include/gmx_lapack.h

   1 /*
   2  *
   3  *                This source code is part of
   4  *
   5  *                 G   R   O   M   A   C   S
   6  *
   7  *          GROningen MAchine for Chemical Simulations
   8  *
   9  * Written by David van der Spoel, Erik Lindahl, Berk Hess, and others.
  10  * Copyright (c) 1991-2000, University of Groningen, The Netherlands.
  11  * Copyright (c) 2001-2008, The GROMACS development team,
  12  * check out http://www.gromacs.org for more information.
  13
  14  * This program is free software; you can redistribute it and/or
  15  * modify it under the terms of the GNU General Public License
  16  * as published by the Free Software Foundation; either version 2
  17  * of the License, or (at your option) any later version.
  18  *
  19  * If you want to redistribute modifications, please consider that
  20  * scientific software is very special. Version control is crucial -
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  24  * files - if they are missing, get the official version at www.gromacs.org.
  25  *
  26  * To help us fund GROMACS development, we humbly ask that you cite
  27  * the papers on the package - you can find them in the top README file.
  28  *
  29  * For more info, check our website at http://www.gromacs.org
  30  *
  31  * And Hey:
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  33  */
  34
  35 #ifndef _GMX_LAPACK_H_
  36 #define _GMX_LAPACK_H_
  37
  38
  39 #ifdef HAVE_CONFIG_H
  40 #include <config.h>
  41 #endif
  42
  43
  44 /** @file
  45  *
  46  *  @brief Header definitions for the standard LAPACK library.
  47  *
  48  * This is the subset of LAPACK routines used for the
  49  * linear algebra operations in Gromacs. Most of the execution time
  50  * will be spent in the BLAS routines, which you hopefully have an
  51  * optimized version of. Gromacs includes reference implementations
  52  * of both BLAS and LAPACK so it compiles everywhere, but you should
  53  * really try to find a vendor or otherwise optimized version at least
  54  * of BLAS for better performance.
  55  *
  56  * Do NOT use this code for other purposes - we only provide this as a
  57  * simple fallback/reference implementation when no optimized BLAS
  58  * is present. If you need an implementation for your own code
  59  * there are several much faster versions out there.
  60  *
  61  * All routines are compatible with the LAPACK/BLAS reference implementations,
  62  * meaning they assume fortran-style matrix row/column organization.
  63  *
  64  * There is plenty of documentation for these routines available
  65  * at http://www.netlib.org/lapack , so there is no point in repeating
  66  * it here.
  67  */
  68
  69
  70
  71 #ifdef __cplusplus
  72 extern "C" {
  73 #endif
  74 #if 0
  75 }
  76 #endif
  77
  78 #ifndef F77_FUNC
  79 #define F77_FUNC(name,NAME) name ## _
  80 #endif
  81
  82 #include "types/simple.h"
  83
  84
  85 /* Double precision */
  86
  87 void
  88 F77_FUNC(dbdsdc,DBDSDC)(const char *uplo, const char *compq, int *n, double *d, double *e, double *u,
  89         int *ldu, double *vt, int *ldvt, double *q, int *iq, double *work,
  90         int *iwork, int *info);
  91
  92 void
  93 F77_FUNC(dgetf2,DGETF2)(int *m, int *n, double *a, int *lda, int *ipiv, int *info);
  94
  95 void
  96 F77_FUNC(dlamrg,DLAMRG)(int *n1, int *n2, double *a, int *dtrd1, int *dtrd2, int *index);
  97
  98 void
  99 F77_FUNC(dlarnv,DLARNV)(int *idist, int *iseed, int *n, double *x);
 100
 101 void
 102 F77_FUNC(dlasd0,DLASD0)(int *n, int *sqre, double *d, double *e, double *u,
 103         int *ldu, double *vt, int *ldvt, int *smlsiz, int *iwork,
 104         double *work, int *info);
 105
 106 void
 107 F77_FUNC(dlasda,DLASDA)(int *icompq, int *smlsiz, int *n, int *sqre, double *d, double *e,
 108         double *u, int *ldu, double *vt, int *k, double *difl, double *difr,
 109         double *z, double *poles, int *givptr, int *givcol, int *ldgcol,
 110         int *perm, double *givnum, double *c, double *s,
 111         double *work, int *iwork, int *info);
 112
 113 void
 114 F77_FUNC(dlasq6,DLASQ6)(int *i0, int *n0, double *z, int *pp, double *dmin, double *dmin1,
 115         double *dmin2, double *dn, double *dnm1, double *dnm2);
 116
 117 void
 118 F77_FUNC(dorgl2,DORGL2)(int *m, int *n, int *k, double *a, int *lda,
 119         double *tau, double *work, int *info);
 120
 121 void
 122 F77_FUNC(dbdsqr,DBDSQR)(const char *uplo, int *n, int *ncvt, int *nru, int *ncc, double *d,
 123         double *e, double *vt, int *ldvt, double *u, int *ldu,
 124         double *c, int *ldc, double *work, int *info);
 125
 126 void
 127 F77_FUNC(dgetrf,DGETRF)(int *m, int *n, double *a, int *lda, int *ipiv, int *info);
 128
 129 void
 130 F77_FUNC(dgetri,DGETRI)(int *n, double *a, int *lda, int *ipiv, double *work,
 131         int *lwork, int *info);
 132
 133 void
 134 F77_FUNC(dgetrs,DGETRS)(const char *trans, int *n, int *nrhs,   double *a, int *lda, int *ipiv,
 135         double *b, int *ldb, int *info);
 136
 137 void
 138 F77_FUNC(dtrtri,DTRTRI)(const char *uplo, const char *diag, int *n, double *a, int *lda, int *info);
 139
 140 void
 141 F77_FUNC(dtrti2,DTRTI2)(const char *uplo, const char *diag, int *n, double *a, int *lda, int *info);
 142
 143 double
 144 F77_FUNC(dlange,DLANGE)(const char *norm, int *m, int *n, double *a, int *lda, double *work);
 145
 146 void
 147 F77_FUNC(dlarrbx,DLARRBX)(int *n, double *d, double *l, double *ld, double *lld, int *ifirst,
 148          int *ilast, double *rtol1, double *rtol2, int *offset, double *w,
 149          double *wgap, double *werr, double *work, int *iwork, int *info);
 150
 151 void
 152 F77_FUNC(dlasd1,DLASD1)(int *nl, int *nr, int *sqre, double *d, double *alpha, double *beta,
 153         double *u, int *ldu, double *vt, int *ldvt, int *idxq, int *iwork,
 154         double *work, int *info);
 155
 156 void
 157 F77_FUNC(dlasdq,DLASDQ)(const char *uplo, int *sqre, int *n, int *ncvt, int *nru, int *ncc,
 158         double *d, double *e, double *vt, int *ldvt, double *u, int *ldu,
 159         double *c, int *ldc, double *work, int *info);
 160
 161 void
 162 F77_FUNC(dlasr,DLASR)(const char *side, const char *pivot, const char *direct, int *m, int *n, double *c,
 163        double *s, double *a, int *lda);
 164
 165 void
 166 F77_FUNC(dorglq,DORGLQ)(int *m, int *n, int *k, double *a, int *lda,
 167         double *tau, double *work, int *lwork, int *info);
 168
 169 void
 170 F77_FUNC(dormtr,DORMTR)(const char *side, const char *uplo, const char *trans, int *m, int *n, double *a,
 171         int *lda, double *tau, double *c, int *ldc,
 172         double *work, int *lwork, int *info);
 173
 174 void
 175 F77_FUNC(dgebd2,DGEBD2)(int *m, int *n, double *a, int *lda, double *d, double *e,
 176         double *tauq, double *taup, double *work, int *info);
 177
 178 void
 179 F77_FUNC(dlabrd,DLABRD)(int *m, int *n, int *nb, double *a, int *lda, double *d,
 180         double *e, double *tauq, double *taup, double *x,
 181         int *ldx, double *y, int *ldy);
 182
 183 double
 184 F77_FUNC(dlanst,DLANST)(const char *norm, int *n, double *d, double *e);
 185
 186 double
 187 F77_FUNC(dlansy,DLANSY)(const char *norm, const char *uplo, int *n, double *a, int *lda, double *work);
 188
 189 void
 190 F77_FUNC(dlarrex,DLARREX)(const char *range, int *n, double *vl, double *vu, int *il, int *iu,
 191          double *d, double *e, double *tol, int *nsplit,
 192          int *isplit, int *m, double *w, int *iblock, int *indexw,
 193          double *gersch, double *work, int *iwork, int *info);
 194
 195 void
 196 F77_FUNC(dlasd2,DLASD2)(int *nl, int *nr, int *sqre, int *k, double *d, double *z,
 197         double *alpha, double *beta, double *u, int *ldu, double *vt,
 198         int *ldvt, double *dsigma, double *u2, int *ldu2, double *vt2,
 199         int *ldvt2, int *idxp, int *idx, int *idxc,
 200         int *idxq, int *coltyp, int *info);
 201
 202 void
 203 F77_FUNC(dlasdt,DLASDT)(int *n, int *lvl, int *nd, int *inode, int *ndiml,
 204         int *ndimr, int *msub);
 205
 206 void
 207 F77_FUNC(dlasrt,DLASRT)(const char *id, int *n, double *d, int *info);
 208
 209 void
 210 F77_FUNC(dlasrt2,DLASRT2)(const char *id, int *n, double *d, int *key, int *info);
 211
 212 void
 213 F77_FUNC(ilasrt2,ILASRT2)(const char *id, int *n, int *d, int *key, int *info);
 214
 215 void
 216 F77_FUNC(dorgqr,DORGQR)(int *m, int *n, int *k, double *a, int *lda, double *tau,
 217         double *work, int *lwork, int *info);
 218
 219 void
 220 F77_FUNC(dstebz,DSTEBZ)(const char *range, const char *order, int *n, double *vl, double *vu,
 221         int *il, int *iu, double *abstol, double *d, double *e,
 222         int *m, int *nsplit, double *w, int *iblock, int *isplit,
 223         double *work, int *iwork, int *info);
 224
 225 void
 226 F77_FUNC(dsteqr,DSTEQR)(const char *compz, int *n, double *d__, double *e,
 227         double *z__,  int *ldz, double *work, int *info);
 228
 229 void
 230 F77_FUNC(dgebrd,DGEBRD)(int *m, int *n, double *a, int *lda, double *d, double *e,
 231         double *tauq, double *taup, double *work, int *lwork, int *info);
 232
 233 void
 234 F77_FUNC(dlacpy,DLACPY)(const char *uplo, int *m, int *n, double *a, int *lda, double *b, int *ldb);
 235
 236 double
 237 F77_FUNC(dlapy2,DLAPY2)(double * x, double * y);
 238
 239
 240 void
 241 F77_FUNC(dlarrfx,DLARRFX)(int *n, double *d, double *l, double *ld, double *lld, int *ifirst,
 242         int *ilast, double *w, double *sigma, double *dplus, double *lplus,
 243         double *work, int *info);
 244
 245 void
 246 F77_FUNC(dlasd3,DLASD3)(int *nl, int *nr, int *sqre, int *k, double *d, double *q, int *ldq,
 247         double *dsigma, double *u, int *ldu, double *u2, int *ldu2,
 248         double *vt, int *ldvt, double *vt2, int *ldvt2, int *idxc,
 249         int *ctot, double *z, int *info);
 250
 251 void
 252 F77_FUNC(dlaset,DLASET)(const char *uplo, int *m, int *n, double *alpha,
 253         double *beta, double *a, int *lda);
 254
 255 void
 256 F77_FUNC(dlassq,DLASSQ)(int *n, double *x, int *incx, double *scale, double *sumsq);
 257
 258 void
 259 F77_FUNC(dorm2l,DORM2L)(const char *side, const char *trans, int *m, int *n, int *k, double *a, int *lda,
 260         double *tau, double *c, int *ldc, double *work, int *info);
 261
 262 void
 263 F77_FUNC(dstegr,DSTEGR)(const char *jobz, const char *range, int *n, double *d, double *e, double *vl,
 264         double *vu, int *il, int *iu, double *abstol, int *m, double *w,
 265         double *z, int *ldz, int *isuppz, double *work,
 266         int *lwork, int *iwork, int *liwork, int *info);
 267
 268 void
 269 F77_FUNC(ssteqr,SSTEQR)(const char *compz, int *n, float *d__, float *e,
 270         float *z__,  int *ldz, float *work, int *info);
 271
 272 void
 273 F77_FUNC(dgelq2,DGELQ2)(int *m, int *n, double *a, int *lda, double *tau, double *work, int *info);
 274
 275 void
 276 F77_FUNC(dlae2,DLAE2)(double *a, double *b, double *c, double *rt1, double *rt2);
 277
 278 void
 279 F77_FUNC(dlaev2,DLAEV2)(double *a, double *b, double *c, double *rt1, double *rt2,
 280         double *cs1, double *cs2);
 281
 282 void
 283 F77_FUNC(dlar1vx,DLAR1VX)(int *n, int *b1, int *bn, double *sigma, double *d, double *l, double *ld,
 284                           double *lld, double *eval, double *gersch, double *z, double *ztz, double *mingma,
 285                           int *r, int *isuppz, double *work);
 286
 287 void
 288 F77_FUNC(dlarrvx,DLARRVX)(int *n, double *d, double *l, int *isplit, int *m, double *w,
 289          int *iblock, int *indexw, double *gersch, double *tol, double *z, int *ldz,
 290          int *isuppz, double *work, int *iwork, int *info);
 291
 292 void
 293 F77_FUNC(dlasd4,DLASD4)(int *n, int *i, double *d, double *z, double *delta,
 294         double *rho, double *sigma, double *work, int *info);
 295
 296 void
 297 F77_FUNC(dlasq1,DLASQ1)(int *n, double *d, double *e, double *work, int *info);
 298
 299
 300 void
 301 F77_FUNC(dlasv2,DLASV2)(double *f, double *g, double *h, double *ssmin, double *ssmax,
 302         double *snr, double *csr, double *snl, double *csl);
 303
 304 void
 305 F77_FUNC(dorm2r,DORM2R)(const char *side, const char *trans, int *m, int *n, int *k, double *a,
 306         int *lda, double *tau, double *c, int *ldc, double *work, int *info);
 307
 308 void
 309 F77_FUNC(dstein,DSTEIN)(int *n, double *d, double *e, int *m, double *w, int *iblock, int *isplit,
 310         double *z, int *ldz, double *work, int *iwork, int *ifail, int *info);
 311
 312 void
 313 F77_FUNC(dgelqf,DGELQF)(int *m, int *n, double *a, int *lda, double *tau,
 314         double *work, int *lwork, int *info);
 315
 316 void
 317 F77_FUNC(dlaebz,DLAEBZ)(int *ijob, int *nitmax, int *n, int *mmax, int *minp, int *nbmin,
 318         double *abstol, double *reltol, double *pivmin, double *d, double *e,
 319         double *e2, int *nval, double *ab, double *c, int *mout, int *nab,
 320         double *work, int *iwork, int *info);
 321
 322 void
 323 F77_FUNC(dlarf,DLARF)(const char *side, int *m, int *n, double *v, int *incv, double *tau,
 324        double *c, int *ldc, double *work);
 325
 326 void
 327 F77_FUNC(dlartg,DLARTG)(double *f, double *g, double *cs, double *sn, double *r);
 328
 329 void
 330 F77_FUNC(dlasd5,DLASD5)(int *i, double *d, double *z, double *delta,
 331         double *rho, double *dsigma, double *work);
 332
 333 void
 334 F77_FUNC(dlasq2,DLASQ2)(int *n, double *z, int *info);
 335
 336 void
 337 F77_FUNC(dlasq3,DLASQ3)(int *i0, int *n0, double *z, int *pp, double *dmin,
 338         double *sigma, double *desig, double *qmax, int *nfail,
 339         int *iter, int *ndiv, int *ieee);
 340
 341 void
 342 F77_FUNC(dlaswp,DLASWP)(int *n, double *a, int *lda, int *k1, int *k2, int *ipiv, int *incx);
 343
 344 void
 345 F77_FUNC(dormbr,DORMBR)(const char *vect, const char *side, const char *trans, int *m, int *n, int *k,
 346         double *a, int *lda, double *tau, double *c, int *ldc, double *work,
 347         int *lwork, int *info);
 348
 349 void
 350 F77_FUNC(dsterf,DSTERF)(int *n, double *d, double *e, int *info);
 351
 352 void
 353 F77_FUNC(dgeqr2,DGEQR2)(int *m, int *n, double *a, int *lda, double *tau,
 354         double *work, int *info);
 355
 356 void
 357 F77_FUNC(dlaed6,DLAED6)(int *kniter, int *orgati, double *rho, double *d,
 358         double *z, double *finit, double *tau, int *info);
 359
 360 void
 361 F77_FUNC(dlarfb,DLARFB)(const char *side, const char *trans, const char *direct, const char *storev, int *m, int *n,
 362         int *k, double *v, int *ldv, double *t, int *ldt, double *c,
 363         int *ldc, double *work, int *ldwork);
 364
 365 void
 366 F77_FUNC(dlaruv,DLARUV)(int *iseed, int *n, double *x);
 367
 368 void
 369 F77_FUNC(dlasd6,DLASD6)(int *icompq, int *nl, int *nr, int *sqre, double *d, double *vf,
 370         double *vl, double *alpha, double *beta, int *idxq, int *perm,
 371         int *givptr, int *givcol, int *ldgcol, double *givnum, int *ldgnum,
 372         double *poles, double *difl, double *difr, double *z, int *k,
 373         double *c, double *s, double *work, int *iwork, int *info);
 374
 375 void
 376 F77_FUNC(dlatrd,DLATRD)(const char *uplo, int *n, int *nb, double *a, int *lda, double *e,
 377         double * tau, double *w, int *ldw);
 378
 379 void
 380 F77_FUNC(dorml2,DORML2)(const char *side, const char *trans, int *m, int *n, int *k, double *a,
 381         int *lda, double *tau, double *c, int *ldc, double *work, int *info);
 382
 383 void
 384 F77_FUNC(dstevr,DSTEVR)(const char *jobz, const char *range, int *n, double *d, double *e, double *vl,
 385         double *vu, int *il, int *iu, double *abstol, int *m, double *w,
 386         double *z, int *ldz, int *isuppz, double *work,
 387         int *lwork, int *iwork, int *liwork, int *info);
 388
 389 void
 390 F77_FUNC(dsytrd,DSYTRD)(const char *uplo, int *n, double *  a, int *lda, double *d,
 391         double *e, double *tau, double *work, int *lwork, int *info);
 392
 393 void
 394 F77_FUNC(dsyevr,DSYEVR)(const char *jobz, const char *range, const char *uplo, int *n,
 395         double *a, int *lda, double *vl, double *vu, int *
 396         il, int *iu, double *abstol, int *m, double *w,
 397         double *z__, int *ldz, int *isuppz, double *work,
 398         int *lwork, int *iwork, int *liwork, int *info);
 399
 400 void
 401 F77_FUNC(dormql,DORMQL)(const char *side, const char *trans, int *m, int *n,
 402         int *k, double *a, int *lda, double *tau, double *
 403         c, int *ldc, double *work, int *lwork, int *info);
 404
 405 void
 406 F77_FUNC(dormqr,DORMQR)(const char *side, const char *trans, int *m, int *n, int *k, double *a,
 407         int *lda, double *tau, double *c, int *ldc,
 408         double *work, int *lwork, int *info);
 409
 410 void
 411 F77_FUNC(dorgbr,DORGBR)(const char *vect, int *m, int *n, int *k, double *a, int *lda,
 412         double *tau, double *work, int *lwork, int *info);
 413
 414 void
 415 F77_FUNC(dlasq5,DLASQ5)(int *i0, int *n0, double *z, int *pp, double *tau, double *dmin,
 416         double *dmin1, double *dmin2, double *dn, double *dnm1,
 417         double *dnm2, int *ieee);
 418
 419 void
 420 F77_FUNC(dlasd8,DLASD8)(int *icompq, int *k, double *d, double *z, double *vf, double *vl,
 421         double *difl, double *difr, int *lddifr, double *dsigma,
 422         double *work, int *info);
 423
 424 void
 425 F77_FUNC(dlascl,DLASCL)(const char *type, int *kl, int *ku, double *cfrom, double *cto, int *m,
 426         int *n, double *a, int *lda, int *info);
 427
 428 void
 429 F77_FUNC(dlarft,DLARFT)(const char *direct, const char *storev, int *n, int *k, double *v,
 430         int *ldv, double *tau, double *t, int *ldt);
 431
 432 void
 433 F77_FUNC(dlagts,DLAGTS)(int *job, int *n, double *a, double *b, double *c, double *d,
 434         int *in, double *y, double *tol, int *info);
 435
 436 void
 437 F77_FUNC(dgesdd,DGESDD)(const char *jobz, int *m, int *n, double *a, int *lda, double *s, double *u,
 438         int *ldu, double *vt, int *ldvt, double *work, int *lwork,
 439         int *iwork, int *info);
 440
 441 void
 442 F77_FUNC(dsytd2,DSYTD2)(const char *uplo, int *n, double *a, int *lda, double *d,
 443         double *e, double *tau, int *info);
 444
 445 void
 446 F77_FUNC(dormlq,DORMLQ)(const char *side, const char *trans, int *m, int *n, int *k, double *a, int *lda,
 447         double *tau, double *c, int *ldc, double *work, int *lwork, int *info);
 448
 449 void
 450 F77_FUNC(dorg2r,DORG2R)(int *m, int *n, int *k, double *a, int *lda, double *tau,
 451         double *work, int *info);
 452
 453 void
 454 F77_FUNC(dlasq4,DLASQ4)(int *i0, int *n0, double *z, int *pp, int *n0in, double *dmin,
 455         double *dmin1, double *dmin2, double *dn, double *dn1,
 456         double *dn2, double *tau, int *ttype);
 457
 458 void
 459 F77_FUNC(dlasd7,DLASD7)(int *icompq, int *nl, int *nr, int *sqre, int *k, double *d, double *z,
 460         double *zw, double *vf, double *vfw, double *vl, double *vlw,
 461         double *alpha, double *beta, double *dsigma, int *idx, int *idxp,
 462         int *idxq, int *perm, int *givptr, int *givcol, int *ldgcol,
 463         double *givnum, int *ldgnum, double *c, double *s, int *info);
 464
 465 void
 466 F77_FUNC(dlas2,DLAS2)(double *f, double *g, double *h, double *ssmin, double *ssmax);
 467
 468 void
 469 F77_FUNC(dlarfg,DLARFG)(int *n, double *alpha, double *x, int *incx, double *tau);
 470
 471 void
 472 F77_FUNC(dlagtf,DLAGTF)(int *n, double *a, double *lambda, double *b, double *c,
 473         double *tol, double *d, int *in, int *info);
 474
 475 void
 476 F77_FUNC(dgeqrf,DGEQRF)(int *m, int *n, double *a, int *lda, double *tau,
 477         double *work, int *lwork, int *info);
 478
 479
 480
 481 /* Single precision */
 482
 483 void
 484 F77_FUNC(sbdsdc,SBDSDC)(const char *uplo, const char *compq, int *n, float *d, float *e, float *u,
 485         int *ldu, float *vt, int *ldvt, float *q, int *iq, float *work,
 486         int *iwork, int *info);
 487
 488 void
 489 F77_FUNC(sgetf2,SGETF2)(int *m, int *n, float *a, int *lda, int *ipiv, int *info);
 490
 491 void
 492 F77_FUNC(slamrg,SLAMRG)(int *n1, int *n2, float *a, int *dtrd1, int *dtrd2, int *index);
 493
 494 void
 495 F77_FUNC(slarnv,SLARNV)(int *idist, int *iseed, int *n, float *x);
 496
 497 void
 498 F77_FUNC(slasd0,SLASD0)(int *n, int *sqre, float *d, float *e, float *u,
 499         int *ldu, float *vt, int *ldvt, int *smlsiz, int *iwork,
 500         float *work, int *info);
 501
 502 void
 503 F77_FUNC(slasda,SLASDA)(int *icompq, int *smlsiz, int *n, int *sqre, float *d, float *e,
 504         float *u, int *ldu, float *vt, int *k, float *difl, float *difr,
 505         float *z, float *poles, int *givptr, int *givcol, int *ldgcol,
 506         int *perm, float *givnum, float *c, float *s,
 507         float *work, int *iwork, int *info);
 508
 509 void
 510 F77_FUNC(slasq6,SLASQ6)(int *i0, int *n0, float *z, int *pp, float *dmin, float *dmin1,
 511         float *dmin2, float *dn, float *dnm1, float *dnm2);
 512
 513 void
 514 F77_FUNC(sorgl2,SORGL2)(int *m, int *n, int *k, float *a, int *lda,
 515         float *tau, float *work, int *info);
 516
 517 void
 518 F77_FUNC(sbdsqr,SBDSQR)(const char *uplo, int *n, int *ncvt, int *nru, int *ncc, float *d,
 519         float *e, float *vt, int *ldvt, float *u, int *ldu,
 520         float *c, int *ldc, float *work, int *info);
 521
 522 void
 523 F77_FUNC(sgetrf,SGETRF)(int *m, int *n, float *a, int *lda, int *ipiv, int *info);
 524
 525 void
 526 F77_FUNC(sgetri,SGETRI)(int *n, float *a, int *lda, int *ipiv, float *work,
 527         int *lwork, int *info);
 528
 529 void
 530 F77_FUNC(sgetrs,SGETRS)(const char *trans, int *n, int *nrhs,   float *a, int *lda, int *ipiv,
 531         float *b, int *ldb, int *info);
 532
 533 void
 534 F77_FUNC(strtri,STRTRI)(const char *uplo, const char *diag, int *n, float *a, int *lda, int *info);
 535
 536 void
 537 F77_FUNC(strti2,STRTI2)(const char *uplo, const char *diag, int *n, float *a, int *lda, int *info);
 538
 539 float
 540 F77_FUNC(slange,SLANGE)(const char *norm, int *m, int *n, float *a, int *lda, float *work);
 541
 542 void
 543 F77_FUNC(slarrbx,SLARRBX)(int *n, float *d, float *l, float *ld, float *lld, int *ifirst,
 544          int *ilast, float *rtol1, float *rtol2, int *offset, float *w,
 545          float *wgap, float *werr, float *work, int *iwork, int *info);
 546
 547 void
 548 F77_FUNC(slasd1,SLASD1)(int *nl, int *nr, int *sqre, float *d, float *alpha, float *beta,
 549         float *u, int *ldu, float *vt, int *ldvt, int *idxq, int *iwork,
 550         float *work, int *info);
 551
 552 void
 553 F77_FUNC(slasdq,SLASDQ)(const char *uplo, int *sqre, int *n, int *ncvt, int *nru, int *ncc,
 554         float *d, float *e, float *vt, int *ldvt, float *u, int *ldu,
 555         float *c, int *ldc, float *work, int *info);
 556
 557 void
 558 F77_FUNC(slasr,SLASR)(const char *side, const char *pivot, const char *direct, int *m, int *n, float *c,
 559        float *s, float *a, int *lda);
 560
 561 void
 562 F77_FUNC(sorglq,SORGLQ)(int *m, int *n, int *k, float *a, int *lda,
 563         float *tau, float *work, int *lwork, int *info);
 564
 565 void
 566 F77_FUNC(sormtr,SORMTR)(const char *side, const char *uplo, const char *trans, int *m, int *n, float *a,
 567         int *lda, float *tau, float *c, int *ldc,
 568         float *work, int *lwork, int *info);
 569
 570 void
 571 F77_FUNC(sgebd2,SGEBD2)(int *m, int *n, float *a, int *lda, float *d, float *e,
 572         float *tauq, float *taup, float *work, int *info);
 573
 574 void
 575 F77_FUNC(slabrd,SLABRD)(int *m, int *n, int *nb, float *a, int *lda, float *d,
 576         float *e, float *tauq, float *taup, float *x,
 577         int *ldx, float *y, int *ldy);
 578
 579 float
 580 F77_FUNC(slanst,SLANST)(const char *norm, int *n, float *d, float *e);
 581
 582 float
 583 F77_FUNC(slansy,SLANSY)(const char *norm, const char *uplo, int *n, float *a, int *lda, float *work);
 584
 585 void
 586 F77_FUNC(slarrex,SLARREX)(const char *range, int *n, float *vl, float *vu, int *il, int *iu,
 587          float *d, float *e, float *tol, int *nsplit,
 588          int *isplit, int *m, float *w, int *iblock, int *indexw,
 589          float *gersch, float *work, int *iwork, int *info);
 590
 591 void
 592 F77_FUNC(slasd2,SLASD2)(int *nl, int *nr, int *sqre, int *k, float *d, float *z,
 593         float *alpha, float *beta, float *u, int *ldu, float *vt,
 594         int *ldvt, float *dsigma, float *u2, int *ldu2, float *vt2,
 595         int *ldvt2, int *idxp, int *idx, int *idxc,
 596         int *idxq, int *coltyp, int *info);
 597
 598 void
 599 F77_FUNC(slasdt,SLASDT)(int *n, int *lvl, int *nd, int *inode, int *ndiml,
 600         int *ndimr, int *msub);
 601
 602 void
 603 F77_FUNC(slasrt,SLASRT)(const char *id, int *n, float *d, int *info);
 604
 605 void
 606 F77_FUNC(slasrt2,SLASRT2)(const char *id, int *n, float *d, int *key, int *info);
 607
 608 void
 609 F77_FUNC(sorgqr,SORGQR)(int *m, int *n, int *k, float *a, int *lda, float *tau,
 610         float *work, int *lwork, int *info);
 611
 612 void
 613 F77_FUNC(sstebz,SSTEBZ)(const char *range, const char *order, int *n, float *vl, float *vu,
 614         int *il, int *iu, float *abstol, float *d, float *e,
 615         int *m, int *nsplit, float *w, int *iblock, int *isplit,
 616         float *work, int *iwork, int *info);
 617
 618 void
 619 F77_FUNC(sgebrd,SGEBRD)(int *m, int *n, float *a, int *lda, float *d, float *e,
 620         float *tauq, float *taup, float *work, int *lwork, int *info);
 621
 622 void
 623 F77_FUNC(slacpy,SLACPY)(const char *uplo, int *m, int *n, float *a, int *lda, float *b, int *ldb);
 624
 625 float
 626 F77_FUNC(slapy2,SLAPY2)(float * x, float * y);
 627
 628 void
 629 F77_FUNC(slarrfx,SLARRFX)(int *n, float *d, float *l, float *ld, float *lld, int *ifirst,
 630         int *ilast, float *w, float *sigma, float *dplus, float *lplus,
 631         float *work, int *info);
 632
 633 void
 634 F77_FUNC(slasd3,SLASD3)(int *nl, int *nr, int *sqre, int *k, float *d, float *q, int *ldq,
 635         float *dsigma, float *u, int *ldu, float *u2, int *ldu2,
 636         float *vt, int *ldvt, float *vt2, int *ldvt2, int *idxc,
 637         int *ctot, float *z, int *info);
 638
 639 void
 640 F77_FUNC(slaset,SLASET)(const char *uplo, int *m, int *n, float *alpha,
 641         float *beta, float *a, int *lda);
 642
 643 void
 644 F77_FUNC(slassq,SLASSQ)(int *n, float *x, int *incx, float *scale, float *sumsq);
 645
 646 void
 647 F77_FUNC(sorm2l,SORM2L)(const char *side, const char *trans, int *m, int *n, int *k, float *a, int *lda,
 648         float *tau, float *c, int *ldc, float *work, int *info);
 649
 650 void
 651 F77_FUNC(sstegr,SSTEGR)(const char *jobz, const char *range, int *n, float *d, float *e, float *vl,
 652         float *vu, int *il, int *iu, float *abstol, int *m, float *w,
 653         float *z, int *ldz, int *isuppz, float *work,
 654         int *lwork, int *iwork, int *liwork, int *info);
 655
 656 void
 657 F77_FUNC(sgelq2,SGELQ2)(int *m, int *n, float *a, int *lda, float *tau, float *work, int *info);
 658
 659 void
 660 F77_FUNC(slae2,SLAE2)(float *a, float *b, float *c, float *rt1, float *rt2);
 661
 662 void
 663 F77_FUNC(slaev2,SLAEV2)(float *a, float *b, float *c, float *rt1, float *rt2,
 664         float *cs1, float *cs2);
 665
 666 void
 667 F77_FUNC(slar1vx,SLAR1VX)(int *n, int *b1, int *bn, float *sigma, float *d, float *l, float *ld,
 668         float *lld, float *eval, float *gersch, float *z, float *ztz, float *mingma,
 669         int *r, int *isuppz, float *work);
 670
 671 void
 672 F77_FUNC(slarrvx,SLARRVX)(int *n, float *d, float *l, int *isplit, int *m, float *w,
 673          int *iblock, int *indexw, float *gersch, float *tol, float *z, int *ldz,
 674          int *isuppz, float *work, int *iwork, int *info);
 675
 676 void
 677 F77_FUNC(slasd4,SLASD4)(int *n, int *i, float *d, float *z, float *delta,
 678         float *rho, float *sigma, float *work, int *info);
 679
 680 void
 681 F77_FUNC(slasq1,SLASQ1)(int *n, float *d, float *e, float *work, int *info);
 682
 683
 684 void
 685 F77_FUNC(slasv2,SLASV2)(float *f, float *g, float *h, float *ssmin, float *ssmax,
 686         float *snr, float *csr, float *snl, float *csl);
 687
 688 void
 689 F77_FUNC(sorm2r,SORM2R)(const char *side, const char *trans, int *m, int *n, int *k, float *a,
 690         int *lda, float *tau, float *c, int *ldc, float *work, int *info);
 691
 692 void
 693 F77_FUNC(sstein,SSTEIN)(int *n, float *d, float *e, int *m, float *w, int *iblock, int *isplit,
 694         float *z, int *ldz, float *work, int *iwork, int *ifail, int *info);
 695
 696 void
 697 F77_FUNC(sgelqf,SGELQF)(int *m, int *n, float *a, int *lda, float *tau,
 698         float *work, int *lwork, int *info);
 699
 700 void
 701 F77_FUNC(slaebz,SLAEBZ)(int *ijob, int *nitmax, int *n, int *mmax, int *minp, int *nbmin,
 702         float *abstol, float *reltol, float *pivmin, float *d, float *e,
 703         float *e2, int *nval, float *ab, float *c, int *mout, int *nab,
 704         float *work, int *iwork, int *info);
 705
 706 void
 707 F77_FUNC(slarf,SLARF)(const char *side, int *m, int *n, float *v, int *incv, float *tau,
 708        float *c, int *ldc, float *work);
 709
 710 void
 711 F77_FUNC(slartg,SLARTG)(float *f, float *g, float *cs, float *sn, float *r);
 712
 713 void
 714 F77_FUNC(slasd5,SLASD5)(int *i, float *d, float *z, float *delta,
 715         float *rho, float *dsigma, float *work);
 716
 717 void
 718 F77_FUNC(slasq2,SLASQ2)(int *n, float *z, int *info);
 719
 720 void
 721 F77_FUNC(slasq3,SLASQ3)(int *i0, int *n0, float *z, int *pp, float *dmin,
 722         float *sigma, float *desig, float *qmax, int *nfail,
 723         int *iter, int *ndiv, int *ieee);
 724
 725 void
 726 F77_FUNC(slaswp,SLASWP)(int *n, float *a, int *lda, int *k1, int *k2, int *ipiv, int *incx);
 727
 728 void
 729 F77_FUNC(sormbr,SORMBR)(const char *vect, const char *side, const char *trans, int *m, int *n, int *k,
 730         float *a, int *lda, float *tau, float *c, int *ldc, float *work,
 731         int *lwork, int *info);
 732
 733 void
 734 F77_FUNC(ssterf,SSTERF)(int *n, float *d, float *e, int *info);
 735
 736 void
 737 F77_FUNC(sgeqr2,SGEQR2)(int *m, int *n, float *a, int *lda, float *tau,
 738         float *work, int *info);
 739
 740 void
 741 F77_FUNC(slaed6,SLAED6)(int *kniter, int *orgati, float *rho, float *d,
 742         float *z, float *finit, float *tau, int *info);
 743
 744 void
 745 F77_FUNC(slarfb,SLARFB)(const char *side, const char *trans, const char *direct, const char *storev, int *m, int *n,
 746         int *k, float *v, int *ldv, float *t, int *ldt, float *c,
 747         int *ldc, float *work, int *ldwork);
 748
 749 void
 750 F77_FUNC(slaruv,SLARUV)(int *iseed, int *n, float *x);
 751
 752 void
 753 F77_FUNC(slasd6,SLASD6)(int *icompq, int *nl, int *nr, int *sqre, float *d, float *vf,
 754         float *vl, float *alpha, float *beta, int *idxq, int *perm,
 755         int *givptr, int *givcol, int *ldgcol, float *givnum, int *ldgnum,
 756         float *poles, float *difl, float *difr, float *z, int *k,
 757         float *c, float *s, float *work, int *iwork, int *info);
 758
 759 void
 760 F77_FUNC(slatrd,SLATRD)(const char *uplo, int *n, int *nb, float *a, int *lda, float *e,
 761         float * tau, float *w, int *ldw);
 762
 763 void
 764 F77_FUNC(sorml2,SORML2)(const char *side, const char *trans, int *m, int *n, int *k, float *a,
 765         int *lda, float *tau, float *c, int *ldc, float *work, int *info);
 766
 767 void
 768 F77_FUNC(sstevr,SSTEVR)(const char *jobz, const char *range, int *n, float *d, float *e, float *vl,
 769         float *vu, int *il, int *iu, float *abstol, int *m, float *w,
 770         float *z, int *ldz, int *isuppz, float *work,
 771         int *lwork, int *iwork, int *liwork, int *info);
 772
 773 void
 774 F77_FUNC(ssytrd,SSYTRD)(const char *uplo, int *n, float *  a, int *lda, float *d,
 775         float *e, float *tau, float *work, int *lwork, int *info);
 776
 777 void
 778 F77_FUNC(ssyevr,SSYEVR)(const char *jobz, const char *range, const char *uplo, int *n,
 779         float *a, int *lda, float *vl, float *vu, int *
 780         il, int *iu, float *abstol, int *m, float *w,
 781         float *z__, int *ldz, int *isuppz, float *work,
 782         int *lwork, int *iwork, int *liwork, int *info);
 783
 784 void
 785 F77_FUNC(sormql,SORMQL)(const char *side, const char *trans, int *m, int *n,
 786         int *k, float *a, int *lda, float *tau, float *
 787         c, int *ldc, float *work, int *lwork, int *info);
 788
 789 void
 790 F77_FUNC(sormqr,SORMQR)(const char *side, const char *trans, int *m, int *n, int *k, float *a,
 791         int *lda, float *tau, float *c, int *ldc,
 792         float *work, int *lwork, int *info);
 793
 794 void
 795 F77_FUNC(sorgbr,SORGBR)(const char *vect, int *m, int *n, int *k, float *a, int *lda,
 796         float *tau, float *work, int *lwork, int *info);
 797
 798 void
 799 F77_FUNC(slasq5,SLASQ5)(int *i0, int *n0, float *z, int *pp, float *tau, float *dmin,
 800         float *dmin1, float *dmin2, float *dn, float *dnm1,
 801         float *dnm2, int *ieee);
 802
 803 void
 804 F77_FUNC(slasd8,SLASD8)(int *icompq, int *k, float *d, float *z, float *vf, float *vl,
 805         float *difl, float *difr, int *lddifr, float *dsigma,
 806         float *work, int *info);
 807
 808 void
 809 F77_FUNC(slascl,SLASCL)(const char *type, int *kl, int *ku, float *cfrom, float *cto, int *m,
 810         int *n, float *a, int *lda, int *info);
 811
 812 void
 813 F77_FUNC(slarft,SLARFT)(const char *direct, const char *storev, int *n, int *k, float *v,
 814         int *ldv, float *tau, float *t, int *ldt);
 815
 816 void
 817 F77_FUNC(slagts,SLAGTS)(int *job, int *n, float *a, float *b, float *c, float *d,
 818         int *in, float *y, float *tol, int *info);
 819
 820 void
 821 F77_FUNC(sgesdd,SGESDD)(const char *jobz, int *m, int *n, float *a, int *lda, float *s, float *u,
 822         int *ldu, float *vt, int *ldvt, float *work, int *lwork,
 823         int *iwork, int *info);
 824
 825 void
 826 F77_FUNC(ssytd2,SSYTD2)(const char *uplo, int *n, float *a, int *lda, float *d,
 827         float *e, float *tau, int *info);
 828
 829 void
 830 F77_FUNC(sormlq,SORMLQ)(const char *side, const char *trans, int *m, int *n, int *k, float *a, int *lda,
 831         float *tau, float *c, int *ldc, float *work, int *lwork, int *info);
 832
 833 void
 834 F77_FUNC(sorg2r,SORG2R)(int *m, int *n, int *k, float *a, int *lda, float *tau,
 835         float *work, int *info);
 836
 837 void
 838 F77_FUNC(slasq4,SLASQ4)(int *i0, int *n0, float *z, int *pp, int *n0in, float *dmin,
 839         float *dmin1, float *dmin2, float *dn, float *dn1,
 840         float *dn2, float *tau, int *ttype);
 841
 842 void
 843 F77_FUNC(slasd7,SLASD7)(int *icompq, int *nl, int *nr, int *sqre, int *k, float *d, float *z,
 844         float *zw, float *vf, float *vfw, float *vl, float *vlw,
 845         float *alpha, float *beta, float *dsigma, int *idx, int *idxp,
 846         int *idxq, int *perm, int *givptr, int *givcol, int *ldgcol,
 847         float *givnum, int *ldgnum, float *c, float *s, int *info);
 848
 849 void
 850 F77_FUNC(slas2,SLAS2)(float *f, float *g, float *h, float *ssmin, float *ssmax);
 851
 852 void
 853 F77_FUNC(slarfg,SLARFG)(int *n, float *alpha, float *x, int *incx, float *tau);
 854
 855 void
 856 F77_FUNC(slagtf,SLAGTF)(int *n, float *a, float *lambda, float *b, float *c,
 857         float *tol, float *d, int *in, int *info);
 858
 859 void
 860 F77_FUNC(sgeqrf,SGEQRF)(int *m, int *n, float *a, int *lda, float *tau,
 861         float *work, int *lwork, int *info);
 862
 863
 864 #ifdef __cplusplus
 865 }
 866 #endif
 867
 868
 869
 870 #endif /* _LAPACK_H_ */