1 /* 2 Factorization code for BAIJ format. 3 */ 4 #include <../src/mat/impls/baij/seq/baij.h> 5 #include <petsc/private/kernels/blockinvert.h> 6 7 /* 8 Version for when blocks are 5 by 5 9 */ 10 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_inplace(Mat C, Mat A, const MatFactorInfo *info) 11 { 12 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data; 13 IS isrow = b->row, isicol = b->icol; 14 const PetscInt *r, *ic, *bi = b->i, *bj = b->j, *ajtmpold, *ajtmp; 15 PetscInt i, j, n = a->mbs, nz, row, idx, ipvt[5]; 16 const PetscInt *diag_offset = b->diag, *ai = a->i, *aj = a->j, *pj; 17 MatScalar *w, *pv, *rtmp, *x, *pc; 18 const MatScalar *v, *aa = a->a; 19 MatScalar p1, p2, p3, p4, m1, m2, m3, m4, m5, m6, m7, m8, m9, x1, x2, x3, x4; 20 MatScalar p5, p6, p7, p8, p9, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16; 21 MatScalar x17, x18, x19, x20, x21, x22, x23, x24, x25, p10, p11, p12, p13, p14; 22 MatScalar p15, p16, p17, p18, p19, p20, p21, p22, p23, p24, p25, m10, m11, m12; 23 MatScalar m13, m14, m15, m16, m17, m18, m19, m20, m21, m22, m23, m24, m25; 24 MatScalar *ba = b->a, work[25]; 25 PetscReal shift = info->shiftamount; 26 PetscBool allowzeropivot, zeropivotdetected; 27 28 PetscFunctionBegin; 29 allowzeropivot = PetscNot(A->erroriffailure); 30 PetscCall(ISGetIndices(isrow, &r)); 31 PetscCall(ISGetIndices(isicol, &ic)); 32 PetscCall(PetscMalloc1(25 * (n + 1), &rtmp)); 33 34 #define PETSC_USE_MEMZERO 1 35 #define PETSC_USE_MEMCPY 1 36 37 for (i = 0; i < n; i++) { 38 nz = bi[i + 1] - bi[i]; 39 ajtmp = bj + bi[i]; 40 for (j = 0; j < nz; j++) { 41 #if defined(PETSC_USE_MEMZERO) 42 PetscCall(PetscArrayzero(rtmp + 25 * ajtmp[j], 25)); 43 #else 44 x = rtmp + 25 * ajtmp[j]; 45 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0; 46 x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0; 47 x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0; 48 #endif 49 } 50 /* load in initial (unfactored row) */ 51 idx = r[i]; 52 nz = ai[idx + 1] - ai[idx]; 53 ajtmpold = aj + ai[idx]; 54 v = aa + 25 * ai[idx]; 55 for (j = 0; j < nz; j++) { 56 #if defined(PETSC_USE_MEMCPY) 57 PetscCall(PetscArraycpy(rtmp + 25 * ic[ajtmpold[j]], v, 25)); 58 #else 59 x = rtmp + 25 * ic[ajtmpold[j]]; 60 x[0] = v[0]; 61 x[1] = v[1]; 62 x[2] = v[2]; 63 x[3] = v[3]; 64 x[4] = v[4]; 65 x[5] = v[5]; 66 x[6] = v[6]; 67 x[7] = v[7]; 68 x[8] = v[8]; 69 x[9] = v[9]; 70 x[10] = v[10]; 71 x[11] = v[11]; 72 x[12] = v[12]; 73 x[13] = v[13]; 74 x[14] = v[14]; 75 x[15] = v[15]; 76 x[16] = v[16]; 77 x[17] = v[17]; 78 x[18] = v[18]; 79 x[19] = v[19]; 80 x[20] = v[20]; 81 x[21] = v[21]; 82 x[22] = v[22]; 83 x[23] = v[23]; 84 x[24] = v[24]; 85 #endif 86 v += 25; 87 } 88 row = *ajtmp++; 89 while (row < i) { 90 pc = rtmp + 25 * row; 91 p1 = pc[0]; 92 p2 = pc[1]; 93 p3 = pc[2]; 94 p4 = pc[3]; 95 p5 = pc[4]; 96 p6 = pc[5]; 97 p7 = pc[6]; 98 p8 = pc[7]; 99 p9 = pc[8]; 100 p10 = pc[9]; 101 p11 = pc[10]; 102 p12 = pc[11]; 103 p13 = pc[12]; 104 p14 = pc[13]; 105 p15 = pc[14]; 106 p16 = pc[15]; 107 p17 = pc[16]; 108 p18 = pc[17]; 109 p19 = pc[18]; 110 p20 = pc[19]; 111 p21 = pc[20]; 112 p22 = pc[21]; 113 p23 = pc[22]; 114 p24 = pc[23]; 115 p25 = pc[24]; 116 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) { 117 pv = ba + 25 * diag_offset[row]; 118 pj = bj + diag_offset[row] + 1; 119 x1 = pv[0]; 120 x2 = pv[1]; 121 x3 = pv[2]; 122 x4 = pv[3]; 123 x5 = pv[4]; 124 x6 = pv[5]; 125 x7 = pv[6]; 126 x8 = pv[7]; 127 x9 = pv[8]; 128 x10 = pv[9]; 129 x11 = pv[10]; 130 x12 = pv[11]; 131 x13 = pv[12]; 132 x14 = pv[13]; 133 x15 = pv[14]; 134 x16 = pv[15]; 135 x17 = pv[16]; 136 x18 = pv[17]; 137 x19 = pv[18]; 138 x20 = pv[19]; 139 x21 = pv[20]; 140 x22 = pv[21]; 141 x23 = pv[22]; 142 x24 = pv[23]; 143 x25 = pv[24]; 144 pc[0] = m1 = p1 * x1 + p6 * x2 + p11 * x3 + p16 * x4 + p21 * x5; 145 pc[1] = m2 = p2 * x1 + p7 * x2 + p12 * x3 + p17 * x4 + p22 * x5; 146 pc[2] = m3 = p3 * x1 + p8 * x2 + p13 * x3 + p18 * x4 + p23 * x5; 147 pc[3] = m4 = p4 * x1 + p9 * x2 + p14 * x3 + p19 * x4 + p24 * x5; 148 pc[4] = m5 = p5 * x1 + p10 * x2 + p15 * x3 + p20 * x4 + p25 * x5; 149 150 pc[5] = m6 = p1 * x6 + p6 * x7 + p11 * x8 + p16 * x9 + p21 * x10; 151 pc[6] = m7 = p2 * x6 + p7 * x7 + p12 * x8 + p17 * x9 + p22 * x10; 152 pc[7] = m8 = p3 * x6 + p8 * x7 + p13 * x8 + p18 * x9 + p23 * x10; 153 pc[8] = m9 = p4 * x6 + p9 * x7 + p14 * x8 + p19 * x9 + p24 * x10; 154 pc[9] = m10 = p5 * x6 + p10 * x7 + p15 * x8 + p20 * x9 + p25 * x10; 155 156 pc[10] = m11 = p1 * x11 + p6 * x12 + p11 * x13 + p16 * x14 + p21 * x15; 157 pc[11] = m12 = p2 * x11 + p7 * x12 + p12 * x13 + p17 * x14 + p22 * x15; 158 pc[12] = m13 = p3 * x11 + p8 * x12 + p13 * x13 + p18 * x14 + p23 * x15; 159 pc[13] = m14 = p4 * x11 + p9 * x12 + p14 * x13 + p19 * x14 + p24 * x15; 160 pc[14] = m15 = p5 * x11 + p10 * x12 + p15 * x13 + p20 * x14 + p25 * x15; 161 162 pc[15] = m16 = p1 * x16 + p6 * x17 + p11 * x18 + p16 * x19 + p21 * x20; 163 pc[16] = m17 = p2 * x16 + p7 * x17 + p12 * x18 + p17 * x19 + p22 * x20; 164 pc[17] = m18 = p3 * x16 + p8 * x17 + p13 * x18 + p18 * x19 + p23 * x20; 165 pc[18] = m19 = p4 * x16 + p9 * x17 + p14 * x18 + p19 * x19 + p24 * x20; 166 pc[19] = m20 = p5 * x16 + p10 * x17 + p15 * x18 + p20 * x19 + p25 * x20; 167 168 pc[20] = m21 = p1 * x21 + p6 * x22 + p11 * x23 + p16 * x24 + p21 * x25; 169 pc[21] = m22 = p2 * x21 + p7 * x22 + p12 * x23 + p17 * x24 + p22 * x25; 170 pc[22] = m23 = p3 * x21 + p8 * x22 + p13 * x23 + p18 * x24 + p23 * x25; 171 pc[23] = m24 = p4 * x21 + p9 * x22 + p14 * x23 + p19 * x24 + p24 * x25; 172 pc[24] = m25 = p5 * x21 + p10 * x22 + p15 * x23 + p20 * x24 + p25 * x25; 173 174 nz = bi[row + 1] - diag_offset[row] - 1; 175 pv += 25; 176 for (j = 0; j < nz; j++) { 177 x1 = pv[0]; 178 x2 = pv[1]; 179 x3 = pv[2]; 180 x4 = pv[3]; 181 x5 = pv[4]; 182 x6 = pv[5]; 183 x7 = pv[6]; 184 x8 = pv[7]; 185 x9 = pv[8]; 186 x10 = pv[9]; 187 x11 = pv[10]; 188 x12 = pv[11]; 189 x13 = pv[12]; 190 x14 = pv[13]; 191 x15 = pv[14]; 192 x16 = pv[15]; 193 x17 = pv[16]; 194 x18 = pv[17]; 195 x19 = pv[18]; 196 x20 = pv[19]; 197 x21 = pv[20]; 198 x22 = pv[21]; 199 x23 = pv[22]; 200 x24 = pv[23]; 201 x25 = pv[24]; 202 x = rtmp + 25 * pj[j]; 203 x[0] -= m1 * x1 + m6 * x2 + m11 * x3 + m16 * x4 + m21 * x5; 204 x[1] -= m2 * x1 + m7 * x2 + m12 * x3 + m17 * x4 + m22 * x5; 205 x[2] -= m3 * x1 + m8 * x2 + m13 * x3 + m18 * x4 + m23 * x5; 206 x[3] -= m4 * x1 + m9 * x2 + m14 * x3 + m19 * x4 + m24 * x5; 207 x[4] -= m5 * x1 + m10 * x2 + m15 * x3 + m20 * x4 + m25 * x5; 208 209 x[5] -= m1 * x6 + m6 * x7 + m11 * x8 + m16 * x9 + m21 * x10; 210 x[6] -= m2 * x6 + m7 * x7 + m12 * x8 + m17 * x9 + m22 * x10; 211 x[7] -= m3 * x6 + m8 * x7 + m13 * x8 + m18 * x9 + m23 * x10; 212 x[8] -= m4 * x6 + m9 * x7 + m14 * x8 + m19 * x9 + m24 * x10; 213 x[9] -= m5 * x6 + m10 * x7 + m15 * x8 + m20 * x9 + m25 * x10; 214 215 x[10] -= m1 * x11 + m6 * x12 + m11 * x13 + m16 * x14 + m21 * x15; 216 x[11] -= m2 * x11 + m7 * x12 + m12 * x13 + m17 * x14 + m22 * x15; 217 x[12] -= m3 * x11 + m8 * x12 + m13 * x13 + m18 * x14 + m23 * x15; 218 x[13] -= m4 * x11 + m9 * x12 + m14 * x13 + m19 * x14 + m24 * x15; 219 x[14] -= m5 * x11 + m10 * x12 + m15 * x13 + m20 * x14 + m25 * x15; 220 221 x[15] -= m1 * x16 + m6 * x17 + m11 * x18 + m16 * x19 + m21 * x20; 222 x[16] -= m2 * x16 + m7 * x17 + m12 * x18 + m17 * x19 + m22 * x20; 223 x[17] -= m3 * x16 + m8 * x17 + m13 * x18 + m18 * x19 + m23 * x20; 224 x[18] -= m4 * x16 + m9 * x17 + m14 * x18 + m19 * x19 + m24 * x20; 225 x[19] -= m5 * x16 + m10 * x17 + m15 * x18 + m20 * x19 + m25 * x20; 226 227 x[20] -= m1 * x21 + m6 * x22 + m11 * x23 + m16 * x24 + m21 * x25; 228 x[21] -= m2 * x21 + m7 * x22 + m12 * x23 + m17 * x24 + m22 * x25; 229 x[22] -= m3 * x21 + m8 * x22 + m13 * x23 + m18 * x24 + m23 * x25; 230 x[23] -= m4 * x21 + m9 * x22 + m14 * x23 + m19 * x24 + m24 * x25; 231 x[24] -= m5 * x21 + m10 * x22 + m15 * x23 + m20 * x24 + m25 * x25; 232 233 pv += 25; 234 } 235 PetscCall(PetscLogFlops(250.0 * nz + 225.0)); 236 } 237 row = *ajtmp++; 238 } 239 /* finished row so stick it into b->a */ 240 pv = ba + 25 * bi[i]; 241 pj = bj + bi[i]; 242 nz = bi[i + 1] - bi[i]; 243 for (j = 0; j < nz; j++) { 244 #if defined(PETSC_USE_MEMCPY) 245 PetscCall(PetscArraycpy(pv, rtmp + 25 * pj[j], 25)); 246 #else 247 x = rtmp + 25 * pj[j]; 248 pv[0] = x[0]; 249 pv[1] = x[1]; 250 pv[2] = x[2]; 251 pv[3] = x[3]; 252 pv[4] = x[4]; 253 pv[5] = x[5]; 254 pv[6] = x[6]; 255 pv[7] = x[7]; 256 pv[8] = x[8]; 257 pv[9] = x[9]; 258 pv[10] = x[10]; 259 pv[11] = x[11]; 260 pv[12] = x[12]; 261 pv[13] = x[13]; 262 pv[14] = x[14]; 263 pv[15] = x[15]; 264 pv[16] = x[16]; 265 pv[17] = x[17]; 266 pv[18] = x[18]; 267 pv[19] = x[19]; 268 pv[20] = x[20]; 269 pv[21] = x[21]; 270 pv[22] = x[22]; 271 pv[23] = x[23]; 272 pv[24] = x[24]; 273 #endif 274 pv += 25; 275 } 276 /* invert diagonal block */ 277 w = ba + 25 * diag_offset[i]; 278 PetscCall(PetscKernel_A_gets_inverse_A_5(w, ipvt, work, shift, allowzeropivot, &zeropivotdetected)); 279 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 280 } 281 282 PetscCall(PetscFree(rtmp)); 283 PetscCall(ISRestoreIndices(isicol, &ic)); 284 PetscCall(ISRestoreIndices(isrow, &r)); 285 286 C->ops->solve = MatSolve_SeqBAIJ_5_inplace; 287 C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_inplace; 288 C->assembled = PETSC_TRUE; 289 290 PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * b->mbs)); /* from inverting diagonal blocks */ 291 PetscFunctionReturn(PETSC_SUCCESS); 292 } 293 294 /* MatLUFactorNumeric_SeqBAIJ_5 - 295 copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented 296 PetscKernel_A_gets_A_times_B() 297 PetscKernel_A_gets_A_minus_B_times_C() 298 PetscKernel_A_gets_inverse_A() 299 */ 300 301 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5(Mat B, Mat A, const MatFactorInfo *info) 302 { 303 Mat C = B; 304 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data; 305 IS isrow = b->row, isicol = b->icol; 306 const PetscInt *r, *ic; 307 PetscInt i, j, k, nz, nzL, row; 308 const PetscInt n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j; 309 const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2; 310 MatScalar *rtmp, *pc, *mwork, *v, *pv, *aa = a->a, work[25]; 311 PetscInt flg, ipvt[5]; 312 PetscReal shift = info->shiftamount; 313 PetscBool allowzeropivot, zeropivotdetected; 314 315 PetscFunctionBegin; 316 allowzeropivot = PetscNot(A->erroriffailure); 317 PetscCall(ISGetIndices(isrow, &r)); 318 PetscCall(ISGetIndices(isicol, &ic)); 319 320 /* generate work space needed by the factorization */ 321 PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork)); 322 PetscCall(PetscArrayzero(rtmp, bs2 * n)); 323 324 for (i = 0; i < n; i++) { 325 /* zero rtmp */ 326 /* L part */ 327 nz = bi[i + 1] - bi[i]; 328 bjtmp = bj + bi[i]; 329 for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2)); 330 331 /* U part */ 332 nz = bdiag[i] - bdiag[i + 1]; 333 bjtmp = bj + bdiag[i + 1] + 1; 334 for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2)); 335 336 /* load in initial (unfactored row) */ 337 nz = ai[r[i] + 1] - ai[r[i]]; 338 ajtmp = aj + ai[r[i]]; 339 v = aa + bs2 * ai[r[i]]; 340 for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ic[ajtmp[j]], v + bs2 * j, bs2)); 341 342 /* elimination */ 343 bjtmp = bj + bi[i]; 344 nzL = bi[i + 1] - bi[i]; 345 for (k = 0; k < nzL; k++) { 346 row = bjtmp[k]; 347 pc = rtmp + bs2 * row; 348 for (flg = 0, j = 0; j < bs2; j++) { 349 if (pc[j] != 0.0) { 350 flg = 1; 351 break; 352 } 353 } 354 if (flg) { 355 pv = b->a + bs2 * bdiag[row]; 356 /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */ 357 PetscCall(PetscKernel_A_gets_A_times_B_5(pc, pv, mwork)); 358 359 pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */ 360 pv = b->a + bs2 * (bdiag[row + 1] + 1); 361 nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */ 362 for (j = 0; j < nz; j++) { 363 /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */ 364 /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */ 365 v = rtmp + bs2 * pj[j]; 366 PetscCall(PetscKernel_A_gets_A_minus_B_times_C_5(v, pc, pv)); 367 pv += bs2; 368 } 369 PetscCall(PetscLogFlops(250.0 * nz + 225)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */ 370 } 371 } 372 373 /* finished row so stick it into b->a */ 374 /* L part */ 375 pv = b->a + bs2 * bi[i]; 376 pj = b->j + bi[i]; 377 nz = bi[i + 1] - bi[i]; 378 for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2)); 379 380 /* Mark diagonal and invert diagonal for simpler triangular solves */ 381 pv = b->a + bs2 * bdiag[i]; 382 pj = b->j + bdiag[i]; 383 PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2)); 384 PetscCall(PetscKernel_A_gets_inverse_A_5(pv, ipvt, work, shift, allowzeropivot, &zeropivotdetected)); 385 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 386 387 /* U part */ 388 pv = b->a + bs2 * (bdiag[i + 1] + 1); 389 pj = b->j + bdiag[i + 1] + 1; 390 nz = bdiag[i] - bdiag[i + 1] - 1; 391 for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2)); 392 } 393 394 PetscCall(PetscFree2(rtmp, mwork)); 395 PetscCall(ISRestoreIndices(isicol, &ic)); 396 PetscCall(ISRestoreIndices(isrow, &r)); 397 398 C->ops->solve = MatSolve_SeqBAIJ_5; 399 C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5; 400 C->assembled = PETSC_TRUE; 401 402 PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * n)); /* from inverting diagonal blocks */ 403 PetscFunctionReturn(PETSC_SUCCESS); 404 } 405 406 /* 407 Version for when blocks are 5 by 5 Using natural ordering 408 */ 409 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_inplace(Mat C, Mat A, const MatFactorInfo *info) 410 { 411 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data; 412 PetscInt i, j, n = a->mbs, *bi = b->i, *bj = b->j, ipvt[5]; 413 PetscInt *ajtmpold, *ajtmp, nz, row; 414 PetscInt *diag_offset = b->diag, *ai = a->i, *aj = a->j, *pj; 415 MatScalar *pv, *v, *rtmp, *pc, *w, *x; 416 MatScalar x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15; 417 MatScalar x16, x17, x18, x19, x20, x21, x22, x23, x24, x25; 418 MatScalar p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12, p13, p14, p15; 419 MatScalar p16, p17, p18, p19, p20, p21, p22, p23, p24, p25; 420 MatScalar m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12, m13, m14, m15; 421 MatScalar m16, m17, m18, m19, m20, m21, m22, m23, m24, m25; 422 MatScalar *ba = b->a, *aa = a->a, work[25]; 423 PetscReal shift = info->shiftamount; 424 PetscBool allowzeropivot, zeropivotdetected; 425 426 PetscFunctionBegin; 427 allowzeropivot = PetscNot(A->erroriffailure); 428 PetscCall(PetscMalloc1(25 * (n + 1), &rtmp)); 429 for (i = 0; i < n; i++) { 430 nz = bi[i + 1] - bi[i]; 431 ajtmp = bj + bi[i]; 432 for (j = 0; j < nz; j++) { 433 x = rtmp + 25 * ajtmp[j]; 434 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0; 435 x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0; 436 x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0; 437 } 438 /* load in initial (unfactored row) */ 439 nz = ai[i + 1] - ai[i]; 440 ajtmpold = aj + ai[i]; 441 v = aa + 25 * ai[i]; 442 for (j = 0; j < nz; j++) { 443 x = rtmp + 25 * ajtmpold[j]; 444 x[0] = v[0]; 445 x[1] = v[1]; 446 x[2] = v[2]; 447 x[3] = v[3]; 448 x[4] = v[4]; 449 x[5] = v[5]; 450 x[6] = v[6]; 451 x[7] = v[7]; 452 x[8] = v[8]; 453 x[9] = v[9]; 454 x[10] = v[10]; 455 x[11] = v[11]; 456 x[12] = v[12]; 457 x[13] = v[13]; 458 x[14] = v[14]; 459 x[15] = v[15]; 460 x[16] = v[16]; 461 x[17] = v[17]; 462 x[18] = v[18]; 463 x[19] = v[19]; 464 x[20] = v[20]; 465 x[21] = v[21]; 466 x[22] = v[22]; 467 x[23] = v[23]; 468 x[24] = v[24]; 469 v += 25; 470 } 471 row = *ajtmp++; 472 while (row < i) { 473 pc = rtmp + 25 * row; 474 p1 = pc[0]; 475 p2 = pc[1]; 476 p3 = pc[2]; 477 p4 = pc[3]; 478 p5 = pc[4]; 479 p6 = pc[5]; 480 p7 = pc[6]; 481 p8 = pc[7]; 482 p9 = pc[8]; 483 p10 = pc[9]; 484 p11 = pc[10]; 485 p12 = pc[11]; 486 p13 = pc[12]; 487 p14 = pc[13]; 488 p15 = pc[14]; 489 p16 = pc[15]; 490 p17 = pc[16]; 491 p18 = pc[17]; 492 p19 = pc[18]; 493 p20 = pc[19]; 494 p21 = pc[20]; 495 p22 = pc[21]; 496 p23 = pc[22]; 497 p24 = pc[23]; 498 p25 = pc[24]; 499 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) { 500 pv = ba + 25 * diag_offset[row]; 501 pj = bj + diag_offset[row] + 1; 502 x1 = pv[0]; 503 x2 = pv[1]; 504 x3 = pv[2]; 505 x4 = pv[3]; 506 x5 = pv[4]; 507 x6 = pv[5]; 508 x7 = pv[6]; 509 x8 = pv[7]; 510 x9 = pv[8]; 511 x10 = pv[9]; 512 x11 = pv[10]; 513 x12 = pv[11]; 514 x13 = pv[12]; 515 x14 = pv[13]; 516 x15 = pv[14]; 517 x16 = pv[15]; 518 x17 = pv[16]; 519 x18 = pv[17]; 520 x19 = pv[18]; 521 x20 = pv[19]; 522 x21 = pv[20]; 523 x22 = pv[21]; 524 x23 = pv[22]; 525 x24 = pv[23]; 526 x25 = pv[24]; 527 pc[0] = m1 = p1 * x1 + p6 * x2 + p11 * x3 + p16 * x4 + p21 * x5; 528 pc[1] = m2 = p2 * x1 + p7 * x2 + p12 * x3 + p17 * x4 + p22 * x5; 529 pc[2] = m3 = p3 * x1 + p8 * x2 + p13 * x3 + p18 * x4 + p23 * x5; 530 pc[3] = m4 = p4 * x1 + p9 * x2 + p14 * x3 + p19 * x4 + p24 * x5; 531 pc[4] = m5 = p5 * x1 + p10 * x2 + p15 * x3 + p20 * x4 + p25 * x5; 532 533 pc[5] = m6 = p1 * x6 + p6 * x7 + p11 * x8 + p16 * x9 + p21 * x10; 534 pc[6] = m7 = p2 * x6 + p7 * x7 + p12 * x8 + p17 * x9 + p22 * x10; 535 pc[7] = m8 = p3 * x6 + p8 * x7 + p13 * x8 + p18 * x9 + p23 * x10; 536 pc[8] = m9 = p4 * x6 + p9 * x7 + p14 * x8 + p19 * x9 + p24 * x10; 537 pc[9] = m10 = p5 * x6 + p10 * x7 + p15 * x8 + p20 * x9 + p25 * x10; 538 539 pc[10] = m11 = p1 * x11 + p6 * x12 + p11 * x13 + p16 * x14 + p21 * x15; 540 pc[11] = m12 = p2 * x11 + p7 * x12 + p12 * x13 + p17 * x14 + p22 * x15; 541 pc[12] = m13 = p3 * x11 + p8 * x12 + p13 * x13 + p18 * x14 + p23 * x15; 542 pc[13] = m14 = p4 * x11 + p9 * x12 + p14 * x13 + p19 * x14 + p24 * x15; 543 pc[14] = m15 = p5 * x11 + p10 * x12 + p15 * x13 + p20 * x14 + p25 * x15; 544 545 pc[15] = m16 = p1 * x16 + p6 * x17 + p11 * x18 + p16 * x19 + p21 * x20; 546 pc[16] = m17 = p2 * x16 + p7 * x17 + p12 * x18 + p17 * x19 + p22 * x20; 547 pc[17] = m18 = p3 * x16 + p8 * x17 + p13 * x18 + p18 * x19 + p23 * x20; 548 pc[18] = m19 = p4 * x16 + p9 * x17 + p14 * x18 + p19 * x19 + p24 * x20; 549 pc[19] = m20 = p5 * x16 + p10 * x17 + p15 * x18 + p20 * x19 + p25 * x20; 550 551 pc[20] = m21 = p1 * x21 + p6 * x22 + p11 * x23 + p16 * x24 + p21 * x25; 552 pc[21] = m22 = p2 * x21 + p7 * x22 + p12 * x23 + p17 * x24 + p22 * x25; 553 pc[22] = m23 = p3 * x21 + p8 * x22 + p13 * x23 + p18 * x24 + p23 * x25; 554 pc[23] = m24 = p4 * x21 + p9 * x22 + p14 * x23 + p19 * x24 + p24 * x25; 555 pc[24] = m25 = p5 * x21 + p10 * x22 + p15 * x23 + p20 * x24 + p25 * x25; 556 557 nz = bi[row + 1] - diag_offset[row] - 1; 558 pv += 25; 559 for (j = 0; j < nz; j++) { 560 x1 = pv[0]; 561 x2 = pv[1]; 562 x3 = pv[2]; 563 x4 = pv[3]; 564 x5 = pv[4]; 565 x6 = pv[5]; 566 x7 = pv[6]; 567 x8 = pv[7]; 568 x9 = pv[8]; 569 x10 = pv[9]; 570 x11 = pv[10]; 571 x12 = pv[11]; 572 x13 = pv[12]; 573 x14 = pv[13]; 574 x15 = pv[14]; 575 x16 = pv[15]; 576 x17 = pv[16]; 577 x18 = pv[17]; 578 x19 = pv[18]; 579 x20 = pv[19]; 580 x21 = pv[20]; 581 x22 = pv[21]; 582 x23 = pv[22]; 583 x24 = pv[23]; 584 x25 = pv[24]; 585 x = rtmp + 25 * pj[j]; 586 x[0] -= m1 * x1 + m6 * x2 + m11 * x3 + m16 * x4 + m21 * x5; 587 x[1] -= m2 * x1 + m7 * x2 + m12 * x3 + m17 * x4 + m22 * x5; 588 x[2] -= m3 * x1 + m8 * x2 + m13 * x3 + m18 * x4 + m23 * x5; 589 x[3] -= m4 * x1 + m9 * x2 + m14 * x3 + m19 * x4 + m24 * x5; 590 x[4] -= m5 * x1 + m10 * x2 + m15 * x3 + m20 * x4 + m25 * x5; 591 592 x[5] -= m1 * x6 + m6 * x7 + m11 * x8 + m16 * x9 + m21 * x10; 593 x[6] -= m2 * x6 + m7 * x7 + m12 * x8 + m17 * x9 + m22 * x10; 594 x[7] -= m3 * x6 + m8 * x7 + m13 * x8 + m18 * x9 + m23 * x10; 595 x[8] -= m4 * x6 + m9 * x7 + m14 * x8 + m19 * x9 + m24 * x10; 596 x[9] -= m5 * x6 + m10 * x7 + m15 * x8 + m20 * x9 + m25 * x10; 597 598 x[10] -= m1 * x11 + m6 * x12 + m11 * x13 + m16 * x14 + m21 * x15; 599 x[11] -= m2 * x11 + m7 * x12 + m12 * x13 + m17 * x14 + m22 * x15; 600 x[12] -= m3 * x11 + m8 * x12 + m13 * x13 + m18 * x14 + m23 * x15; 601 x[13] -= m4 * x11 + m9 * x12 + m14 * x13 + m19 * x14 + m24 * x15; 602 x[14] -= m5 * x11 + m10 * x12 + m15 * x13 + m20 * x14 + m25 * x15; 603 604 x[15] -= m1 * x16 + m6 * x17 + m11 * x18 + m16 * x19 + m21 * x20; 605 x[16] -= m2 * x16 + m7 * x17 + m12 * x18 + m17 * x19 + m22 * x20; 606 x[17] -= m3 * x16 + m8 * x17 + m13 * x18 + m18 * x19 + m23 * x20; 607 x[18] -= m4 * x16 + m9 * x17 + m14 * x18 + m19 * x19 + m24 * x20; 608 x[19] -= m5 * x16 + m10 * x17 + m15 * x18 + m20 * x19 + m25 * x20; 609 610 x[20] -= m1 * x21 + m6 * x22 + m11 * x23 + m16 * x24 + m21 * x25; 611 x[21] -= m2 * x21 + m7 * x22 + m12 * x23 + m17 * x24 + m22 * x25; 612 x[22] -= m3 * x21 + m8 * x22 + m13 * x23 + m18 * x24 + m23 * x25; 613 x[23] -= m4 * x21 + m9 * x22 + m14 * x23 + m19 * x24 + m24 * x25; 614 x[24] -= m5 * x21 + m10 * x22 + m15 * x23 + m20 * x24 + m25 * x25; 615 pv += 25; 616 } 617 PetscCall(PetscLogFlops(250.0 * nz + 225.0)); 618 } 619 row = *ajtmp++; 620 } 621 /* finished row so stick it into b->a */ 622 pv = ba + 25 * bi[i]; 623 pj = bj + bi[i]; 624 nz = bi[i + 1] - bi[i]; 625 for (j = 0; j < nz; j++) { 626 x = rtmp + 25 * pj[j]; 627 pv[0] = x[0]; 628 pv[1] = x[1]; 629 pv[2] = x[2]; 630 pv[3] = x[3]; 631 pv[4] = x[4]; 632 pv[5] = x[5]; 633 pv[6] = x[6]; 634 pv[7] = x[7]; 635 pv[8] = x[8]; 636 pv[9] = x[9]; 637 pv[10] = x[10]; 638 pv[11] = x[11]; 639 pv[12] = x[12]; 640 pv[13] = x[13]; 641 pv[14] = x[14]; 642 pv[15] = x[15]; 643 pv[16] = x[16]; 644 pv[17] = x[17]; 645 pv[18] = x[18]; 646 pv[19] = x[19]; 647 pv[20] = x[20]; 648 pv[21] = x[21]; 649 pv[22] = x[22]; 650 pv[23] = x[23]; 651 pv[24] = x[24]; 652 pv += 25; 653 } 654 /* invert diagonal block */ 655 w = ba + 25 * diag_offset[i]; 656 PetscCall(PetscKernel_A_gets_inverse_A_5(w, ipvt, work, shift, allowzeropivot, &zeropivotdetected)); 657 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 658 } 659 660 PetscCall(PetscFree(rtmp)); 661 662 C->ops->solve = MatSolve_SeqBAIJ_5_NaturalOrdering_inplace; 663 C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering_inplace; 664 C->assembled = PETSC_TRUE; 665 666 PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * b->mbs)); /* from inverting diagonal blocks */ 667 PetscFunctionReturn(PETSC_SUCCESS); 668 } 669 670 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering(Mat B, Mat A, const MatFactorInfo *info) 671 { 672 Mat C = B; 673 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data; 674 PetscInt i, j, k, nz, nzL, row; 675 const PetscInt n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j; 676 const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2; 677 MatScalar *rtmp, *pc, *mwork, *v, *vv, *pv, *aa = a->a, work[25]; 678 PetscInt flg, ipvt[5]; 679 PetscReal shift = info->shiftamount; 680 PetscBool allowzeropivot, zeropivotdetected; 681 682 PetscFunctionBegin; 683 allowzeropivot = PetscNot(A->erroriffailure); 684 685 /* generate work space needed by the factorization */ 686 PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork)); 687 PetscCall(PetscArrayzero(rtmp, bs2 * n)); 688 689 for (i = 0; i < n; i++) { 690 /* zero rtmp */ 691 /* L part */ 692 nz = bi[i + 1] - bi[i]; 693 bjtmp = bj + bi[i]; 694 for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2)); 695 696 /* U part */ 697 nz = bdiag[i] - bdiag[i + 1]; 698 bjtmp = bj + bdiag[i + 1] + 1; 699 for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2)); 700 701 /* load in initial (unfactored row) */ 702 nz = ai[i + 1] - ai[i]; 703 ajtmp = aj + ai[i]; 704 v = aa + bs2 * ai[i]; 705 for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ajtmp[j], v + bs2 * j, bs2)); 706 707 /* elimination */ 708 bjtmp = bj + bi[i]; 709 nzL = bi[i + 1] - bi[i]; 710 for (k = 0; k < nzL; k++) { 711 row = bjtmp[k]; 712 pc = rtmp + bs2 * row; 713 for (flg = 0, j = 0; j < bs2; j++) { 714 if (pc[j] != 0.0) { 715 flg = 1; 716 break; 717 } 718 } 719 if (flg) { 720 pv = b->a + bs2 * bdiag[row]; 721 /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */ 722 PetscCall(PetscKernel_A_gets_A_times_B_5(pc, pv, mwork)); 723 724 pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */ 725 pv = b->a + bs2 * (bdiag[row + 1] + 1); 726 nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */ 727 for (j = 0; j < nz; j++) { 728 /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */ 729 /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */ 730 vv = rtmp + bs2 * pj[j]; 731 PetscCall(PetscKernel_A_gets_A_minus_B_times_C_5(vv, pc, pv)); 732 pv += bs2; 733 } 734 PetscCall(PetscLogFlops(250.0 * nz + 225)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */ 735 } 736 } 737 738 /* finished row so stick it into b->a */ 739 /* L part */ 740 pv = b->a + bs2 * bi[i]; 741 pj = b->j + bi[i]; 742 nz = bi[i + 1] - bi[i]; 743 for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2)); 744 745 /* Mark diagonal and invert diagonal for simpler triangular solves */ 746 pv = b->a + bs2 * bdiag[i]; 747 pj = b->j + bdiag[i]; 748 PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2)); 749 PetscCall(PetscKernel_A_gets_inverse_A_5(pv, ipvt, work, shift, allowzeropivot, &zeropivotdetected)); 750 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 751 752 /* U part */ 753 pv = b->a + bs2 * (bdiag[i + 1] + 1); 754 pj = b->j + bdiag[i + 1] + 1; 755 nz = bdiag[i] - bdiag[i + 1] - 1; 756 for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2)); 757 } 758 PetscCall(PetscFree2(rtmp, mwork)); 759 760 C->ops->solve = MatSolve_SeqBAIJ_5_NaturalOrdering; 761 C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering; 762 C->assembled = PETSC_TRUE; 763 764 PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * n)); /* from inverting diagonal blocks */ 765 PetscFunctionReturn(PETSC_SUCCESS); 766 } 767