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
  23  * be called official GROMACS. Details are found in the README & COPYING
  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 /* Suppress Cygwin compiler warnings from using newlib version of
  76  * ctype.h */
  77 #ifdef GMX_CYGWIN
  78 #undef toupper
  79 #endif
  80
  81 #ifndef F77_FUNC
  82 #define F77_FUNC(name,NAME) name ## _
  83 #endif
  84
  85
  86
  87 /* Double precision */
  88
  89 void
  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);
  93
  94 void
  95 F77_FUNC(dgetf2,DGETF2)(int *m, int *n, double *a, int *lda, int *ipiv, int *info);
  96
  97 void
  98 F77_FUNC(dlamrg,DLAMRG)(int *n1, int *n2, double *a, int *dtrd1, int *dtrd2, int *index);
  99
 100 void
 101 F77_FUNC(dlarnv,DLARNV)(int *idist, int *iseed, int *n, double *x);
 102
 103 void
 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);
 107
 108 void
 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);
 114
 115 void
 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);
 118
 119 void
 120 F77_FUNC(dorgl2,DORGL2)(int *m, int *n, int *k, double *a, int *lda,
 121         double *tau, double *work, int *info);
 122
 123 void
 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);
 127
 128 void
 129 F77_FUNC(dgetrf,DGETRF)(int *m, int *n, double *a, int *lda, int *ipiv, int *info);
 130
 131 void
 132 F77_FUNC(dgetri,DGETRI)(int *n, double *a, int *lda, int *ipiv, double *work,
 133         int *lwork, int *info);
 134
 135 void
 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);
 138
 139 void
 140 F77_FUNC(dtrtri,DTRTRI)(const char *uplo, const char *diag, int *n, double *a, int *lda, int *info);
 141
 142 void
 143 F77_FUNC(dtrti2,DTRTI2)(const char *uplo, const char *diag, int *n, double *a, int *lda, int *info);
 144
 145 double
 146 F77_FUNC(dlange,DLANGE)(const char *norm, int *m, int *n, double *a, int *lda, double *work);
 147
 148 void
 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);
 152
 153 void
 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);
 157
 158 void
 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);
 162
 163 void
 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);
 166
 167 void
 168 F77_FUNC(dorglq,DORGLQ)(int *m, int *n, int *k, double *a, int *lda,
 169         double *tau, double *work, int *lwork, int *info);
 170
 171 void
 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);
 175
 176 void
 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);
 179
 180 void
 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);
 184
 185 double
 186 F77_FUNC(dlanst,DLANST)(const char *norm, int *n, double *d, double *e);
 187
 188 double
 189 F77_FUNC(dlansy,DLANSY)(const char *norm, const char *uplo, int *n, double *a, int *lda, double *work);
 190
 191 void
 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);
 196
 197 void
 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);
 203
 204 void
 205 F77_FUNC(dlasdt,DLASDT)(int *n, int *lvl, int *nd, int *inode, int *ndiml,
 206         int *ndimr, int *msub);
 207
 208 void
 209 F77_FUNC(dlasrt,DLASRT)(const char *id, int *n, double *d, int *info);
 210
 211 void
 212 F77_FUNC(dlasrt2,DLASRT2)(const char *id, int *n, double *d, int *key, int *info);
 213
 214 void
 215 F77_FUNC(ilasrt2,ILASRT2)(const char *id, int *n, int *d, int *key, int *info);
 216
 217 void
 218 F77_FUNC(dorgqr,DORGQR)(int *m, int *n, int *k, double *a, int *lda, double *tau,
 219         double *work, int *lwork, int *info);
 220
 221 void
 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);
 226
 227 void
 228 F77_FUNC(dsteqr,DSTEQR)(const char *compz, int *n, double *d__, double *e,
 229         double *z__,  int *ldz, double *work, int *info);
 230
 231 void
 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);
 234
 235 void
 236 F77_FUNC(dlacpy,DLACPY)(const char *uplo, int *m, int *n, double *a, int *lda, double *b, int *ldb);
 237
 238 double
 239 F77_FUNC(dlapy2,DLAPY2)(double * x, double * y);
 240
 241
 242 void
 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);
 246
 247 void
 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);
 252
 253 void
 254 F77_FUNC(dlaset,DLASET)(const char *uplo, int *m, int *n, double *alpha,
 255         double *beta, double *a, int *lda);
 256
 257 void
 258 F77_FUNC(dlassq,DLASSQ)(int *n, double *x, int *incx, double *scale, double *sumsq);
 259
 260 void
 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);
 263
 264 void
 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);
 269
 270 void
 271 F77_FUNC(ssteqr,SSTEQR)(const char *compz, int *n, float *d__, float *e,
 272         float *z__,  int *ldz, float *work, int *info);
 273
 274 void
 275 F77_FUNC(dgelq2,DGELQ2)(int *m, int *n, double *a, int *lda, double *tau, double *work, int *info);
 276
 277 void
 278 F77_FUNC(dlae2,DLAE2)(double *a, double *b, double *c, double *rt1, double *rt2);
 279
 280 void
 281 F77_FUNC(dlaev2,DLAEV2)(double *a, double *b, double *c, double *rt1, double *rt2,
 282         double *cs1, double *cs2);
 283
 284 void
 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);
 288
 289 void
 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);
 293
 294 void
 295 F77_FUNC(dlasd4,DLASD4)(int *n, int *i, double *d, double *z, double *delta,
 296         double *rho, double *sigma, double *work, int *info);
 297
 298 void
 299 F77_FUNC(dlasq1,DLASQ1)(int *n, double *d, double *e, double *work, int *info);
 300
 301
 302 void
 303 F77_FUNC(dlasv2,DLASV2)(double *f, double *g, double *h, double *ssmin, double *ssmax,
 304         double *snr, double *csr, double *snl, double *csl);
 305
 306 void
 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);
 309
 310 void
 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);
 313
 314 void
 315 F77_FUNC(dgelqf,DGELQF)(int *m, int *n, double *a, int *lda, double *tau,
 316         double *work, int *lwork, int *info);
 317
 318 void
 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);
 323
 324 void
 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);
 327
 328 void
 329 F77_FUNC(dlartg,DLARTG)(double *f, double *g, double *cs, double *sn, double *r);
 330
 331 void
 332 F77_FUNC(dlasd5,DLASD5)(int *i, double *d, double *z, double *delta,
 333         double *rho, double *dsigma, double *work);
 334
 335 void
 336 F77_FUNC(dlasq2,DLASQ2)(int *n, double *z, int *info);
 337
 338 void
 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);
 342
 343 void
 344 F77_FUNC(dlaswp,DLASWP)(int *n, double *a, int *lda, int *k1, int *k2, int *ipiv, int *incx);
 345
 346 void
 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);
 350
 351 void
 352 F77_FUNC(dsterf,DSTERF)(int *n, double *d, double *e, int *info);
 353
 354 void
 355 F77_FUNC(dgeqr2,DGEQR2)(int *m, int *n, double *a, int *lda, double *tau,
 356         double *work, int *info);
 357
 358 void
 359 F77_FUNC(dlaed6,DLAED6)(int *kniter, int *orgati, double *rho, double *d,
 360         double *z, double *finit, double *tau, int *info);
 361
 362 void
 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);
 366
 367 void
 368 F77_FUNC(dlaruv,DLARUV)(int *iseed, int *n, double *x);
 369
 370 void
 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);
 376
 377 void
 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);
 380
 381 void
 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);
 384
 385 void
 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);
 390
 391 void
 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);
 394
 395 void
 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);
 401
 402 void
 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);
 406
 407 void
 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);
 411
 412 void
 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);
 415
 416 void
 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);
 420
 421 void
 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);
 425
 426 void
 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);
 429
 430 void
 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);
 433
 434 void
 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);
 437
 438 void
 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);
 442
 443 void
 444 F77_FUNC(dsytd2,DSYTD2)(const char *uplo, int *n, double *a, int *lda, double *d,
 445         double *e, double *tau, int *info);
 446
 447 void
 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);
 450
 451 void
 452 F77_FUNC(dorg2r,DORG2R)(int *m, int *n, int *k, double *a, int *lda, double *tau,
 453         double *work, int *info);
 454
 455 void
 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);
 459
 460 void
 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);
 466
 467 void
 468 F77_FUNC(dlas2,DLAS2)(double *f, double *g, double *h, double *ssmin, double *ssmax);
 469
 470 void
 471 F77_FUNC(dlarfg,DLARFG)(int *n, double *alpha, double *x, int *incx, double *tau);
 472
 473 void
 474 F77_FUNC(dlagtf,DLAGTF)(int *n, double *a, double *lambda, double *b, double *c,
 475         double *tol, double *d, int *in, int *info);
 476
 477 void
 478 F77_FUNC(dgeqrf,DGEQRF)(int *m, int *n, double *a, int *lda, double *tau,
 479         double *work, int *lwork, int *info);
 480
 481
 482
 483 /* Single precision */
 484
 485 void
 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);
 489
 490 void
 491 F77_FUNC(sgetf2,SGETF2)(int *m, int *n, float *a, int *lda, int *ipiv, int *info);
 492
 493 void
 494 F77_FUNC(slamrg,SLAMRG)(int *n1, int *n2, float *a, int *dtrd1, int *dtrd2, int *index);
 495
 496 void
 497 F77_FUNC(slarnv,SLARNV)(int *idist, int *iseed, int *n, float *x);
 498
 499 void
 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);
 503
 504 void
 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);
 510
 511 void
 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);
 514
 515 void
 516 F77_FUNC(sorgl2,SORGL2)(int *m, int *n, int *k, float *a, int *lda,
 517         float *tau, float *work, int *info);
 518
 519 void
 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);
 523
 524 void
 525 F77_FUNC(sgetrf,SGETRF)(int *m, int *n, float *a, int *lda, int *ipiv, int *info);
 526
 527 void
 528 F77_FUNC(sgetri,SGETRI)(int *n, float *a, int *lda, int *ipiv, float *work,
 529         int *lwork, int *info);
 530
 531 void
 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);
 534
 535 void
 536 F77_FUNC(strtri,STRTRI)(const char *uplo, const char *diag, int *n, float *a, int *lda, int *info);
 537
 538 void
 539 F77_FUNC(strti2,STRTI2)(const char *uplo, const char *diag, int *n, float *a, int *lda, int *info);
 540
 541 float
 542 F77_FUNC(slange,SLANGE)(const char *norm, int *m, int *n, float *a, int *lda, float *work);
 543
 544 void
 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);
 548
 549 void
 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);
 553
 554 void
 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);
 558
 559 void
 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);
 562
 563 void
 564 F77_FUNC(sorglq,SORGLQ)(int *m, int *n, int *k, float *a, int *lda,
 565         float *tau, float *work, int *lwork, int *info);
 566
 567 void
 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);
 571
 572 void
 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);
 575
 576 void
 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);
 580
 581 float
 582 F77_FUNC(slanst,SLANST)(const char *norm, int *n, float *d, float *e);
 583
 584 float
 585 F77_FUNC(slansy,SLANSY)(const char *norm, const char *uplo, int *n, float *a, int *lda, float *work);
 586
 587 void
 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);
 592
 593 void
 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);
 599
 600 void
 601 F77_FUNC(slasdt,SLASDT)(int *n, int *lvl, int *nd, int *inode, int *ndiml,
 602         int *ndimr, int *msub);
 603
 604 void
 605 F77_FUNC(slasrt,SLASRT)(const char *id, int *n, float *d, int *info);
 606
 607 void
 608 F77_FUNC(slasrt2,SLASRT2)(const char *id, int *n, float *d, int *key, int *info);
 609
 610 void
 611 F77_FUNC(sorgqr,SORGQR)(int *m, int *n, int *k, float *a, int *lda, float *tau,
 612         float *work, int *lwork, int *info);
 613
 614 void
 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);
 619
 620 void
 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);
 623
 624 void
 625 F77_FUNC(slacpy,SLACPY)(const char *uplo, int *m, int *n, float *a, int *lda, float *b, int *ldb);
 626
 627 float
 628 F77_FUNC(slapy2,SLAPY2)(float * x, float * y);
 629
 630 void
 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);
 634
 635 void
 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);
 640
 641 void
 642 F77_FUNC(slaset,SLASET)(const char *uplo, int *m, int *n, float *alpha,
 643         float *beta, float *a, int *lda);
 644
 645 void
 646 F77_FUNC(slassq,SLASSQ)(int *n, float *x, int *incx, float *scale, float *sumsq);
 647
 648 void
 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);
 651
 652 void
 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);
 657
 658 void
 659 F77_FUNC(sgelq2,SGELQ2)(int *m, int *n, float *a, int *lda, float *tau, float *work, int *info);
 660
 661 void
 662 F77_FUNC(slae2,SLAE2)(float *a, float *b, float *c, float *rt1, float *rt2);
 663
 664 void
 665 F77_FUNC(slaev2,SLAEV2)(float *a, float *b, float *c, float *rt1, float *rt2,
 666         float *cs1, float *cs2);
 667
 668 void
 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);
 672
 673 void
 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);
 677
 678 void
 679 F77_FUNC(slasd4,SLASD4)(int *n, int *i, float *d, float *z, float *delta,
 680         float *rho, float *sigma, float *work, int *info);
 681
 682 void
 683 F77_FUNC(slasq1,SLASQ1)(int *n, float *d, float *e, float *work, int *info);
 684
 685
 686 void
 687 F77_FUNC(slasv2,SLASV2)(float *f, float *g, float *h, float *ssmin, float *ssmax,
 688         float *snr, float *csr, float *snl, float *csl);
 689
 690 void
 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);
 693
 694 void
 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);
 697
 698 void
 699 F77_FUNC(sgelqf,SGELQF)(int *m, int *n, float *a, int *lda, float *tau,
 700         float *work, int *lwork, int *info);
 701
 702 void
 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);
 707
 708 void
 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);
 711
 712 void
 713 F77_FUNC(slartg,SLARTG)(float *f, float *g, float *cs, float *sn, float *r);
 714
 715 void
 716 F77_FUNC(slasd5,SLASD5)(int *i, float *d, float *z, float *delta,
 717         float *rho, float *dsigma, float *work);
 718
 719 void
 720 F77_FUNC(slasq2,SLASQ2)(int *n, float *z, int *info);
 721
 722 void
 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);
 726
 727 void
 728 F77_FUNC(slaswp,SLASWP)(int *n, float *a, int *lda, int *k1, int *k2, int *ipiv, int *incx);
 729
 730 void
 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);
 734
 735 void
 736 F77_FUNC(ssterf,SSTERF)(int *n, float *d, float *e, int *info);
 737
 738 void
 739 F77_FUNC(sgeqr2,SGEQR2)(int *m, int *n, float *a, int *lda, float *tau,
 740         float *work, int *info);
 741
 742 void
 743 F77_FUNC(slaed6,SLAED6)(int *kniter, int *orgati, float *rho, float *d,
 744         float *z, float *finit, float *tau, int *info);
 745
 746 void
 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);
 750
 751 void
 752 F77_FUNC(slaruv,SLARUV)(int *iseed, int *n, float *x);
 753
 754 void
 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);
 760
 761 void
 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);
 764
 765 void
 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);
 768
 769 void
 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);
 774
 775 void
 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);
 778
 779 void
 780 F77_FUNC(ssyevr,SSYEVR)(const char *jobz, const char *range, const char *uplo, int *n,
 781         float *a, int *lda, float *vl, float *vu, int *
 782         il, int *iu, float *abstol, int *m, float *w,
 783         float *z__, int *ldz, int *isuppz, float *work,
 784         int *lwork, int *iwork, int *liwork, int *info);
 785
 786 void
 787 F77_FUNC(sormql,SORMQL)(const char *side, const char *trans, int *m, int *n,
 788         int *k, float *a, int *lda, float *tau, float *
 789         c, int *ldc, float *work, int *lwork, int *info);
 790
 791 void
 792 F77_FUNC(sormqr,SORMQR)(const char *side, const char *trans, int *m, int *n, int *k, float *a,
 793         int *lda, float *tau, float *c, int *ldc,
 794         float *work, int *lwork, int *info);
 795
 796 void
 797 F77_FUNC(sorgbr,SORGBR)(const char *vect, int *m, int *n, int *k, float *a, int *lda,
 798         float *tau, float *work, int *lwork, int *info);
 799
 800 void
 801 F77_FUNC(slasq5,SLASQ5)(int *i0, int *n0, float *z, int *pp, float *tau, float *dmin,
 802         float *dmin1, float *dmin2, float *dn, float *dnm1,
 803         float *dnm2, int *ieee);
 804
 805 void
 806 F77_FUNC(slasd8,SLASD8)(int *icompq, int *k, float *d, float *z, float *vf, float *vl,
 807         float *difl, float *difr, int *lddifr, float *dsigma,
 808         float *work, int *info);
 809
 810 void
 811 F77_FUNC(slascl,SLASCL)(const char *type, int *kl, int *ku, float *cfrom, float *cto, int *m,
 812         int *n, float *a, int *lda, int *info);
 813
 814 void
 815 F77_FUNC(slarft,SLARFT)(const char *direct, const char *storev, int *n, int *k, float *v,
 816         int *ldv, float *tau, float *t, int *ldt);
 817
 818 void
 819 F77_FUNC(slagts,SLAGTS)(int *job, int *n, float *a, float *b, float *c, float *d,
 820         int *in, float *y, float *tol, int *info);
 821
 822 void
 823 F77_FUNC(sgesdd,SGESDD)(const char *jobz, int *m, int *n, float *a, int *lda, float *s, float *u,
 824         int *ldu, float *vt, int *ldvt, float *work, int *lwork,
 825         int *iwork, int *info);
 826
 827 void
 828 F77_FUNC(ssytd2,SSYTD2)(const char *uplo, int *n, float *a, int *lda, float *d,
 829         float *e, float *tau, int *info);
 830
 831 void
 832 F77_FUNC(sormlq,SORMLQ)(const char *side, const char *trans, int *m, int *n, int *k, float *a, int *lda,
 833         float *tau, float *c, int *ldc, float *work, int *lwork, int *info);
 834
 835 void
 836 F77_FUNC(sorg2r,SORG2R)(int *m, int *n, int *k, float *a, int *lda, float *tau,
 837         float *work, int *info);
 838
 839 void
 840 F77_FUNC(slasq4,SLASQ4)(int *i0, int *n0, float *z, int *pp, int *n0in, float *dmin,
 841         float *dmin1, float *dmin2, float *dn, float *dn1,
 842         float *dn2, float *tau, int *ttype);
 843
 844 void
 845 F77_FUNC(slasd7,SLASD7)(int *icompq, int *nl, int *nr, int *sqre, int *k, float *d, float *z,
 846         float *zw, float *vf, float *vfw, float *vl, float *vlw,
 847         float *alpha, float *beta, float *dsigma, int *idx, int *idxp,
 848         int *idxq, int *perm, int *givptr, int *givcol, int *ldgcol,
 849         float *givnum, int *ldgnum, float *c, float *s, int *info);
 850
 851 void
 852 F77_FUNC(slas2,SLAS2)(float *f, float *g, float *h, float *ssmin, float *ssmax);
 853
 854 void
 855 F77_FUNC(slarfg,SLARFG)(int *n, float *alpha, float *x, int *incx, float *tau);
 856
 857 void
 858 F77_FUNC(slagtf,SLAGTF)(int *n, float *a, float *lambda, float *b, float *c,
 859         float *tol, float *d, int *in, int *info);
 860
 861 void
 862 F77_FUNC(sgeqrf,SGEQRF)(int *m, int *n, float *a, int *lda, float *tau,
 863         float *work, int *lwork, int *info);
 864
 865
 866 #ifdef __cplusplus
 867 }
 868 #endif
 869
 870
 871
 872 #endif /* _LAPACK_H_ */