From 13dfe14e171941b3ca82cd858973e3681d7b254e Mon Sep 17 00:00:00 2001 From: Alberto Ruiz Date: Sun, 30 Sep 2007 10:38:59 +0000 Subject: move LAPACK under LinearAlgebra --- lib/LinearAlgebra/LAPACK/clapack.h | 5079 +++++++++++++++++++++++++++++++++ lib/LinearAlgebra/LAPACK/f2c.h | 223 ++ lib/LinearAlgebra/LAPACK/lapack-aux.c | 656 +++++ lib/LinearAlgebra/LAPACK/lapack-aux.h | 46 + 4 files changed, 6004 insertions(+) create mode 100644 lib/LinearAlgebra/LAPACK/clapack.h create mode 100644 lib/LinearAlgebra/LAPACK/f2c.h create mode 100644 lib/LinearAlgebra/LAPACK/lapack-aux.c create mode 100644 lib/LinearAlgebra/LAPACK/lapack-aux.h (limited to 'lib/LinearAlgebra/LAPACK') diff --git a/lib/LinearAlgebra/LAPACK/clapack.h b/lib/LinearAlgebra/LAPACK/clapack.h new file mode 100644 index 0000000..cad9a4c --- /dev/null +++ b/lib/LinearAlgebra/LAPACK/clapack.h @@ -0,0 +1,5079 @@ +#ifndef __CLAPACK_H +#define __CLAPACK_H + +/* 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 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 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 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 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 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 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 cgesv_(integer *n, integer *nrhs, complex *a, integer * + lda, integer *ipiv, complex *b, integer *ldb, 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 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 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 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 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 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 chgeqz_(char *job, char *compq, char *compz, integer *n, + integer *ilo, integer *ihi, complex *a, integer *lda, complex *b, + integer *ldb, complex *alpha, complex *beta, complex *q, integer *ldq, + complex *z__, integer *ldz, complex *work, integer *lwork, real * + rwork, integer *info); + +/* 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 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 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); + +/* 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 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 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 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 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 * + sigma, real *d__, real *l, real *ld, real *lld, real *gersch, complex + *z__, real *ztz, real *mingma, integer *r__, integer *isuppz, 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 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 *d__, real *l, integer *isplit, + integer *m, real *w, integer *iblock, real *gersch, real *tol, + complex *z__, integer *ldz, integer *isuppz, real *work, integer * + iwork, integer *info); + +/* 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 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 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 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 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 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 cptcon_(integer *n, real *d__, complex *e, real *anorm, + real *rcond, real *rwork, 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 csrot_(integer *n, complex *cx, integer *incx, complex * + cy, integer *incy, real *c__, real *s); + +/* 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 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 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 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 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 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 ctgevc_(char *side, char *howmny, logical *select, + integer *n, complex *a, integer *lda, complex *b, integer *ldb, + 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 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 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 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 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 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 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 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 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 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 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 + delctg, 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 + delctg, 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 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 *a, integer *lda, doublereal * + b, integer *ldb, 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); + +/* 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 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 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 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__); + +/* 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 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); + +/* Subroutine */ int dlamc4_(integer *emin, doublereal *start, integer *base); + +/* Subroutine */ int dlamc5_(integer *beta, integer *p, integer *emin, + logical *ieee, integer *emax, doublereal *rmax); + +/* Subroutine */ int dlamrg_(integer *n1, integer *n2, doublereal *a, integer + *dtrd1, integer *dtrd2, integer *index); + +/* 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); + +/* 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 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 + *sigma, doublereal *d__, doublereal *l, doublereal *ld, doublereal * + lld, doublereal *gersch, doublereal *z__, doublereal *ztz, doublereal + *mingma, integer *r__, integer *isuppz, 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 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 dlarrb_(integer *n, doublereal *d__, doublereal *l, + doublereal *ld, doublereal *lld, integer *ifirst, integer *ilast, + doublereal *sigma, doublereal *reltol, doublereal *w, doublereal * + wgap, doublereal *werr, doublereal *work, integer *iwork, integer * + info); + +/* Subroutine */ int dlarre_(integer *n, doublereal *d__, doublereal *e, + doublereal *tol, integer *nsplit, integer *isplit, integer *m, + doublereal *w, doublereal *woff, doublereal *gersch, doublereal *work, + integer *info); + +/* Subroutine */ int dlarrf_(integer *n, doublereal *d__, doublereal *l, + doublereal *ld, doublereal *lld, integer *ifirst, integer *ilast, + doublereal *w, doublereal *dplus, doublereal *lplus, doublereal *work, + integer *iwork, integer *info); + +/* Subroutine */ int dlarrv_(integer *n, doublereal *d__, doublereal *l, + integer *isplit, integer *m, doublereal *w, integer *iblock, + doublereal *gersch, doublereal *tol, doublereal *z__, integer *ldz, + integer *isuppz, doublereal *work, integer *iwork, integer *info); + +/* 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 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 dlasd9_(integer *icompq, integer *ldu, integer *k, + doublereal *d__, doublereal *z__, doublereal *vf, doublereal *vl, + doublereal *difl, doublereal *difr, 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); + +/* 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); + +/* 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 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 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 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 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 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 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 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 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 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 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 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 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 dtgevc_(char *side, char *howmny, logical *select, + integer *n, doublereal *a, integer *lda, doublereal *b, integer *ldb, + 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 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 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); + +integer icmax1_(integer *n, complex *cx, integer *incx); + +integer ieeeck_(integer *ispec, real *zero, real *one); + +integer ilaenv_(integer *ispec, char *name__, char *opts, integer *n1, + integer *n2, integer *n3, integer *n4, ftnlen name_len, ftnlen + opts_len); + +integer izmax1_(integer *n, doublecomplex *cx, integer *incx); + +/* 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); + +/* 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 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 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 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 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 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 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 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 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 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 *a, integer *lda, real *b, integer * + ldb, 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); + +/* 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 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 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 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__); + +/* 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 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); + +/* Subroutine */ int slamc4_(integer *emin, real *start, integer *base); + +/* Subroutine */ int slamc5_(integer *beta, integer *p, integer *emin, + logical *ieee, integer *emax, real *rmax); + +/* Subroutine */ int slamrg_(integer *n1, integer *n2, real *a, integer * + strd1, integer *strd2, integer *index); + +/* 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); + +/* 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 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 * + sigma, real *d__, real *l, real *ld, real *lld, real *gersch, real * + z__, real *ztz, real *mingma, integer *r__, integer *isuppz, 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 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 slarrb_(integer *n, real *d__, real *l, real *ld, real * + lld, integer *ifirst, integer *ilast, real *sigma, real *reltol, real + *w, real *wgap, real *werr, real *work, integer *iwork, integer *info); + +/* Subroutine */ int slarre_(integer *n, real *d__, real *e, real *tol, + integer *nsplit, integer *isplit, integer *m, real *w, real *woff, + real *gersch, real *work, integer *info); + +/* Subroutine */ int slarrf_(integer *n, real *d__, real *l, real *ld, real * + lld, integer *ifirst, integer *ilast, real *w, real *dplus, real * + lplus, real *work, integer *iwork, integer *info); + +/* Subroutine */ int slarrv_(integer *n, real *d__, real *l, integer *isplit, + integer *m, real *w, integer *iblock, real *gersch, real *tol, real * + z__, integer *ldz, integer *isuppz, real *work, integer *iwork, + integer *info); + +/* 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 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 slasd9_(integer *icompq, integer *ldu, integer *k, real * + d__, real *z__, real *vf, real *vl, real *difl, real *difr, 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); + +/* 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); + +/* 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 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 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 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 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 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 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 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 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 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 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 stgevc_(char *side, char *howmny, logical *select, + integer *n, real *a, integer *lda, real *b, integer *ldb, 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 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 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 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 zdrot_(integer *n, doublecomplex *cx, integer *incx, + doublecomplex *cy, integer *incy, doublereal *c__, doublereal *s); + +/* 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 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 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 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 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 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 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 zgesv_(integer *n, integer *nrhs, doublecomplex *a, + integer *lda, integer *ipiv, doublecomplex *b, integer *ldb, 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 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 + delctg, 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 + delctg, 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 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 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 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 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 zhgeqz_(char *job, char *compq, char *compz, integer *n, + integer *ilo, integer *ihi, doublecomplex *a, integer *lda, + doublecomplex *b, integer *ldb, 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 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 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); + +/* 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 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 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 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 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 + *sigma, doublereal *d__, doublereal *l, doublereal *ld, doublereal * + lld, doublereal *gersch, doublecomplex *z__, doublereal *ztz, + doublereal *mingma, integer *r__, integer *isuppz, 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 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 *d__, doublereal *l, + integer *isplit, integer *m, doublereal *w, integer *iblock, + doublereal *gersch, doublereal *tol, doublecomplex *z__, integer *ldz, + integer *isuppz, doublereal *work, integer *iwork, integer *info); + +/* 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 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 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 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 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 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 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 zptcon_(integer *n, doublereal *d__, doublecomplex *e, + doublereal *anorm, doublereal *rcond, doublereal *rwork, 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 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 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 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 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 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 ztgevc_(char *side, char *howmny, logical *select, + integer *n, doublecomplex *a, integer *lda, doublecomplex *b, integer + *ldb, 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 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 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); + +#endif /* __CLAPACK_H */ diff --git a/lib/LinearAlgebra/LAPACK/f2c.h b/lib/LinearAlgebra/LAPACK/f2c.h new file mode 100644 index 0000000..b94ee7c --- /dev/null +++ b/lib/LinearAlgebra/LAPACK/f2c.h @@ -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 long int integer; +typedef unsigned long int uinteger; +typedef char *address; +typedef short int shortint; +typedef float real; +typedef double doublereal; +typedef struct { real r, i; } complex; +typedef struct { doublereal r, i; } doublecomplex; +typedef long int logical; +typedef short int shortlogical; +typedef char logical1; +typedef char integer1; +#ifdef INTEGER_STAR_8 /* Adjust for integer*8. */ +typedef long long longint; /* system-dependent */ +typedef unsigned long long 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 long int flag; +typedef long int ftnlen; +typedef long 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 diff --git a/lib/LinearAlgebra/LAPACK/lapack-aux.c b/lib/LinearAlgebra/LAPACK/lapack-aux.c new file mode 100644 index 0000000..4ef9a6e --- /dev/null +++ b/lib/LinearAlgebra/LAPACK/lapack-aux.c @@ -0,0 +1,656 @@ +#include +#include +#include +#include +#include +#include "lapack-aux.h" + +#define MACRO(B) do {B} while (0) +#define ERROR(CODE) MACRO(return CODE;) +#define REQUIRES(COND, CODE) MACRO(if(!(COND)) {ERROR(CODE);}) + +#define MIN(A,B) ((A)<(B)?(A):(B)) +#define MAX(A,B) ((A)>(B)?(A):(B)) + +#ifdef DBGL +#define DEBUGMSG(M) printf("LAPACK Wrapper "M"\n: "); size_t t0 = time(NULL); +#define OK MACRO(printf("%ld s\n",time(0)-t0); return 0;); +#else +#define DEBUGMSG(M) +#define OK return 0; +#endif + +#define CHECK(RES,CODE) MACRO(if(RES) return CODE;) + +#define BAD_SIZE 2000 +#define BAD_CODE 2001 +#define MEM 2002 +#define BAD_FILE 2003 +#define SINGULAR 2004 +#define NOCONVER 2005 +#define NODEFPOS 2006 + +//////////////////// real svd //////////////////////////////////// + +int svd_l_R(KDMAT(a),DMAT(u), DVEC(s),DMAT(v)) { + integer m = ar; + integer n = ac; + integer q = MIN(m,n); + REQUIRES(ur==m && uc==m && sn==q && vr==n && vc==n,BAD_SIZE); + DEBUGMSG("svd_l_R"); + double *B = (double*)malloc(m*n*sizeof(double)); + CHECK(!B,MEM); + memcpy(B,ap,m*n*sizeof(double)); + integer lwork = -1; + integer res; + // ask for optimal lwork + double ans; + //printf("ask zgesvd\n"); + char* job = "A"; + dgesvd_ (job,job, + &m,&n,B,&m, + sp, + up,&m, + vp,&n, + &ans, &lwork, + &res); + lwork = ceil(ans); + //printf("ans = %d\n",lwork); + double * work = (double*)malloc(lwork*sizeof(double)); + CHECK(!work,MEM); + //printf("dgesdd\n"); + dgesvd_ (job,job, + &m,&n,B,&m, + sp, + up,&m, + vp,&n, + work, &lwork, + &res); + CHECK(res,res); + free(work); + free(B); + OK +} + +// (alternative version) + +int svd_l_Rdd(KDMAT(a),DMAT(u), DVEC(s),DMAT(v)) { + integer m = ar; + integer n = ac; + integer q = MIN(m,n); + REQUIRES(ur==m && uc==m && sn==q && vr==n && vc==n,BAD_SIZE); + DEBUGMSG("svd_l_Rdd"); + double *B = (double*)malloc(m*n*sizeof(double)); + CHECK(!B,MEM); + memcpy(B,ap,m*n*sizeof(double)); + integer* iwk = (integer*) malloc(8*q*sizeof(int)); + CHECK(!iwk,MEM); + integer lwk = -1; + integer res; + // ask for optimal lwk + double ans; + //printf("ask dgesdd\n"); + dgesdd_ ("A",&m,&n,B,&m,sp,up,&m,vp,&n,&ans,&lwk,iwk,&res); + lwk = 2*ceil(ans); // ????? otherwise 50x100 rejects lwk + //printf("lwk = %d\n",lwk); + double * workv = (double*)malloc(lwk*sizeof(double)); + CHECK(!workv,MEM); + //printf("dgesdd\n"); + dgesdd_ ("A",&m,&n,B,&m,sp,up,&m,vp,&n,workv,&lwk,iwk,&res); + CHECK(res,res); + free(iwk); + free(workv); + free(B); + OK +} + +//////////////////// complex svd //////////////////////////////////// + +// not in clapack.h + +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); + +int svd_l_C(KCMAT(a),CMAT(u), DVEC(s),CMAT(v)) { + integer m = ar; + integer n = ac; + integer q = MIN(m,n); + REQUIRES(ur==m && uc==m && sn==q && vr==n && vc==n,BAD_SIZE); + DEBUGMSG("svd_l_C"); + double *B = (double*)malloc(2*m*n*sizeof(double)); + CHECK(!B,MEM); + memcpy(B,ap,m*n*2*sizeof(double)); + + double *rwork = (double*) malloc(5*q*sizeof(double)); + CHECK(!rwork,MEM); + integer lwork = -1; + integer res; + // ask for optimal lwork + doublecomplex ans; + //printf("ask zgesvd\n"); + char* job = "A"; + zgesvd_ (job,job, + &m,&n,(doublecomplex*)B,&m, + sp, + (doublecomplex*)up,&m, + (doublecomplex*)vp,&n, + &ans, &lwork, + rwork, + &res); + lwork = ceil(ans.r); + //printf("ans = %d\n",lwork); + doublecomplex * work = (doublecomplex*)malloc(lwork*2*sizeof(double)); + CHECK(!work,MEM); + //printf("zgesvd\n"); + zgesvd_ (job,job, + &m,&n,(doublecomplex*)B,&m, + sp, + (doublecomplex*)up,&m, + (doublecomplex*)vp,&n, + work, &lwork, + rwork, + &res); + CHECK(res,res); + free(work); + free(rwork); + free(B); + OK +} + + + +//////////////////// general complex eigensystem //////////// + +int eig_l_C(KCMAT(a),CMAT(u), CVEC(s),CMAT(v)) { + integer n = ar; + REQUIRES(n>=2 && ac==n && (ur==1 || (ur==n && uc==n)) && sn==n && (vr==1 || (vr==n && vc==n)),BAD_SIZE); + DEBUGMSG("eig_l_C"); + double *B = (double*)malloc(2*n*n*sizeof(double)); + CHECK(!B,MEM); + memcpy(B,ap,n*n*2*sizeof(double)); + + double *rwork = (double*) malloc(2*n*sizeof(double)); + CHECK(!rwork,MEM); + integer lwork = -1; + char jobvl = ur==1?'N':'V'; + char jobvr = vr==1?'N':'V'; + integer res; + // ask for optimal lwork + doublecomplex ans; + //printf("ask zgeev\n"); + zgeev_ (&jobvl,&jobvr, + &n,(doublecomplex*)B,&n, + (doublecomplex*)sp, + (doublecomplex*)up,&n, + (doublecomplex*)vp,&n, + &ans, &lwork, + rwork, + &res); + lwork = ceil(ans.r); + //printf("ans = %d\n",lwork); + doublecomplex * work = (doublecomplex*)malloc(lwork*2*sizeof(double)); + CHECK(!work,MEM); + //printf("zgeev\n"); + zgeev_ (&jobvl,&jobvr, + &n,(doublecomplex*)B,&n, + (doublecomplex*)sp, + (doublecomplex*)up,&n, + (doublecomplex*)vp,&n, + work, &lwork, + rwork, + &res); + CHECK(res,res); + free(work); + free(rwork); + free(B); + OK +} + + + +//////////////////// general real eigensystem //////////// + +int eig_l_R(KDMAT(a),DMAT(u), CVEC(s),DMAT(v)) { + integer n = ar; + REQUIRES(n>=2 && ac == n && (ur==1 || (ur==n && uc==n)) && sn==n && (vr==1 || (vr==n && vc==n)),BAD_SIZE); + DEBUGMSG("eig_l_R"); + double *B = (double*)malloc(n*n*sizeof(double)); + CHECK(!B,MEM); + memcpy(B,ap,n*n*sizeof(double)); + integer lwork = -1; + char jobvl = ur==1?'N':'V'; + char jobvr = vr==1?'N':'V'; + integer res; + // ask for optimal lwork + double ans; + //printf("ask dgeev\n"); + dgeev_ (&jobvl,&jobvr, + &n,B,&n, + sp, sp+n, + up,&n, + vp,&n, + &ans, &lwork, + &res); + lwork = ceil(ans); + //printf("ans = %d\n",lwork); + double * work = (double*)malloc(lwork*sizeof(double)); + CHECK(!work,MEM); + //printf("dgeev\n"); + dgeev_ (&jobvl,&jobvr, + &n,B,&n, + sp, sp+n, + up,&n, + vp,&n, + work, &lwork, + &res); + CHECK(res,res); + free(work); + free(B); + OK +} + + +//////////////////// symmetric real eigensystem //////////// + + +int eig_l_S(KDMAT(a),DVEC(s),DMAT(v)) { + integer n = ar; + REQUIRES(n>=2 && ac == n && sn==n && (vr==1 || (vr==n && vc==n)),BAD_SIZE); + DEBUGMSG("eig_l_S"); + memcpy(vp,ap,n*n*sizeof(double)); + integer lwork = -1; + char jobz = vr==1?'N':'V'; + char uplo = 'U'; + integer res; + // ask for optimal lwork + double ans; + //printf("ask dsyev\n"); + dsyev_ (&jobz,&uplo, + &n,vp,&n, + sp, + &ans, &lwork, + &res); + lwork = ceil(ans); + //printf("ans = %d\n",lwork); + double * work = (double*)malloc(lwork*sizeof(double)); + CHECK(!work,MEM); + dsyev_ (&jobz,&uplo, + &n,vp,&n, + sp, + work, &lwork, + &res); + CHECK(res,res); + free(work); + OK +} + +//////////////////// hermitian complex eigensystem //////////// + +int eig_l_H(KCMAT(a),DVEC(s),CMAT(v)) { + integer n = ar; + REQUIRES(n>=2 && ac==n && sn==n && (vr==1 || (vr==n && vc==n)),BAD_SIZE); + DEBUGMSG("eig_l_H"); + memcpy(vp,ap,2*n*n*sizeof(double)); + double *rwork = (double*) malloc((3*n-2)*sizeof(double)); + CHECK(!rwork,MEM); + integer lwork = -1; + char jobz = vr==1?'N':'V'; + char uplo = 'U'; + integer res; + // ask for optimal lwork + doublecomplex ans; + //printf("ask zheev\n"); + zheev_ (&jobz,&uplo, + &n,(doublecomplex*)vp,&n, + sp, + &ans, &lwork, + rwork, + &res); + lwork = ceil(ans.r); + //printf("ans = %d\n",lwork); + doublecomplex * work = (doublecomplex*)malloc(lwork*2*sizeof(double)); + CHECK(!work,MEM); + zheev_ (&jobz,&uplo, + &n,(doublecomplex*)vp,&n, + sp, + work, &lwork, + rwork, + &res); + CHECK(res,res); + free(work); + free(rwork); + OK +} + +//////////////////// general real linear system //////////// + +int linearSolveR_l(KDMAT(a),KDMAT(b),DMAT(x)) { + integer n = ar; + integer nhrs = bc; + REQUIRES(n>=1 && ar==ac && ar==br,BAD_SIZE); + DEBUGMSG("linearSolveR_l"); + double*AC = (double*)malloc(n*n*sizeof(double)); + memcpy(AC,ap,n*n*sizeof(double)); + memcpy(xp,bp,n*nhrs*sizeof(double)); + integer * ipiv = (integer*)malloc(n*sizeof(integer)); + integer res; + dgesv_ (&n,&nhrs, + AC, &n, + ipiv, + xp, &n, + &res); + if(res>0) { + return SINGULAR; + } + CHECK(res,res); + free(ipiv); + free(AC); + OK +} + +//////////////////// general complex linear system //////////// + +int linearSolveC_l(KCMAT(a),KCMAT(b),CMAT(x)) { + integer n = ar; + integer nhrs = bc; + REQUIRES(n>=1 && ar==ac && ar==br,BAD_SIZE); + DEBUGMSG("linearSolveC_l"); + double*AC = (double*)malloc(2*n*n*sizeof(double)); + memcpy(AC,ap,2*n*n*sizeof(double)); + memcpy(xp,bp,2*n*nhrs*sizeof(double)); + integer * ipiv = (integer*)malloc(n*sizeof(integer)); + integer res; + zgesv_ (&n,&nhrs, + (doublecomplex*)AC, &n, + ipiv, + (doublecomplex*)xp, &n, + &res); + if(res>0) { + return SINGULAR; + } + CHECK(res,res); + free(ipiv); + free(AC); + OK +} + +//////////////////// least squares real linear system //////////// + +int linearSolveLSR_l(KDMAT(a),KDMAT(b),DMAT(x)) { + integer m = ar; + integer n = ac; + integer nrhs = bc; + integer ldb = xr; + REQUIRES(m>=1 && n>=1 && ar==br && xr==MAX(m,n) && xc == bc, BAD_SIZE); + DEBUGMSG("linearSolveLSR_l"); + double*AC = (double*)malloc(m*n*sizeof(double)); + memcpy(AC,ap,m*n*sizeof(double)); + if (m>=n) { + memcpy(xp,bp,m*nrhs*sizeof(double)); + } else { + int k; + for(k = 0; k0) { + return SINGULAR; + } + CHECK(res,res); + free(work); + free(AC); + OK +} + +//////////////////// least squares complex linear system //////////// + +int linearSolveLSC_l(KCMAT(a),KCMAT(b),CMAT(x)) { + integer m = ar; + integer n = ac; + integer nrhs = bc; + integer ldb = xr; + REQUIRES(m>=1 && n>=1 && ar==br && xr==MAX(m,n) && xc == bc, BAD_SIZE); + DEBUGMSG("linearSolveLSC_l"); + double*AC = (double*)malloc(2*m*n*sizeof(double)); + memcpy(AC,ap,2*m*n*sizeof(double)); + memcpy(AC,ap,2*m*n*sizeof(double)); + if (m>=n) { + memcpy(xp,bp,2*m*nrhs*sizeof(double)); + } else { + int k; + for(k = 0; k0) { + return SINGULAR; + } + CHECK(res,res); + free(work); + free(AC); + OK +} + +//////////////////// least squares real linear system using SVD //////////// + +int linearSolveSVDR_l(double rcond,KDMAT(a),KDMAT(b),DMAT(x)) { + integer m = ar; + integer n = ac; + integer nrhs = bc; + integer ldb = xr; + REQUIRES(m>=1 && n>=1 && ar==br && xr==MAX(m,n) && xc == bc, BAD_SIZE); + DEBUGMSG("linearSolveSVDR_l"); + double*AC = (double*)malloc(m*n*sizeof(double)); + double*S = (double*)malloc(MIN(m,n)*sizeof(double)); + memcpy(AC,ap,m*n*sizeof(double)); + if (m>=n) { + memcpy(xp,bp,m*nrhs*sizeof(double)); + } else { + int k; + for(k = 0; k0) { + return NOCONVER; + } + CHECK(res,res); + free(work); + free(S); + free(AC); + OK +} + +//////////////////// least squares complex linear system using SVD //////////// + +// not in clapack.h + +int zgelss_(integer *m, integer *n, integer *nhrs, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, doublereal *s, + doublereal *rcond, integer* rank, + doublecomplex *work, integer* lwork, doublereal* rwork, + integer *info); + +int linearSolveSVDC_l(double rcond, KCMAT(a),KCMAT(b),CMAT(x)) { + integer m = ar; + integer n = ac; + integer nrhs = bc; + integer ldb = xr; + REQUIRES(m>=1 && n>=1 && ar==br && xr==MAX(m,n) && xc == bc, BAD_SIZE); + DEBUGMSG("linearSolveSVDC_l"); + double*AC = (double*)malloc(2*m*n*sizeof(double)); + double*S = (double*)malloc(MIN(m,n)*sizeof(double)); + double*RWORK = (double*)malloc(5*MIN(m,n)*sizeof(double)); + memcpy(AC,ap,2*m*n*sizeof(double)); + if (m>=n) { + memcpy(xp,bp,2*m*nrhs*sizeof(double)); + } else { + int k; + for(k = 0; k0) { + return NOCONVER; + } + CHECK(res,res); + free(work); + free(RWORK); + free(S); + free(AC); + OK +} + +//////////////////// Cholesky factorization ///////////////////////// + +int chol_l_H(KCMAT(a),CMAT(l)) { + integer n = ar; + REQUIRES(n>=1 && ac == n && lr==n && lc==n,BAD_SIZE); + DEBUGMSG("chol_l_H"); + memcpy(lp,ap,n*n*sizeof(doublecomplex)); + char uplo = 'U'; + integer res; + zpotrf_ (&uplo,&n,(doublecomplex*)lp,&n,&res); + CHECK(res>0,NODEFPOS); + CHECK(res,res); + doublecomplex zero = {0.,0.}; + int r,c; + for (r=0; r=1 && ac == n && lr==n && lc==n,BAD_SIZE); + DEBUGMSG("chol_l_S"); + memcpy(lp,ap,n*n*sizeof(double)); + char uplo = 'U'; + integer res; + dpotrf_ (&uplo,&n,lp,&n,&res); + CHECK(res>0,NODEFPOS); + CHECK(res,res); + int r,c; + for (r=0; r=1 && n >=1 && rr== m && rc == n && taun == mn, BAD_SIZE); + DEBUGMSG("qr_l_R"); + double *WORK = (double*)malloc(m*sizeof(double)); + CHECK(!WORK,MEM); + memcpy(rp,ap,m*n*sizeof(double)); + integer res; + dgeqr2_ (&m,&n,rp,&m,taup,WORK,&res); + CHECK(res,res); + free(WORK); + OK +} + +int qr_l_C(KCMAT(a), CVEC(tau), CMAT(r)) { + integer m = ar; + integer n = ac; + integer mn = MIN(m,n); + REQUIRES(m>=1 && n >=1 && rr== m && rc == n && taun == mn, BAD_SIZE); + DEBUGMSG("qr_l_C"); + doublecomplex *WORK = (doublecomplex*)malloc(m*sizeof(doublecomplex)); + CHECK(!WORK,MEM); + memcpy(rp,ap,m*n*sizeof(doublecomplex)); + integer res; + zgeqr2_ (&m,&n,(doublecomplex*)rp,&m,(doublecomplex*)taup,WORK,&res); + CHECK(res,res); + free(WORK); + OK +} diff --git a/lib/LinearAlgebra/LAPACK/lapack-aux.h b/lib/LinearAlgebra/LAPACK/lapack-aux.h new file mode 100644 index 0000000..ea71847 --- /dev/null +++ b/lib/LinearAlgebra/LAPACK/lapack-aux.h @@ -0,0 +1,46 @@ +#include "f2c.h" +#include "clapack.h" + +#define DVEC(A) int A##n, double*A##p +#define CVEC(A) int A##n, double*A##p +#define DMAT(A) int A##r, int A##c, double* A##p +#define CMAT(A) int A##r, int A##c, double* A##p + +// const pointer versions for the parameters +#define KDVEC(A) int A##n, const double*A##p +#define KCVEC(A) int A##n, const double*A##p +#define KDMAT(A) int A##r, int A##c, const double* A##p +#define KCMAT(A) int A##r, int A##c, const double* A##p + +int svd_l_R(KDMAT(x),DMAT(u),DVEC(s),DMAT(v)); +int svd_l_Rdd(KDMAT(x),DMAT(u),DVEC(s),DMAT(v)); + +int svd_l_C(KCMAT(a),CMAT(u),DVEC(s),CMAT(v)); + +int eig_l_C(KCMAT(a),CMAT(u),CVEC(s),CMAT(v)); + +int eig_l_R(KDMAT(a),DMAT(u),CVEC(s),DMAT(v)); + +int eig_l_S(KDMAT(a),DVEC(s),DMAT(v)); + +int eig_l_H(KCMAT(a),DVEC(s),CMAT(v)); + +int linearSolveR_l(KDMAT(a),KDMAT(b),DMAT(x)); + +int linearSolveC_l(KCMAT(a),KCMAT(b),CMAT(x)); + +int linearSolveLSR_l(KDMAT(a),KDMAT(b),DMAT(x)); + +int linearSolveLSC_l(KCMAT(a),KCMAT(b),CMAT(x)); + +int linearSolveSVDR_l(double,KDMAT(a),KDMAT(b),DMAT(x)); + +int linearSolveSVDC_l(double,KCMAT(a),KCMAT(b),CMAT(x)); + +int chol_l_H(KCMAT(a),CMAT(r)); + +int chol_l_S(KDMAT(a),DMAT(r)); + +int qr_l_R(KDMAT(a), DVEC(tau), DMAT(r)); + +int qr_l_C(KCMAT(a), CVEC(tau), CMAT(r)); -- cgit v1.2.3