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32 * Gallium Rubidium Oxygen Manganese Argon Carbon Silicon
35 #ifndef _GMX_LAPACK_H_
36 #define _GMX_LAPACK_H_
38 #include "visibility.h"
41 * @brief Header definitions for the standard LAPACK library.
43 * This is the subset of LAPACK routines used for the
44 * linear algebra operations in Gromacs. Most of the execution time
45 * will be spent in the BLAS routines, which you hopefully have an
46 * optimized version of. Gromacs includes reference implementations
47 * of both BLAS and LAPACK so it compiles everywhere, but you should
48 * really try to find a vendor or otherwise optimized version at least
49 * of BLAS for better performance.
51 * Do NOT use this code for other purposes - we only provide this as a
52 * simple fallback/reference implementation when no optimized BLAS
53 * is present. If you need an implementation for your own code
54 * there are several much faster versions out there.
56 * All routines are compatible with the LAPACK/BLAS reference implementations,
57 * meaning they assume fortran-style matrix row/column organization.
59 * There is plenty of documentation for these routines available
60 * at http://www.netlib.org/lapack , so there is no point in repeating
73 #include "types/simple.h"
75 /* Suppress Cygwin compiler warnings from using newlib version of
82 #define F77_FUNC(name,NAME) name ## _
87 /* Double precision */
90 F77_FUNC(dbdsdc,DBDSDC)(const char *uplo, const char *compq, int *n, double *d, double *e, double *u,
91 int *ldu, double *vt, int *ldvt, double *q, int *iq, double *work,
92 int *iwork, int *info);
95 F77_FUNC(dgetf2,DGETF2)(int *m, int *n, double *a, int *lda, int *ipiv, int *info);
98 F77_FUNC(dlamrg,DLAMRG)(int *n1, int *n2, double *a, int *dtrd1, int *dtrd2, int *index);
101 F77_FUNC(dlarnv,DLARNV)(int *idist, int *iseed, int *n, double *x);
104 F77_FUNC(dlasd0,DLASD0)(int *n, int *sqre, double *d, double *e, double *u,
105 int *ldu, double *vt, int *ldvt, int *smlsiz, int *iwork,
106 double *work, int *info);
109 F77_FUNC(dlasda,DLASDA)(int *icompq, int *smlsiz, int *n, int *sqre, double *d, double *e,
110 double *u, int *ldu, double *vt, int *k, double *difl, double *difr,
111 double *z, double *poles, int *givptr, int *givcol, int *ldgcol,
112 int *perm, double *givnum, double *c, double *s,
113 double *work, int *iwork, int *info);
116 F77_FUNC(dlasq6,DLASQ6)(int *i0, int *n0, double *z, int *pp, double *dmin, double *dmin1,
117 double *dmin2, double *dn, double *dnm1, double *dnm2);
120 F77_FUNC(dorgl2,DORGL2)(int *m, int *n, int *k, double *a, int *lda,
121 double *tau, double *work, int *info);
124 F77_FUNC(dbdsqr,DBDSQR)(const char *uplo, int *n, int *ncvt, int *nru, int *ncc, double *d,
125 double *e, double *vt, int *ldvt, double *u, int *ldu,
126 double *c, int *ldc, double *work, int *info);
129 F77_FUNC(dgetrf,DGETRF)(int *m, int *n, double *a, int *lda, int *ipiv, int *info);
132 F77_FUNC(dgetri,DGETRI)(int *n, double *a, int *lda, int *ipiv, double *work,
133 int *lwork, int *info);
136 F77_FUNC(dgetrs,DGETRS)(const char *trans, int *n, int *nrhs, double *a, int *lda, int *ipiv,
137 double *b, int *ldb, int *info);
140 F77_FUNC(dtrtri,DTRTRI)(const char *uplo, const char *diag, int *n, double *a, int *lda, int *info);
143 F77_FUNC(dtrti2,DTRTI2)(const char *uplo, const char *diag, int *n, double *a, int *lda, int *info);
146 F77_FUNC(dlange,DLANGE)(const char *norm, int *m, int *n, double *a, int *lda, double *work);
149 F77_FUNC(dlarrbx,DLARRBX)(int *n, double *d, double *l, double *ld, double *lld, int *ifirst,
150 int *ilast, double *rtol1, double *rtol2, int *offset, double *w,
151 double *wgap, double *werr, double *work, int *iwork, int *info);
154 F77_FUNC(dlasd1,DLASD1)(int *nl, int *nr, int *sqre, double *d, double *alpha, double *beta,
155 double *u, int *ldu, double *vt, int *ldvt, int *idxq, int *iwork,
156 double *work, int *info);
159 F77_FUNC(dlasdq,DLASDQ)(const char *uplo, int *sqre, int *n, int *ncvt, int *nru, int *ncc,
160 double *d, double *e, double *vt, int *ldvt, double *u, int *ldu,
161 double *c, int *ldc, double *work, int *info);
164 F77_FUNC(dlasr,DLASR)(const char *side, const char *pivot, const char *direct, int *m, int *n, double *c,
165 double *s, double *a, int *lda);
168 F77_FUNC(dorglq,DORGLQ)(int *m, int *n, int *k, double *a, int *lda,
169 double *tau, double *work, int *lwork, int *info);
172 F77_FUNC(dormtr,DORMTR)(const char *side, const char *uplo, const char *trans, int *m, int *n, double *a,
173 int *lda, double *tau, double *c, int *ldc,
174 double *work, int *lwork, int *info);
177 F77_FUNC(dgebd2,DGEBD2)(int *m, int *n, double *a, int *lda, double *d, double *e,
178 double *tauq, double *taup, double *work, int *info);
181 F77_FUNC(dlabrd,DLABRD)(int *m, int *n, int *nb, double *a, int *lda, double *d,
182 double *e, double *tauq, double *taup, double *x,
183 int *ldx, double *y, int *ldy);
186 F77_FUNC(dlanst,DLANST)(const char *norm, int *n, double *d, double *e);
189 F77_FUNC(dlansy,DLANSY)(const char *norm, const char *uplo, int *n, double *a, int *lda, double *work);
192 F77_FUNC(dlarrex,DLARREX)(const char *range, int *n, double *vl, double *vu, int *il, int *iu,
193 double *d, double *e, double *tol, int *nsplit,
194 int *isplit, int *m, double *w, int *iblock, int *indexw,
195 double *gersch, double *work, int *iwork, int *info);
198 F77_FUNC(dlasd2,DLASD2)(int *nl, int *nr, int *sqre, int *k, double *d, double *z,
199 double *alpha, double *beta, double *u, int *ldu, double *vt,
200 int *ldvt, double *dsigma, double *u2, int *ldu2, double *vt2,
201 int *ldvt2, int *idxp, int *idx, int *idxc,
202 int *idxq, int *coltyp, int *info);
205 F77_FUNC(dlasdt,DLASDT)(int *n, int *lvl, int *nd, int *inode, int *ndiml,
206 int *ndimr, int *msub);
209 F77_FUNC(dlasrt,DLASRT)(const char *id, int *n, double *d, int *info);
212 F77_FUNC(dlasrt2,DLASRT2)(const char *id, int *n, double *d, int *key, int *info);
215 F77_FUNC(ilasrt2,ILASRT2)(const char *id, int *n, int *d, int *key, int *info);
218 F77_FUNC(dorgqr,DORGQR)(int *m, int *n, int *k, double *a, int *lda, double *tau,
219 double *work, int *lwork, int *info);
222 F77_FUNC(dstebz,DSTEBZ)(const char *range, const char *order, int *n, double *vl, double *vu,
223 int *il, int *iu, double *abstol, double *d, double *e,
224 int *m, int *nsplit, double *w, int *iblock, int *isplit,
225 double *work, int *iwork, int *info);
228 F77_FUNC(dsteqr,DSTEQR)(const char *compz, int *n, double *d__, double *e,
229 double *z__, int *ldz, double *work, int *info);
232 F77_FUNC(dgebrd,DGEBRD)(int *m, int *n, double *a, int *lda, double *d, double *e,
233 double *tauq, double *taup, double *work, int *lwork, int *info);
236 F77_FUNC(dlacpy,DLACPY)(const char *uplo, int *m, int *n, double *a, int *lda, double *b, int *ldb);
239 F77_FUNC(dlapy2,DLAPY2)(double * x, double * y);
243 F77_FUNC(dlarrfx,DLARRFX)(int *n, double *d, double *l, double *ld, double *lld, int *ifirst,
244 int *ilast, double *w, double *sigma, double *dplus, double *lplus,
245 double *work, int *info);
248 F77_FUNC(dlasd3,DLASD3)(int *nl, int *nr, int *sqre, int *k, double *d, double *q, int *ldq,
249 double *dsigma, double *u, int *ldu, double *u2, int *ldu2,
250 double *vt, int *ldvt, double *vt2, int *ldvt2, int *idxc,
251 int *ctot, double *z, int *info);
254 F77_FUNC(dlaset,DLASET)(const char *uplo, int *m, int *n, double *alpha,
255 double *beta, double *a, int *lda);
258 F77_FUNC(dlassq,DLASSQ)(int *n, double *x, int *incx, double *scale, double *sumsq);
261 F77_FUNC(dorm2l,DORM2L)(const char *side, const char *trans, int *m, int *n, int *k, double *a, int *lda,
262 double *tau, double *c, int *ldc, double *work, int *info);
265 F77_FUNC(dstegr,DSTEGR)(const char *jobz, const char *range, int *n, double *d, double *e, double *vl,
266 double *vu, int *il, int *iu, double *abstol, int *m, double *w,
267 double *z, int *ldz, int *isuppz, double *work,
268 int *lwork, int *iwork, int *liwork, int *info);
271 F77_FUNC(ssteqr,SSTEQR)(const char *compz, int *n, float *d__, float *e,
272 float *z__, int *ldz, float *work, int *info);
275 F77_FUNC(dgelq2,DGELQ2)(int *m, int *n, double *a, int *lda, double *tau, double *work, int *info);
278 F77_FUNC(dlae2,DLAE2)(double *a, double *b, double *c, double *rt1, double *rt2);
281 F77_FUNC(dlaev2,DLAEV2)(double *a, double *b, double *c, double *rt1, double *rt2,
282 double *cs1, double *cs2);
285 F77_FUNC(dlar1vx,DLAR1VX)(int *n, int *b1, int *bn, double *sigma, double *d, double *l, double *ld,
286 double *lld, double *eval, double *gersch, double *z, double *ztz, double *mingma,
287 int *r, int *isuppz, double *work);
290 F77_FUNC(dlarrvx,DLARRVX)(int *n, double *d, double *l, int *isplit, int *m, double *w,
291 int *iblock, int *indexw, double *gersch, double *tol, double *z, int *ldz,
292 int *isuppz, double *work, int *iwork, int *info);
295 F77_FUNC(dlasd4,DLASD4)(int *n, int *i, double *d, double *z, double *delta,
296 double *rho, double *sigma, double *work, int *info);
299 F77_FUNC(dlasq1,DLASQ1)(int *n, double *d, double *e, double *work, int *info);
303 F77_FUNC(dlasv2,DLASV2)(double *f, double *g, double *h, double *ssmin, double *ssmax,
304 double *snr, double *csr, double *snl, double *csl);
307 F77_FUNC(dorm2r,DORM2R)(const char *side, const char *trans, int *m, int *n, int *k, double *a,
308 int *lda, double *tau, double *c, int *ldc, double *work, int *info);
311 F77_FUNC(dstein,DSTEIN)(int *n, double *d, double *e, int *m, double *w, int *iblock, int *isplit,
312 double *z, int *ldz, double *work, int *iwork, int *ifail, int *info);
315 F77_FUNC(dgelqf,DGELQF)(int *m, int *n, double *a, int *lda, double *tau,
316 double *work, int *lwork, int *info);
319 F77_FUNC(dlaebz,DLAEBZ)(int *ijob, int *nitmax, int *n, int *mmax, int *minp, int *nbmin,
320 double *abstol, double *reltol, double *pivmin, double *d, double *e,
321 double *e2, int *nval, double *ab, double *c, int *mout, int *nab,
322 double *work, int *iwork, int *info);
325 F77_FUNC(dlarf,DLARF)(const char *side, int *m, int *n, double *v, int *incv, double *tau,
326 double *c, int *ldc, double *work);
329 F77_FUNC(dlartg,DLARTG)(double *f, double *g, double *cs, double *sn, double *r);
332 F77_FUNC(dlasd5,DLASD5)(int *i, double *d, double *z, double *delta,
333 double *rho, double *dsigma, double *work);
336 F77_FUNC(dlasq2,DLASQ2)(int *n, double *z, int *info);
339 F77_FUNC(dlasq3,DLASQ3)(int *i0, int *n0, double *z, int *pp, double *dmin,
340 double *sigma, double *desig, double *qmax, int *nfail,
341 int *iter, int *ndiv, int *ieee);
344 F77_FUNC(dlaswp,DLASWP)(int *n, double *a, int *lda, int *k1, int *k2, int *ipiv, int *incx);
347 F77_FUNC(dormbr,DORMBR)(const char *vect, const char *side, const char *trans, int *m, int *n, int *k,
348 double *a, int *lda, double *tau, double *c, int *ldc, double *work,
349 int *lwork, int *info);
352 F77_FUNC(dsterf,DSTERF)(int *n, double *d, double *e, int *info);
355 F77_FUNC(dgeqr2,DGEQR2)(int *m, int *n, double *a, int *lda, double *tau,
356 double *work, int *info);
359 F77_FUNC(dlaed6,DLAED6)(int *kniter, int *orgati, double *rho, double *d,
360 double *z, double *finit, double *tau, int *info);
363 F77_FUNC(dlarfb,DLARFB)(const char *side, const char *trans, const char *direct, const char *storev, int *m, int *n,
364 int *k, double *v, int *ldv, double *t, int *ldt, double *c,
365 int *ldc, double *work, int *ldwork);
368 F77_FUNC(dlaruv,DLARUV)(int *iseed, int *n, double *x);
371 F77_FUNC(dlasd6,DLASD6)(int *icompq, int *nl, int *nr, int *sqre, double *d, double *vf,
372 double *vl, double *alpha, double *beta, int *idxq, int *perm,
373 int *givptr, int *givcol, int *ldgcol, double *givnum, int *ldgnum,
374 double *poles, double *difl, double *difr, double *z, int *k,
375 double *c, double *s, double *work, int *iwork, int *info);
378 F77_FUNC(dlatrd,DLATRD)(const char *uplo, int *n, int *nb, double *a, int *lda, double *e,
379 double * tau, double *w, int *ldw);
382 F77_FUNC(dorml2,DORML2)(const char *side, const char *trans, int *m, int *n, int *k, double *a,
383 int *lda, double *tau, double *c, int *ldc, double *work, int *info);
386 F77_FUNC(dstevr,DSTEVR)(const char *jobz, const char *range, int *n, double *d, double *e, double *vl,
387 double *vu, int *il, int *iu, double *abstol, int *m, double *w,
388 double *z, int *ldz, int *isuppz, double *work,
389 int *lwork, int *iwork, int *liwork, int *info);
392 F77_FUNC(dsytrd,DSYTRD)(const char *uplo, int *n, double * a, int *lda, double *d,
393 double *e, double *tau, double *work, int *lwork, int *info);
396 F77_FUNC(dsyevr,DSYEVR)(const char *jobz, const char *range, const char *uplo, int *n,
397 double *a, int *lda, double *vl, double *vu, int *
398 il, int *iu, double *abstol, int *m, double *w,
399 double *z__, int *ldz, int *isuppz, double *work,
400 int *lwork, int *iwork, int *liwork, int *info);
403 F77_FUNC(dormql,DORMQL)(const char *side, const char *trans, int *m, int *n,
404 int *k, double *a, int *lda, double *tau, double *
405 c, int *ldc, double *work, int *lwork, int *info);
408 F77_FUNC(dormqr,DORMQR)(const char *side, const char *trans, int *m, int *n, int *k, double *a,
409 int *lda, double *tau, double *c, int *ldc,
410 double *work, int *lwork, int *info);
413 F77_FUNC(dorgbr,DORGBR)(const char *vect, int *m, int *n, int *k, double *a, int *lda,
414 double *tau, double *work, int *lwork, int *info);
417 F77_FUNC(dlasq5,DLASQ5)(int *i0, int *n0, double *z, int *pp, double *tau, double *dmin,
418 double *dmin1, double *dmin2, double *dn, double *dnm1,
419 double *dnm2, int *ieee);
422 F77_FUNC(dlasd8,DLASD8)(int *icompq, int *k, double *d, double *z, double *vf, double *vl,
423 double *difl, double *difr, int *lddifr, double *dsigma,
424 double *work, int *info);
427 F77_FUNC(dlascl,DLASCL)(const char *type, int *kl, int *ku, double *cfrom, double *cto, int *m,
428 int *n, double *a, int *lda, int *info);
431 F77_FUNC(dlarft,DLARFT)(const char *direct, const char *storev, int *n, int *k, double *v,
432 int *ldv, double *tau, double *t, int *ldt);
435 F77_FUNC(dlagts,DLAGTS)(int *job, int *n, double *a, double *b, double *c, double *d,
436 int *in, double *y, double *tol, int *info);
439 F77_FUNC(dgesdd,DGESDD)(const char *jobz, int *m, int *n, double *a, int *lda, double *s, double *u,
440 int *ldu, double *vt, int *ldvt, double *work, int *lwork,
441 int *iwork, int *info);
444 F77_FUNC(dsytd2,DSYTD2)(const char *uplo, int *n, double *a, int *lda, double *d,
445 double *e, double *tau, int *info);
448 F77_FUNC(dormlq,DORMLQ)(const char *side, const char *trans, int *m, int *n, int *k, double *a, int *lda,
449 double *tau, double *c, int *ldc, double *work, int *lwork, int *info);
452 F77_FUNC(dorg2r,DORG2R)(int *m, int *n, int *k, double *a, int *lda, double *tau,
453 double *work, int *info);
456 F77_FUNC(dlasq4,DLASQ4)(int *i0, int *n0, double *z, int *pp, int *n0in, double *dmin,
457 double *dmin1, double *dmin2, double *dn, double *dn1,
458 double *dn2, double *tau, int *ttype);
461 F77_FUNC(dlasd7,DLASD7)(int *icompq, int *nl, int *nr, int *sqre, int *k, double *d, double *z,
462 double *zw, double *vf, double *vfw, double *vl, double *vlw,
463 double *alpha, double *beta, double *dsigma, int *idx, int *idxp,
464 int *idxq, int *perm, int *givptr, int *givcol, int *ldgcol,
465 double *givnum, int *ldgnum, double *c, double *s, int *info);
468 F77_FUNC(dlas2,DLAS2)(double *f, double *g, double *h, double *ssmin, double *ssmax);
471 F77_FUNC(dlarfg,DLARFG)(int *n, double *alpha, double *x, int *incx, double *tau);
474 F77_FUNC(dlagtf,DLAGTF)(int *n, double *a, double *lambda, double *b, double *c,
475 double *tol, double *d, int *in, int *info);
478 F77_FUNC(dgeqrf,DGEQRF)(int *m, int *n, double *a, int *lda, double *tau,
479 double *work, int *lwork, int *info);
483 /* Single precision */
486 F77_FUNC(sbdsdc,SBDSDC)(const char *uplo, const char *compq, int *n, float *d, float *e, float *u,
487 int *ldu, float *vt, int *ldvt, float *q, int *iq, float *work,
488 int *iwork, int *info);
491 F77_FUNC(sgetf2,SGETF2)(int *m, int *n, float *a, int *lda, int *ipiv, int *info);
494 F77_FUNC(slamrg,SLAMRG)(int *n1, int *n2, float *a, int *dtrd1, int *dtrd2, int *index);
497 F77_FUNC(slarnv,SLARNV)(int *idist, int *iseed, int *n, float *x);
500 F77_FUNC(slasd0,SLASD0)(int *n, int *sqre, float *d, float *e, float *u,
501 int *ldu, float *vt, int *ldvt, int *smlsiz, int *iwork,
502 float *work, int *info);
505 F77_FUNC(slasda,SLASDA)(int *icompq, int *smlsiz, int *n, int *sqre, float *d, float *e,
506 float *u, int *ldu, float *vt, int *k, float *difl, float *difr,
507 float *z, float *poles, int *givptr, int *givcol, int *ldgcol,
508 int *perm, float *givnum, float *c, float *s,
509 float *work, int *iwork, int *info);
512 F77_FUNC(slasq6,SLASQ6)(int *i0, int *n0, float *z, int *pp, float *dmin, float *dmin1,
513 float *dmin2, float *dn, float *dnm1, float *dnm2);
516 F77_FUNC(sorgl2,SORGL2)(int *m, int *n, int *k, float *a, int *lda,
517 float *tau, float *work, int *info);
520 F77_FUNC(sbdsqr,SBDSQR)(const char *uplo, int *n, int *ncvt, int *nru, int *ncc, float *d,
521 float *e, float *vt, int *ldvt, float *u, int *ldu,
522 float *c, int *ldc, float *work, int *info);
525 F77_FUNC(sgetrf,SGETRF)(int *m, int *n, float *a, int *lda, int *ipiv, int *info);
528 F77_FUNC(sgetri,SGETRI)(int *n, float *a, int *lda, int *ipiv, float *work,
529 int *lwork, int *info);
532 F77_FUNC(sgetrs,SGETRS)(const char *trans, int *n, int *nrhs, float *a, int *lda, int *ipiv,
533 float *b, int *ldb, int *info);
536 F77_FUNC(strtri,STRTRI)(const char *uplo, const char *diag, int *n, float *a, int *lda, int *info);
539 F77_FUNC(strti2,STRTI2)(const char *uplo, const char *diag, int *n, float *a, int *lda, int *info);
542 F77_FUNC(slange,SLANGE)(const char *norm, int *m, int *n, float *a, int *lda, float *work);
545 F77_FUNC(slarrbx,SLARRBX)(int *n, float *d, float *l, float *ld, float *lld, int *ifirst,
546 int *ilast, float *rtol1, float *rtol2, int *offset, float *w,
547 float *wgap, float *werr, float *work, int *iwork, int *info);
550 F77_FUNC(slasd1,SLASD1)(int *nl, int *nr, int *sqre, float *d, float *alpha, float *beta,
551 float *u, int *ldu, float *vt, int *ldvt, int *idxq, int *iwork,
552 float *work, int *info);
555 F77_FUNC(slasdq,SLASDQ)(const char *uplo, int *sqre, int *n, int *ncvt, int *nru, int *ncc,
556 float *d, float *e, float *vt, int *ldvt, float *u, int *ldu,
557 float *c, int *ldc, float *work, int *info);
560 F77_FUNC(slasr,SLASR)(const char *side, const char *pivot, const char *direct, int *m, int *n, float *c,
561 float *s, float *a, int *lda);
564 F77_FUNC(sorglq,SORGLQ)(int *m, int *n, int *k, float *a, int *lda,
565 float *tau, float *work, int *lwork, int *info);
568 F77_FUNC(sormtr,SORMTR)(const char *side, const char *uplo, const char *trans, int *m, int *n, float *a,
569 int *lda, float *tau, float *c, int *ldc,
570 float *work, int *lwork, int *info);
573 F77_FUNC(sgebd2,SGEBD2)(int *m, int *n, float *a, int *lda, float *d, float *e,
574 float *tauq, float *taup, float *work, int *info);
577 F77_FUNC(slabrd,SLABRD)(int *m, int *n, int *nb, float *a, int *lda, float *d,
578 float *e, float *tauq, float *taup, float *x,
579 int *ldx, float *y, int *ldy);
582 F77_FUNC(slanst,SLANST)(const char *norm, int *n, float *d, float *e);
585 F77_FUNC(slansy,SLANSY)(const char *norm, const char *uplo, int *n, float *a, int *lda, float *work);
588 F77_FUNC(slarrex,SLARREX)(const char *range, int *n, float *vl, float *vu, int *il, int *iu,
589 float *d, float *e, float *tol, int *nsplit,
590 int *isplit, int *m, float *w, int *iblock, int *indexw,
591 float *gersch, float *work, int *iwork, int *info);
594 F77_FUNC(slasd2,SLASD2)(int *nl, int *nr, int *sqre, int *k, float *d, float *z,
595 float *alpha, float *beta, float *u, int *ldu, float *vt,
596 int *ldvt, float *dsigma, float *u2, int *ldu2, float *vt2,
597 int *ldvt2, int *idxp, int *idx, int *idxc,
598 int *idxq, int *coltyp, int *info);
601 F77_FUNC(slasdt,SLASDT)(int *n, int *lvl, int *nd, int *inode, int *ndiml,
602 int *ndimr, int *msub);
605 F77_FUNC(slasrt,SLASRT)(const char *id, int *n, float *d, int *info);
608 F77_FUNC(slasrt2,SLASRT2)(const char *id, int *n, float *d, int *key, int *info);
611 F77_FUNC(sorgqr,SORGQR)(int *m, int *n, int *k, float *a, int *lda, float *tau,
612 float *work, int *lwork, int *info);
615 F77_FUNC(sstebz,SSTEBZ)(const char *range, const char *order, int *n, float *vl, float *vu,
616 int *il, int *iu, float *abstol, float *d, float *e,
617 int *m, int *nsplit, float *w, int *iblock, int *isplit,
618 float *work, int *iwork, int *info);
621 F77_FUNC(sgebrd,SGEBRD)(int *m, int *n, float *a, int *lda, float *d, float *e,
622 float *tauq, float *taup, float *work, int *lwork, int *info);
625 F77_FUNC(slacpy,SLACPY)(const char *uplo, int *m, int *n, float *a, int *lda, float *b, int *ldb);
628 F77_FUNC(slapy2,SLAPY2)(float * x, float * y);
631 F77_FUNC(slarrfx,SLARRFX)(int *n, float *d, float *l, float *ld, float *lld, int *ifirst,
632 int *ilast, float *w, float *sigma, float *dplus, float *lplus,
633 float *work, int *info);
636 F77_FUNC(slasd3,SLASD3)(int *nl, int *nr, int *sqre, int *k, float *d, float *q, int *ldq,
637 float *dsigma, float *u, int *ldu, float *u2, int *ldu2,
638 float *vt, int *ldvt, float *vt2, int *ldvt2, int *idxc,
639 int *ctot, float *z, int *info);
642 F77_FUNC(slaset,SLASET)(const char *uplo, int *m, int *n, float *alpha,
643 float *beta, float *a, int *lda);
646 F77_FUNC(slassq,SLASSQ)(int *n, float *x, int *incx, float *scale, float *sumsq);
649 F77_FUNC(sorm2l,SORM2L)(const char *side, const char *trans, int *m, int *n, int *k, float *a, int *lda,
650 float *tau, float *c, int *ldc, float *work, int *info);
653 F77_FUNC(sstegr,SSTEGR)(const char *jobz, const char *range, int *n, float *d, float *e, float *vl,
654 float *vu, int *il, int *iu, float *abstol, int *m, float *w,
655 float *z, int *ldz, int *isuppz, float *work,
656 int *lwork, int *iwork, int *liwork, int *info);
659 F77_FUNC(sgelq2,SGELQ2)(int *m, int *n, float *a, int *lda, float *tau, float *work, int *info);
662 F77_FUNC(slae2,SLAE2)(float *a, float *b, float *c, float *rt1, float *rt2);
665 F77_FUNC(slaev2,SLAEV2)(float *a, float *b, float *c, float *rt1, float *rt2,
666 float *cs1, float *cs2);
669 F77_FUNC(slar1vx,SLAR1VX)(int *n, int *b1, int *bn, float *sigma, float *d, float *l, float *ld,
670 float *lld, float *eval, float *gersch, float *z, float *ztz, float *mingma,
671 int *r, int *isuppz, float *work);
674 F77_FUNC(slarrvx,SLARRVX)(int *n, float *d, float *l, int *isplit, int *m, float *w,
675 int *iblock, int *indexw, float *gersch, float *tol, float *z, int *ldz,
676 int *isuppz, float *work, int *iwork, int *info);
679 F77_FUNC(slasd4,SLASD4)(int *n, int *i, float *d, float *z, float *delta,
680 float *rho, float *sigma, float *work, int *info);
683 F77_FUNC(slasq1,SLASQ1)(int *n, float *d, float *e, float *work, int *info);
687 F77_FUNC(slasv2,SLASV2)(float *f, float *g, float *h, float *ssmin, float *ssmax,
688 float *snr, float *csr, float *snl, float *csl);
691 F77_FUNC(sorm2r,SORM2R)(const char *side, const char *trans, int *m, int *n, int *k, float *a,
692 int *lda, float *tau, float *c, int *ldc, float *work, int *info);
695 F77_FUNC(sstein,SSTEIN)(int *n, float *d, float *e, int *m, float *w, int *iblock, int *isplit,
696 float *z, int *ldz, float *work, int *iwork, int *ifail, int *info);
699 F77_FUNC(sgelqf,SGELQF)(int *m, int *n, float *a, int *lda, float *tau,
700 float *work, int *lwork, int *info);
703 F77_FUNC(slaebz,SLAEBZ)(int *ijob, int *nitmax, int *n, int *mmax, int *minp, int *nbmin,
704 float *abstol, float *reltol, float *pivmin, float *d, float *e,
705 float *e2, int *nval, float *ab, float *c, int *mout, int *nab,
706 float *work, int *iwork, int *info);
709 F77_FUNC(slarf,SLARF)(const char *side, int *m, int *n, float *v, int *incv, float *tau,
710 float *c, int *ldc, float *work);
713 F77_FUNC(slartg,SLARTG)(float *f, float *g, float *cs, float *sn, float *r);
716 F77_FUNC(slasd5,SLASD5)(int *i, float *d, float *z, float *delta,
717 float *rho, float *dsigma, float *work);
720 F77_FUNC(slasq2,SLASQ2)(int *n, float *z, int *info);
723 F77_FUNC(slasq3,SLASQ3)(int *i0, int *n0, float *z, int *pp, float *dmin,
724 float *sigma, float *desig, float *qmax, int *nfail,
725 int *iter, int *ndiv, int *ieee);
728 F77_FUNC(slaswp,SLASWP)(int *n, float *a, int *lda, int *k1, int *k2, int *ipiv, int *incx);
731 F77_FUNC(sormbr,SORMBR)(const char *vect, const char *side, const char *trans, int *m, int *n, int *k,
732 float *a, int *lda, float *tau, float *c, int *ldc, float *work,
733 int *lwork, int *info);
736 F77_FUNC(ssterf,SSTERF)(int *n, float *d, float *e, int *info);
739 F77_FUNC(sgeqr2,SGEQR2)(int *m, int *n, float *a, int *lda, float *tau,
740 float *work, int *info);
743 F77_FUNC(slaed6,SLAED6)(int *kniter, int *orgati, float *rho, float *d,
744 float *z, float *finit, float *tau, int *info);
747 F77_FUNC(slarfb,SLARFB)(const char *side, const char *trans, const char *direct, const char *storev, int *m, int *n,
748 int *k, float *v, int *ldv, float *t, int *ldt, float *c,
749 int *ldc, float *work, int *ldwork);
752 F77_FUNC(slaruv,SLARUV)(int *iseed, int *n, float *x);
755 F77_FUNC(slasd6,SLASD6)(int *icompq, int *nl, int *nr, int *sqre, float *d, float *vf,
756 float *vl, float *alpha, float *beta, int *idxq, int *perm,
757 int *givptr, int *givcol, int *ldgcol, float *givnum, int *ldgnum,
758 float *poles, float *difl, float *difr, float *z, int *k,
759 float *c, float *s, float *work, int *iwork, int *info);
762 F77_FUNC(slatrd,SLATRD)(const char *uplo, int *n, int *nb, float *a, int *lda, float *e,
763 float * tau, float *w, int *ldw);
766 F77_FUNC(sorml2,SORML2)(const char *side, const char *trans, int *m, int *n, int *k, float *a,
767 int *lda, float *tau, float *c, int *ldc, float *work, int *info);
770 F77_FUNC(sstevr,SSTEVR)(const char *jobz, const char *range, int *n, float *d, float *e, float *vl,
771 float *vu, int *il, int *iu, float *abstol, int *m, float *w,
772 float *z, int *ldz, int *isuppz, float *work,
773 int *lwork, int *iwork, int *liwork, int *info);
776 F77_FUNC(ssytrd,SSYTRD)(const char *uplo, int *n, float * a, int *lda, float *d,
777 float *e, float *tau, float *work, int *lwork, int *info);
781 F77_FUNC(ssyevr,SSYEVR)(const char *jobz, const char *range, const char *uplo, int *n,
782 float *a, int *lda, float *vl, float *vu, int *
783 il, int *iu, float *abstol, int *m, float *w,
784 float *z__, int *ldz, int *isuppz, float *work,
785 int *lwork, int *iwork, int *liwork, int *info);
788 F77_FUNC(sormql,SORMQL)(const char *side, const char *trans, int *m, int *n,
789 int *k, float *a, int *lda, float *tau, float *
790 c, int *ldc, float *work, int *lwork, int *info);
793 F77_FUNC(sormqr,SORMQR)(const char *side, const char *trans, int *m, int *n, int *k, float *a,
794 int *lda, float *tau, float *c, int *ldc,
795 float *work, int *lwork, int *info);
798 F77_FUNC(sorgbr,SORGBR)(const char *vect, int *m, int *n, int *k, float *a, int *lda,
799 float *tau, float *work, int *lwork, int *info);
802 F77_FUNC(slasq5,SLASQ5)(int *i0, int *n0, float *z, int *pp, float *tau, float *dmin,
803 float *dmin1, float *dmin2, float *dn, float *dnm1,
804 float *dnm2, int *ieee);
807 F77_FUNC(slasd8,SLASD8)(int *icompq, int *k, float *d, float *z, float *vf, float *vl,
808 float *difl, float *difr, int *lddifr, float *dsigma,
809 float *work, int *info);
812 F77_FUNC(slascl,SLASCL)(const char *type, int *kl, int *ku, float *cfrom, float *cto, int *m,
813 int *n, float *a, int *lda, int *info);
816 F77_FUNC(slarft,SLARFT)(const char *direct, const char *storev, int *n, int *k, float *v,
817 int *ldv, float *tau, float *t, int *ldt);
820 F77_FUNC(slagts,SLAGTS)(int *job, int *n, float *a, float *b, float *c, float *d,
821 int *in, float *y, float *tol, int *info);
824 F77_FUNC(sgesdd,SGESDD)(const char *jobz, int *m, int *n, float *a, int *lda, float *s, float *u,
825 int *ldu, float *vt, int *ldvt, float *work, int *lwork,
826 int *iwork, int *info);
829 F77_FUNC(ssytd2,SSYTD2)(const char *uplo, int *n, float *a, int *lda, float *d,
830 float *e, float *tau, int *info);
833 F77_FUNC(sormlq,SORMLQ)(const char *side, const char *trans, int *m, int *n, int *k, float *a, int *lda,
834 float *tau, float *c, int *ldc, float *work, int *lwork, int *info);
837 F77_FUNC(sorg2r,SORG2R)(int *m, int *n, int *k, float *a, int *lda, float *tau,
838 float *work, int *info);
841 F77_FUNC(slasq4,SLASQ4)(int *i0, int *n0, float *z, int *pp, int *n0in, float *dmin,
842 float *dmin1, float *dmin2, float *dn, float *dn1,
843 float *dn2, float *tau, int *ttype);
846 F77_FUNC(slasd7,SLASD7)(int *icompq, int *nl, int *nr, int *sqre, int *k, float *d, float *z,
847 float *zw, float *vf, float *vfw, float *vl, float *vlw,
848 float *alpha, float *beta, float *dsigma, int *idx, int *idxp,
849 int *idxq, int *perm, int *givptr, int *givcol, int *ldgcol,
850 float *givnum, int *ldgnum, float *c, float *s, int *info);
853 F77_FUNC(slas2,SLAS2)(float *f, float *g, float *h, float *ssmin, float *ssmax);
856 F77_FUNC(slarfg,SLARFG)(int *n, float *alpha, float *x, int *incx, float *tau);
859 F77_FUNC(slagtf,SLAGTF)(int *n, float *a, float *lambda, float *b, float *c,
860 float *tol, float *d, int *in, int *info);
863 F77_FUNC(sgeqrf,SGEQRF)(int *m, int *n, float *a, int *lda, float *tau,
864 float *work, int *lwork, int *info);
873 #endif /* _LAPACK_H_ */