1 /* 2 Inverts 2 by 2 matrix using gaussian elimination with partial pivoting. 3 4 Used by the sparse factorization routines in 5 src/mat/impls/baij/seq 6 7 This is a combination of the Linpack routines 8 dgefa() and dgedi() specialized for a size of 2. 9 10 */ 11 #include <petscsys.h> 12 #include <petsc/private/kernels/blockinvert.h> 13 14 PetscErrorCode PetscKernel_A_gets_inverse_A_2(MatScalar *a, PetscReal shift, PetscBool allowzeropivot, PetscBool *zeropivotdetected) 15 { 16 PetscInt i__2, i__3, kp1, j, k, l, ll, i, ipvt[2], k3; 17 PetscInt k4, j3; 18 MatScalar *aa, *ax, *ay, work[4], stmp; 19 MatReal tmp, max; 20 21 PetscFunctionBegin; 22 if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE; 23 shift = .25 * shift * (1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[3])); 24 25 /* Parameter adjustments */ 26 a -= 3; 27 28 k = 1; 29 kp1 = k + 1; 30 k3 = 2 * k; 31 k4 = k3 + k; 32 33 /* find l = pivot index */ 34 i__2 = 3 - k; 35 aa = &a[k4]; 36 max = PetscAbsScalar(aa[0]); 37 l = 1; 38 for (ll = 1; ll < i__2; ll++) { 39 tmp = PetscAbsScalar(aa[ll]); 40 if (tmp > max) { 41 max = tmp; 42 l = ll + 1; 43 } 44 } 45 l += k - 1; 46 ipvt[k - 1] = l; 47 48 if (a[l + k3] == 0.0) { 49 if (shift == 0.0) { 50 PetscCheck(allowzeropivot, PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT, k - 1); 51 PetscCall(PetscInfo(NULL, "Zero pivot, row %" PetscInt_FMT "\n", k - 1)); 52 if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE; 53 } else { 54 a[l + k3] = shift; 55 } 56 } 57 58 /* interchange if necessary */ 59 if (l != k) { 60 stmp = a[l + k3]; 61 a[l + k3] = a[k4]; 62 a[k4] = stmp; 63 } 64 65 /* compute multipliers */ 66 stmp = -1. / a[k4]; 67 i__2 = 2 - k; 68 aa = &a[1 + k4]; 69 for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp; 70 71 /* row elimination with column indexing */ 72 ax = &a[k4 + 1]; 73 for (j = kp1; j <= 2; ++j) { 74 j3 = 2 * j; 75 stmp = a[l + j3]; 76 if (l != k) { 77 a[l + j3] = a[k + j3]; 78 a[k + j3] = stmp; 79 } 80 81 i__3 = 2 - k; 82 ay = &a[1 + k + j3]; 83 for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll]; 84 } 85 86 ipvt[1] = 2; 87 if (a[6] == 0.0) { 88 PetscCheck(PetscLikely(allowzeropivot), PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 1"); 89 PetscCall(PetscInfo(NULL, "Zero pivot, row 1\n")); 90 if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE; 91 } 92 93 /* Now form the inverse */ 94 /* compute inverse(u) */ 95 for (k = 1; k <= 2; ++k) { 96 k3 = 2 * k; 97 k4 = k3 + k; 98 a[k4] = 1.0 / a[k4]; 99 stmp = -a[k4]; 100 i__2 = k - 1; 101 aa = &a[k3 + 1]; 102 for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp; 103 kp1 = k + 1; 104 if (2 < kp1) continue; 105 ax = aa; 106 for (j = kp1; j <= 2; ++j) { 107 j3 = 2 * j; 108 stmp = a[k + j3]; 109 a[k + j3] = 0.0; 110 ay = &a[j3 + 1]; 111 for (ll = 0; ll < k; ll++) ay[ll] += stmp * ax[ll]; 112 } 113 } 114 115 /* form inverse(u)*inverse(l) */ 116 k = 1; 117 k3 = 2 * k; 118 kp1 = k + 1; 119 aa = a + k3; 120 for (i = kp1; i <= 2; ++i) { 121 work[i - 1] = aa[i]; 122 aa[i] = 0.0; 123 } 124 for (j = kp1; j <= 2; ++j) { 125 stmp = work[j - 1]; 126 ax = &a[2 * j + 1]; 127 ay = &a[k3 + 1]; 128 ay[0] += stmp * ax[0]; 129 ay[1] += stmp * ax[1]; 130 } 131 l = ipvt[k - 1]; 132 if (l != k) { 133 ax = &a[k3 + 1]; 134 ay = &a[2 * l + 1]; 135 stmp = ax[0]; 136 ax[0] = ay[0]; 137 ay[0] = stmp; 138 stmp = ax[1]; 139 ax[1] = ay[1]; 140 ay[1] = stmp; 141 } 142 PetscFunctionReturn(PETSC_SUCCESS); 143 } 144 145 /* Gaussian elimination with partial pivoting */ 146 PetscErrorCode PetscKernel_A_gets_inverse_A_9(MatScalar *a, PetscReal shift, PetscBool allowzeropivot, PetscBool *zeropivotdetected) 147 { 148 PetscInt i__2, i__3, kp1, j, k, l, ll, i, ipvt[9], kb, k3; 149 PetscInt k4, j3; 150 MatScalar *aa, *ax, *ay, work[81], stmp; 151 MatReal tmp, max; 152 153 PetscFunctionBegin; 154 if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE; 155 156 /* Parameter adjustments */ 157 a -= 10; 158 159 for (k = 1; k <= 8; ++k) { 160 kp1 = k + 1; 161 k3 = 9 * k; 162 k4 = k3 + k; 163 164 /* find l = pivot index */ 165 i__2 = 10 - k; 166 aa = &a[k4]; 167 max = PetscAbsScalar(aa[0]); 168 l = 1; 169 for (ll = 1; ll < i__2; ll++) { 170 tmp = PetscAbsScalar(aa[ll]); 171 if (tmp > max) { 172 max = tmp; 173 l = ll + 1; 174 } 175 } 176 l += k - 1; 177 ipvt[k - 1] = l; 178 179 if (a[l + k3] == 0.0) { 180 if (shift == 0.0) { 181 PetscCheck(allowzeropivot, PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT, k - 1); 182 PetscCall(PetscInfo(NULL, "Zero pivot, row %" PetscInt_FMT "\n", k - 1)); 183 if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE; 184 } else { 185 a[l + k3] = shift; 186 } 187 } 188 189 /* interchange if necessary */ 190 if (l != k) { 191 stmp = a[l + k3]; 192 a[l + k3] = a[k4]; 193 a[k4] = stmp; 194 } 195 196 /* compute multipliers */ 197 stmp = -1. / a[k4]; 198 i__2 = 9 - k; 199 aa = &a[1 + k4]; 200 for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp; 201 202 /* row elimination with column indexing */ 203 ax = &a[k4 + 1]; 204 for (j = kp1; j <= 9; ++j) { 205 j3 = 9 * j; 206 stmp = a[l + j3]; 207 if (l != k) { 208 a[l + j3] = a[k + j3]; 209 a[k + j3] = stmp; 210 } 211 212 i__3 = 9 - k; 213 ay = &a[1 + k + j3]; 214 for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll]; 215 } 216 } 217 ipvt[8] = 9; 218 if (a[90] == 0.0) { 219 PetscCheck(PetscLikely(allowzeropivot), PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 8"); 220 PetscCall(PetscInfo(NULL, "Zero pivot, row 8\n")); 221 if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE; 222 } 223 224 /* Now form the inverse */ 225 /* compute inverse(u) */ 226 for (k = 1; k <= 9; ++k) { 227 k3 = 9 * k; 228 k4 = k3 + k; 229 a[k4] = 1.0 / a[k4]; 230 stmp = -a[k4]; 231 i__2 = k - 1; 232 aa = &a[k3 + 1]; 233 for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp; 234 kp1 = k + 1; 235 if (9 < kp1) continue; 236 ax = aa; 237 for (j = kp1; j <= 9; ++j) { 238 j3 = 9 * j; 239 stmp = a[k + j3]; 240 a[k + j3] = 0.0; 241 ay = &a[j3 + 1]; 242 for (ll = 0; ll < k; ll++) ay[ll] += stmp * ax[ll]; 243 } 244 } 245 246 /* form inverse(u)*inverse(l) */ 247 for (kb = 1; kb <= 8; ++kb) { 248 k = 9 - kb; 249 k3 = 9 * k; 250 kp1 = k + 1; 251 aa = a + k3; 252 for (i = kp1; i <= 9; ++i) { 253 work[i - 1] = aa[i]; 254 aa[i] = 0.0; 255 } 256 for (j = kp1; j <= 9; ++j) { 257 stmp = work[j - 1]; 258 ax = &a[9 * j + 1]; 259 ay = &a[k3 + 1]; 260 ay[0] += stmp * ax[0]; 261 ay[1] += stmp * ax[1]; 262 ay[2] += stmp * ax[2]; 263 ay[3] += stmp * ax[3]; 264 ay[4] += stmp * ax[4]; 265 ay[5] += stmp * ax[5]; 266 ay[6] += stmp * ax[6]; 267 ay[7] += stmp * ax[7]; 268 ay[8] += stmp * ax[8]; 269 } 270 l = ipvt[k - 1]; 271 if (l != k) { 272 ax = &a[k3 + 1]; 273 ay = &a[9 * l + 1]; 274 stmp = ax[0]; 275 ax[0] = ay[0]; 276 ay[0] = stmp; 277 stmp = ax[1]; 278 ax[1] = ay[1]; 279 ay[1] = stmp; 280 stmp = ax[2]; 281 ax[2] = ay[2]; 282 ay[2] = stmp; 283 stmp = ax[3]; 284 ax[3] = ay[3]; 285 ay[3] = stmp; 286 stmp = ax[4]; 287 ax[4] = ay[4]; 288 ay[4] = stmp; 289 stmp = ax[5]; 290 ax[5] = ay[5]; 291 ay[5] = stmp; 292 stmp = ax[6]; 293 ax[6] = ay[6]; 294 ay[6] = stmp; 295 stmp = ax[7]; 296 ax[7] = ay[7]; 297 ay[7] = stmp; 298 stmp = ax[8]; 299 ax[8] = ay[8]; 300 ay[8] = stmp; 301 } 302 } 303 PetscFunctionReturn(PETSC_SUCCESS); 304 } 305 306 /* 307 Inverts 15 by 15 matrix using gaussian elimination with partial pivoting. 308 309 Used by the sparse factorization routines in 310 src/mat/impls/baij/seq 311 312 This is a combination of the Linpack routines 313 dgefa() and dgedi() specialized for a size of 15. 314 315 */ 316 317 PetscErrorCode PetscKernel_A_gets_inverse_A_15(MatScalar *a, PetscInt *ipvt, MatScalar *work, PetscReal shift, PetscBool allowzeropivot, PetscBool *zeropivotdetected) 318 { 319 PetscInt i__2, i__3, kp1, j, k, l, ll, i, kb, k3; 320 PetscInt k4, j3; 321 MatScalar *aa, *ax, *ay, stmp; 322 MatReal tmp, max; 323 324 PetscFunctionBegin; 325 if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE; 326 327 /* Parameter adjustments */ 328 a -= 16; 329 330 for (k = 1; k <= 14; ++k) { 331 kp1 = k + 1; 332 k3 = 15 * k; 333 k4 = k3 + k; 334 335 /* find l = pivot index */ 336 i__2 = 16 - k; 337 aa = &a[k4]; 338 max = PetscAbsScalar(aa[0]); 339 l = 1; 340 for (ll = 1; ll < i__2; ll++) { 341 tmp = PetscAbsScalar(aa[ll]); 342 if (tmp > max) { 343 max = tmp; 344 l = ll + 1; 345 } 346 } 347 l += k - 1; 348 ipvt[k - 1] = l; 349 350 if (a[l + k3] == 0.0) { 351 if (shift == 0.0) { 352 PetscCheck(allowzeropivot, PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT, k - 1); 353 PetscCall(PetscInfo(NULL, "Zero pivot, row %" PetscInt_FMT "\n", k - 1)); 354 if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE; 355 } else { 356 a[l + k3] = shift; 357 } 358 } 359 360 /* interchange if necessary */ 361 if (l != k) { 362 stmp = a[l + k3]; 363 a[l + k3] = a[k4]; 364 a[k4] = stmp; 365 } 366 367 /* compute multipliers */ 368 stmp = -1. / a[k4]; 369 i__2 = 15 - k; 370 aa = &a[1 + k4]; 371 for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp; 372 373 /* row elimination with column indexing */ 374 ax = &a[k4 + 1]; 375 for (j = kp1; j <= 15; ++j) { 376 j3 = 15 * j; 377 stmp = a[l + j3]; 378 if (l != k) { 379 a[l + j3] = a[k + j3]; 380 a[k + j3] = stmp; 381 } 382 383 i__3 = 15 - k; 384 ay = &a[1 + k + j3]; 385 for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll]; 386 } 387 } 388 ipvt[14] = 15; 389 if (a[240] == 0.0) { 390 PetscCheck(PetscLikely(allowzeropivot), PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 14"); 391 PetscCall(PetscInfo(NULL, "Zero pivot, row 14\n")); 392 if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE; 393 } 394 395 /* Now form the inverse */ 396 /* compute inverse(u) */ 397 for (k = 1; k <= 15; ++k) { 398 k3 = 15 * k; 399 k4 = k3 + k; 400 a[k4] = 1.0 / a[k4]; 401 stmp = -a[k4]; 402 i__2 = k - 1; 403 aa = &a[k3 + 1]; 404 for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp; 405 kp1 = k + 1; 406 if (15 < kp1) continue; 407 ax = aa; 408 for (j = kp1; j <= 15; ++j) { 409 j3 = 15 * j; 410 stmp = a[k + j3]; 411 a[k + j3] = 0.0; 412 ay = &a[j3 + 1]; 413 for (ll = 0; ll < k; ll++) ay[ll] += stmp * ax[ll]; 414 } 415 } 416 417 /* form inverse(u)*inverse(l) */ 418 for (kb = 1; kb <= 14; ++kb) { 419 k = 15 - kb; 420 k3 = 15 * k; 421 kp1 = k + 1; 422 aa = a + k3; 423 for (i = kp1; i <= 15; ++i) { 424 work[i - 1] = aa[i]; 425 aa[i] = 0.0; 426 } 427 for (j = kp1; j <= 15; ++j) { 428 stmp = work[j - 1]; 429 ax = &a[15 * j + 1]; 430 ay = &a[k3 + 1]; 431 ay[0] += stmp * ax[0]; 432 ay[1] += stmp * ax[1]; 433 ay[2] += stmp * ax[2]; 434 ay[3] += stmp * ax[3]; 435 ay[4] += stmp * ax[4]; 436 ay[5] += stmp * ax[5]; 437 ay[6] += stmp * ax[6]; 438 ay[7] += stmp * ax[7]; 439 ay[8] += stmp * ax[8]; 440 ay[9] += stmp * ax[9]; 441 ay[10] += stmp * ax[10]; 442 ay[11] += stmp * ax[11]; 443 ay[12] += stmp * ax[12]; 444 ay[13] += stmp * ax[13]; 445 ay[14] += stmp * ax[14]; 446 } 447 l = ipvt[k - 1]; 448 if (l != k) { 449 ax = &a[k3 + 1]; 450 ay = &a[15 * l + 1]; 451 stmp = ax[0]; 452 ax[0] = ay[0]; 453 ay[0] = stmp; 454 stmp = ax[1]; 455 ax[1] = ay[1]; 456 ay[1] = stmp; 457 stmp = ax[2]; 458 ax[2] = ay[2]; 459 ay[2] = stmp; 460 stmp = ax[3]; 461 ax[3] = ay[3]; 462 ay[3] = stmp; 463 stmp = ax[4]; 464 ax[4] = ay[4]; 465 ay[4] = stmp; 466 stmp = ax[5]; 467 ax[5] = ay[5]; 468 ay[5] = stmp; 469 stmp = ax[6]; 470 ax[6] = ay[6]; 471 ay[6] = stmp; 472 stmp = ax[7]; 473 ax[7] = ay[7]; 474 ay[7] = stmp; 475 stmp = ax[8]; 476 ax[8] = ay[8]; 477 ay[8] = stmp; 478 stmp = ax[9]; 479 ax[9] = ay[9]; 480 ay[9] = stmp; 481 stmp = ax[10]; 482 ax[10] = ay[10]; 483 ay[10] = stmp; 484 stmp = ax[11]; 485 ax[11] = ay[11]; 486 ay[11] = stmp; 487 stmp = ax[12]; 488 ax[12] = ay[12]; 489 ay[12] = stmp; 490 stmp = ax[13]; 491 ax[13] = ay[13]; 492 ay[13] = stmp; 493 stmp = ax[14]; 494 ax[14] = ay[14]; 495 ay[14] = stmp; 496 } 497 } 498 PetscFunctionReturn(PETSC_SUCCESS); 499 } 500