer *n, doublecomplex *x, doublecomplex + *y, doublecomplex *w); + +/* Subroutine */ int zlabrd_(integer *m, integer *n, integer *nb, + doublecomplex *a, integer *lda, doublereal *d__, doublereal *e, + doublecomplex *tauq, doublecomplex *taup, doublecomplex *x, integer * + ldx, doublecomplex *y, integer *ldy); + +/* Subroutine */ int zlacgv_(integer *n, doublecomplex *x, integer *incx); + +/* Subroutine */ int zlacn2_(integer *n, doublecomplex *v, doublecomplex *x, + doublereal *est, integer *kase, integer *isave); + +/* Subroutine */ int zlacon_(integer *n, doublecomplex *v, doublecomplex *x, + doublereal *est, integer *kase); + +/* Subroutine */ int zlacp2_(char *uplo, integer *m, integer *n, doublereal * + a, integer *lda, doublecomplex *b, integer *ldb); + +/* Subroutine */ int zlacpy_(char *uplo, integer *m, integer *n, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb); + +/* Subroutine */ int zlacrm_(integer *m, integer *n, doublecomplex *a, + integer *lda, doublereal *b, integer *ldb, doublecomplex *c__, + integer *ldc, doublereal *rwork); + +/* Subroutine */ int zlacrt_(integer *n, doublecomplex *cx, integer *incx, + doublecomplex *cy, integer *incy, doublecomplex *c__, doublecomplex * + s); + +/* Double Complex */ VOID zladiv_(doublecomplex * ret_val, doublecomplex *x, + doublecomplex *y); + +/* Subroutine */ int zlaed0_(integer *qsiz, integer *n, doublereal *d__, + doublereal *e, doublecomplex *q, integer *ldq, doublecomplex *qstore, + integer *ldqs, doublereal *rwork, integer *iwork, integer *info); + +/* Subroutine */ int zlaed7_(integer *n, integer *cutpnt, integer *qsiz, + integer *tlvls, integer *curlvl, integer *curpbm, doublereal *d__, + doublecomplex *q, integer *ldq, doublereal *rho, integer *indxq, + doublereal *qstore, integer *qptr, integer *prmptr, integer *perm, + integer *givptr, integer *givcol, doublereal *givnum, doublecomplex * + work, doublereal *rwork, integer *iwork, integer *info); + +/* Subroutine */ int zlaed8_(integer *k, integer *n, integer *qsiz, + doublecomplex *q, integer *ldq, doublereal *d__, doublereal *rho, + integer *cutpnt, doublereal *z__, doublereal *dlamda, doublecomplex * + q2, integer *ldq2, doublereal *w, integer *indxp, integer *indx, + integer *indxq, integer *perm, integer *givptr, integer *givcol, + doublereal *givnum, integer *info); + +/* Subroutine */ int zlaein_(logical *rightv, logical *noinit, integer *n, + doublecomplex *h__, integer *ldh, doublecomplex *w, doublecomplex *v, + doublecomplex *b, integer *ldb, doublereal *rwork, doublereal *eps3, + doublereal *smlnum, integer *info); + +/* Subroutine */ int zlaesy_(doublecomplex *a, doublecomplex *b, + doublecomplex *c__, doublecomplex *rt1, doublecomplex *rt2, + doublecomplex *evscal, doublecomplex *cs1, doublecomplex *sn1); + +/* Subroutine */ int zlaev2_(doublecomplex *a, doublecomplex *b, + doublecomplex *c__, doublereal *rt1, doublereal *rt2, doublereal *cs1, + doublecomplex *sn1); + +/* Subroutine */ int zlag2c_(integer *m, integer *n, doublecomplex *a, + integer *lda, complex *sa, integer *ldsa, integer *info); + +/* Subroutine */ int zlags2_(logical *upper, doublereal *a1, doublecomplex * + a2, doublereal *a3, doublereal *b1, doublecomplex *b2, doublereal *b3, + doublereal *csu, doublecomplex *snu, doublereal *csv, doublecomplex * + snv, doublereal *csq, doublecomplex *snq); + +/* Subroutine */ int zlagtm_(char *trans, integer *n, integer *nrhs, + doublereal *alpha, doublecomplex *dl, doublecomplex *d__, + doublecomplex *du, doublecomplex *x, integer *ldx, doublereal *beta, + doublecomplex *b, integer *ldb); + +/* Subroutine */ int zlahef_(char *uplo, integer *n, integer *nb, integer *kb, + doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *w, + integer *ldw, integer *info); + +/* Subroutine */ int zlahqr_(logical *wantt, logical *wantz, integer *n, + integer *ilo, integer *ihi, doublecomplex *h__, integer *ldh, + doublecomplex *w, integer *iloz, integer *ihiz, doublecomplex *z__, + integer *ldz, integer *info); + +/* Subroutine */ int zlahr2_(integer *n, integer *k, integer *nb, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *t, + integer *ldt, doublecomplex *y, integer *ldy); + +/* Subroutine */ int zlahrd_(integer *n, integer *k, integer *nb, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *t, + integer *ldt, doublecomplex *y, integer *ldy); + +/* Subroutine */ int zlaic1_(integer *job, integer *j, doublecomplex *x, + doublereal *sest, doublecomplex *w, doublecomplex *gamma, doublereal * + sestpr, doublecomplex *s, doublecomplex *c__); + +/* Subroutine */ int zlals0_(integer *icompq, integer *nl, integer *nr, + integer *sqre, integer *nrhs, doublecomplex *b, integer *ldb, + doublecomplex *bx, integer *ldbx, integer *perm, integer *givptr, + integer *givcol, integer *ldgcol, doublereal *givnum, integer *ldgnum, + doublereal *poles, doublereal *difl, doublereal *difr, doublereal * + z__, integer *k, doublereal *c__, doublereal *s, doublereal *rwork, + integer *info); + +/* Subroutine */ int zlalsa_(integer *icompq, integer *smlsiz, integer *n, + integer *nrhs, doublecomplex *b, integer *ldb, doublecomplex *bx, + integer *ldbx, doublereal *u, integer *ldu, doublereal *vt, integer * + k, doublereal *difl, doublereal *difr, doublereal *z__, doublereal * + poles, integer *givptr, integer *givcol, integer *ldgcol, integer * + perm, doublereal *givnum, doublereal *c__, doublereal *s, doublereal * + rwork, integer *iwork, integer *info); + +/* Subroutine */ int zlalsd_(char *uplo, integer *smlsiz, integer *n, integer + *nrhs, doublereal *d__, doublereal *e, doublecomplex *b, integer *ldb, + doublereal *rcond, integer *rank, doublecomplex *work, doublereal * + rwork, integer *iwork, integer *info); + +doublereal zlangb_(char *norm, integer *n, integer *kl, integer *ku, + doublecomplex *ab, integer *ldab, doublereal *work); + +doublereal zlange_(char *norm, integer *m, integer *n, doublecomplex *a, + integer *lda, doublereal *work); + +doublereal zlangt_(char *norm, integer *n, doublecomplex *dl, doublecomplex * + d__, doublecomplex *du); + +doublereal zlanhb_(char *norm, char *uplo, integer *n, integer *k, + doublecomplex *ab, integer *ldab, doublereal *work); + +doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, + integer *lda, doublereal *work); + +doublereal zlanhf_(char *norm, char *transr, char *uplo, integer *n, + doublecomplex *a, doublereal *work); + +doublereal zlanhp_(char *norm, char *uplo, integer *n, doublecomplex *ap, + doublereal *work); + +doublereal zlanhs_(char *norm, integer *n, doublecomplex *a, integer *lda, + doublereal *work); + +doublereal zlanht_(char *norm, integer *n, doublereal *d__, doublecomplex *e); + +doublereal zlansb_(char *norm, char *uplo, integer *n, integer *k, + doublecomplex *ab, integer *ldab, doublereal *work); + +doublereal zlansp_(char *norm, char *uplo, integer *n, doublecomplex *ap, + doublereal *work); + +doublereal zlansy_(char *norm, char *uplo, integer *n, doublecomplex *a, + integer *lda, doublereal *work); + +doublereal zlantb_(char *norm, char *uplo, char *diag, integer *n, integer *k, + doublecomplex *ab, integer *ldab, doublereal *work); + +doublereal zlantp_(char *norm, char *uplo, char *diag, integer *n, + doublecomplex *ap, doublereal *work); + +doublereal zlantr_(char *norm, char *uplo, char *diag, integer *m, integer *n, + doublecomplex *a, integer *lda, doublereal *work); + +/* Subroutine */ int zlapll_(integer *n, doublecomplex *x, integer *incx, + doublecomplex *y, integer *incy, doublereal *ssmin); + +/* Subroutine */ int zlapmt_(logical *forwrd, integer *m, integer *n, + doublecomplex *x, integer *ldx, integer *k); + +/* Subroutine */ int zlaqgb_(integer *m, integer *n, integer *kl, integer *ku, + doublecomplex *ab, integer *ldab, doublereal *r__, doublereal *c__, + doublereal *rowcnd, doublereal *colcnd, doublereal *amax, char *equed); + +/* Subroutine */ int zlaqge_(integer *m, integer *n, doublecomplex *a, + integer *lda, doublereal *r__, doublereal *c__, doublereal *rowcnd, + doublereal *colcnd, doublereal *amax, char *equed); + +/* Subroutine */ int zlaqhb_(char *uplo, integer *n, integer *kd, + doublecomplex *ab, integer *ldab, doublereal *s, doublereal *scond, + doublereal *amax, char *equed); + +/* Subroutine */ int zlaqhe_(char *uplo, integer *n, doublecomplex *a, + integer *lda, doublereal *s, doublereal *scond, doublereal *amax, + char *equed); + +/* Subroutine */ int zlaqhp_(char *uplo, integer *n, doublecomplex *ap, + doublereal *s, doublereal *scond, doublereal *amax, char *equed); + +/* Subroutine */ int zlaqp2_(integer *m, integer *n, integer *offset, + doublecomplex *a, integer *lda, integer *jpvt, doublecomplex *tau, + doublereal *vn1, doublereal *vn2, doublecomplex *work); + +/* Subroutine */ int zlaqps_(integer *m, integer *n, integer *offset, integer + *nb, integer *kb, doublecomplex *a, integer *lda, integer *jpvt, + doublecomplex *tau, doublereal *vn1, doublereal *vn2, doublecomplex * + auxv, doublecomplex *f, integer *ldf); + +/* Subroutine */ int zlaqr0_(logical *wantt, logical *wantz, integer *n, + integer *ilo, integer *ihi, doublecomplex *h__, integer *ldh, + doublecomplex *w, integer *iloz, integer *ihiz, doublecomplex *z__, + integer *ldz, doublecomplex *work, integer *lwork, integer *info); + +/* Subroutine */ int zlaqr1_(integer *n, doublecomplex *h__, integer *ldh, + doublecomplex *s1, doublecomplex *s2, doublecomplex *v); + +/* Subroutine */ int zlaqr2_(logical *wantt, logical *wantz, integer *n, + integer *ktop, integer *kbot, integer *nw, doublecomplex *h__, + integer *ldh, integer *iloz, integer *ihiz, doublecomplex *z__, + integer *ldz, integer *ns, integer *nd, doublecomplex *sh, + doublecomplex *v, integer *ldv, integer *nh, doublecomplex *t, + integer *ldt, integer *nv, doublecomplex *wv, integer *ldwv, + doublecomplex *work, integer *lwork); + +/* Subroutine */ int zlaqr3_(logical *wantt, logical *wantz, integer *n, + integer *ktop, integer *kbot, integer *nw, doublecomplex *h__, + integer *ldh, integer *iloz, integer *ihiz, doublecomplex *z__, + integer *ldz, integer *ns, integer *nd, doublecomplex *sh, + doublecomplex *v, integer *ldv, integer *nh, doublecomplex *t, + integer *ldt, integer *nv, doublecomplex *wv, integer *ldwv, + doublecomplex *work, integer *lwork); + +/* Subroutine */ int zlaqr4_(logical *wantt, logical *wantz, integer *n, + integer *ilo, integer *ihi, doublecomplex *h__, integer *ldh, + doublecomplex *w, integer *iloz, integer *ihiz, doublecomplex *z__, + integer *ldz, doublecomplex *work, integer *lwork, integer *info); + +/* Subroutine */ int zlaqr5_(logical *wantt, logical *wantz, integer *kacc22, + integer *n, integer *ktop, integer *kbot, integer *nshfts, + doublecomplex *s, doublecomplex *h__, integer *ldh, integer *iloz, + integer *ihiz, doublecomplex *z__, integer *ldz, doublecomplex *v, + integer *ldv, doublecomplex *u, integer *ldu, integer *nv, + doublecomplex *wv, integer *ldwv, integer *nh, doublecomplex *wh, + integer *ldwh); + +/* Subroutine */ int zlaqsb_(char *uplo, integer *n, integer *kd, + doublecomplex *ab, integer *ldab, doublereal *s, doublereal *scond, + doublereal *amax, char *equed); + +/* Subroutine */ int zlaqsp_(char *uplo, integer *n, doublecomplex *ap, + doublereal *s, doublereal *scond, doublereal *amax, char *equed); + +/* Subroutine */ int zlaqsy_(char *uplo, integer *n, doublecomplex *a, + integer *lda, doublereal *s, doublereal *scond, doublereal *amax, + char *equed); + +/* Subroutine */ int zlar1v_(integer *n, integer *b1, integer *bn, doublereal + *lambda, doublereal *d__, doublereal *l, doublereal *ld, doublereal * + lld, doublereal *pivmin, doublereal *gaptol, doublecomplex *z__, + logical *wantnc, integer *negcnt, doublereal *ztz, doublereal *mingma, + integer *r__, integer *isuppz, doublereal *nrminv, doublereal *resid, + doublereal *rqcorr, doublereal *work); + +/* Subroutine */ int zlar2v_(integer *n, doublecomplex *x, doublecomplex *y, + doublecomplex *z__, integer *incx, doublereal *c__, doublecomplex *s, + integer *incc); + +/* Subroutine */ int zlarcm_(integer *m, integer *n, doublereal *a, integer * + lda, doublecomplex *b, integer *ldb, doublecomplex *c__, integer *ldc, + doublereal *rwork); + +/* Subroutine */ int zlarf_(char *side, integer *m, integer *n, doublecomplex + *v, integer *incv, doublecomplex *tau, doublecomplex *c__, integer * + ldc, doublecomplex *work); + +/* Subroutine */ int zlarfb_(char *side, char *trans, char *direct, char * + storev, integer *m, integer *n, integer *k, doublecomplex *v, integer + *ldv, doublecomplex *t, integer *ldt, doublecomplex *c__, integer * + ldc, doublecomplex *work, integer *ldwork); + +/* Subroutine */ int zlarfg_(integer *n, doublecomplex *alpha, doublecomplex * + x, integer *incx, doublecomplex *tau); + +/* Subroutine */ int zlarfp_(integer *n, doublecomplex *alpha, doublecomplex * + x, integer *incx, doublecomplex *tau); + +/* Subroutine */ int zlarft_(char *direct, char *storev, integer *n, integer * + k, doublecomplex *v, integer *ldv, doublecomplex *tau, doublecomplex * + t, integer *ldt); + +/* Subroutine */ int zlarfx_(char *side, integer *m, integer *n, + doublecomplex *v, doublecomplex *tau, doublecomplex *c__, integer * + ldc, doublecomplex *work); + +/* Subroutine */ int zlargv_(integer *n, doublecomplex *x, integer *incx, + doublecomplex *y, integer *incy, doublereal *c__, integer *incc); + +/* Subroutine */ int zlarnv_(integer *idist, integer *iseed, integer *n, + doublecomplex *x); + +/* Subroutine */ int zlarrv_(integer *n, doublereal *vl, doublereal *vu, + doublereal *d__, doublereal *l, doublereal *pivmin, integer *isplit, + integer *m, integer *dol, integer *dou, doublereal *minrgp, + doublereal *rtol1, doublereal *rtol2, doublereal *w, doublereal *werr, + doublereal *wgap, integer *iblock, integer *indexw, doublereal *gers, + doublecomplex *z__, integer *ldz, integer *isuppz, doublereal *work, + integer *iwork, integer *info); + +/* Subroutine */ int zlarscl2_(integer *m, integer *n, doublereal *d__, + doublecomplex *x, integer *ldx); + +/* Subroutine */ int zlartg_(doublecomplex *f, doublecomplex *g, doublereal * + cs, doublecomplex *sn, doublecomplex *r__); + +/* Subroutine */ int zlartv_(integer *n, doublecomplex *x, integer *incx, + doublecomplex *y, integer *incy, doublereal *c__, doublecomplex *s, + integer *incc); + +/* Subroutine */ int zlarz_(char *side, integer *m, integer *n, integer *l, + doublecomplex *v, integer *incv, doublecomplex *tau, doublecomplex * + c__, integer *ldc, doublecomplex *work); + +/* Subroutine */ int zlarzb_(char *side, char *trans, char *direct, char * + storev, integer *m, integer *n, integer *k, integer *l, doublecomplex + *v, integer *ldv, doublecomplex *t, integer *ldt, doublecomplex *c__, + integer *ldc, doublecomplex *work, integer *ldwork); + +/* Subroutine */ int zlarzt_(char *direct, char *storev, integer *n, integer * + k, doublecomplex *v, integer *ldv, doublecomplex *tau, doublecomplex * + t, integer *ldt); + +/* Subroutine */ int zlascl_(char *type__, integer *kl, integer *ku, + doublereal *cfrom, doublereal *cto, integer *m, integer *n, + doublecomplex *a, integer *lda, integer *info); + +/* Subroutine */ int zlascl2_(integer *m, integer *n, doublereal *d__, + doublecomplex *x, integer *ldx); + +/* Subroutine */ int zlaset_(char *uplo, integer *m, integer *n, + doublecomplex *alpha, doublecomplex *beta, doublecomplex *a, integer * + lda); + +/* Subroutine */ int zlasr_(char *side, char *pivot, char *direct, integer *m, + integer *n, doublereal *c__, doublereal *s, doublecomplex *a, + integer *lda); + +/* Subroutine */ int zlassq_(integer *n, doublecomplex *x, integer *incx, + doublereal *scale, doublereal *sumsq); + +/* Subroutine */ int zlaswp_(integer *n, doublecomplex *a, integer *lda, + integer *k1, integer *k2, integer *ipiv, integer *incx); + +/* Subroutine */ int zlasyf_(char *uplo, integer *n, integer *nb, integer *kb, + doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *w, + integer *ldw, integer *info); + +/* Subroutine */ int zlat2c_(char *uplo, integer *n, doublecomplex *a, + integer *lda, complex *sa, integer *ldsa, integer *info); + +/* Subroutine */ int zlatbs_(char *uplo, char *trans, char *diag, char * + normin, integer *n, integer *kd, doublecomplex *ab, integer *ldab, + doublecomplex *x, doublereal *scale, doublereal *cnorm, integer *info); + +/* Subroutine */ int zlatdf_(integer *ijob, integer *n, doublecomplex *z__, + integer *ldz, doublecomplex *rhs, doublereal *rdsum, doublereal * + rdscal, integer *ipiv, integer *jpiv); + +/* Subroutine */ int zlatps_(char *uplo, char *trans, char *diag, char * + normin, integer *n, doublecomplex *ap, doublecomplex *x, doublereal * + scale, doublereal *cnorm, integer *info); + +/* Subroutine */ int zlatrd_(char *uplo, integer *n, integer *nb, + doublecomplex *a, integer *lda, doublereal *e, doublecomplex *tau, + doublecomplex *w, integer *ldw); + +/* Subroutine */ int zlatrs_(char *uplo, char *trans, char *diag, char * + normin, integer *n, doublecomplex *a, integer *lda, doublecomplex *x, + doublereal *scale, doublereal *cnorm, integer *info); + +/* Subroutine */ int zlatrz_(integer *m, integer *n, integer *l, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work); + +/* Subroutine */ int zlatzm_(char *side, integer *m, integer *n, + doublecomplex *v, integer *incv, doublecomplex *tau, doublecomplex * + c1, doublecomplex *c2, integer *ldc, doublecomplex *work); + +/* Subroutine */ int zlauu2_(char *uplo, integer *n, doublecomplex *a, + integer *lda, integer *info); + +/* Subroutine */ int zlauum_(char *uplo, integer *n, doublecomplex *a, + integer *lda, integer *info); + +/* Subroutine */ int zpbcon_(char *uplo, integer *n, integer *kd, + doublecomplex *ab, integer *ldab, doublereal *anorm, doublereal * + rcond, doublecomplex *work, doublereal *rwork, integer *info); + +/* Subroutine */ int zpbequ_(char *uplo, integer *n, integer *kd, + doublecomplex *ab, integer *ldab, doublereal *s, doublereal *scond, + doublereal *amax, integer *info); + +/* Subroutine */ int zpbrfs_(char *uplo, integer *n, integer *kd, integer * + nrhs, doublecomplex *ab, integer *ldab, doublecomplex *afb, integer * + ldafb, doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, + doublereal *ferr, doublereal *berr, doublecomplex *work, doublereal * + rwork, integer *info); + +/* Subroutine */ int zpbstf_(char *uplo, integer *n, integer *kd, + doublecomplex *ab, integer *ldab, integer *info); + +/* Subroutine */ int zpbsv_(char *uplo, integer *n, integer *kd, integer * + nrhs, doublecomplex *ab, integer *ldab, doublecomplex *b, integer * + ldb, integer *info); + +/* Subroutine */ int zpbsvx_(char *fact, char *uplo, integer *n, integer *kd, + integer *nrhs, doublecomplex *ab, integer *ldab, doublecomplex *afb, + integer *ldafb, char *equed, doublereal *s, doublecomplex *b, integer + *ldb, doublecomplex *x, integer *ldx, doublereal *rcond, doublereal * + ferr, doublereal *berr, doublecomplex *work, doublereal *rwork, + integer *info); + +/* Subroutine */ int zpbtf2_(char *uplo, integer *n, integer *kd, + doublecomplex *ab, integer *ldab, integer *info); + +/* Subroutine */ int zpbtrf_(char *uplo, integer *n, integer *kd, + doublecomplex *ab, integer *ldab, integer *info); + +/* Subroutine */ int zpbtrs_(char *uplo, integer *n, integer *kd, integer * + nrhs, doublecomplex *ab, integer *ldab, doublecomplex *b, integer * + ldb, integer *info); + +/* Subroutine */ int zpftrf_(char *transr, char *uplo, integer *n, + doublecomplex *a, integer *info); + +/* Subroutine */ int zpftri_(char *transr, char *uplo, integer *n, + doublecomplex *a, integer *info); + +/* Subroutine */ int zpftrs_(char *transr, char *uplo, integer *n, integer * + nrhs, doublecomplex *a, doublecomplex *b, integer *ldb, integer *info); + +/* Subroutine */ int zpocon_(char *uplo, integer *n, doublecomplex *a, + integer *lda, doublereal *anorm, doublereal *rcond, doublecomplex * + work, doublereal *rwork, integer *info); + +/* Subroutine */ int zpoequ_(integer *n, doublecomplex *a, integer *lda, + doublereal *s, doublereal *scond, doublereal *amax, integer *info); + +/* Subroutine */ int zpoequb_(integer *n, doublecomplex *a, integer *lda, + doublereal *s, doublereal *scond, doublereal *amax, integer *info); + +/* Subroutine */ int zporfs_(char *uplo, integer *n, integer *nrhs, + doublecomplex *a, integer *lda, doublecomplex *af, integer *ldaf, + doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, + doublereal *ferr, doublereal *berr, doublecomplex *work, doublereal * + rwork, integer *info); + +/* Subroutine */ int zporfsx_(char *uplo, char *equed, integer *n, integer * + nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * + ldaf, doublereal *s, doublecomplex *b, integer *ldb, doublecomplex *x, + integer *ldx, doublereal *rcond, doublereal *berr, integer * + n_err_bnds__, doublereal *err_bnds_norm__, doublereal * + err_bnds_comp__, integer *nparams, doublereal *params, doublecomplex * + work, doublereal *rwork, integer *info); + +/* Subroutine */ int zposv_(char *uplo, integer *n, integer *nrhs, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + integer *info); + +/* Subroutine */ int zposvx_(char *fact, char *uplo, integer *n, integer * + nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * + ldaf, char *equed, doublereal *s, doublecomplex *b, integer *ldb, + doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *ferr, + doublereal *berr, doublecomplex *work, doublereal *rwork, integer * + info); + +/* Subroutine */ int zposvxx_(char *fact, char *uplo, integer *n, integer * + nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * + ldaf, char *equed, doublereal *s, doublecomplex *b, integer *ldb, + doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *rpvgrw, + doublereal *berr, integer *n_err_bnds__, doublereal *err_bnds_norm__, + doublereal *err_bnds_comp__, integer *nparams, doublereal *params, + doublecomplex *work, doublereal *rwork, integer *info); + +/* Subroutine */ int zpotf2_(char *uplo, integer *n, doublecomplex *a, + integer *lda, integer *info); + +/* Subroutine */ int zpotrf_(char *uplo, integer *n, doublecomplex *a, + integer *lda, integer *info); + +/* Subroutine */ int zpotri_(char *uplo, integer *n, doublecomplex *a, + integer *lda, integer *info); + +/* Subroutine */ int zpotrs_(char *uplo, integer *n, integer *nrhs, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + integer *info); + +/* Subroutine */ int zppcon_(char *uplo, integer *n, doublecomplex *ap, + doublereal *anorm, doublereal *rcond, doublecomplex *work, doublereal + *rwork, integer *info); + +/* Subroutine */ int zppequ_(char *uplo, integer *n, doublecomplex *ap, + doublereal *s, doublereal *scond, doublereal *amax, integer *info); + +/* Subroutine */ int zpprfs_(char *uplo, integer *n, integer *nrhs, + doublecomplex *ap, doublecomplex *afp, doublecomplex *b, integer *ldb, + doublecomplex *x, integer *ldx, doublereal *ferr, doublereal *berr, + doublecomplex *work, doublereal *rwork, integer *info); + +/* Subroutine */ int zppsv_(char *uplo, integer *n, integer *nrhs, + doublecomplex *ap, doublecomplex *b, integer *ldb, integer *info); + +/* Subroutine */ int zppsvx_(char *fact, char *uplo, integer *n, integer * + nrhs, doublecomplex *ap, doublecomplex *afp, char *equed, doublereal * + s, doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, + doublereal *rcond, doublereal *ferr, doublereal *berr, doublecomplex * + work, doublereal *rwork, integer *info); + +/* Subroutine */ int zpptrf_(char *uplo, integer *n, doublecomplex *ap, + integer *info); + +/* Subroutine */ int zpptri_(char *uplo, integer *n, doublecomplex *ap, + integer *info); + +/* Subroutine */ int zpptrs_(char *uplo, integer *n, integer *nrhs, + doublecomplex *ap, doublecomplex *b, integer *ldb, integer *info); + +/* Subroutine */ int zpstf2_(char *uplo, integer *n, doublecomplex *a, + integer *lda, integer *piv, integer *rank, doublereal *tol, + doublereal *work, integer *info); + +/* Subroutine */ int zpstrf_(char *uplo, integer *n, doublecomplex *a, + integer *lda, integer *piv, integer *rank, doublereal *tol, + doublereal *work, integer *info); + +/* Subroutine */ int zptcon_(integer *n, doublereal *d__, doublecomplex *e, + doublereal *anorm, doublereal *rcond, doublereal *rwork, integer * + info); + +/* Subroutine */ int zpteqr_(char *compz, integer *n, doublereal *d__, + doublereal *e, doublecomplex *z__, integer *ldz, doublereal *work, + integer *info); + +/* Subroutine */ int zptrfs_(char *uplo, integer *n, integer *nrhs, + doublereal *d__, doublecomplex *e, doublereal *df, doublecomplex *ef, + doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, + doublereal *ferr, doublereal *berr, doublecomplex *work, doublereal * + rwork, integer *info); + +/* Subroutine */ int zptsv_(integer *n, integer *nrhs, doublereal *d__, + doublecomplex *e, doublecomplex *b, integer *ldb, integer *info); + +/* Subroutine */ int zptsvx_(char *fact, integer *n, integer *nrhs, + doublereal *d__, doublecomplex *e, doublereal *df, doublecomplex *ef, + doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, + doublereal *rcond, doublereal *ferr, doublereal *berr, doublecomplex * + work, doublereal *rwork, integer *info); + +/* Subroutine */ int zpttrf_(integer *n, doublereal *d__, doublecomplex *e, + integer *info); + +/* Subroutine */ int zpttrs_(char *uplo, integer *n, integer *nrhs, + doublereal *d__, doublecomplex *e, doublecomplex *b, integer *ldb, + integer *info); + +/* Subroutine */ int zptts2_(integer *iuplo, integer *n, integer *nrhs, + doublereal *d__, doublecomplex *e, doublecomplex *b, integer *ldb); + +/* Subroutine */ int zrot_(integer *n, doublecomplex *cx, integer *incx, + doublecomplex *cy, integer *incy, doublereal *c__, doublecomplex *s); + +/* Subroutine */ int zspcon_(char *uplo, integer *n, doublecomplex *ap, + integer *ipiv, doublereal *anorm, doublereal *rcond, doublecomplex * + work, integer *info); + +/* Subroutine */ int zspmv_(char *uplo, integer *n, doublecomplex *alpha, + doublecomplex *ap, doublecomplex *x, integer *incx, doublecomplex * + beta, doublecomplex *y, integer *incy); + +/* Subroutine */ int zspr_(char *uplo, integer *n, doublecomplex *alpha, + doublecomplex *x, integer *incx, doublecomplex *ap); + +/* Subroutine */ int zsprfs_(char *uplo, integer *n, integer *nrhs, + doublecomplex *ap, doublecomplex *afp, integer *ipiv, doublecomplex * + b, integer *ldb, doublecomplex *x, integer *ldx, doublereal *ferr, + doublereal *berr, doublecomplex *work, doublereal *rwork, integer * + info); + +/* Subroutine */ int zspsv_(char *uplo, integer *n, integer *nrhs, + doublecomplex *ap, integer *ipiv, doublecomplex *b, integer *ldb, + integer *info); + +/* Subroutine */ int zspsvx_(char *fact, char *uplo, integer *n, integer * + nrhs, doublecomplex *ap, doublecomplex *afp, integer *ipiv, + doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, + doublereal *rcond, doublereal *ferr, doublereal *berr, doublecomplex * + work, doublereal *rwork, integer *info); + +/* Subroutine */ int zsptrf_(char *uplo, integer *n, doublecomplex *ap, + integer *ipiv, integer *info); + +/* Subroutine */ int zsptri_(char *uplo, integer *n, doublecomplex *ap, + integer *ipiv, doublecomplex *work, integer *info); + +/* Subroutine */ int zsptrs_(char *uplo, integer *n, integer *nrhs, + doublecomplex *ap, integer *ipiv, doublecomplex *b, integer *ldb, + integer *info); + +/* Subroutine */ int zstedc_(char *compz, integer *n, doublereal *d__, + doublereal *e, doublecomplex *z__, integer *ldz, doublecomplex *work, + integer *lwork, doublereal *rwork, integer *lrwork, integer *iwork, + integer *liwork, integer *info); + +/* Subroutine */ int zstegr_(char *jobz, char *range, integer *n, doublereal * + d__, doublereal *e, doublereal *vl, doublereal *vu, integer *il, + integer *iu, doublereal *abstol, integer *m, doublereal *w, + doublecomplex *z__, integer *ldz, integer *isuppz, doublereal *work, + integer *lwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int zstein_(integer *n, doublereal *d__, doublereal *e, + integer *m, doublereal *w, integer *iblock, integer *isplit, + doublecomplex *z__, integer *ldz, doublereal *work, integer *iwork, + integer *ifail, integer *info); + +/* Subroutine */ int zstemr_(char *jobz, char *range, integer *n, doublereal * + d__, doublereal *e, doublereal *vl, doublereal *vu, integer *il, + integer *iu, integer *m, doublereal *w, doublecomplex *z__, integer * + ldz, integer *nzc, integer *isuppz, logical *tryrac, doublereal *work, + integer *lwork, integer *iwork, integer *liwork, integer *info); + +/* Subroutine */ int zsteqr_(char *compz, integer *n, doublereal *d__, + doublereal *e, doublecomplex *z__, integer *ldz, doublereal *work, + integer *info); + +/* Subroutine */ int zsycon_(char *uplo, integer *n, doublecomplex *a, + integer *lda, integer *ipiv, doublereal *anorm, doublereal *rcond, + doublecomplex *work, integer *info); + +/* Subroutine */ int zsyequb_(char *uplo, integer *n, doublecomplex *a, + integer *lda, doublereal *s, doublereal *scond, doublereal *amax, + doublecomplex *work, integer *info); + +/* Subroutine */ int zsymv_(char *uplo, integer *n, doublecomplex *alpha, + doublecomplex *a, integer *lda, doublecomplex *x, integer *incx, + doublecomplex *beta, doublecomplex *y, integer *incy); + +/* Subroutine */ int zsyr_(char *uplo, integer *n, doublecomplex *alpha, + doublecomplex *x, integer *incx, doublecomplex *a, integer *lda); + +/* Subroutine */ int zsyrfs_(char *uplo, integer *n, integer *nrhs, + doublecomplex *a, integer *lda, doublecomplex *af, integer *ldaf, + integer *ipiv, doublecomplex *b, integer *ldb, doublecomplex *x, + integer *ldx, doublereal *ferr, doublereal *berr, doublecomplex *work, + doublereal *rwork, integer *info); + +/* Subroutine */ int zsyrfsx_(char *uplo, char *equed, integer *n, integer * + nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * + ldaf, integer *ipiv, doublereal *s, doublecomplex *b, integer *ldb, + doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *berr, + integer *n_err_bnds__, doublereal *err_bnds_norm__, doublereal * + err_bnds_comp__, integer *nparams, doublereal *params, doublecomplex * + work, doublereal *rwork, integer *info); + +/* Subroutine */ int zsysv_(char *uplo, integer *n, integer *nrhs, + doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *b, + integer *ldb, doublecomplex *work, integer *lwork, integer *info); + +/* Subroutine */ int zsysvx_(char *fact, char *uplo, integer *n, integer * + nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * + ldaf, integer *ipiv, doublecomplex *b, integer *ldb, doublecomplex *x, + integer *ldx, doublereal *rcond, doublereal *ferr, doublereal *berr, + doublecomplex *work, integer *lwork, doublereal *rwork, integer *info); + +/* Subroutine */ int zsysvxx_(char *fact, char *uplo, integer *n, integer * + nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * + ldaf, integer *ipiv, char *equed, doublereal *s, doublecomplex *b, + integer *ldb, doublecomplex *x, integer *ldx, doublereal *rcond, + doublereal *rpvgrw, doublereal *berr, integer *n_err_bnds__, + doublereal *err_bnds_norm__, doublereal *err_bnds_comp__, integer * + nparams, doublereal *params, doublecomplex *work, doublereal *rwork, + integer *info); + +/* Subroutine */ int zsytf2_(char *uplo, integer *n, doublecomplex *a, + integer *lda, integer *ipiv, integer *info); + +/* Subroutine */ int zsytrf_(char *uplo, integer *n, doublecomplex *a, + integer *lda, integer *ipiv, doublecomplex *work, integer *lwork, + integer *info); + +/* Subroutine */ int zsytri_(char *uplo, integer *n, doublecomplex *a, + integer *lda, integer *ipiv, doublecomplex *work, integer *info); + +/* Subroutine */ int zsytrs_(char *uplo, integer *n, integer *nrhs, + doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *b, + integer *ldb, integer *info); + +/* Subroutine */ int ztbcon_(char *norm, char *uplo, char *diag, integer *n, + integer *kd, doublecomplex *ab, integer *ldab, doublereal *rcond, + doublecomplex *work, doublereal *rwork, integer *info); + +/* Subroutine */ int ztbrfs_(char *uplo, char *trans, char *diag, integer *n, + integer *kd, integer *nrhs, doublecomplex *ab, integer *ldab, + doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, + doublereal *ferr, doublereal *berr, doublecomplex *work, doublereal * + rwork, integer *info); + +/* Subroutine */ int ztbtrs_(char *uplo, char *trans, char *diag, integer *n, + integer *kd, integer *nrhs, doublecomplex *ab, integer *ldab, + doublecomplex *b, integer *ldb, integer *info); + +/* Subroutine */ int ztfsm_(char *transr, char *side, char *uplo, char *trans, + char *diag, integer *m, integer *n, doublecomplex *alpha, + doublecomplex *a, doublecomplex *b, integer *ldb); + +/* Subroutine */ int ztftri_(char *transr, char *uplo, char *diag, integer *n, + doublecomplex *a, integer *info); + +/* Subroutine */ int ztfttp_(char *transr, char *uplo, integer *n, + doublecomplex *arf, doublecomplex *ap, integer *info); + +/* Subroutine */ int ztfttr_(char *transr, char *uplo, integer *n, + doublecomplex *arf, doublecomplex *a, integer *lda, integer *info); + +/* Subroutine */ int ztgevc_(char *side, char *howmny, logical *select, + integer *n, doublecomplex *s, integer *lds, doublecomplex *p, integer + *ldp, doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer * + ldvr, integer *mm, integer *m, doublecomplex *work, doublereal *rwork, + integer *info); + +/* Subroutine */ int ztgex2_(logical *wantq, logical *wantz, integer *n, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + doublecomplex *q, integer *ldq, doublecomplex *z__, integer *ldz, + integer *j1, integer *info); + +/* Subroutine */ int ztgexc_(logical *wantq, logical *wantz, integer *n, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + doublecomplex *q, integer *ldq, doublecomplex *z__, integer *ldz, + integer *ifst, integer *ilst, integer *info); + +/* Subroutine */ int ztgsen_(integer *ijob, logical *wantq, logical *wantz, + logical *select, integer *n, doublecomplex *a, integer *lda, + doublecomplex *b, integer *ldb, doublecomplex *alpha, doublecomplex * + beta, doublecomplex *q, integer *ldq, doublecomplex *z__, integer * + ldz, integer *m, doublereal *pl, doublereal *pr, doublereal *dif, + doublecomplex *work, integer *lwork, integer *iwork, integer *liwork, + integer *info); + +/* Subroutine */ int ztgsja_(char *jobu, char *jobv, char *jobq, integer *m, + integer *p, integer *n, integer *k, integer *l, doublecomplex *a, + integer *lda, doublecomplex *b, integer *ldb, doublereal *tola, + doublereal *tolb, doublereal *alpha, doublereal *beta, doublecomplex * + u, integer *ldu, doublecomplex *v, integer *ldv, doublecomplex *q, + integer *ldq, doublecomplex *work, integer *ncycle, integer *info); + +/* Subroutine */ int ztgsna_(char *job, char *howmny, logical *select, + integer *n, doublecomplex *a, integer *lda, doublecomplex *b, integer + *ldb, doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer * + ldvr, doublereal *s, doublereal *dif, integer *mm, integer *m, + doublecomplex *work, integer *lwork, integer *iwork, integer *info); + +/* Subroutine */ int ztgsy2_(char *trans, integer *ijob, integer *m, integer * + n, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + doublecomplex *c__, integer *ldc, doublecomplex *d__, integer *ldd, + doublecomplex *e, integer *lde, doublecomplex *f, integer *ldf, + doublereal *scale, doublereal *rdsum, doublereal *rdscal, integer * + info); + +/* Subroutine */ int ztgsyl_(char *trans, integer *ijob, integer *m, integer * + n, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + doublecomplex *c__, integer *ldc, doublecomplex *d__, integer *ldd, + doublecomplex *e, integer *lde, doublecomplex *f, integer *ldf, + doublereal *scale, doublereal *dif, doublecomplex *work, integer * + lwork, integer *iwork, integer *info); + +/* Subroutine */ int ztpcon_(char *norm, char *uplo, char *diag, integer *n, + doublecomplex *ap, doublereal *rcond, doublecomplex *work, doublereal + *rwork, integer *info); + +/* Subroutine */ int ztprfs_(char *uplo, char *trans, char *diag, integer *n, + integer *nrhs, doublecomplex *ap, doublecomplex *b, integer *ldb, + doublecomplex *x, integer *ldx, doublereal *ferr, doublereal *berr, + doublecomplex *work, doublereal *rwork, integer *info); + +/* Subroutine */ int ztptri_(char *uplo, char *diag, integer *n, + doublecomplex *ap, integer *info); + +/* Subroutine */ int ztptrs_(char *uplo, char *trans, char *diag, integer *n, + integer *nrhs, doublecomplex *ap, doublecomplex *b, integer *ldb, + integer *info); + +/* Subroutine */ int ztpttf_(char *transr, char *uplo, integer *n, + doublecomplex *ap, doublecomplex *arf, integer *info); + +/* Subroutine */ int ztpttr_(char *uplo, integer *n, doublecomplex *ap, + doublecomplex *a, integer *lda, integer *info); + +/* Subroutine */ int ztrcon_(char *norm, char *uplo, char *diag, integer *n, + doublecomplex *a, integer *lda, doublereal *rcond, doublecomplex * + work, doublereal *rwork, integer *info); + +/* Subroutine */ int ztrevc_(char *side, char *howmny, logical *select, + integer *n, doublecomplex *t, integer *ldt, doublecomplex *vl, + integer *ldvl, doublecomplex *vr, integer *ldvr, integer *mm, integer + *m, doublecomplex *work, doublereal *rwork, integer *info); + +/* Subroutine */ int ztrexc_(char *compq, integer *n, doublecomplex *t, + integer *ldt, doublecomplex *q, integer *ldq, integer *ifst, integer * + ilst, integer *info); + +/* Subroutine */ int ztrrfs_(char *uplo, char *trans, char *diag, integer *n, + integer *nrhs, doublecomplex *a, integer *lda, doublecomplex *b, + integer *ldb, doublecomplex *x, integer *ldx, doublereal *ferr, + doublereal *berr, doublecomplex *work, doublereal *rwork, integer * + info); + +/* Subroutine */ int ztrsen_(char *job, char *compq, logical *select, integer + *n, doublecomplex *t, integer *ldt, doublecomplex *q, integer *ldq, + doublecomplex *w, integer *m, doublereal *s, doublereal *sep, + doublecomplex *work, integer *lwork, integer *info); + +/* Subroutine */ int ztrsna_(char *job, char *howmny, logical *select, + integer *n, doublecomplex *t, integer *ldt, doublecomplex *vl, + integer *ldvl, doublecomplex *vr, integer *ldvr, doublereal *s, + doublereal *sep, integer *mm, integer *m, doublecomplex *work, + integer *ldwork, doublereal *rwork, integer *info); + +/* Subroutine */ int ztrsyl_(char *trana, char *tranb, integer *isgn, integer + *m, integer *n, doublecomplex *a, integer *lda, doublecomplex *b, + integer *ldb, doublecomplex *c__, integer *ldc, doublereal *scale, + integer *info); + +/* Subroutine */ int ztrti2_(char *uplo, char *diag, integer *n, + doublecomplex *a, integer *lda, integer *info); + +/* Subroutine */ int ztrtri_(char *uplo, char *diag, integer *n, + doublecomplex *a, integer *lda, integer *info); + +/* Subroutine */ int ztrtrs_(char *uplo, char *trans, char *diag, integer *n, + integer *nrhs, doublecomplex *a, integer *lda, doublecomplex *b, + integer *ldb, integer *info); + +/* Subroutine */ int ztrttf_(char *transr, char *uplo, integer *n, + doublecomplex *a, integer *lda, doublecomplex *arf, integer *info); + +/* Subroutine */ int ztrttp_(char *uplo, integer *n, doublecomplex *a, + integer *lda, doublecomplex *ap, integer *info); + +/* Subroutine */ int ztzrqf_(integer *m, integer *n, doublecomplex *a, + integer *lda, doublecomplex *tau, integer *info); + +/* Subroutine */ int ztzrzf_(integer *m, integer *n, doublecomplex *a, + integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork, + integer *info); + +/* Subroutine */ int zung2l_(integer *m, integer *n, integer *k, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *info); + +/* Subroutine */ int zung2r_(integer *m, integer *n, integer *k, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *info); + +/* Subroutine */ int zungbr_(char *vect, integer *m, integer *n, integer *k, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *lwork, integer *info); + +/* Subroutine */ int zunghr_(integer *n, integer *ilo, integer *ihi, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *lwork, integer *info); + +/* Subroutine */ int zungl2_(integer *m, integer *n, integer *k, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *info); + +/* Subroutine */ int zunglq_(integer *m, integer *n, integer *k, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *lwork, integer *info); + +/* Subroutine */ int zungql_(integer *m, integer *n, integer *k, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *lwork, integer *info); + +/* Subroutine */ int zungqr_(integer *m, integer *n, integer *k, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *lwork, integer *info); + +/* Subroutine */ int zungr2_(integer *m, integer *n, integer *k, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *info); + +/* Subroutine */ int zungrq_(integer *m, integer *n, integer *k, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *lwork, integer *info); + +/* Subroutine */ int zungtr_(char *uplo, integer *n, doublecomplex *a, + integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork, + integer *info); + +/* Subroutine */ int zunm2l_(char *side, char *trans, integer *m, integer *n, + integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *c__, integer *ldc, doublecomplex *work, integer *info); + +/* Subroutine */ int zunm2r_(char *side, char *trans, integer *m, integer *n, + integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *c__, integer *ldc, doublecomplex *work, integer *info); + +/* Subroutine */ int zunmbr_(char *vect, char *side, char *trans, integer *m, + integer *n, integer *k, doublecomplex *a, integer *lda, doublecomplex + *tau, doublecomplex *c__, integer *ldc, doublecomplex *work, integer * + lwork, integer *info); + +/* Subroutine */ int zunmhr_(char *side, char *trans, integer *m, integer *n, + integer *ilo, integer *ihi, doublecomplex *a, integer *lda, + doublecomplex *tau, doublecomplex *c__, integer *ldc, doublecomplex * + work, integer *lwork, integer *info); + +/* Subroutine */ int zunml2_(char *side, char *trans, integer *m, integer *n, + integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *c__, integer *ldc, doublecomplex *work, integer *info); + +/* Subroutine */ int zunmlq_(char *side, char *trans, integer *m, integer *n, + integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork, + integer *info); + +/* Subroutine */ int zunmql_(char *side, char *trans, integer *m, integer *n, + integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork, + integer *info); + +/* Subroutine */ int zunmqr_(char *side, char *trans, integer *m, integer *n, + integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork, + integer *info); + +/* Subroutine */ int zunmr2_(char *side, char *trans, integer *m, integer *n, + integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *c__, integer *ldc, doublecomplex *work, integer *info); + +/* Subroutine */ int zunmr3_(char *side, char *trans, integer *m, integer *n, + integer *k, integer *l, doublecomplex *a, integer *lda, doublecomplex + *tau, doublecomplex *c__, integer *ldc, doublecomplex *work, integer * + info); + +/* Subroutine */ int zunmrq_(char *side, char *trans, integer *m, integer *n, + integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork, + integer *info); + +/* Subroutine */ int zunmrz_(char *side, char *trans, integer *m, integer *n, + integer *k, integer *l, doublecomplex *a, integer *lda, doublecomplex + *tau, doublecomplex *c__, integer *ldc, doublecomplex *work, integer * + lwork, integer *info); + +/* Subroutine */ int zunmtr_(char *side, char *uplo, char *trans, integer *m, + integer *n, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork, + integer *info); + +/* Subroutine */ int zupgtr_(char *uplo, integer *n, doublecomplex *ap, + doublecomplex *tau, doublecomplex *q, integer *ldq, doublecomplex * + work, integer *info); + +/* Subroutine */ int zupmtr_(char *side, char *uplo, char *trans, integer *m, + integer *n, doublecomplex *ap, doublecomplex *tau, doublecomplex *c__, + integer *ldc, doublecomplex *work, integer *info); + +/* Subroutine */ int dlamc1_(integer *beta, integer *t, logical *rnd, logical + *ieee1); + +doublereal dsecnd_(); + +/* Subroutine */ int ilaver_(integer *vers_major__, integer *vers_minor__, + integer *vers_patch__); + +logical lsame_(char *ca, char *cb); + +doublereal second_(); + +doublereal slamch_(char *cmach); + +/* Subroutine */ int slamc1_(integer *beta, integer *t, logical *rnd, logical + *ieee1); + +/* Subroutine */ int slamc2_(integer *beta, integer *t, logical *rnd, real * + eps, integer *emin, real *rmin, integer *emax, real *rmax); + +doublereal slamc3_(real *a, real *b); + +/* Subroutine */ int slamc4_(integer *emin, real *start, integer *base); + +/* Subroutine */ int slamc5_(integer *beta, integer *p, integer *emin, + logical *ieee, integer *emax, real *rmax); + + +doublereal dlamch_(char *cmach); + +/* Subroutine */ int dlamc1_(integer *beta, integer *t, logical *rnd, logical + *ieee1); + +/* Subroutine */ int dlamc2_(integer *beta, integer *t, logical *rnd, + doublereal *eps, integer *emin, doublereal *rmin, integer *emax, + doublereal *rmax); + +doublereal dlamc3_(doublereal *a, doublereal *b); + +/* Subroutine */ int dlamc4_(integer *emin, doublereal *start, integer *base); + +/* Subroutine */ int dlamc5_(integer *beta, integer *p, integer *emin, + logical *ieee, integer *emax, doublereal *rmax); + +integer ilaenv_(integer *ispec, char *name__, char *opts, integer *n1, + integer *n2, integer *n3, integer *n4); + +#ifdef __cplusplus +} +#endif + + +#endif /* __CLAPACK_H */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/clapack/include/f2c.h Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,223 @@ +/* f2c.h -- Standard Fortran to C header file */ + +/** barf [ba:rf] 2. "He suggested using FORTRAN, and everybody barfed." + + - From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */ + +#ifndef F2C_INCLUDE +#define F2C_INCLUDE + +typedef int integer; +typedef unsigned int uinteger; +typedef char *address; +typedef short shortint; +typedef float real; +typedef double doublereal; +typedef struct { real r, i; } complex; +typedef struct { doublereal r, i; } doublecomplex; +typedef int logical; +typedef short shortlogical; +typedef char logical1; +typedef char integer1; +#ifdef INTEGER_STAR_8 /* Adjust for integer*8. */ +typedef int64_t longint; /* system-dependent */ +typedef uint64_t ulongint; /* system-dependent */ +#define qbit_clear(a,b) ((a) & ~((ulongint)1 << (b))) +#define qbit_set(a,b) ((a) | ((ulongint)1 << (b))) +#endif + +#define TRUE_ (1) +#define FALSE_ (0) + +/* Extern is for use with -E */ +#ifndef Extern +#define Extern extern +#endif + +/* I/O stuff */ + +#ifdef f2c_i2 +/* for -i2 */ +typedef short flag; +typedef short ftnlen; +typedef short ftnint; +#else +typedef int flag; +typedef int ftnlen; +typedef int ftnint; +#endif + +/*external read, write*/ +typedef struct +{ flag cierr; + ftnint ciunit; + flag ciend; + char *cifmt; + ftnint cirec; +} cilist; + +/*internal read, write*/ +typedef struct +{ flag icierr; + char *iciunit; + flag iciend; + char *icifmt; + ftnint icirlen; + ftnint icirnum; +} icilist; + +/*open*/ +typedef struct +{ flag oerr; + ftnint ounit; + char *ofnm; + ftnlen ofnmlen; + char *osta; + char *oacc; + char *ofm; + ftnint orl; + char *oblnk; +} olist; + +/*close*/ +typedef struct +{ flag cerr; + ftnint cunit; + char *csta; +} cllist; + +/*rewind, backspace, endfile*/ +typedef struct +{ flag aerr; + ftnint aunit; +} alist; + +/* inquire */ +typedef struct +{ flag inerr; + ftnint inunit; + char *infile; + ftnlen infilen; + ftnint *inex; /*parameters in standard's order*/ + ftnint *inopen; + ftnint *innum; + ftnint *innamed; + char *inname; + ftnlen innamlen; + char *inacc; + ftnlen inacclen; + char *inseq; + ftnlen inseqlen; + char *indir; + ftnlen indirlen; + char *infmt; + ftnlen infmtlen; + char *inform; + ftnint informlen; + char *inunf; + ftnlen inunflen; + ftnint *inrecl; + ftnint *innrec; + char *inblank; + ftnlen inblanklen; +} inlist; + +#define VOID void + +union Multitype { /* for multiple entry points */ + integer1 g; + shortint h; + integer i; + /* longint j; */ + real r; + doublereal d; + complex c; + doublecomplex z; + }; + +typedef union Multitype Multitype; + +/*typedef long int Long;*/ /* No longer used; formerly in Namelist */ + +struct Vardesc { /* for Namelist */ + char *name; + char *addr; + ftnlen *dims; + int type; + }; +typedef struct Vardesc Vardesc; + +struct Namelist { + char *name; + Vardesc **vars; + int nvars; + }; +typedef struct Namelist Namelist; + +#define abs(x) ((x) >= 0 ? (x) : -(x)) +#define dabs(x) (doublereal)abs(x) +#define min(a,b) ((a) <= (b) ? (a) : (b)) +#define max(a,b) ((a) >= (b) ? (a) : (b)) +#define dmin(a,b) (doublereal)min(a,b) +#define dmax(a,b) (doublereal)max(a,b) +#define bit_test(a,b) ((a) >> (b) & 1) +#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b))) +#define bit_set(a,b) ((a) | ((uinteger)1 << (b))) + +/* procedure parameter types for -A and -C++ */ + +#define F2C_proc_par_types 1 +#ifdef __cplusplus +typedef int /* Unknown procedure type */ (*U_fp)(...); +typedef shortint (*J_fp)(...); +typedef integer (*I_fp)(...); +typedef real (*R_fp)(...); +typedef doublereal (*D_fp)(...), (*E_fp)(...); +typedef /* Complex */ VOID (*C_fp)(...); +typedef /* Double Complex */ VOID (*Z_fp)(...); +typedef logical (*L_fp)(...); +typedef shortlogical (*K_fp)(...); +typedef /* Character */ VOID (*H_fp)(...); +typedef /* Subroutine */ int (*S_fp)(...); +#else +typedef int /* Unknown procedure type */ (*U_fp)(); +typedef shortint (*J_fp)(); +typedef integer (*I_fp)(); +typedef real (*R_fp)(); +typedef doublereal (*D_fp)(), (*E_fp)(); +typedef /* Complex */ VOID (*C_fp)(); +typedef /* Double Complex */ VOID (*Z_fp)(); +typedef logical (*L_fp)(); +typedef shortlogical (*K_fp)(); +typedef /* Character */ VOID (*H_fp)(); +typedef /* Subroutine */ int (*S_fp)(); +#endif +/* E_fp is for real functions when -R is not specified */ +typedef VOID C_f; /* complex function */ +typedef VOID H_f; /* character function */ +typedef VOID Z_f; /* double complex function */ +typedef doublereal E_f; /* real function with -R not specified */ + +/* undef any lower-case symbols that your C compiler predefines, e.g.: */ + +#ifndef Skip_f2c_Undefs +#undef cray +#undef gcos +#undef mc68010 +#undef mc68020 +#undef mips +#undef pdp11 +#undef sgi +#undef sparc +#undef sun +#undef sun2 +#undef sun3 +#undef sun4 +#undef u370 +#undef u3b +#undef u3b2 +#undef u3b5 +#undef unix +#undef vax +#endif +#endif
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/clapack/src/dgetf2.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,193 @@ +/* dgetf2.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static doublereal c_b8 = -1.; + +/* Subroutine */ int dgetf2_(integer *m, integer *n, doublereal *a, integer * + lda, integer *ipiv, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + doublereal d__1; + + /* Local variables */ + integer i__, j, jp; + extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *), dscal_(integer *, doublereal *, doublereal *, integer + *); + doublereal sfmin; + extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, + doublereal *, integer *); + extern doublereal dlamch_(char *); + extern integer idamax_(integer *, doublereal *, integer *); + extern /* Subroutine */ int xerbla_(char *, integer *); + + +/* -- LAPACK routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* DGETF2 computes an LU factorization of a general m-by-n matrix A */ +/* using partial pivoting with row interchanges. */ + +/* The factorization has the form */ +/* A = P * L * U */ +/* where P is a permutation matrix, L is lower triangular with unit */ +/* diagonal elements (lower trapezoidal if m > n), and U is upper */ +/* triangular (upper trapezoidal if m < n). */ + +/* This is the right-looking Level 2 BLAS version of the algorithm. */ + +/* Arguments */ +/* ========= */ + +/* M (input) INTEGER */ +/* The number of rows of the matrix A. M >= 0. */ + +/* N (input) INTEGER */ +/* The number of columns of the matrix A. N >= 0. */ + +/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */ +/* On entry, the m by n matrix to be factored. */ +/* On exit, the factors L and U from the factorization */ +/* A = P*L*U; the unit diagonal elements of L are not stored. */ + +/* LDA (input) INTEGER */ +/* The leading dimension of the array A. LDA >= max(1,M). */ + +/* IPIV (output) INTEGER array, dimension (min(M,N)) */ +/* The pivot indices; for 1 <= i <= min(M,N), row i of the */ +/* matrix was interchanged with row IPIV(i). */ + +/* INFO (output) INTEGER */ +/* = 0: successful exit */ +/* < 0: if INFO = -k, the k-th argument had an illegal value */ +/* > 0: if INFO = k, U(k,k) is exactly zero. The factorization */ +/* has been completed, but the factor U is exactly */ +/* singular, and division by zero will occur if it is used */ +/* to solve a system of equations. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --ipiv; + + /* Function Body */ + *info = 0; + if (*m < 0) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*m)) { + *info = -4; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_("DGETF2", &i__1); + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0) { + return 0; + } + +/* Compute machine safe minimum */ + + sfmin = dlamch_("S"); + + i__1 = min(*m,*n); + for (j = 1; j <= i__1; ++j) { + +/* Find pivot and test for singularity. */ + + i__2 = *m - j + 1; + jp = j - 1 + idamax_(&i__2, &a[j + j * a_dim1], &c__1); + ipiv[j] = jp; + if (a[jp + j * a_dim1] != 0.) { + +/* Apply the interchange to columns 1:N. */ + + if (jp != j) { + dswap_(n, &a[j + a_dim1], lda, &a[jp + a_dim1], lda); + } + +/* Compute elements J+1:M of J-th column. */ + + if (j < *m) { + if ((d__1 = a[j + j * a_dim1], abs(d__1)) >= sfmin) { + i__2 = *m - j; + d__1 = 1. / a[j + j * a_dim1]; + dscal_(&i__2, &d__1, &a[j + 1 + j * a_dim1], &c__1); + } else { + i__2 = *m - j; + for (i__ = 1; i__ <= i__2; ++i__) { + a[j + i__ + j * a_dim1] /= a[j + j * a_dim1]; +/* L20: */ + } + } + } + + } else if (*info == 0) { + + *info = j; + } + + if (j < min(*m,*n)) { + +/* Update trailing submatrix. */ + + i__2 = *m - j; + i__3 = *n - j; + dger_(&i__2, &i__3, &c_b8, &a[j + 1 + j * a_dim1], &c__1, &a[j + ( + j + 1) * a_dim1], lda, &a[j + 1 + (j + 1) * a_dim1], lda); + } +/* L10: */ + } + return 0; + +/* End of DGETF2 */ + +} /* dgetf2_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/clapack/src/dgetrf.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,219 @@ +/* dgetrf.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static doublereal c_b16 = 1.; +static doublereal c_b19 = -1.; + +/* Subroutine */ int dgetrf_(integer *m, integer *n, doublereal *a, integer * + lda, integer *ipiv, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; + + /* Local variables */ + integer i__, j, jb, nb; + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *); + integer iinfo; + extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *), dgetf2_( + integer *, integer *, doublereal *, integer *, integer *, integer + *), xerbla_(char *, integer *); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *); + extern /* Subroutine */ int dlaswp_(integer *, doublereal *, integer *, + integer *, integer *, integer *, integer *); + + +/* -- LAPACK routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* DGETRF computes an LU factorization of a general M-by-N matrix A */ +/* using partial pivoting with row interchanges. */ + +/* The factorization has the form */ +/* A = P * L * U */ +/* where P is a permutation matrix, L is lower triangular with unit */ +/* diagonal elements (lower trapezoidal if m > n), and U is upper */ +/* triangular (upper trapezoidal if m < n). */ + +/* This is the right-looking Level 3 BLAS version of the algorithm. */ + +/* Arguments */ +/* ========= */ + +/* M (input) INTEGER */ +/* The number of rows of the matrix A. M >= 0. */ + +/* N (input) INTEGER */ +/* The number of columns of the matrix A. N >= 0. */ + +/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */ +/* On entry, the M-by-N matrix to be factored. */ +/* On exit, the factors L and U from the factorization */ +/* A = P*L*U; the unit diagonal elements of L are not stored. */ + +/* LDA (input) INTEGER */ +/* The leading dimension of the array A. LDA >= max(1,M). */ + +/* IPIV (output) INTEGER array, dimension (min(M,N)) */ +/* The pivot indices; for 1 <= i <= min(M,N), row i of the */ +/* matrix was interchanged with row IPIV(i). */ + +/* INFO (output) INTEGER */ +/* = 0: successful exit */ +/* < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > 0: if INFO = i, U(i,i) is exactly zero. The factorization */ +/* has been completed, but the factor U is exactly */ +/* singular, and division by zero will occur if it is used */ +/* to solve a system of equations. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --ipiv; + + /* Function Body */ + *info = 0; + if (*m < 0) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*m)) { + *info = -4; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_("DGETRF", &i__1); + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0) { + return 0; + } + +/* Determine the block size for this environment. */ + + nb = ilaenv_(&c__1, "DGETRF", " ", m, n, &c_n1, &c_n1); + if (nb <= 1 || nb >= min(*m,*n)) { + +/* Use unblocked code. */ + + dgetf2_(m, n, &a[a_offset], lda, &ipiv[1], info); + } else { + +/* Use blocked code. */ + + i__1 = min(*m,*n); + i__2 = nb; + for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { +/* Computing MIN */ + i__3 = min(*m,*n) - j + 1; + jb = min(i__3,nb); + +/* Factor diagonal and subdiagonal blocks and test for exact */ +/* singularity. */ + + i__3 = *m - j + 1; + dgetf2_(&i__3, &jb, &a[j + j * a_dim1], lda, &ipiv[j], &iinfo); + +/* Adjust INFO and the pivot indices. */ + + if (*info == 0 && iinfo > 0) { + *info = iinfo + j - 1; + } +/* Computing MIN */ + i__4 = *m, i__5 = j + jb - 1; + i__3 = min(i__4,i__5); + for (i__ = j; i__ <= i__3; ++i__) { + ipiv[i__] = j - 1 + ipiv[i__]; +/* L10: */ + } + +/* Apply interchanges to columns 1:J-1. */ + + i__3 = j - 1; + i__4 = j + jb - 1; + dlaswp_(&i__3, &a[a_offset], lda, &j, &i__4, &ipiv[1], &c__1); + + if (j + jb <= *n) { + +/* Apply interchanges to columns J+JB:N. */ + + i__3 = *n - j - jb + 1; + i__4 = j + jb - 1; + dlaswp_(&i__3, &a[(j + jb) * a_dim1 + 1], lda, &j, &i__4, & + ipiv[1], &c__1); + +/* Compute block row of U. */ + + i__3 = *n - j - jb + 1; + dtrsm_("Left", "Lower", "No transpose", "Unit", &jb, &i__3, & + c_b16, &a[j + j * a_dim1], lda, &a[j + (j + jb) * + a_dim1], lda); + if (j + jb <= *m) { + +/* Update trailing submatrix. */ + + i__3 = *m - j - jb + 1; + i__4 = *n - j - jb + 1; + dgemm_("No transpose", "No transpose", &i__3, &i__4, &jb, + &c_b19, &a[j + jb + j * a_dim1], lda, &a[j + (j + + jb) * a_dim1], lda, &c_b16, &a[j + jb + (j + jb) * + a_dim1], lda); + } + } +/* L20: */ + } + } + return 0; + +/* End of DGETRF */ + +} /* dgetrf_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/clapack/src/dgetri.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,264 @@ +/* dgetri.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__2 = 2; +static doublereal c_b20 = -1.; +static doublereal c_b22 = 1.; + +/* Subroutine */ int dgetri_(integer *n, doublereal *a, integer *lda, integer + *ipiv, doublereal *work, integer *lwork, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + + /* Local variables */ + integer i__, j, jb, nb, jj, jp, nn, iws; + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *), + dgemv_(char *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *); + integer nbmin; + extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, + doublereal *, integer *), dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *), xerbla_( + char *, integer *); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *); + integer ldwork; + extern /* Subroutine */ int dtrtri_(char *, char *, integer *, doublereal + *, integer *, integer *); + integer lwkopt; + logical lquery; + + +/* -- LAPACK routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* DGETRI computes the inverse of a matrix using the LU factorization */ +/* computed by DGETRF. */ + +/* This method inverts U and then computes inv(A) by solving the system */ +/* inv(A)*L = inv(U) for inv(A). */ + +/* Arguments */ +/* ========= */ + +/* N (input) INTEGER */ +/* The order of the matrix A. N >= 0. */ + +/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */ +/* On entry, the factors L and U from the factorization */ +/* A = P*L*U as computed by DGETRF. */ +/* On exit, if INFO = 0, the inverse of the original matrix A. */ + +/* LDA (input) INTEGER */ +/* The leading dimension of the array A. LDA >= max(1,N). */ + +/* IPIV (input) INTEGER array, dimension (N) */ +/* The pivot indices from DGETRF; for 1<=i<=N, row i of the */ +/* matrix was interchanged with row IPIV(i). */ + +/* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* On exit, if INFO=0, then WORK(1) returns the optimal LWORK. */ + +/* LWORK (input) INTEGER */ +/* The dimension of the array WORK. LWORK >= max(1,N). */ +/* For optimal performance LWORK >= N*NB, where NB is */ +/* the optimal blocksize returned by ILAENV. */ + +/* If LWORK = -1, then a workspace query is assumed; the routine */ +/* only calculates the optimal size of the WORK array, returns */ +/* this value as the first entry of the WORK array, and no error */ +/* message related to LWORK is issued by XERBLA. */ + +/* INFO (output) INTEGER */ +/* = 0: successful exit */ +/* < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > 0: if INFO = i, U(i,i) is exactly zero; the matrix is */ +/* singular and its inverse could not be computed. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --ipiv; + --work; + + /* Function Body */ + *info = 0; + nb = ilaenv_(&c__1, "DGETRI", " ", n, &c_n1, &c_n1, &c_n1); + lwkopt = *n * nb; + work[1] = (doublereal) lwkopt; + lquery = *lwork == -1; + if (*n < 0) { + *info = -1; + } else if (*lda < max(1,*n)) { + *info = -3; + } else if (*lwork < max(1,*n) && ! lquery) { + *info = -6; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_("DGETRI", &i__1); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + +/* Form inv(U). If INFO > 0 from DTRTRI, then U is singular, */ +/* and the inverse is not computed. */ + + dtrtri_("Upper", "Non-unit", n, &a[a_offset], lda, info); + if (*info > 0) { + return 0; + } + + nbmin = 2; + ldwork = *n; + if (nb > 1 && nb < *n) { +/* Computing MAX */ + i__1 = ldwork * nb; + iws = max(i__1,1); + if (*lwork < iws) { + nb = *lwork / ldwork; +/* Computing MAX */ + i__1 = 2, i__2 = ilaenv_(&c__2, "DGETRI", " ", n, &c_n1, &c_n1, & + c_n1); + nbmin = max(i__1,i__2); + } + } else { + iws = *n; + } + +/* Solve the equation inv(A)*L = inv(U) for inv(A). */ + + if (nb < nbmin || nb >= *n) { + +/* Use unblocked code. */ + + for (j = *n; j >= 1; --j) { + +/* Copy current column of L to WORK and replace with zeros. */ + + i__1 = *n; + for (i__ = j + 1; i__ <= i__1; ++i__) { + work[i__] = a[i__ + j * a_dim1]; + a[i__ + j * a_dim1] = 0.; +/* L10: */ + } + +/* Compute current column of inv(A). */ + + if (j < *n) { + i__1 = *n - j; + dgemv_("No transpose", n, &i__1, &c_b20, &a[(j + 1) * a_dim1 + + 1], lda, &work[j + 1], &c__1, &c_b22, &a[j * a_dim1 + + 1], &c__1); + } +/* L20: */ + } + } else { + +/* Use blocked code. */ + + nn = (*n - 1) / nb * nb + 1; + i__1 = -nb; + for (j = nn; i__1 < 0 ? j >= 1 : j <= 1; j += i__1) { +/* Computing MIN */ + i__2 = nb, i__3 = *n - j + 1; + jb = min(i__2,i__3); + +/* Copy current block column of L to WORK and replace with */ +/* zeros. */ + + i__2 = j + jb - 1; + for (jj = j; jj <= i__2; ++jj) { + i__3 = *n; + for (i__ = jj + 1; i__ <= i__3; ++i__) { + work[i__ + (jj - j) * ldwork] = a[i__ + jj * a_dim1]; + a[i__ + jj * a_dim1] = 0.; +/* L30: */ + } +/* L40: */ + } + +/* Compute current block column of inv(A). */ + + if (j + jb <= *n) { + i__2 = *n - j - jb + 1; + dgemm_("No transpose", "No transpose", n, &jb, &i__2, &c_b20, + &a[(j + jb) * a_dim1 + 1], lda, &work[j + jb], & + ldwork, &c_b22, &a[j * a_dim1 + 1], lda); + } + dtrsm_("Right", "Lower", "No transpose", "Unit", n, &jb, &c_b22, & + work[j], &ldwork, &a[j * a_dim1 + 1], lda); +/* L50: */ + } + } + +/* Apply column interchanges. */ + + for (j = *n - 1; j >= 1; --j) { + jp = ipiv[j]; + if (jp != j) { + dswap_(n, &a[j * a_dim1 + 1], &c__1, &a[jp * a_dim1 + 1], &c__1); + } +/* L60: */ + } + + work[1] = (doublereal) iws; + return 0; + +/* End of DGETRI */ + +} /* dgetri_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/clapack/src/dlaswp.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,158 @@ +/* dlaswp.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +/* Subroutine */ int dlaswp_(integer *n, doublereal *a, integer *lda, integer + *k1, integer *k2, integer *ipiv, integer *incx) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4; + + /* Local variables */ + integer i__, j, k, i1, i2, n32, ip, ix, ix0, inc; + doublereal temp; + + +/* -- LAPACK auxiliary routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* DLASWP performs a series of row interchanges on the matrix A. */ +/* One row interchange is initiated for each of rows K1 through K2 of A. */ + +/* Arguments */ +/* ========= */ + +/* N (input) INTEGER */ +/* The number of columns of the matrix A. */ + +/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */ +/* On entry, the matrix of column dimension N to which the row */ +/* interchanges will be applied. */ +/* On exit, the permuted matrix. */ + +/* LDA (input) INTEGER */ +/* The leading dimension of the array A. */ + +/* K1 (input) INTEGER */ +/* The first element of IPIV for which a row interchange will */ +/* be done. */ + +/* K2 (input) INTEGER */ +/* The last element of IPIV for which a row interchange will */ +/* be done. */ + +/* IPIV (input) INTEGER array, dimension (K2*abs(INCX)) */ +/* The vector of pivot indices. Only the elements in positions */ +/* K1 through K2 of IPIV are accessed. */ +/* IPIV(K) = L implies rows K and L are to be interchanged. */ + +/* INCX (input) INTEGER */ +/* The increment between successive values of IPIV. If IPIV */ +/* is negative, the pivots are applied in reverse order. */ + +/* Further Details */ +/* =============== */ + +/* Modified by */ +/* R. C. Whaley, Computer Science Dept., Univ. of Tenn., Knoxville, USA */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Interchange row I with row IPIV(I) for each of rows K1 through K2. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --ipiv; + + /* Function Body */ + if (*incx > 0) { + ix0 = *k1; + i1 = *k1; + i2 = *k2; + inc = 1; + } else if (*incx < 0) { + ix0 = (1 - *k2) * *incx + 1; + i1 = *k2; + i2 = *k1; + inc = -1; + } else { + return 0; + } + + n32 = *n / 32 << 5; + if (n32 != 0) { + i__1 = n32; + for (j = 1; j <= i__1; j += 32) { + ix = ix0; + i__2 = i2; + i__3 = inc; + for (i__ = i1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__3) + { + ip = ipiv[ix]; + if (ip != i__) { + i__4 = j + 31; + for (k = j; k <= i__4; ++k) { + temp = a[i__ + k * a_dim1]; + a[i__ + k * a_dim1] = a[ip + k * a_dim1]; + a[ip + k * a_dim1] = temp; +/* L10: */ + } + } + ix += *incx; +/* L20: */ + } +/* L30: */ + } + } + if (n32 != *n) { + ++n32; + ix = ix0; + i__1 = i2; + i__3 = inc; + for (i__ = i1; i__3 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__3) { + ip = ipiv[ix]; + if (ip != i__) { + i__2 = *n; + for (k = n32; k <= i__2; ++k) { + temp = a[i__ + k * a_dim1]; + a[i__ + k * a_dim1] = a[ip + k * a_dim1]; + a[ip + k * a_dim1] = temp; +/* L40: */ + } + } + ix += *incx; +/* L50: */ + } + } + + return 0; + +/* End of DLASWP */ + +} /* dlaswp_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/clapack/src/dtrti2.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,183 @@ +/* dtrti2.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* Subroutine */ int dtrti2_(char *uplo, char *diag, integer *n, doublereal * + a, integer *lda, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + + /* Local variables */ + integer j; + doublereal ajj; + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); + extern logical lsame_(char *, char *); + logical upper; + extern /* Subroutine */ int dtrmv_(char *, char *, char *, integer *, + doublereal *, integer *, doublereal *, integer *), xerbla_(char *, integer *); + logical nounit; + + +/* -- LAPACK routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* DTRTI2 computes the inverse of a real upper or lower triangular */ +/* matrix. */ + +/* This is the Level 2 BLAS version of the algorithm. */ + +/* Arguments */ +/* ========= */ + +/* UPLO (input) CHARACTER*1 */ +/* Specifies whether the matrix A is upper or lower triangular. */ +/* = 'U': Upper triangular */ +/* = 'L': Lower triangular */ + +/* DIAG (input) CHARACTER*1 */ +/* Specifies whether or not the matrix A is unit triangular. */ +/* = 'N': Non-unit triangular */ +/* = 'U': Unit triangular */ + +/* N (input) INTEGER */ +/* The order of the matrix A. N >= 0. */ + +/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */ +/* On entry, the triangular matrix A. If UPLO = 'U', the */ +/* leading n by n upper triangular part of the array A contains */ +/* the upper triangular matrix, and the strictly lower */ +/* triangular part of A is not referenced. If UPLO = 'L', the */ +/* leading n by n lower triangular part of the array A contains */ +/* the lower triangular matrix, and the strictly upper */ +/* triangular part of A is not referenced. If DIAG = 'U', the */ +/* diagonal elements of A are also not referenced and are */ +/* assumed to be 1. */ + +/* On exit, the (triangular) inverse of the original matrix, in */ +/* the same storage format. */ + +/* LDA (input) INTEGER */ +/* The leading dimension of the array A. LDA >= max(1,N). */ + +/* INFO (output) INTEGER */ +/* = 0: successful exit */ +/* < 0: if INFO = -k, the k-th argument had an illegal value */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + *info = 0; + upper = lsame_(uplo, "U"); + nounit = lsame_(diag, "N"); + if (! upper && ! lsame_(uplo, "L")) { + *info = -1; + } else if (! nounit && ! lsame_(diag, "U")) { + *info = -2; + } else if (*n < 0) { + *info = -3; + } else if (*lda < max(1,*n)) { + *info = -5; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_("DTRTI2", &i__1); + return 0; + } + + if (upper) { + +/* Compute inverse of upper triangular matrix. */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (nounit) { + a[j + j * a_dim1] = 1. / a[j + j * a_dim1]; + ajj = -a[j + j * a_dim1]; + } else { + ajj = -1.; + } + +/* Compute elements 1:j-1 of j-th column. */ + + i__2 = j - 1; + dtrmv_("Upper", "No transpose", diag, &i__2, &a[a_offset], lda, & + a[j * a_dim1 + 1], &c__1); + i__2 = j - 1; + dscal_(&i__2, &ajj, &a[j * a_dim1 + 1], &c__1); +/* L10: */ + } + } else { + +/* Compute inverse of lower triangular matrix. */ + + for (j = *n; j >= 1; --j) { + if (nounit) { + a[j + j * a_dim1] = 1. / a[j + j * a_dim1]; + ajj = -a[j + j * a_dim1]; + } else { + ajj = -1.; + } + if (j < *n) { + +/* Compute elements j+1:n of j-th column. */ + + i__1 = *n - j; + dtrmv_("Lower", "No transpose", diag, &i__1, &a[j + 1 + (j + + 1) * a_dim1], lda, &a[j + 1 + j * a_dim1], &c__1); + i__1 = *n - j; + dscal_(&i__1, &ajj, &a[j + 1 + j * a_dim1], &c__1); + } +/* L20: */ + } + } + + return 0; + +/* End of DTRTI2 */ + +} /* dtrti2_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/clapack/src/dtrtri.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,242 @@ +/* dtrtri.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__2 = 2; +static doublereal c_b18 = 1.; +static doublereal c_b22 = -1.; + +/* Subroutine */ int dtrtri_(char *uplo, char *diag, integer *n, doublereal * + a, integer *lda, integer *info) +{ + /* System generated locals */ + address a__1[2]; + integer a_dim1, a_offset, i__1, i__2[2], i__3, i__4, i__5; + char ch__1[2]; + + /* Builtin functions */ + /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + + /* Local variables */ + integer j, jb, nb, nn; + extern logical lsame_(char *, char *); + extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *), dtrsm_( + char *, char *, char *, char *, integer *, integer *, doublereal * +, doublereal *, integer *, doublereal *, integer *); + logical upper; + extern /* Subroutine */ int dtrti2_(char *, char *, integer *, doublereal + *, integer *, integer *), xerbla_(char *, integer + *); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *); + logical nounit; + + +/* -- LAPACK routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* DTRTRI computes the inverse of a real upper or lower triangular */ +/* matrix A. */ + +/* This is the Level 3 BLAS version of the algorithm. */ + +/* Arguments */ +/* ========= */ + +/* UPLO (input) CHARACTER*1 */ +/* = 'U': A is upper triangular; */ +/* = 'L': A is lower triangular. */ + +/* DIAG (input) CHARACTER*1 */ +/* = 'N': A is non-unit triangular; */ +/* = 'U': A is unit triangular. */ + +/* N (input) INTEGER */ +/* The order of the matrix A. N >= 0. */ + +/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */ +/* On entry, the triangular matrix A. If UPLO = 'U', the */ +/* leading N-by-N upper triangular part of the array A contains */ +/* the upper triangular matrix, and the strictly lower */ +/* triangular part of A is not referenced. If UPLO = 'L', the */ +/* leading N-by-N lower triangular part of the array A contains */ +/* the lower triangular matrix, and the strictly upper */ +/* triangular part of A is not referenced. If DIAG = 'U', the */ +/* diagonal elements of A are also not referenced and are */ +/* assumed to be 1. */ +/* On exit, the (triangular) inverse of the original matrix, in */ +/* the same storage format. */ + +/* LDA (input) INTEGER */ +/* The leading dimension of the array A. LDA >= max(1,N). */ + +/* INFO (output) INTEGER */ +/* = 0: successful exit */ +/* < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > 0: if INFO = i, A(i,i) is exactly zero. The triangular */ +/* matrix is singular and its inverse can not be computed. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + *info = 0; + upper = lsame_(uplo, "U"); + nounit = lsame_(diag, "N"); + if (! upper && ! lsame_(uplo, "L")) { + *info = -1; + } else if (! nounit && ! lsame_(diag, "U")) { + *info = -2; + } else if (*n < 0) { + *info = -3; + } else if (*lda < max(1,*n)) { + *info = -5; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_("DTRTRI", &i__1); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + +/* Check for singularity if non-unit. */ + + if (nounit) { + i__1 = *n; + for (*info = 1; *info <= i__1; ++(*info)) { + if (a[*info + *info * a_dim1] == 0.) { + return 0; + } +/* L10: */ + } + *info = 0; + } + +/* Determine the block size for this environment. */ + +/* Writing concatenation */ + i__2[0] = 1, a__1[0] = uplo; + i__2[1] = 1, a__1[1] = diag; + s_cat(ch__1, a__1, i__2, &c__2, (ftnlen)2); + nb = ilaenv_(&c__1, "DTRTRI", ch__1, n, &c_n1, &c_n1, &c_n1); + if (nb <= 1 || nb >= *n) { + +/* Use unblocked code */ + + dtrti2_(uplo, diag, n, &a[a_offset], lda, info); + } else { + +/* Use blocked code */ + + if (upper) { + +/* Compute inverse of upper triangular matrix */ + + i__1 = *n; + i__3 = nb; + for (j = 1; i__3 < 0 ? j >= i__1 : j <= i__1; j += i__3) { +/* Computing MIN */ + i__4 = nb, i__5 = *n - j + 1; + jb = min(i__4,i__5); + +/* Compute rows 1:j-1 of current block column */ + + i__4 = j - 1; + dtrmm_("Left", "Upper", "No transpose", diag, &i__4, &jb, & + c_b18, &a[a_offset], lda, &a[j * a_dim1 + 1], lda); + i__4 = j - 1; + dtrsm_("Right", "Upper", "No transpose", diag, &i__4, &jb, & + c_b22, &a[j + j * a_dim1], lda, &a[j * a_dim1 + 1], + lda); + +/* Compute inverse of current diagonal block */ + + dtrti2_("Upper", diag, &jb, &a[j + j * a_dim1], lda, info); +/* L20: */ + } + } else { + +/* Compute inverse of lower triangular matrix */ + + nn = (*n - 1) / nb * nb + 1; + i__3 = -nb; + for (j = nn; i__3 < 0 ? j >= 1 : j <= 1; j += i__3) { +/* Computing MIN */ + i__1 = nb, i__4 = *n - j + 1; + jb = min(i__1,i__4); + if (j + jb <= *n) { + +/* Compute rows j+jb:n of current block column */ + + i__1 = *n - j - jb + 1; + dtrmm_("Left", "Lower", "No transpose", diag, &i__1, &jb, + &c_b18, &a[j + jb + (j + jb) * a_dim1], lda, &a[j + + jb + j * a_dim1], lda); + i__1 = *n - j - jb + 1; + dtrsm_("Right", "Lower", "No transpose", diag, &i__1, &jb, + &c_b22, &a[j + j * a_dim1], lda, &a[j + jb + j * + a_dim1], lda); + } + +/* Compute inverse of current diagonal block */ + + dtrti2_("Lower", diag, &jb, &a[j + j * a_dim1], lda, info); +/* L30: */ + } + } + } + + return 0; + +/* End of DTRTRI */ + +} /* dtrtri_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/clapack/src/exit_.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,43 @@ +/* This gives the effect of + + subroutine exit(rc) + integer*4 rc + stop + end + + * with the added side effect of supplying rc as the program's exit code. + */ + +#include "f2c.h" +#undef abs +#undef min +#undef max +#ifndef KR_headers +#include "stdlib.h" +#ifdef __cplusplus +extern "C" { +#endif +#ifdef __cplusplus +extern "C" { +#endif +extern void f_exit(void); +#endif + + void +#ifdef KR_headers +exit_(rc) integer *rc; +#else +exit_(integer *rc) +#endif +{ +#ifdef NO_ONEXIT + f_exit(); +#endif + exit(*rc); + } +#ifdef __cplusplus +} +#endif +#ifdef __cplusplus +} +#endif
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/clapack/src/f77_aloc.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,44 @@ +#include "f2c.h" +#undef abs +#undef min +#undef max +#include "stdio.h" + +static integer memfailure = 3; + +#ifdef KR_headers +extern char *malloc(); +extern void exit_(); + + char * +F77_aloc(Len, whence) integer Len; char *whence; +#else +#include "stdlib.h" +#ifdef __cplusplus +extern "C" { +#endif +#ifdef __cplusplus +extern "C" { +#endif +extern void exit_(integer*); +#ifdef __cplusplus + } +#endif + + char * +F77_aloc(integer Len, const char *whence) +#endif +{ + char *rv; + unsigned int uLen = (unsigned int) Len; /* for K&R C */ + + if (!(rv = (char*)malloc(uLen))) { + fprintf(stderr, "malloc(%u) failure in %s\n", + uLen, whence); + exit_(&memfailure); + } + return rv; + } +#ifdef __cplusplus +} +#endif
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/clapack/src/i_nint.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,19 @@ +#include "f2c.h" + +#ifdef KR_headers +double floor(); +integer i_nint(x) real *x; +#else +#undef abs +#include "math.h" +#ifdef __cplusplus +extern "C" { +#endif +integer i_nint(real *x) +#endif +{ +return (integer)(*x >= 0 ? floor(*x + .5) : -floor(.5 - *x)); +} +#ifdef __cplusplus +} +#endif
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/clapack/src/ieeeck.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,166 @@ +/* ieeeck.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +integer ieeeck_(integer *ispec, real *zero, real *one) +{ + /* System generated locals */ + integer ret_val; + + /* Local variables */ + real nan1, nan2, nan3, nan4, nan5, nan6, neginf, posinf, negzro, newzro; + + +/* -- LAPACK auxiliary routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* IEEECK is called from the ILAENV to verify that Infinity and */ +/* possibly NaN arithmetic is safe (i.e. will not trap). */ + +/* Arguments */ +/* ========= */ + +/* ISPEC (input) INTEGER */ +/* Specifies whether to test just for inifinity arithmetic */ +/* or whether to test for infinity and NaN arithmetic. */ +/* = 0: Verify infinity arithmetic only. */ +/* = 1: Verify infinity and NaN arithmetic. */ + +/* ZERO (input) REAL */ +/* Must contain the value 0.0 */ +/* This is passed to prevent the compiler from optimizing */ +/* away this code. */ + +/* ONE (input) REAL */ +/* Must contain the value 1.0 */ +/* This is passed to prevent the compiler from optimizing */ +/* away this code. */ + +/* RETURN VALUE: INTEGER */ +/* = 0: Arithmetic failed to produce the correct answers */ +/* = 1: Arithmetic produced the correct answers */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. Executable Statements .. */ + ret_val = 1; + + posinf = *one / *zero; + if (posinf <= *one) { + ret_val = 0; + return ret_val; + } + + neginf = -(*one) / *zero; + if (neginf >= *zero) { + ret_val = 0; + return ret_val; + } + + negzro = *one / (neginf + *one); + if (negzro != *zero) { + ret_val = 0; + return ret_val; + } + + neginf = *one / negzro; + if (neginf >= *zero) { + ret_val = 0; + return ret_val; + } + + newzro = negzro + *zero; + if (newzro != *zero) { + ret_val = 0; + return ret_val; + } + + posinf = *one / newzro; + if (posinf <= *one) { + ret_val = 0; + return ret_val; + } + + neginf *= posinf; + if (neginf >= *zero) { + ret_val = 0; + return ret_val; + } + + posinf *= posinf; + if (posinf <= *one) { + ret_val = 0; + return ret_val; + } + + + + +/* Return if we were only asked to check infinity arithmetic */ + + if (*ispec == 0) { + return ret_val; + } + + nan1 = posinf + neginf; + + nan2 = posinf / neginf; + + nan3 = posinf / posinf; + + nan4 = posinf * *zero; + + nan5 = neginf * negzro; + + nan6 = nan5 * 0.f; + + if (nan1 == nan1) { + ret_val = 0; + return ret_val; + } + + if (nan2 == nan2) { + ret_val = 0; + return ret_val; + } + + if (nan3 == nan3) { + ret_val = 0; + return ret_val; + } + + if (nan4 == nan4) { + ret_val = 0; + return ret_val; + } + + if (nan5 == nan5) { + ret_val = 0; + return ret_val; + } + + if (nan6 == nan6) { + ret_val = 0; + return ret_val; + } + + return ret_val; +} /* ieeeck_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/clapack/src/ilaenv.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,642 @@ +#include "f2c.h" +#include "string.h" + +/* Table of constant values */ + +static integer c__0 = 0; +static real c_b163 = 0.f; +static real c_b164 = 1.f; +static integer c__1 = 1; + +integer ilaenv_(integer *ispec, char *name__, char *opts, integer *n1, + integer *n2, integer *n3, integer *n4) +{ + /* System generated locals */ + integer ret_val; + + /* Builtin functions */ + /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); + integer s_cmp(char *, char *, ftnlen, ftnlen); + + /* Local variables */ + static integer i__; + static char c1[1], c2[2], c3[3], c4[2]; + static integer ic, nb, iz, nx; + static logical cname; + static integer nbmin; + static logical sname; + extern integer ieeeck_(integer *, real *, real *); + static char subnam[6]; + extern integer iparmq_(integer *, char *, char *, integer *, integer *, + integer *, integer *); + + ftnlen name_len, opts_len; + + name_len = strlen (name__); + opts_len = strlen (opts); + + +/* -- LAPACK auxiliary routine (version 3.1.1) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* January 2007 */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* ILAENV is called from the LAPACK routines to choose problem-dependent */ +/* parameters for the local environment. See ISPEC for a description of */ +/* the parameters. */ + +/* ILAENV returns an INTEGER */ +/* if ILAENV >= 0: ILAENV returns the value of the parameter specified by ISPEC */ +/* if ILAENV < 0: if ILAENV = -k, the k-th argument had an illegal value. */ + +/* This version provides a set of parameters which should give good, */ +/* but not optimal, performance on many of the currently available */ +/* computers. Users are encouraged to modify this subroutine to set */ +/* the tuning parameters for their particular machine using the option */ +/* and problem size information in the arguments. */ + +/* This routine will not function correctly if it is converted to all */ +/* lower case. Converting it to all upper case is allowed. */ + +/* Arguments */ +/* ========= */ + +/* ISPEC (input) INTEGER */ +/* Specifies the parameter to be returned as the value of */ +/* ILAENV. */ +/* = 1: the optimal blocksize; if this value is 1, an unblocked */ +/* algorithm will give the best performance. */ +/* = 2: the minimum block size for which the block routine */ +/* should be used; if the usable block size is less than */ +/* this value, an unblocked routine should be used. */ +/* = 3: the crossover point (in a block routine, for N less */ +/* than this value, an unblocked routine should be used) */ +/* = 4: the number of shifts, used in the nonsymmetric */ +/* eigenvalue routines (DEPRECATED) */ +/* = 5: the minimum column dimension for blocking to be used; */ +/* rectangular blocks must have dimension at least k by m, */ +/* where k is given by ILAENV(2,...) and m by ILAENV(5,...) */ +/* = 6: the crossover point for the SVD (when reducing an m by n */ +/* matrix to bidiagonal form, if max(m,n)/min(m,n) exceeds */ +/* this value, a QR factorization is used first to reduce */ +/* the matrix to a triangular form.) */ +/* = 7: the number of processors */ +/* = 8: the crossover point for the multishift QR method */ +/* for nonsymmetric eigenvalue problems (DEPRECATED) */ +/* = 9: maximum size of the subproblems at the bottom of the */ +/* computation tree in the divide-and-conquer algorithm */ +/* (used by xGELSD and xGESDD) */ +/* =10: ieee NaN arithmetic can be trusted not to trap */ +/* =11: infinity arithmetic can be trusted not to trap */ +/* 12 <= ISPEC <= 16: */ +/* xHSEQR or one of its subroutines, */ +/* see IPARMQ for detailed explanation */ + +/* NAME (input) CHARACTER*(*) */ +/* The name of the calling subroutine, in either upper case or */ +/* lower case. */ + +/* OPTS (input) CHARACTER*(*) */ +/* The character options to the subroutine NAME, concatenated */ +/* into a single character string. For example, UPLO = 'U', */ +/* TRANS = 'T', and DIAG = 'N' for a triangular routine would */ +/* be specified as OPTS = 'UTN'. */ + +/* N1 (input) INTEGER */ +/* N2 (input) INTEGER */ +/* N3 (input) INTEGER */ +/* N4 (input) INTEGER */ +/* Problem dimensions for the subroutine NAME; these may not all */ +/* be required. */ + +/* Further Details */ +/* =============== */ + +/* The following conventions have been used when calling ILAENV from the */ +/* LAPACK routines: */ +/* 1) OPTS is a concatenation of all of the character options to */ +/* subroutine NAME, in the same order that they appear in the */ +/* argument list for NAME, even if they are not used in determining */ +/* the value of the parameter specified by ISPEC. */ +/* 2) The problem dimensions N1, N2, N3, N4 are specified in the order */ +/* that they appear in the argument list for NAME. N1 is used */ +/* first, N2 second, and so on, and unused problem dimensions are */ +/* passed a value of -1. */ +/* 3) The parameter value returned by ILAENV is checked for validity in */ +/* the calling subroutine. For example, ILAENV is used to retrieve */ +/* the optimal blocksize for STRTRI as follows: */ + +/* NB = ILAENV( 1, 'STRTRI', UPLO // DIAG, N, -1, -1, -1 ) */ +/* IF( NB.LE.1 ) NB = MAX( 1, N ) */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + switch (*ispec) { + case 1: goto L10; + case 2: goto L10; + case 3: goto L10; + case 4: goto L80; + case 5: goto L90; + case 6: goto L100; + case 7: goto L110; + case 8: goto L120; + case 9: goto L130; + case 10: goto L140; + case 11: goto L150; + case 12: goto L160; + case 13: goto L160; + case 14: goto L160; + case 15: goto L160; + case 16: goto L160; + } + +/* Invalid value for ISPEC */ + + ret_val = -1; + return ret_val; + +L10: + +/* Convert NAME to upper case if the first character is lower case. */ + + ret_val = 1; + s_copy(subnam, name__, (ftnlen)6, name_len); + ic = *(unsigned char *)subnam; + iz = 'Z'; + if (iz == 90 || iz == 122) { + +/* ASCII character set */ + + if (ic >= 97 && ic <= 122) { + *(unsigned char *)subnam = (char) (ic - 32); + for (i__ = 2; i__ <= 6; ++i__) { + ic = *(unsigned char *)&subnam[i__ - 1]; + if (ic >= 97 && ic <= 122) { + *(unsigned char *)&subnam[i__ - 1] = (char) (ic - 32); + } +/* L20: */ + } + } + + } else if (iz == 233 || iz == 169) { + +/* EBCDIC character set */ + + if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || ic >= 162 && + ic <= 169) { + *(unsigned char *)subnam = (char) (ic + 64); + for (i__ = 2; i__ <= 6; ++i__) { + ic = *(unsigned char *)&subnam[i__ - 1]; + if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || ic >= + 162 && ic <= 169) { + *(unsigned char *)&subnam[i__ - 1] = (char) (ic + 64); + } +/* L30: */ + } + } + + } else if (iz == 218 || iz == 250) { + +/* Prime machines: ASCII+128 */ + + if (ic >= 225 && ic <= 250) { + *(unsigned char *)subnam = (char) (ic - 32); + for (i__ = 2; i__ <= 6; ++i__) { + ic = *(unsigned char *)&subnam[i__ - 1]; + if (ic >= 225 && ic <= 250) { + *(unsigned char *)&subnam[i__ - 1] = (char) (ic - 32); + } +/* L40: */ + } + } + } + + *(unsigned char *)c1 = *(unsigned char *)subnam; + sname = *(unsigned char *)c1 == 'S' || *(unsigned char *)c1 == 'D'; + cname = *(unsigned char *)c1 == 'C' || *(unsigned char *)c1 == 'Z'; + if (! (cname || sname)) { + return ret_val; + } + s_copy(c2, subnam + 1, (ftnlen)2, (ftnlen)2); + s_copy(c3, subnam + 3, (ftnlen)3, (ftnlen)3); + s_copy(c4, c3 + 1, (ftnlen)2, (ftnlen)2); + + switch (*ispec) { + case 1: goto L50; + case 2: goto L60; + case 3: goto L70; + } + +L50: + +/* ISPEC = 1: block size */ + +/* In these examples, separate code is provided for setting NB for */ +/* real and complex. We assume that NB will take the same value in */ +/* single or double precision. */ + + nb = 1; + + if (s_cmp(c2, "GE", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, "TRF", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 64; + } else { + nb = 64; + } + } else if (s_cmp(c3, "QRF", (ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, + "RQF", (ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, "LQF", (ftnlen) + 3, (ftnlen)3) == 0 || s_cmp(c3, "QLF", (ftnlen)3, (ftnlen)3) + == 0) { + if (sname) { + nb = 32; + } else { + nb = 32; + } + } else if (s_cmp(c3, "HRD", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 32; + } else { + nb = 32; + } + } else if (s_cmp(c3, "BRD", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 32; + } else { + nb = 32; + } + } else if (s_cmp(c3, "TRI", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 64; + } else { + nb = 64; + } + } + } else if (s_cmp(c2, "PO", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, "TRF", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 64; + } else { + nb = 64; + } + } + } else if (s_cmp(c2, "SY", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, "TRF", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 64; + } else { + nb = 64; + } + } else if (sname && s_cmp(c3, "TRD", (ftnlen)3, (ftnlen)3) == 0) { + nb = 32; + } else if (sname && s_cmp(c3, "GST", (ftnlen)3, (ftnlen)3) == 0) { + nb = 64; + } + } else if (cname && s_cmp(c2, "HE", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, "TRF", (ftnlen)3, (ftnlen)3) == 0) { + nb = 64; + } else if (s_cmp(c3, "TRD", (ftnlen)3, (ftnlen)3) == 0) { + nb = 32; + } else if (s_cmp(c3, "GST", (ftnlen)3, (ftnlen)3) == 0) { + nb = 64; + } + } else if (sname && s_cmp(c2, "OR", (ftnlen)2, (ftnlen)2) == 0) { + if (*(unsigned char *)c3 == 'G') { + if (s_cmp(c4, "QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, "QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, "HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, "TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nb = 32; + } + } else if (*(unsigned char *)c3 == 'M') { + if (s_cmp(c4, "QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, "QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, "HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, "TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nb = 32; + } + } + } else if (cname && s_cmp(c2, "UN", (ftnlen)2, (ftnlen)2) == 0) { + if (*(unsigned char *)c3 == 'G') { + if (s_cmp(c4, "QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, "QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, "HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, "TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nb = 32; + } + } else if (*(unsigned char *)c3 == 'M') { + if (s_cmp(c4, "QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, "QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, "HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, "TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nb = 32; + } + } + } else if (s_cmp(c2, "GB", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, "TRF", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + if (*n4 <= 64) { + nb = 1; + } else { + nb = 32; + } + } else { + if (*n4 <= 64) { + nb = 1; + } else { + nb = 32; + } + } + } + } else if (s_cmp(c2, "PB", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, "TRF", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + if (*n2 <= 64) { + nb = 1; + } else { + nb = 32; + } + } else { + if (*n2 <= 64) { + nb = 1; + } else { + nb = 32; + } + } + } + } else if (s_cmp(c2, "TR", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, "TRI", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 64; + } else { + nb = 64; + } + } + } else if (s_cmp(c2, "LA", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, "UUM", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 64; + } else { + nb = 64; + } + } + } else if (sname && s_cmp(c2, "ST", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, "EBZ", (ftnlen)3, (ftnlen)3) == 0) { + nb = 1; + } + } + ret_val = nb; + return ret_val; + +L60: + +/* ISPEC = 2: minimum block size */ + + nbmin = 2; + if (s_cmp(c2, "GE", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, "QRF", (ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, "RQF", ( + ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, "LQF", (ftnlen)3, ( + ftnlen)3) == 0 || s_cmp(c3, "QLF", (ftnlen)3, (ftnlen)3) == 0) + { + if (sname) { + nbmin = 2; + } else { + nbmin = 2; + } + } else if (s_cmp(c3, "HRD", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nbmin = 2; + } else { + nbmin = 2; + } + } else if (s_cmp(c3, "BRD", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nbmin = 2; + } else { + nbmin = 2; + } + } else if (s_cmp(c3, "TRI", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nbmin = 2; + } else { + nbmin = 2; + } + } + } else if (s_cmp(c2, "SY", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, "TRF", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nbmin = 8; + } else { + nbmin = 8; + } + } else if (sname && s_cmp(c3, "TRD", (ftnlen)3, (ftnlen)3) == 0) { + nbmin = 2; + } + } else if (cname && s_cmp(c2, "HE", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, "TRD", (ftnlen)3, (ftnlen)3) == 0) { + nbmin = 2; + } + } else if (sname && s_cmp(c2, "OR", (ftnlen)2, (ftnlen)2) == 0) { + if (*(unsigned char *)c3 == 'G') { + if (s_cmp(c4, "QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, "QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, "HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, "TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nbmin = 2; + } + } else if (*(unsigned char *)c3 == 'M') { + if (s_cmp(c4, "QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, "QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, "HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, "TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nbmin = 2; + } + } + } else if (cname && s_cmp(c2, "UN", (ftnlen)2, (ftnlen)2) == 0) { + if (*(unsigned char *)c3 == 'G') { + if (s_cmp(c4, "QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, "QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, "HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, "TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nbmin = 2; + } + } else if (*(unsigned char *)c3 == 'M') { + if (s_cmp(c4, "QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, "QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, "HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, "TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nbmin = 2; + } + } + } + ret_val = nbmin; + return ret_val; + +L70: + +/* ISPEC = 3: crossover point */ + + nx = 0; + if (s_cmp(c2, "GE", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, "QRF", (ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, "RQF", ( + ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, "LQF", (ftnlen)3, ( + ftnlen)3) == 0 || s_cmp(c3, "QLF", (ftnlen)3, (ftnlen)3) == 0) + { + if (sname) { + nx = 128; + } else { + nx = 128; + } + } else if (s_cmp(c3, "HRD", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nx = 128; + } else { + nx = 128; + } + } else if (s_cmp(c3, "BRD", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nx = 128; + } else { + nx = 128; + } + } + } else if (s_cmp(c2, "SY", (ftnlen)2, (ftnlen)2) == 0) { + if (sname && s_cmp(c3, "TRD", (ftnlen)3, (ftnlen)3) == 0) { + nx = 32; + } + } else if (cname && s_cmp(c2, "HE", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, "TRD", (ftnlen)3, (ftnlen)3) == 0) { + nx = 32; + } + } else if (sname && s_cmp(c2, "OR", (ftnlen)2, (ftnlen)2) == 0) { + if (*(unsigned char *)c3 == 'G') { + if (s_cmp(c4, "QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, "QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, "HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, "TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nx = 128; + } + } + } else if (cname && s_cmp(c2, "UN", (ftnlen)2, (ftnlen)2) == 0) { + if (*(unsigned char *)c3 == 'G') { + if (s_cmp(c4, "QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, "QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, "HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, "TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, "BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nx = 128; + } + } + } + ret_val = nx; + return ret_val; + +L80: + +/* ISPEC = 4: number of shifts (used by xHSEQR) */ + + ret_val = 6; + return ret_val; + +L90: + +/* ISPEC = 5: minimum column dimension (not used) */ + + ret_val = 2; + return ret_val; + +L100: + +/* ISPEC = 6: crossover point for SVD (used by xGELSS and xGESVD) */ + + ret_val = (integer) ((real) min(*n1,*n2) * 1.6f); + return ret_val; + +L110: + +/* ISPEC = 7: number of processors (not used) */ + + ret_val = 1; + return ret_val; + +L120: + +/* ISPEC = 8: crossover point for multishift (used by xHSEQR) */ + + ret_val = 50; + return ret_val; + +L130: + +/* ISPEC = 9: maximum size of the subproblems at the bottom of the */ +/* computation tree in the divide-and-conquer algorithm */ +/* (used by xGELSD and xGESDD) */ + + ret_val = 25; + return ret_val; + +L140: + +/* ISPEC = 10: ieee NaN arithmetic can be trusted not to trap */ + +/* ILAENV = 0 */ + ret_val = 1; + if (ret_val == 1) { + ret_val = ieeeck_(&c__0, &c_b163, &c_b164); + } + return ret_val; + +L150: + +/* ISPEC = 11: infinity arithmetic can be trusted not to trap */ + +/* ILAENV = 0 */ + ret_val = 1; + if (ret_val == 1) { + ret_val = ieeeck_(&c__1, &c_b163, &c_b164); + } + return ret_val; + +L160: + +/* 12 <= ISPEC <= 16: xHSEQR or one of its subroutines. */ + + ret_val = iparmq_(ispec, name__, opts, n1, n2, n3, n4) + ; + return ret_val; + +/* End of ILAENV */ + +} /* ilaenv_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/clapack/src/iparmq.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,282 @@ +/* iparmq.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer + *ilo, integer *ihi, integer *lwork) +{ + /* System generated locals */ + integer ret_val, i__1, i__2; + real r__1; + + /* Builtin functions */ + double log(doublereal); + integer i_nint(real *); + + /* Local variables */ + integer nh, ns; + + +/* -- LAPACK auxiliary routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ + +/* Purpose */ +/* ======= */ + +/* This program sets problem and machine dependent parameters */ +/* useful for xHSEQR and its subroutines. It is called whenever */ +/* ILAENV is called with 12 <= ISPEC <= 16 */ + +/* Arguments */ +/* ========= */ + +/* ISPEC (input) integer scalar */ +/* ISPEC specifies which tunable parameter IPARMQ should */ +/* return. */ + +/* ISPEC=12: (INMIN) Matrices of order nmin or less */ +/* are sent directly to xLAHQR, the implicit */ +/* double shift QR algorithm. NMIN must be */ +/* at least 11. */ + +/* ISPEC=13: (INWIN) Size of the deflation window. */ +/* This is best set greater than or equal to */ +/* the number of simultaneous shifts NS. */ +/* Larger matrices benefit from larger deflation */ +/* windows. */ + +/* ISPEC=14: (INIBL) Determines when to stop nibbling and */ +/* invest in an (expensive) multi-shift QR sweep. */ +/* If the aggressive early deflation subroutine */ +/* finds LD converged eigenvalues from an order */ +/* NW deflation window and LD.GT.(NW*NIBBLE)/100, */ +/* then the next QR sweep is skipped and early */ +/* deflation is applied immediately to the */ +/* remaining active diagonal block. Setting */ +/* IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a */ +/* multi-shift QR sweep whenever early deflation */ +/* finds a converged eigenvalue. Setting */ +/* IPARMQ(ISPEC=14) greater than or equal to 100 */ +/* prevents TTQRE from skipping a multi-shift */ +/* QR sweep. */ + +/* ISPEC=15: (NSHFTS) The number of simultaneous shifts in */ +/* a multi-shift QR iteration. */ + +/* ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the */ +/* following meanings. */ +/* 0: During the multi-shift QR sweep, */ +/* xLAQR5 does not accumulate reflections and */ +/* does not use matrix-matrix multiply to */ +/* update the far-from-diagonal matrix */ +/* entries. */ +/* 1: During the multi-shift QR sweep, */ +/* xLAQR5 and/or xLAQRaccumulates reflections and uses */ +/* matrix-matrix multiply to update the */ +/* far-from-diagonal matrix entries. */ +/* 2: During the multi-shift QR sweep. */ +/* xLAQR5 accumulates reflections and takes */ +/* advantage of 2-by-2 block structure during */ +/* matrix-matrix multiplies. */ +/* (If xTRMM is slower than xGEMM, then */ +/* IPARMQ(ISPEC=16)=1 may be more efficient than */ +/* IPARMQ(ISPEC=16)=2 despite the greater level of */ +/* arithmetic work implied by the latter choice.) */ + +/* NAME (input) character string */ +/* Name of the calling subroutine */ + +/* OPTS (input) character string */ +/* This is a concatenation of the string arguments to */ +/* TTQRE. */ + +/* N (input) integer scalar */ +/* N is the order of the Hessenberg matrix H. */ + +/* ILO (input) INTEGER */ +/* IHI (input) INTEGER */ +/* It is assumed that H is already upper triangular */ +/* in rows and columns 1:ILO-1 and IHI+1:N. */ + +/* LWORK (input) integer scalar */ +/* The amount of workspace available. */ + +/* Further Details */ +/* =============== */ + +/* Little is known about how best to choose these parameters. */ +/* It is possible to use different values of the parameters */ +/* for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR. */ + +/* It is probably best to choose different parameters for */ +/* different matrices and different parameters at different */ +/* times during the iteration, but this has not been */ +/* implemented --- yet. */ + + +/* The best choices of most of the parameters depend */ +/* in an ill-understood way on the relative execution */ +/* rate of xLAQR3 and xLAQR5 and on the nature of each */ +/* particular eigenvalue problem. Experiment may be the */ +/* only practical way to determine which choices are most */ +/* effective. */ + +/* Following is a list of default values supplied by IPARMQ. */ +/* These defaults may be adjusted in order to attain better */ +/* performance in any particular computational environment. */ + +/* IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point. */ +/* Default: 75. (Must be at least 11.) */ + +/* IPARMQ(ISPEC=13) Recommended deflation window size. */ +/* This depends on ILO, IHI and NS, the */ +/* number of simultaneous shifts returned */ +/* by IPARMQ(ISPEC=15). The default for */ +/* (IHI-ILO+1).LE.500 is NS. The default */ +/* for (IHI-ILO+1).GT.500 is 3*NS/2. */ + +/* IPARMQ(ISPEC=14) Nibble crossover point. Default: 14. */ + +/* IPARMQ(ISPEC=15) Number of simultaneous shifts, NS. */ +/* a multi-shift QR iteration. */ + +/* If IHI-ILO+1 is ... */ + +/* greater than ...but less ... the */ +/* or equal to ... than default is */ + +/* 0 30 NS = 2+ */ +/* 30 60 NS = 4+ */ +/* 60 150 NS = 10 */ +/* 150 590 NS = ** */ +/* 590 3000 NS = 64 */ +/* 3000 6000 NS = 128 */ +/* 6000 infinity NS = 256 */ + +/* (+) By default matrices of this order are */ +/* passed to the implicit double shift routine */ +/* xLAHQR. See IPARMQ(ISPEC=12) above. These */ +/* values of NS are used only in case of a rare */ +/* xLAHQR failure. */ + +/* (**) The asterisks (**) indicate an ad-hoc */ +/* function increasing from 10 to 64. */ + +/* IPARMQ(ISPEC=16) Select structured matrix multiply. */ +/* (See ISPEC=16 above for details.) */ +/* Default: 3. */ + +/* ================================================================ */ +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + if (*ispec == 15 || *ispec == 13 || *ispec == 16) { + +/* ==== Set the number simultaneous shifts ==== */ + + nh = *ihi - *ilo + 1; + ns = 2; + if (nh >= 30) { + ns = 4; + } + if (nh >= 60) { + ns = 10; + } + if (nh >= 150) { +/* Computing MAX */ + r__1 = log((real) nh) / log(2.f); + i__1 = 10, i__2 = nh / i_nint(&r__1); + ns = max(i__1,i__2); + } + if (nh >= 590) { + ns = 64; + } + if (nh >= 3000) { + ns = 128; + } + if (nh >= 6000) { + ns = 256; + } +/* Computing MAX */ + i__1 = 2, i__2 = ns - ns % 2; + ns = max(i__1,i__2); + } + + if (*ispec == 12) { + + +/* ===== Matrices of order smaller than NMIN get sent */ +/* . to xLAHQR, the classic double shift algorithm. */ +/* . This must be at least 11. ==== */ + + ret_val = 75; + + } else if (*ispec == 14) { + +/* ==== INIBL: skip a multi-shift qr iteration and */ +/* . whenever aggressive early deflation finds */ +/* . at least (NIBBLE*(window size)/100) deflations. ==== */ + + ret_val = 14; + + } else if (*ispec == 15) { + +/* ==== NSHFTS: The number of simultaneous shifts ===== */ + + ret_val = ns; + + } else if (*ispec == 13) { + +/* ==== NW: deflation window size. ==== */ + + if (nh <= 500) { + ret_val = ns; + } else { + ret_val = ns * 3 / 2; + } + + } else if (*ispec == 16) { + +/* ==== IACC22: Whether to accumulate reflections */ +/* . before updating the far-from-diagonal elements */ +/* . and whether to use 2-by-2 block structure while */ +/* . doing it. A small amount of work could be saved */ +/* . by making this choice dependent also upon the */ +/* . NH=IHI-ILO+1. */ + + ret_val = 0; + if (ns >= 14) { + ret_val = 1; + } + if (ns >= 14) { + ret_val = 2; + } + + } else { +/* ===== invalid value of ispec ===== */ + ret_val = -1; + + } + +/* ==== End of IPARMQ ==== */ + + return ret_val; +} /* iparmq_ */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/clapack/src/pow_di.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,41 @@ +#include "f2c.h" +#ifdef __cplusplus +extern "C" { +#endif + +#ifdef KR_headers +double pow_di(ap, bp) doublereal *ap; integer *bp; +#else +double pow_di(doublereal *ap, integer *bp) +#endif +{ +double pow, x; +integer n; +unsigned long u; + +pow = 1; +x = *ap; +n = *bp; + +if(n != 0) + { + if(n < 0) + { + n = -n; + x = 1/x; + } + for(u = n; ; ) + { + if(u & 01) + pow *= x; + if(u >>= 1) + x *= x; + else + break; + } + } +return(pow); +} +#ifdef __cplusplus +} +#endif
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/clapack/src/s_cat.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,86 @@ +/* Unless compiled with -DNO_OVERWRITE, this variant of s_cat allows the + * target of a concatenation to appear on its right-hand side (contrary + * to the Fortran 77 Standard, but in accordance with Fortran 90). + */ + +#include "f2c.h" +#ifndef NO_OVERWRITE +#include "stdio.h" +#undef abs +#ifdef KR_headers + extern char *F77_aloc(); + extern void free(); + extern void exit_(); +#else +#undef min +#undef max +#include "stdlib.h" +extern +#ifdef __cplusplus + "C" +#endif + char *F77_aloc(ftnlen, const char*); +#endif +#include "string.h" +#endif /* NO_OVERWRITE */ + +#ifdef __cplusplus +extern "C" { +#endif + + VOID +#ifdef KR_headers +s_cat(lp, rpp, rnp, np, ll) char *lp, *rpp[]; ftnint rnp[], *np; ftnlen ll; +#else +s_cat(char *lp, char *rpp[], ftnint rnp[], ftnint *np, ftnlen ll) +#endif +{ + ftnlen i, nc; + char *rp; + ftnlen n = *np; +#ifndef NO_OVERWRITE + ftnlen L, m; + char *lp0, *lp1; + + lp0 = 0; + lp1 = lp; + L = ll; + i = 0; + while(i < n) { + rp = rpp[i]; + m = rnp[i++]; + if (rp >= lp1 || rp + m <= lp) { + if ((L -= m) <= 0) { + n = i; + break; + } + lp1 += m; + continue; + } + lp0 = lp; + lp = lp1 = F77_aloc(L = ll, "s_cat"); + break; + } + lp1 = lp; +#endif /* NO_OVERWRITE */ + for(i = 0 ; i < n ; ++i) { + nc = ll; + if(rnp[i] < nc) + nc = rnp[i]; + ll -= nc; + rp = rpp[i]; + while(--nc >= 0) + *lp++ = *rp++; + } + while(--ll >= 0) + *lp++ = ' '; +#ifndef NO_OVERWRITE + if (lp0) { + memcpy(lp0, lp1, L); + free(lp1); + } +#endif + } +#ifdef __cplusplus +} +#endif
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/clapack/src/s_cmp.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,50 @@ +#include "f2c.h" +#ifdef __cplusplus +extern "C" { +#endif + +/* compare two strings */ + +#ifdef KR_headers +integer s_cmp(a0, b0, la, lb) char *a0, *b0; ftnlen la, lb; +#else +integer s_cmp(char *a0, char *b0, ftnlen la, ftnlen lb) +#endif +{ +register unsigned char *a, *aend, *b, *bend; +a = (unsigned char *)a0; +b = (unsigned char *)b0; +aend = a + la; +bend = b + lb; + +if(la <= lb) + { + while(a < aend) + if(*a != *b) + return( *a - *b ); + else + { ++a; ++b; } + + while(b < bend) + if(*b != ' ') + return( ' ' - *b ); + else ++b; + } + +else + { + while(b < bend) + if(*a == *b) + { ++a; ++b; } + else + return( *a - *b ); + while(a < aend) + if(*a != ' ') + return(*a - ' '); + else ++a; + } +return(0); +} +#ifdef __cplusplus +} +#endif
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/clapack/src/s_copy.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,57 @@ +/* Unless compiled with -DNO_OVERWRITE, this variant of s_copy allows the + * target of an assignment to appear on its right-hand side (contrary + * to the Fortran 77 Standard, but in accordance with Fortran 90), + * as in a(2:5) = a(4:7) . + */ + +#include "f2c.h" +#ifdef __cplusplus +extern "C" { +#endif + +/* assign strings: a = b */ + +#ifdef KR_headers +VOID s_copy(a, b, la, lb) register char *a, *b; ftnlen la, lb; +#else +void s_copy(register char *a, register char *b, ftnlen la, ftnlen lb) +#endif +{ + register char *aend, *bend; + + aend = a + la; + + if(la <= lb) +#ifndef NO_OVERWRITE + if (a <= b || a >= b + la) +#endif + while(a < aend) + *a++ = *b++; +#ifndef NO_OVERWRITE + else + for(b += la; a < aend; ) + *--aend = *--b; +#endif + + else { + bend = b + lb; +#ifndef NO_OVERWRITE + if (a <= b || a >= bend) +#endif + while(b < bend) + *a++ = *b++; +#ifndef NO_OVERWRITE + else { + a += lb; + while(b < bend) + *--a = *--bend; + a += lb; + } +#endif + while(a < aend) + *a++ = ' '; + } + } +#ifdef __cplusplus +} +#endif
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ext/clapack/src/xerbla.c Fri Sep 30 16:24:24 2016 +0100 @@ -0,0 +1,65 @@ +/* xerbla.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" +#include "stdio.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* Subroutine */ int xerbla_(char *srname, integer *info) +{ + + +/* -- LAPACK auxiliary routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* XERBLA is an error handler for the LAPACK routines. */ +/* It is called by an LAPACK routine if an input parameter has an */ +/* invalid value. A message is printed and execution stops. */ + +/* Installers may consider modifying the STOP statement in order to */ +/* call system-specific exception-handling facilities. */ + +/* Arguments */ +/* ========= */ + +/* SRNAME (input) CHARACTER*(*) */ +/* The name of the routine which called XERBLA. */ + +/* INFO (input) INTEGER */ +/* The position of the invalid parameter in the parameter list */ +/* of the calling routine. */ + +/* ===================================================================== */ + +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + printf("** On entry to %6s, parameter number %2i had an illegal value\n", + srname, *info); + + +/* End of XERBLA */ + + return 0; +} /* xerbla_ */
--- a/maths/Polyfit.h Thu May 26 14:17:00 2016 +0100 +++ b/maths/Polyfit.h Fri Sep 30 16:24:24 2016 +0100 @@ -292,7 +292,7 @@ double big, t; double pivot; double determ; - int irow, icol; + int irow = 0, icol = 0; int ncol(b.size()); int nv = 1; // single constant vector for(int i = 0; i < ncol; ++i)