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