1 #define PETSCMAT_DLL 2 3 /* 4 Inverts 2 by 2 matrix using partial pivoting. 5 6 Used by the sparse factorization routines in 7 src/mat/impls/baij/seq 8 9 10 This is a combination of the Linpack routines 11 dgefa() and dgedi() specialized for a size of 2. 12 13 */ 14 #include "petscsys.h" 15 16 #undef __FUNCT__ 17 #define __FUNCT__ "Kernel_A_gets_inverse_A_2" 18 PetscErrorCode Kernel_A_gets_inverse_A_2(MatScalar *a,PetscReal shift) 19 { 20 PetscInt i__2,i__3,kp1,j,k,l,ll,i,ipvt[2],k3; 21 PetscInt k4,j3; 22 MatScalar *aa,*ax,*ay,work[4],stmp; 23 MatReal tmp,max; 24 25 /* gaussian elimination with partial pivoting */ 26 27 PetscFunctionBegin; 28 /* Parameter adjustments */ 29 a -= 3; 30 31 /*for (k = 1; k <= 1; ++k) {*/ 32 k = 1; 33 kp1 = k + 1; 34 k3 = 2*k; 35 k4 = k3 + k; 36 /* find l = pivot index */ 37 38 i__2 = 3 - k; 39 aa = &a[k4]; 40 max = PetscAbsScalar(aa[0]); 41 l = 1; 42 for (ll=1; ll<i__2; ll++) { 43 tmp = PetscAbsScalar(aa[ll]); 44 if (tmp > max) { max = tmp; l = ll+1;} 45 } 46 l += k - 1; 47 ipvt[k-1] = l; 48 49 if (a[l + k3] == 0.0) { 50 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1); 51 } 52 53 /* interchange if necessary */ 54 55 if (l != k) { 56 stmp = a[l + k3]; 57 a[l + k3] = a[k4]; 58 a[k4] = stmp; 59 } 60 61 /* compute multipliers */ 62 63 stmp = -1. / a[k4]; 64 i__2 = 2 - k; 65 aa = &a[1 + k4]; 66 for (ll=0; ll<i__2; ll++) { 67 aa[ll] *= stmp; 68 } 69 70 /* row elimination with column indexing */ 71 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++) { 84 ay[ll] += stmp*ax[ll]; 85 } 86 } 87 /*}*/ 88 ipvt[1] = 2; 89 if (a[6] == 0.0) { 90 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",1); 91 } 92 93 /* 94 Now form the inverse 95 */ 96 97 /* compute inverse(u) */ 98 99 for (k = 1; k <= 2; ++k) { 100 k3 = 2*k; 101 k4 = k3 + k; 102 a[k4] = 1.0 / a[k4]; 103 stmp = -a[k4]; 104 i__2 = k - 1; 105 aa = &a[k3 + 1]; 106 for (ll=0; ll<i__2; ll++) aa[ll] *= stmp; 107 kp1 = k + 1; 108 if (2 < kp1) continue; 109 ax = aa; 110 for (j = kp1; j <= 2; ++j) { 111 j3 = 2*j; 112 stmp = a[k + j3]; 113 a[k + j3] = 0.0; 114 ay = &a[j3 + 1]; 115 for (ll=0; ll<k; ll++) { 116 ay[ll] += stmp*ax[ll]; 117 } 118 } 119 } 120 121 /* form inverse(u)*inverse(l) */ 122 123 /*for (kb = 1; kb <= 1; ++kb) {*/ 124 125 k = 1; 126 k3 = 2*k; 127 kp1 = k + 1; 128 aa = a + k3; 129 for (i = kp1; i <= 2; ++i) { 130 work[i-1] = aa[i]; 131 aa[i] = 0.0; 132 } 133 for (j = kp1; j <= 2; ++j) { 134 stmp = work[j-1]; 135 ax = &a[2*j + 1]; 136 ay = &a[k3 + 1]; 137 ay[0] += stmp*ax[0]; 138 ay[1] += stmp*ax[1]; 139 } 140 l = ipvt[k-1]; 141 if (l != k) { 142 ax = &a[k3 + 1]; 143 ay = &a[2*l + 1]; 144 stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp; 145 stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp; 146 } 147 148 PetscFunctionReturn(0); 149 } 150 151 #undef __FUNCT__ 152 #define __FUNCT__ "Kernel_A_gets_inverse_A_9" 153 PetscErrorCode Kernel_A_gets_inverse_A_9(MatScalar *a,PetscReal shift) 154 { 155 PetscInt i__2,i__3,kp1,j,k,l,ll,i,ipvt[9],kb,k3; 156 PetscInt k4,j3; 157 MatScalar *aa,*ax,*ay,work[81],stmp; 158 MatReal tmp,max; 159 160 /* gaussian elimination with partial pivoting */ 161 162 PetscFunctionBegin; 163 /* Parameter adjustments */ 164 a -= 10; 165 166 for (k = 1; k <= 8; ++k) { 167 kp1 = k + 1; 168 k3 = 9*k; 169 k4 = k3 + k; 170 /* find l = pivot index */ 171 172 i__2 = 10 - k; 173 aa = &a[k4]; 174 max = PetscAbsScalar(aa[0]); 175 l = 1; 176 for (ll=1; ll<i__2; ll++) { 177 tmp = PetscAbsScalar(aa[ll]); 178 if (tmp > max) { max = tmp; l = ll+1;} 179 } 180 l += k - 1; 181 ipvt[k-1] = l; 182 183 if (a[l + k3] == 0.0) { 184 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1); 185 } 186 187 /* interchange if necessary */ 188 189 if (l != k) { 190 stmp = a[l + k3]; 191 a[l + k3] = a[k4]; 192 a[k4] = stmp; 193 } 194 195 /* compute multipliers */ 196 197 stmp = -1. / a[k4]; 198 i__2 = 9 - k; 199 aa = &a[1 + k4]; 200 for (ll=0; ll<i__2; ll++) { 201 aa[ll] *= stmp; 202 } 203 204 /* row elimination with column indexing */ 205 206 ax = &a[k4+1]; 207 for (j = kp1; j <= 9; ++j) { 208 j3 = 9*j; 209 stmp = a[l + j3]; 210 if (l != k) { 211 a[l + j3] = a[k + j3]; 212 a[k + j3] = stmp; 213 } 214 215 i__3 = 9 - k; 216 ay = &a[1+k+j3]; 217 for (ll=0; ll<i__3; ll++) { 218 ay[ll] += stmp*ax[ll]; 219 } 220 } 221 } 222 ipvt[8] = 9; 223 if (a[90] == 0.0) { 224 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",6); 225 } 226 227 /* 228 Now form the inverse 229 */ 230 231 /* compute inverse(u) */ 232 233 for (k = 1; k <= 9; ++k) { 234 k3 = 9*k; 235 k4 = k3 + k; 236 a[k4] = 1.0 / a[k4]; 237 stmp = -a[k4]; 238 i__2 = k - 1; 239 aa = &a[k3 + 1]; 240 for (ll=0; ll<i__2; ll++) aa[ll] *= stmp; 241 kp1 = k + 1; 242 if (9 < kp1) continue; 243 ax = aa; 244 for (j = kp1; j <= 9; ++j) { 245 j3 = 9*j; 246 stmp = a[k + j3]; 247 a[k + j3] = 0.0; 248 ay = &a[j3 + 1]; 249 for (ll=0; ll<k; ll++) { 250 ay[ll] += stmp*ax[ll]; 251 } 252 } 253 } 254 255 /* form inverse(u)*inverse(l) */ 256 257 for (kb = 1; kb <= 8; ++kb) { 258 k = 9 - kb; 259 k3 = 9*k; 260 kp1 = k + 1; 261 aa = a + k3; 262 for (i = kp1; i <= 9; ++i) { 263 work[i-1] = aa[i]; 264 aa[i] = 0.0; 265 } 266 for (j = kp1; j <= 9; ++j) { 267 stmp = work[j-1]; 268 ax = &a[9*j + 1]; 269 ay = &a[k3 + 1]; 270 ay[0] += stmp*ax[0]; 271 ay[1] += stmp*ax[1]; 272 ay[2] += stmp*ax[2]; 273 ay[3] += stmp*ax[3]; 274 ay[4] += stmp*ax[4]; 275 ay[5] += stmp*ax[5]; 276 ay[6] += stmp*ax[6]; 277 ay[7] += stmp*ax[7]; 278 ay[8] += stmp*ax[8]; 279 } 280 l = ipvt[k-1]; 281 if (l != k) { 282 ax = &a[k3 + 1]; 283 ay = &a[9*l + 1]; 284 stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp; 285 stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp; 286 stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp; 287 stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp; 288 stmp = ax[4]; ax[4] = ay[4]; ay[4] = stmp; 289 stmp = ax[5]; ax[5] = ay[5]; ay[5] = stmp; 290 stmp = ax[6]; ax[6] = ay[6]; ay[6] = stmp; 291 stmp = ax[7]; ax[7] = ay[7]; ay[7] = stmp; 292 stmp = ax[8]; ax[8] = ay[8]; ay[8] = stmp; 293 } 294 } 295 PetscFunctionReturn(0); 296 } 297 298 /* 299 Inverts 15 by 15 matrix using partial pivoting. 300 301 Used by the sparse factorization routines in 302 src/mat/impls/baij/seq 303 304 This is a combination of the Linpack routines 305 dgefa() and dgedi() specialized for a size of 15. 306 307 */ 308 #include "petsc.h" 309 310 #undef __FUNCT__ 311 #define __FUNCT__ "Kernel_A_gets_inverse_A_15" 312 PetscErrorCode Kernel_A_gets_inverse_A_15(MatScalar *a,PetscInt *ipvt,MatScalar *work,PetscReal shift) 313 { 314 PetscInt i__2,i__3,kp1,j,k,l,ll,i,kb,k3; 315 PetscInt k4,j3; 316 MatScalar *aa,*ax,*ay,stmp; 317 MatReal tmp,max; 318 319 /* gaussian elimination with partial pivoting */ 320 321 PetscFunctionBegin; 322 /* Parameter adjustments */ 323 a -= 16; 324 325 for (k = 1; k <= 14; ++k) { 326 kp1 = k + 1; 327 k3 = 15*k; 328 k4 = k3 + k; 329 /* find l = pivot index */ 330 331 i__2 = 16 - k; 332 aa = &a[k4]; 333 max = PetscAbsScalar(aa[0]); 334 l = 1; 335 for (ll=1; ll<i__2; ll++) { 336 tmp = PetscAbsScalar(aa[ll]); 337 if (tmp > max) { max = tmp; l = ll+1;} 338 } 339 l += k - 1; 340 ipvt[k-1] = l; 341 342 if (a[l + k3] == 0.0) { 343 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1); 344 } 345 346 /* interchange if necessary */ 347 348 if (l != k) { 349 stmp = a[l + k3]; 350 a[l + k3] = a[k4]; 351 a[k4] = stmp; 352 } 353 354 /* compute multipliers */ 355 356 stmp = -1. / a[k4]; 357 i__2 = 15 - k; 358 aa = &a[1 + k4]; 359 for (ll=0; ll<i__2; ll++) { 360 aa[ll] *= stmp; 361 } 362 363 /* row elimination with column indexing */ 364 365 ax = &a[k4+1]; 366 for (j = kp1; j <= 15; ++j) { 367 j3 = 15*j; 368 stmp = a[l + j3]; 369 if (l != k) { 370 a[l + j3] = a[k + j3]; 371 a[k + j3] = stmp; 372 } 373 374 i__3 = 15 - k; 375 ay = &a[1+k+j3]; 376 for (ll=0; ll<i__3; ll++) { 377 ay[ll] += stmp*ax[ll]; 378 } 379 } 380 } 381 ipvt[14] = 15; 382 if (a[240] == 0.0) { 383 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",6); 384 } 385 386 /* 387 Now form the inverse 388 */ 389 390 /* compute inverse(u) */ 391 392 for (k = 1; k <= 15; ++k) { 393 k3 = 15*k; 394 k4 = k3 + k; 395 a[k4] = 1.0 / a[k4]; 396 stmp = -a[k4]; 397 i__2 = k - 1; 398 aa = &a[k3 + 1]; 399 for (ll=0; ll<i__2; ll++) aa[ll] *= stmp; 400 kp1 = k + 1; 401 if (15 < kp1) continue; 402 ax = aa; 403 for (j = kp1; j <= 15; ++j) { 404 j3 = 15*j; 405 stmp = a[k + j3]; 406 a[k + j3] = 0.0; 407 ay = &a[j3 + 1]; 408 for (ll=0; ll<k; ll++) { 409 ay[ll] += stmp*ax[ll]; 410 } 411 } 412 } 413 414 /* form inverse(u)*inverse(l) */ 415 416 for (kb = 1; kb <= 14; ++kb) { 417 k = 15 - kb; 418 k3 = 15*k; 419 kp1 = k + 1; 420 aa = a + k3; 421 for (i = kp1; i <= 15; ++i) { 422 work[i-1] = aa[i]; 423 aa[i] = 0.0; 424 } 425 for (j = kp1; j <= 15; ++j) { 426 stmp = work[j-1]; 427 ax = &a[15*j + 1]; 428 ay = &a[k3 + 1]; 429 ay[0] += stmp*ax[0]; 430 ay[1] += stmp*ax[1]; 431 ay[2] += stmp*ax[2]; 432 ay[3] += stmp*ax[3]; 433 ay[4] += stmp*ax[4]; 434 ay[5] += stmp*ax[5]; 435 ay[6] += stmp*ax[6]; 436 ay[7] += stmp*ax[7]; 437 ay[8] += stmp*ax[8]; 438 ay[9] += stmp*ax[9]; 439 ay[10] += stmp*ax[10]; 440 ay[11] += stmp*ax[11]; 441 ay[12] += stmp*ax[12]; 442 ay[13] += stmp*ax[13]; 443 ay[14] += stmp*ax[14]; 444 } 445 l = ipvt[k-1]; 446 if (l != k) { 447 ax = &a[k3 + 1]; 448 ay = &a[15*l + 1]; 449 stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp; 450 stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp; 451 stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp; 452 stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp; 453 stmp = ax[4]; ax[4] = ay[4]; ay[4] = stmp; 454 stmp = ax[5]; ax[5] = ay[5]; ay[5] = stmp; 455 stmp = ax[6]; ax[6] = ay[6]; ay[6] = stmp; 456 stmp = ax[7]; ax[7] = ay[7]; ay[7] = stmp; 457 stmp = ax[8]; ax[8] = ay[8]; ay[8] = stmp; 458 stmp = ax[9]; ax[9] = ay[9]; ay[9] = stmp; 459 stmp = ax[10]; ax[10] = ay[10]; ay[10] = stmp; 460 stmp = ax[11]; ax[11] = ay[11]; ay[11] = stmp; 461 stmp = ax[12]; ax[12] = ay[12]; ay[12] = stmp; 462 stmp = ax[13]; ax[13] = ay[13]; ay[13] = stmp; 463 stmp = ax[14]; ax[14] = ay[14]; ay[14] = stmp; 464 } 465 } 466 PetscFunctionReturn(0); 467 } 468