/usr/include/gsl/gsl_linalg.h is in libgsl0-dev 1.16+dfsg-1ubuntu1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 | /* linalg/gsl_linalg.h
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2006, 2007 Gerard Jungman, Brian Gough, Patrick Alken
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
#ifndef __GSL_LINALG_H__
#define __GSL_LINALG_H__
#include <gsl/gsl_mode.h>
#include <gsl/gsl_permutation.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_matrix.h>
#undef __BEGIN_DECLS
#undef __END_DECLS
#ifdef __cplusplus
#define __BEGIN_DECLS extern "C" {
#define __END_DECLS }
#else
#define __BEGIN_DECLS /* empty */
#define __END_DECLS /* empty */
#endif
__BEGIN_DECLS
typedef enum
{
GSL_LINALG_MOD_NONE = 0,
GSL_LINALG_MOD_TRANSPOSE = 1,
GSL_LINALG_MOD_CONJUGATE = 2
}
gsl_linalg_matrix_mod_t;
/* Note: You can now use the gsl_blas_dgemm function instead of matmult */
/* Simple implementation of matrix multiply.
* Calculates C = A.B
*
* exceptions: GSL_EBADLEN
*/
int gsl_linalg_matmult (const gsl_matrix * A,
const gsl_matrix * B,
gsl_matrix * C);
/* Simple implementation of matrix multiply.
* Allows transposition of either matrix, so it
* can compute A.B or Trans(A).B or A.Trans(B) or Trans(A).Trans(B)
*
* exceptions: GSL_EBADLEN
*/
int gsl_linalg_matmult_mod (const gsl_matrix * A,
gsl_linalg_matrix_mod_t modA,
const gsl_matrix * B,
gsl_linalg_matrix_mod_t modB,
gsl_matrix * C);
/* Calculate the matrix exponential by the scaling and
* squaring method described in Moler + Van Loan,
* SIAM Rev 20, 801 (1978). The mode argument allows
* choosing an optimal strategy, from the table
* given in the paper, for a given precision.
*
* exceptions: GSL_ENOTSQR, GSL_EBADLEN
*/
int gsl_linalg_exponential_ss(
const gsl_matrix * A,
gsl_matrix * eA,
gsl_mode_t mode
);
/* Householder Transformations */
double gsl_linalg_householder_transform (gsl_vector * v);
gsl_complex gsl_linalg_complex_householder_transform (gsl_vector_complex * v);
int gsl_linalg_householder_hm (double tau,
const gsl_vector * v,
gsl_matrix * A);
int gsl_linalg_householder_mh (double tau,
const gsl_vector * v,
gsl_matrix * A);
int gsl_linalg_householder_hv (double tau,
const gsl_vector * v,
gsl_vector * w);
int gsl_linalg_householder_hm1 (double tau,
gsl_matrix * A);
int gsl_linalg_complex_householder_hm (gsl_complex tau,
const gsl_vector_complex * v,
gsl_matrix_complex * A);
int gsl_linalg_complex_householder_mh (gsl_complex tau,
const gsl_vector_complex * v,
gsl_matrix_complex * A);
int gsl_linalg_complex_householder_hv (gsl_complex tau,
const gsl_vector_complex * v,
gsl_vector_complex * w);
/* Hessenberg reduction */
int gsl_linalg_hessenberg_decomp(gsl_matrix *A, gsl_vector *tau);
int gsl_linalg_hessenberg_unpack(gsl_matrix * H, gsl_vector * tau,
gsl_matrix * U);
int gsl_linalg_hessenberg_unpack_accum(gsl_matrix * H, gsl_vector * tau,
gsl_matrix * U);
int gsl_linalg_hessenberg_set_zero(gsl_matrix * H);
int gsl_linalg_hessenberg_submatrix(gsl_matrix *M, gsl_matrix *A,
size_t top, gsl_vector *tau);
/* To support gsl-1.9 interface: DEPRECATED */
int gsl_linalg_hessenberg(gsl_matrix *A, gsl_vector *tau);
/* Hessenberg-Triangular reduction */
int gsl_linalg_hesstri_decomp(gsl_matrix * A, gsl_matrix * B,
gsl_matrix * U, gsl_matrix * V,
gsl_vector * work);
/* Singular Value Decomposition
* exceptions:
*/
int
gsl_linalg_SV_decomp (gsl_matrix * A,
gsl_matrix * V,
gsl_vector * S,
gsl_vector * work);
int
gsl_linalg_SV_decomp_mod (gsl_matrix * A,
gsl_matrix * X,
gsl_matrix * V,
gsl_vector * S,
gsl_vector * work);
int gsl_linalg_SV_decomp_jacobi (gsl_matrix * A,
gsl_matrix * Q,
gsl_vector * S);
int
gsl_linalg_SV_solve (const gsl_matrix * U,
const gsl_matrix * Q,
const gsl_vector * S,
const gsl_vector * b,
gsl_vector * x);
int gsl_linalg_SV_leverage(const gsl_matrix *U, gsl_vector *h);
/* LU Decomposition, Gaussian elimination with partial pivoting
*/
int gsl_linalg_LU_decomp (gsl_matrix * A, gsl_permutation * p, int *signum);
int gsl_linalg_LU_solve (const gsl_matrix * LU,
const gsl_permutation * p,
const gsl_vector * b,
gsl_vector * x);
int gsl_linalg_LU_svx (const gsl_matrix * LU,
const gsl_permutation * p,
gsl_vector * x);
int gsl_linalg_LU_refine (const gsl_matrix * A,
const gsl_matrix * LU,
const gsl_permutation * p,
const gsl_vector * b,
gsl_vector * x,
gsl_vector * residual);
int gsl_linalg_LU_invert (const gsl_matrix * LU,
const gsl_permutation * p,
gsl_matrix * inverse);
double gsl_linalg_LU_det (gsl_matrix * LU, int signum);
double gsl_linalg_LU_lndet (gsl_matrix * LU);
int gsl_linalg_LU_sgndet (gsl_matrix * lu, int signum);
/* Complex LU Decomposition */
int gsl_linalg_complex_LU_decomp (gsl_matrix_complex * A,
gsl_permutation * p,
int *signum);
int gsl_linalg_complex_LU_solve (const gsl_matrix_complex * LU,
const gsl_permutation * p,
const gsl_vector_complex * b,
gsl_vector_complex * x);
int gsl_linalg_complex_LU_svx (const gsl_matrix_complex * LU,
const gsl_permutation * p,
gsl_vector_complex * x);
int gsl_linalg_complex_LU_refine (const gsl_matrix_complex * A,
const gsl_matrix_complex * LU,
const gsl_permutation * p,
const gsl_vector_complex * b,
gsl_vector_complex * x,
gsl_vector_complex * residual);
int gsl_linalg_complex_LU_invert (const gsl_matrix_complex * LU,
const gsl_permutation * p,
gsl_matrix_complex * inverse);
gsl_complex gsl_linalg_complex_LU_det (gsl_matrix_complex * LU,
int signum);
double gsl_linalg_complex_LU_lndet (gsl_matrix_complex * LU);
gsl_complex gsl_linalg_complex_LU_sgndet (gsl_matrix_complex * LU,
int signum);
/* QR decomposition */
int gsl_linalg_QR_decomp (gsl_matrix * A,
gsl_vector * tau);
int gsl_linalg_QR_solve (const gsl_matrix * QR,
const gsl_vector * tau,
const gsl_vector * b,
gsl_vector * x);
int gsl_linalg_QR_svx (const gsl_matrix * QR,
const gsl_vector * tau,
gsl_vector * x);
int gsl_linalg_QR_lssolve (const gsl_matrix * QR,
const gsl_vector * tau,
const gsl_vector * b,
gsl_vector * x,
gsl_vector * residual);
int gsl_linalg_QR_QRsolve (gsl_matrix * Q,
gsl_matrix * R,
const gsl_vector * b,
gsl_vector * x);
int gsl_linalg_QR_Rsolve (const gsl_matrix * QR,
const gsl_vector * b,
gsl_vector * x);
int gsl_linalg_QR_Rsvx (const gsl_matrix * QR,
gsl_vector * x);
int gsl_linalg_QR_update (gsl_matrix * Q,
gsl_matrix * R,
gsl_vector * w,
const gsl_vector * v);
int gsl_linalg_QR_QTvec (const gsl_matrix * QR,
const gsl_vector * tau,
gsl_vector * v);
int gsl_linalg_QR_Qvec (const gsl_matrix * QR,
const gsl_vector * tau,
gsl_vector * v);
int gsl_linalg_QR_QTmat (const gsl_matrix * QR,
const gsl_vector * tau,
gsl_matrix * A);
int gsl_linalg_QR_unpack (const gsl_matrix * QR,
const gsl_vector * tau,
gsl_matrix * Q,
gsl_matrix * R);
int gsl_linalg_R_solve (const gsl_matrix * R,
const gsl_vector * b,
gsl_vector * x);
int gsl_linalg_R_svx (const gsl_matrix * R,
gsl_vector * x);
/* Q R P^T decomposition */
int gsl_linalg_QRPT_decomp (gsl_matrix * A,
gsl_vector * tau,
gsl_permutation * p,
int *signum,
gsl_vector * norm);
int gsl_linalg_QRPT_decomp2 (const gsl_matrix * A,
gsl_matrix * q, gsl_matrix * r,
gsl_vector * tau,
gsl_permutation * p,
int *signum,
gsl_vector * norm);
int gsl_linalg_QRPT_solve (const gsl_matrix * QR,
const gsl_vector * tau,
const gsl_permutation * p,
const gsl_vector * b,
gsl_vector * x);
int gsl_linalg_QRPT_svx (const gsl_matrix * QR,
const gsl_vector * tau,
const gsl_permutation * p,
gsl_vector * x);
int gsl_linalg_QRPT_QRsolve (const gsl_matrix * Q,
const gsl_matrix * R,
const gsl_permutation * p,
const gsl_vector * b,
gsl_vector * x);
int gsl_linalg_QRPT_Rsolve (const gsl_matrix * QR,
const gsl_permutation * p,
const gsl_vector * b,
gsl_vector * x);
int gsl_linalg_QRPT_Rsvx (const gsl_matrix * QR,
const gsl_permutation * p,
gsl_vector * x);
int gsl_linalg_QRPT_update (gsl_matrix * Q,
gsl_matrix * R,
const gsl_permutation * p,
gsl_vector * u,
const gsl_vector * v);
/* LQ decomposition */
int gsl_linalg_LQ_decomp (gsl_matrix * A, gsl_vector * tau);
int gsl_linalg_LQ_solve_T (const gsl_matrix * LQ, const gsl_vector * tau,
const gsl_vector * b, gsl_vector * x);
int gsl_linalg_LQ_svx_T (const gsl_matrix * LQ, const gsl_vector * tau,
gsl_vector * x);
int gsl_linalg_LQ_lssolve_T (const gsl_matrix * LQ, const gsl_vector * tau,
const gsl_vector * b, gsl_vector * x,
gsl_vector * residual);
int gsl_linalg_LQ_Lsolve_T (const gsl_matrix * LQ, const gsl_vector * b,
gsl_vector * x);
int gsl_linalg_LQ_Lsvx_T (const gsl_matrix * LQ, gsl_vector * x);
int gsl_linalg_L_solve_T (const gsl_matrix * L, const gsl_vector * b,
gsl_vector * x);
int gsl_linalg_LQ_vecQ (const gsl_matrix * LQ, const gsl_vector * tau,
gsl_vector * v);
int gsl_linalg_LQ_vecQT (const gsl_matrix * LQ, const gsl_vector * tau,
gsl_vector * v);
int gsl_linalg_LQ_unpack (const gsl_matrix * LQ, const gsl_vector * tau,
gsl_matrix * Q, gsl_matrix * L);
int gsl_linalg_LQ_update (gsl_matrix * Q, gsl_matrix * R,
const gsl_vector * v, gsl_vector * w);
int gsl_linalg_LQ_LQsolve (gsl_matrix * Q, gsl_matrix * L,
const gsl_vector * b, gsl_vector * x);
/* P^T L Q decomposition */
int gsl_linalg_PTLQ_decomp (gsl_matrix * A, gsl_vector * tau,
gsl_permutation * p, int *signum,
gsl_vector * norm);
int gsl_linalg_PTLQ_decomp2 (const gsl_matrix * A, gsl_matrix * q,
gsl_matrix * r, gsl_vector * tau,
gsl_permutation * p, int *signum,
gsl_vector * norm);
int gsl_linalg_PTLQ_solve_T (const gsl_matrix * QR,
const gsl_vector * tau,
const gsl_permutation * p,
const gsl_vector * b,
gsl_vector * x);
int gsl_linalg_PTLQ_svx_T (const gsl_matrix * LQ,
const gsl_vector * tau,
const gsl_permutation * p,
gsl_vector * x);
int gsl_linalg_PTLQ_LQsolve_T (const gsl_matrix * Q, const gsl_matrix * L,
const gsl_permutation * p,
const gsl_vector * b,
gsl_vector * x);
int gsl_linalg_PTLQ_Lsolve_T (const gsl_matrix * LQ,
const gsl_permutation * p,
const gsl_vector * b,
gsl_vector * x);
int gsl_linalg_PTLQ_Lsvx_T (const gsl_matrix * LQ,
const gsl_permutation * p,
gsl_vector * x);
int gsl_linalg_PTLQ_update (gsl_matrix * Q, gsl_matrix * L,
const gsl_permutation * p,
const gsl_vector * v, gsl_vector * w);
/* Cholesky Decomposition */
int gsl_linalg_cholesky_decomp (gsl_matrix * A);
int gsl_linalg_cholesky_solve (const gsl_matrix * cholesky,
const gsl_vector * b,
gsl_vector * x);
int gsl_linalg_cholesky_svx (const gsl_matrix * cholesky,
gsl_vector * x);
int gsl_linalg_cholesky_invert(gsl_matrix * cholesky);
/* Cholesky decomposition with unit-diagonal triangular parts.
* A = L D L^T, where diag(L) = (1,1,...,1).
* Upon exit, A contains L and L^T as for Cholesky, and
* the diagonal of A is (1,1,...,1). The vector Dis set
* to the diagonal elements of the diagonal matrix D.
*/
int gsl_linalg_cholesky_decomp_unit(gsl_matrix * A, gsl_vector * D);
/* Complex Cholesky Decomposition */
int gsl_linalg_complex_cholesky_decomp (gsl_matrix_complex * A);
int gsl_linalg_complex_cholesky_solve (const gsl_matrix_complex * cholesky,
const gsl_vector_complex * b,
gsl_vector_complex * x);
int gsl_linalg_complex_cholesky_svx (const gsl_matrix_complex * cholesky,
gsl_vector_complex * x);
int gsl_linalg_complex_cholesky_invert(gsl_matrix_complex * cholesky);
/* Symmetric to symmetric tridiagonal decomposition */
int gsl_linalg_symmtd_decomp (gsl_matrix * A,
gsl_vector * tau);
int gsl_linalg_symmtd_unpack (const gsl_matrix * A,
const gsl_vector * tau,
gsl_matrix * Q,
gsl_vector * diag,
gsl_vector * subdiag);
int gsl_linalg_symmtd_unpack_T (const gsl_matrix * A,
gsl_vector * diag,
gsl_vector * subdiag);
/* Hermitian to symmetric tridiagonal decomposition */
int gsl_linalg_hermtd_decomp (gsl_matrix_complex * A,
gsl_vector_complex * tau);
int gsl_linalg_hermtd_unpack (const gsl_matrix_complex * A,
const gsl_vector_complex * tau,
gsl_matrix_complex * U,
gsl_vector * diag,
gsl_vector * sudiag);
int gsl_linalg_hermtd_unpack_T (const gsl_matrix_complex * A,
gsl_vector * diag,
gsl_vector * subdiag);
/* Linear Solve Using Householder Transformations
* exceptions:
*/
int gsl_linalg_HH_solve (gsl_matrix * A, const gsl_vector * b, gsl_vector * x);
int gsl_linalg_HH_svx (gsl_matrix * A, gsl_vector * x);
/* Linear solve for a symmetric tridiagonal system.
* The input vectors represent the NxN matrix as follows:
*
* diag[0] offdiag[0] 0 ...
* offdiag[0] diag[1] offdiag[1] ...
* 0 offdiag[1] diag[2] ...
* 0 0 offdiag[2] ...
* ... ... ... ...
*/
int gsl_linalg_solve_symm_tridiag (const gsl_vector * diag,
const gsl_vector * offdiag,
const gsl_vector * b,
gsl_vector * x);
/* Linear solve for a nonsymmetric tridiagonal system.
* The input vectors represent the NxN matrix as follows:
*
* diag[0] abovediag[0] 0 ...
* belowdiag[0] diag[1] abovediag[1] ...
* 0 belowdiag[1] diag[2] ...
* 0 0 belowdiag[2] ...
* ... ... ... ...
*/
int gsl_linalg_solve_tridiag (const gsl_vector * diag,
const gsl_vector * abovediag,
const gsl_vector * belowdiag,
const gsl_vector * b,
gsl_vector * x);
/* Linear solve for a symmetric cyclic tridiagonal system.
* The input vectors represent the NxN matrix as follows:
*
* diag[0] offdiag[0] 0 ..... offdiag[N-1]
* offdiag[0] diag[1] offdiag[1] .....
* 0 offdiag[1] diag[2] .....
* 0 0 offdiag[2] .....
* ... ...
* offdiag[N-1] ...
*/
int gsl_linalg_solve_symm_cyc_tridiag (const gsl_vector * diag,
const gsl_vector * offdiag,
const gsl_vector * b,
gsl_vector * x);
/* Linear solve for a nonsymmetric cyclic tridiagonal system.
* The input vectors represent the NxN matrix as follows:
*
* diag[0] abovediag[0] 0 ..... belowdiag[N-1]
* belowdiag[0] diag[1] abovediag[1] .....
* 0 belowdiag[1] diag[2]
* 0 0 belowdiag[2] .....
* ... ...
* abovediag[N-1] ...
*/
int gsl_linalg_solve_cyc_tridiag (const gsl_vector * diag,
const gsl_vector * abovediag,
const gsl_vector * belowdiag,
const gsl_vector * b,
gsl_vector * x);
/* Bidiagonal decomposition */
int gsl_linalg_bidiag_decomp (gsl_matrix * A,
gsl_vector * tau_U,
gsl_vector * tau_V);
int gsl_linalg_bidiag_unpack (const gsl_matrix * A,
const gsl_vector * tau_U,
gsl_matrix * U,
const gsl_vector * tau_V,
gsl_matrix * V,
gsl_vector * diag,
gsl_vector * superdiag);
int gsl_linalg_bidiag_unpack2 (gsl_matrix * A,
gsl_vector * tau_U,
gsl_vector * tau_V,
gsl_matrix * V);
int gsl_linalg_bidiag_unpack_B (const gsl_matrix * A,
gsl_vector * diag,
gsl_vector * superdiag);
/* Balancing */
int gsl_linalg_balance_matrix (gsl_matrix * A, gsl_vector * D);
int gsl_linalg_balance_accum (gsl_matrix * A, gsl_vector * D);
int gsl_linalg_balance_columns (gsl_matrix * A, gsl_vector * D);
__END_DECLS
#endif /* __GSL_LINALG_H__ */
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