src/gromacs/linearalgebra/gmx_lapack.h

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