Mercurial > hg > CbC > CbC_gcc
annotate gcc/lambda-mat.c @ 56:3c8a44c06a95
Added tag gcc-4.4.5 for changeset 77e2b8dfacca
| author | ryoma <e075725@ie.u-ryukyu.ac.jp> |
|---|---|
| date | Fri, 12 Feb 2010 23:41:23 +0900 |
| parents | 77e2b8dfacca |
| children | b7f97abdc517 |
| rev | line source |
|---|---|
| 0 | 1 /* Integer matrix math routines |
| 2 Copyright (C) 2003, 2004, 2005, 2007, 2008 Free Software Foundation, Inc. | |
| 3 Contributed by Daniel Berlin <dberlin@dberlin.org>. | |
| 4 | |
| 5 This file is part of GCC. | |
| 6 | |
| 7 GCC is free software; you can redistribute it and/or modify it under | |
| 8 the terms of the GNU General Public License as published by the Free | |
| 9 Software Foundation; either version 3, or (at your option) any later | |
| 10 version. | |
| 11 | |
| 12 GCC is distributed in the hope that it will be useful, but WITHOUT ANY | |
| 13 WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 15 for more details. | |
| 16 | |
| 17 You should have received a copy of the GNU General Public License | |
| 18 along with GCC; see the file COPYING3. If not see | |
| 19 <http://www.gnu.org/licenses/>. */ | |
| 20 | |
| 21 #include "config.h" | |
| 22 #include "system.h" | |
| 23 #include "coretypes.h" | |
| 24 #include "tm.h" | |
| 25 #include "ggc.h" | |
| 26 #include "tree.h" | |
| 27 #include "tree-flow.h" | |
| 28 #include "lambda.h" | |
| 29 | |
|
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30 static void lambda_matrix_get_column (lambda_matrix, int, int, |
| 0 | 31 lambda_vector); |
| 32 | |
| 33 /* Allocate a matrix of M rows x N cols. */ | |
| 34 | |
| 35 lambda_matrix | |
| 36 lambda_matrix_new (int m, int n) | |
| 37 { | |
| 38 lambda_matrix mat; | |
| 39 int i; | |
| 40 | |
| 41 mat = GGC_NEWVEC (lambda_vector, m); | |
|
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42 |
| 0 | 43 for (i = 0; i < m; i++) |
| 44 mat[i] = lambda_vector_new (n); | |
| 45 | |
| 46 return mat; | |
| 47 } | |
| 48 | |
| 49 /* Copy the elements of M x N matrix MAT1 to MAT2. */ | |
| 50 | |
| 51 void | |
| 52 lambda_matrix_copy (lambda_matrix mat1, lambda_matrix mat2, | |
| 53 int m, int n) | |
| 54 { | |
| 55 int i; | |
| 56 | |
| 57 for (i = 0; i < m; i++) | |
| 58 lambda_vector_copy (mat1[i], mat2[i], n); | |
| 59 } | |
| 60 | |
| 61 /* Store the N x N identity matrix in MAT. */ | |
| 62 | |
| 63 void | |
| 64 lambda_matrix_id (lambda_matrix mat, int size) | |
| 65 { | |
| 66 int i, j; | |
| 67 | |
| 68 for (i = 0; i < size; i++) | |
| 69 for (j = 0; j < size; j++) | |
| 70 mat[i][j] = (i == j) ? 1 : 0; | |
| 71 } | |
| 72 | |
| 73 /* Return true if MAT is the identity matrix of SIZE */ | |
| 74 | |
| 75 bool | |
| 76 lambda_matrix_id_p (lambda_matrix mat, int size) | |
| 77 { | |
| 78 int i, j; | |
| 79 for (i = 0; i < size; i++) | |
| 80 for (j = 0; j < size; j++) | |
| 81 { | |
| 82 if (i == j) | |
| 83 { | |
| 84 if (mat[i][j] != 1) | |
| 85 return false; | |
| 86 } | |
| 87 else | |
| 88 { | |
| 89 if (mat[i][j] != 0) | |
| 90 return false; | |
| 91 } | |
| 92 } | |
| 93 return true; | |
| 94 } | |
| 95 | |
| 96 /* Negate the elements of the M x N matrix MAT1 and store it in MAT2. */ | |
| 97 | |
| 98 void | |
| 99 lambda_matrix_negate (lambda_matrix mat1, lambda_matrix mat2, int m, int n) | |
| 100 { | |
| 101 int i; | |
| 102 | |
| 103 for (i = 0; i < m; i++) | |
| 104 lambda_vector_negate (mat1[i], mat2[i], n); | |
| 105 } | |
| 106 | |
| 107 /* Take the transpose of matrix MAT1 and store it in MAT2. | |
| 108 MAT1 is an M x N matrix, so MAT2 must be N x M. */ | |
| 109 | |
| 110 void | |
| 111 lambda_matrix_transpose (lambda_matrix mat1, lambda_matrix mat2, int m, int n) | |
| 112 { | |
| 113 int i, j; | |
| 114 | |
| 115 for (i = 0; i < n; i++) | |
| 116 for (j = 0; j < m; j++) | |
| 117 mat2[i][j] = mat1[j][i]; | |
| 118 } | |
| 119 | |
| 120 | |
| 121 /* Add two M x N matrices together: MAT3 = MAT1+MAT2. */ | |
| 122 | |
| 123 void | |
| 124 lambda_matrix_add (lambda_matrix mat1, lambda_matrix mat2, | |
| 125 lambda_matrix mat3, int m, int n) | |
| 126 { | |
| 127 int i; | |
| 128 | |
| 129 for (i = 0; i < m; i++) | |
| 130 lambda_vector_add (mat1[i], mat2[i], mat3[i], n); | |
| 131 } | |
| 132 | |
| 133 /* MAT3 = CONST1 * MAT1 + CONST2 * MAT2. All matrices are M x N. */ | |
| 134 | |
| 135 void | |
| 136 lambda_matrix_add_mc (lambda_matrix mat1, int const1, | |
| 137 lambda_matrix mat2, int const2, | |
| 138 lambda_matrix mat3, int m, int n) | |
| 139 { | |
| 140 int i; | |
| 141 | |
| 142 for (i = 0; i < m; i++) | |
| 143 lambda_vector_add_mc (mat1[i], const1, mat2[i], const2, mat3[i], n); | |
| 144 } | |
| 145 | |
| 146 /* Multiply two matrices: MAT3 = MAT1 * MAT2. | |
| 147 MAT1 is an M x R matrix, and MAT2 is R x N. The resulting MAT2 | |
| 148 must therefore be M x N. */ | |
| 149 | |
| 150 void | |
| 151 lambda_matrix_mult (lambda_matrix mat1, lambda_matrix mat2, | |
| 152 lambda_matrix mat3, int m, int r, int n) | |
| 153 { | |
| 154 | |
| 155 int i, j, k; | |
| 156 | |
| 157 for (i = 0; i < m; i++) | |
| 158 { | |
| 159 for (j = 0; j < n; j++) | |
| 160 { | |
| 161 mat3[i][j] = 0; | |
| 162 for (k = 0; k < r; k++) | |
| 163 mat3[i][j] += mat1[i][k] * mat2[k][j]; | |
| 164 } | |
| 165 } | |
| 166 } | |
| 167 | |
| 168 /* Get column COL from the matrix MAT and store it in VEC. MAT has | |
| 169 N rows, so the length of VEC must be N. */ | |
| 170 | |
| 171 static void | |
| 172 lambda_matrix_get_column (lambda_matrix mat, int n, int col, | |
| 173 lambda_vector vec) | |
| 174 { | |
| 175 int i; | |
| 176 | |
| 177 for (i = 0; i < n; i++) | |
| 178 vec[i] = mat[i][col]; | |
| 179 } | |
| 180 | |
| 181 /* Delete rows r1 to r2 (not including r2). */ | |
| 182 | |
| 183 void | |
| 184 lambda_matrix_delete_rows (lambda_matrix mat, int rows, int from, int to) | |
| 185 { | |
| 186 int i; | |
| 187 int dist; | |
| 188 dist = to - from; | |
| 189 | |
| 190 for (i = to; i < rows; i++) | |
| 191 mat[i - dist] = mat[i]; | |
| 192 | |
| 193 for (i = rows - dist; i < rows; i++) | |
| 194 mat[i] = NULL; | |
| 195 } | |
| 196 | |
| 197 /* Swap rows R1 and R2 in matrix MAT. */ | |
| 198 | |
| 199 void | |
| 200 lambda_matrix_row_exchange (lambda_matrix mat, int r1, int r2) | |
| 201 { | |
| 202 lambda_vector row; | |
| 203 | |
| 204 row = mat[r1]; | |
| 205 mat[r1] = mat[r2]; | |
| 206 mat[r2] = row; | |
| 207 } | |
| 208 | |
| 209 /* Add a multiple of row R1 of matrix MAT with N columns to row R2: | |
| 210 R2 = R2 + CONST1 * R1. */ | |
| 211 | |
| 212 void | |
| 213 lambda_matrix_row_add (lambda_matrix mat, int n, int r1, int r2, int const1) | |
| 214 { | |
| 215 int i; | |
| 216 | |
| 217 if (const1 == 0) | |
| 218 return; | |
| 219 | |
| 220 for (i = 0; i < n; i++) | |
| 221 mat[r2][i] += const1 * mat[r1][i]; | |
| 222 } | |
| 223 | |
| 224 /* Negate row R1 of matrix MAT which has N columns. */ | |
| 225 | |
| 226 void | |
| 227 lambda_matrix_row_negate (lambda_matrix mat, int n, int r1) | |
| 228 { | |
| 229 lambda_vector_negate (mat[r1], mat[r1], n); | |
| 230 } | |
| 231 | |
| 232 /* Multiply row R1 of matrix MAT with N columns by CONST1. */ | |
| 233 | |
| 234 void | |
| 235 lambda_matrix_row_mc (lambda_matrix mat, int n, int r1, int const1) | |
| 236 { | |
| 237 int i; | |
| 238 | |
| 239 for (i = 0; i < n; i++) | |
| 240 mat[r1][i] *= const1; | |
| 241 } | |
| 242 | |
| 243 /* Exchange COL1 and COL2 in matrix MAT. M is the number of rows. */ | |
| 244 | |
| 245 void | |
| 246 lambda_matrix_col_exchange (lambda_matrix mat, int m, int col1, int col2) | |
| 247 { | |
| 248 int i; | |
| 249 int tmp; | |
| 250 for (i = 0; i < m; i++) | |
| 251 { | |
| 252 tmp = mat[i][col1]; | |
| 253 mat[i][col1] = mat[i][col2]; | |
| 254 mat[i][col2] = tmp; | |
| 255 } | |
| 256 } | |
| 257 | |
| 258 /* Add a multiple of column C1 of matrix MAT with M rows to column C2: | |
| 259 C2 = C2 + CONST1 * C1. */ | |
| 260 | |
| 261 void | |
| 262 lambda_matrix_col_add (lambda_matrix mat, int m, int c1, int c2, int const1) | |
| 263 { | |
| 264 int i; | |
| 265 | |
| 266 if (const1 == 0) | |
| 267 return; | |
| 268 | |
| 269 for (i = 0; i < m; i++) | |
| 270 mat[i][c2] += const1 * mat[i][c1]; | |
| 271 } | |
| 272 | |
| 273 /* Negate column C1 of matrix MAT which has M rows. */ | |
| 274 | |
| 275 void | |
| 276 lambda_matrix_col_negate (lambda_matrix mat, int m, int c1) | |
| 277 { | |
| 278 int i; | |
| 279 | |
| 280 for (i = 0; i < m; i++) | |
| 281 mat[i][c1] *= -1; | |
| 282 } | |
| 283 | |
| 284 /* Multiply column C1 of matrix MAT with M rows by CONST1. */ | |
| 285 | |
| 286 void | |
| 287 lambda_matrix_col_mc (lambda_matrix mat, int m, int c1, int const1) | |
| 288 { | |
| 289 int i; | |
| 290 | |
| 291 for (i = 0; i < m; i++) | |
| 292 mat[i][c1] *= const1; | |
| 293 } | |
| 294 | |
| 295 /* Compute the inverse of the N x N matrix MAT and store it in INV. | |
| 296 | |
| 297 We don't _really_ compute the inverse of MAT. Instead we compute | |
| 298 det(MAT)*inv(MAT), and we return det(MAT) to the caller as the function | |
| 299 result. This is necessary to preserve accuracy, because we are dealing | |
| 300 with integer matrices here. | |
| 301 | |
| 302 The algorithm used here is a column based Gauss-Jordan elimination on MAT | |
| 303 and the identity matrix in parallel. The inverse is the result of applying | |
| 304 the same operations on the identity matrix that reduce MAT to the identity | |
| 305 matrix. | |
| 306 | |
| 307 When MAT is a 2 x 2 matrix, we don't go through the whole process, because | |
| 308 it is easily inverted by inspection and it is a very common case. */ | |
| 309 | |
| 310 static int lambda_matrix_inverse_hard (lambda_matrix, lambda_matrix, int); | |
| 311 | |
| 312 int | |
| 313 lambda_matrix_inverse (lambda_matrix mat, lambda_matrix inv, int n) | |
| 314 { | |
| 315 if (n == 2) | |
| 316 { | |
| 317 int a, b, c, d, det; | |
| 318 a = mat[0][0]; | |
| 319 b = mat[1][0]; | |
| 320 c = mat[0][1]; | |
|
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321 d = mat[1][1]; |
| 0 | 322 inv[0][0] = d; |
| 323 inv[0][1] = -c; | |
| 324 inv[1][0] = -b; | |
| 325 inv[1][1] = a; | |
| 326 det = (a * d - b * c); | |
| 327 if (det < 0) | |
| 328 { | |
| 329 det *= -1; | |
| 330 inv[0][0] *= -1; | |
| 331 inv[1][0] *= -1; | |
| 332 inv[0][1] *= -1; | |
| 333 inv[1][1] *= -1; | |
| 334 } | |
| 335 return det; | |
| 336 } | |
| 337 else | |
| 338 return lambda_matrix_inverse_hard (mat, inv, n); | |
| 339 } | |
| 340 | |
| 341 /* If MAT is not a special case, invert it the hard way. */ | |
| 342 | |
| 343 static int | |
| 344 lambda_matrix_inverse_hard (lambda_matrix mat, lambda_matrix inv, int n) | |
| 345 { | |
| 346 lambda_vector row; | |
| 347 lambda_matrix temp; | |
| 348 int i, j; | |
| 349 int determinant; | |
| 350 | |
| 351 temp = lambda_matrix_new (n, n); | |
| 352 lambda_matrix_copy (mat, temp, n, n); | |
| 353 lambda_matrix_id (inv, n); | |
| 354 | |
| 355 /* Reduce TEMP to a lower triangular form, applying the same operations on | |
| 356 INV which starts as the identity matrix. N is the number of rows and | |
| 357 columns. */ | |
| 358 for (j = 0; j < n; j++) | |
| 359 { | |
| 360 row = temp[j]; | |
| 361 | |
| 362 /* Make every element in the current row positive. */ | |
| 363 for (i = j; i < n; i++) | |
| 364 if (row[i] < 0) | |
| 365 { | |
| 366 lambda_matrix_col_negate (temp, n, i); | |
| 367 lambda_matrix_col_negate (inv, n, i); | |
| 368 } | |
| 369 | |
| 370 /* Sweep the upper triangle. Stop when only the diagonal element in the | |
| 371 current row is nonzero. */ | |
| 372 while (lambda_vector_first_nz (row, n, j + 1) < n) | |
| 373 { | |
| 374 int min_col = lambda_vector_min_nz (row, n, j); | |
| 375 lambda_matrix_col_exchange (temp, n, j, min_col); | |
| 376 lambda_matrix_col_exchange (inv, n, j, min_col); | |
| 377 | |
| 378 for (i = j + 1; i < n; i++) | |
| 379 { | |
| 380 int factor; | |
| 381 | |
| 382 factor = -1 * row[i]; | |
| 383 if (row[j] != 1) | |
| 384 factor /= row[j]; | |
| 385 | |
| 386 lambda_matrix_col_add (temp, n, j, i, factor); | |
| 387 lambda_matrix_col_add (inv, n, j, i, factor); | |
| 388 } | |
| 389 } | |
| 390 } | |
| 391 | |
| 392 /* Reduce TEMP from a lower triangular to the identity matrix. Also compute | |
| 393 the determinant, which now is simply the product of the elements on the | |
| 394 diagonal of TEMP. If one of these elements is 0, the matrix has 0 as an | |
| 395 eigenvalue so it is singular and hence not invertible. */ | |
| 396 determinant = 1; | |
| 397 for (j = n - 1; j >= 0; j--) | |
| 398 { | |
| 399 int diagonal; | |
| 400 | |
| 401 row = temp[j]; | |
| 402 diagonal = row[j]; | |
| 403 | |
| 404 /* The matrix must not be singular. */ | |
| 405 gcc_assert (diagonal); | |
| 406 | |
| 407 determinant = determinant * diagonal; | |
| 408 | |
| 409 /* If the diagonal is not 1, then multiply the each row by the | |
| 410 diagonal so that the middle number is now 1, rather than a | |
| 411 rational. */ | |
| 412 if (diagonal != 1) | |
| 413 { | |
| 414 for (i = 0; i < j; i++) | |
| 415 lambda_matrix_col_mc (inv, n, i, diagonal); | |
| 416 for (i = j + 1; i < n; i++) | |
| 417 lambda_matrix_col_mc (inv, n, i, diagonal); | |
| 418 | |
| 419 row[j] = diagonal = 1; | |
| 420 } | |
| 421 | |
| 422 /* Sweep the lower triangle column wise. */ | |
| 423 for (i = j - 1; i >= 0; i--) | |
| 424 { | |
| 425 if (row[i]) | |
| 426 { | |
| 427 int factor = -row[i]; | |
| 428 lambda_matrix_col_add (temp, n, j, i, factor); | |
| 429 lambda_matrix_col_add (inv, n, j, i, factor); | |
| 430 } | |
| 431 | |
| 432 } | |
| 433 } | |
| 434 | |
| 435 return determinant; | |
| 436 } | |
| 437 | |
| 438 /* Decompose a N x N matrix MAT to a product of a lower triangular H | |
| 439 and a unimodular U matrix such that MAT = H.U. N is the size of | |
| 440 the rows of MAT. */ | |
| 441 | |
| 442 void | |
| 443 lambda_matrix_hermite (lambda_matrix mat, int n, | |
| 444 lambda_matrix H, lambda_matrix U) | |
| 445 { | |
| 446 lambda_vector row; | |
| 447 int i, j, factor, minimum_col; | |
| 448 | |
| 449 lambda_matrix_copy (mat, H, n, n); | |
| 450 lambda_matrix_id (U, n); | |
| 451 | |
| 452 for (j = 0; j < n; j++) | |
| 453 { | |
| 454 row = H[j]; | |
| 455 | |
| 456 /* Make every element of H[j][j..n] positive. */ | |
| 457 for (i = j; i < n; i++) | |
| 458 { | |
| 459 if (row[i] < 0) | |
| 460 { | |
| 461 lambda_matrix_col_negate (H, n, i); | |
| 462 lambda_vector_negate (U[i], U[i], n); | |
| 463 } | |
| 464 } | |
| 465 | |
| 466 /* Stop when only the diagonal element is nonzero. */ | |
| 467 while (lambda_vector_first_nz (row, n, j + 1) < n) | |
| 468 { | |
| 469 minimum_col = lambda_vector_min_nz (row, n, j); | |
| 470 lambda_matrix_col_exchange (H, n, j, minimum_col); | |
| 471 lambda_matrix_row_exchange (U, j, minimum_col); | |
| 472 | |
| 473 for (i = j + 1; i < n; i++) | |
| 474 { | |
| 475 factor = row[i] / row[j]; | |
| 476 lambda_matrix_col_add (H, n, j, i, -1 * factor); | |
| 477 lambda_matrix_row_add (U, n, i, j, factor); | |
| 478 } | |
| 479 } | |
| 480 } | |
| 481 } | |
| 482 | |
| 483 /* Given an M x N integer matrix A, this function determines an M x | |
| 484 M unimodular matrix U, and an M x N echelon matrix S such that | |
| 485 "U.A = S". This decomposition is also known as "right Hermite". | |
|
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486 |
| 0 | 487 Ref: Algorithm 2.1 page 33 in "Loop Transformations for |
| 488 Restructuring Compilers" Utpal Banerjee. */ | |
| 489 | |
| 490 void | |
| 491 lambda_matrix_right_hermite (lambda_matrix A, int m, int n, | |
| 492 lambda_matrix S, lambda_matrix U) | |
| 493 { | |
| 494 int i, j, i0 = 0; | |
| 495 | |
| 496 lambda_matrix_copy (A, S, m, n); | |
| 497 lambda_matrix_id (U, m); | |
| 498 | |
| 499 for (j = 0; j < n; j++) | |
| 500 { | |
| 501 if (lambda_vector_first_nz (S[j], m, i0) < m) | |
| 502 { | |
| 503 ++i0; | |
| 504 for (i = m - 1; i >= i0; i--) | |
| 505 { | |
| 506 while (S[i][j] != 0) | |
| 507 { | |
| 508 int sigma, factor, a, b; | |
| 509 | |
| 510 a = S[i-1][j]; | |
| 511 b = S[i][j]; | |
| 512 sigma = (a * b < 0) ? -1: 1; | |
| 513 a = abs (a); | |
| 514 b = abs (b); | |
| 515 factor = sigma * (a / b); | |
| 516 | |
| 517 lambda_matrix_row_add (S, n, i, i-1, -factor); | |
| 518 lambda_matrix_row_exchange (S, i, i-1); | |
| 519 | |
| 520 lambda_matrix_row_add (U, m, i, i-1, -factor); | |
| 521 lambda_matrix_row_exchange (U, i, i-1); | |
| 522 } | |
| 523 } | |
| 524 } | |
| 525 } | |
| 526 } | |
| 527 | |
| 528 /* Given an M x N integer matrix A, this function determines an M x M | |
| 529 unimodular matrix V, and an M x N echelon matrix S such that "A = | |
| 530 V.S". This decomposition is also known as "left Hermite". | |
|
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parents:
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531 |
| 0 | 532 Ref: Algorithm 2.2 page 36 in "Loop Transformations for |
| 533 Restructuring Compilers" Utpal Banerjee. */ | |
| 534 | |
| 535 void | |
| 536 lambda_matrix_left_hermite (lambda_matrix A, int m, int n, | |
| 537 lambda_matrix S, lambda_matrix V) | |
| 538 { | |
| 539 int i, j, i0 = 0; | |
| 540 | |
| 541 lambda_matrix_copy (A, S, m, n); | |
| 542 lambda_matrix_id (V, m); | |
| 543 | |
| 544 for (j = 0; j < n; j++) | |
| 545 { | |
| 546 if (lambda_vector_first_nz (S[j], m, i0) < m) | |
| 547 { | |
| 548 ++i0; | |
| 549 for (i = m - 1; i >= i0; i--) | |
| 550 { | |
| 551 while (S[i][j] != 0) | |
| 552 { | |
| 553 int sigma, factor, a, b; | |
| 554 | |
| 555 a = S[i-1][j]; | |
| 556 b = S[i][j]; | |
| 557 sigma = (a * b < 0) ? -1: 1; | |
| 558 a = abs (a); | |
| 559 b = abs (b); | |
| 560 factor = sigma * (a / b); | |
| 561 | |
| 562 lambda_matrix_row_add (S, n, i, i-1, -factor); | |
| 563 lambda_matrix_row_exchange (S, i, i-1); | |
| 564 | |
| 565 lambda_matrix_col_add (V, m, i-1, i, factor); | |
| 566 lambda_matrix_col_exchange (V, m, i, i-1); | |
| 567 } | |
| 568 } | |
| 569 } | |
| 570 } | |
| 571 } | |
| 572 | |
| 573 /* When it exists, return the first nonzero row in MAT after row | |
| 574 STARTROW. Otherwise return rowsize. */ | |
| 575 | |
| 576 int | |
| 577 lambda_matrix_first_nz_vec (lambda_matrix mat, int rowsize, int colsize, | |
| 578 int startrow) | |
| 579 { | |
| 580 int j; | |
| 581 bool found = false; | |
| 582 | |
| 583 for (j = startrow; (j < rowsize) && !found; j++) | |
| 584 { | |
| 585 if ((mat[j] != NULL) | |
| 586 && (lambda_vector_first_nz (mat[j], colsize, startrow) < colsize)) | |
| 587 found = true; | |
| 588 } | |
| 589 | |
| 590 if (found) | |
| 591 return j - 1; | |
| 592 return rowsize; | |
| 593 } | |
| 594 | |
| 595 /* Calculate the projection of E sub k to the null space of B. */ | |
| 596 | |
| 597 void | |
| 598 lambda_matrix_project_to_null (lambda_matrix B, int rowsize, | |
| 599 int colsize, int k, lambda_vector x) | |
| 600 { | |
| 601 lambda_matrix M1, M2, M3, I; | |
| 602 int determinant; | |
| 603 | |
| 604 /* Compute c(I-B^T inv(B B^T) B) e sub k. */ | |
| 605 | |
| 606 /* M1 is the transpose of B. */ | |
| 607 M1 = lambda_matrix_new (colsize, colsize); | |
| 608 lambda_matrix_transpose (B, M1, rowsize, colsize); | |
| 609 | |
| 610 /* M2 = B * B^T */ | |
| 611 M2 = lambda_matrix_new (colsize, colsize); | |
| 612 lambda_matrix_mult (B, M1, M2, rowsize, colsize, rowsize); | |
| 613 | |
| 614 /* M3 = inv(M2) */ | |
| 615 M3 = lambda_matrix_new (colsize, colsize); | |
| 616 determinant = lambda_matrix_inverse (M2, M3, rowsize); | |
| 617 | |
| 618 /* M2 = B^T (inv(B B^T)) */ | |
| 619 lambda_matrix_mult (M1, M3, M2, colsize, rowsize, rowsize); | |
| 620 | |
| 621 /* M1 = B^T (inv(B B^T)) B */ | |
| 622 lambda_matrix_mult (M2, B, M1, colsize, rowsize, colsize); | |
| 623 lambda_matrix_negate (M1, M1, colsize, colsize); | |
| 624 | |
| 625 I = lambda_matrix_new (colsize, colsize); | |
| 626 lambda_matrix_id (I, colsize); | |
| 627 | |
| 628 lambda_matrix_add_mc (I, determinant, M1, 1, M2, colsize, colsize); | |
| 629 | |
| 630 lambda_matrix_get_column (M2, colsize, k - 1, x); | |
| 631 | |
| 632 } | |
| 633 | |
| 634 /* Multiply a vector VEC by a matrix MAT. | |
| 635 MAT is an M*N matrix, and VEC is a vector with length N. The result | |
| 636 is stored in DEST which must be a vector of length M. */ | |
| 637 | |
| 638 void | |
| 639 lambda_matrix_vector_mult (lambda_matrix matrix, int m, int n, | |
| 640 lambda_vector vec, lambda_vector dest) | |
| 641 { | |
| 642 int i, j; | |
| 643 | |
| 644 lambda_vector_clear (dest, m); | |
| 645 for (i = 0; i < m; i++) | |
| 646 for (j = 0; j < n; j++) | |
| 647 dest[i] += matrix[i][j] * vec[j]; | |
| 648 } | |
| 649 | |
| 650 /* Print out an M x N matrix MAT to OUTFILE. */ | |
| 651 | |
| 652 void | |
| 653 print_lambda_matrix (FILE * outfile, lambda_matrix matrix, int m, int n) | |
| 654 { | |
| 655 int i; | |
| 656 | |
| 657 for (i = 0; i < m; i++) | |
| 658 print_lambda_vector (outfile, matrix[i], n); | |
| 659 fprintf (outfile, "\n"); | |
| 660 } | |
| 661 |