1 2 /* 3 Factorization code for BAIJ format. 4 */ 5 #include <../src/mat/impls/baij/seq/baij.h> 6 #include <petsc/private/kernels/blockinvert.h> 7 8 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2(Mat B,Mat A,const MatFactorInfo *info) 9 { 10 Mat C =B; 11 Mat_SeqBAIJ *a =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data; 12 IS isrow = b->row,isicol = b->icol; 13 PetscErrorCode ierr; 14 const PetscInt *r,*ic; 15 PetscInt i,j,k,nz,nzL,row,*pj; 16 const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,bs2=a->bs2; 17 const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag; 18 MatScalar *rtmp,*pc,*mwork,*pv; 19 MatScalar *aa=a->a,*v; 20 PetscInt flg; 21 PetscReal shift = info->shiftamount; 22 PetscBool allowzeropivot,zeropivotdetected; 23 24 PetscFunctionBegin; 25 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 26 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 27 allowzeropivot = PetscNot(A->erroriffailure); 28 29 /* generate work space needed by the factorization */ 30 ierr = PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);CHKERRQ(ierr); 31 ierr = PetscArrayzero(rtmp,bs2*n);CHKERRQ(ierr); 32 33 for (i=0; i<n; i++) { 34 /* zero rtmp */ 35 /* L part */ 36 nz = bi[i+1] - bi[i]; 37 bjtmp = bj + bi[i]; 38 for (j=0; j<nz; j++) { 39 ierr = PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);CHKERRQ(ierr); 40 } 41 42 /* U part */ 43 nz = bdiag[i] - bdiag[i+1]; 44 bjtmp = bj + bdiag[i+1]+1; 45 for (j=0; j<nz; j++) { 46 ierr = PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);CHKERRQ(ierr); 47 } 48 49 /* load in initial (unfactored row) */ 50 nz = ai[r[i]+1] - ai[r[i]]; 51 ajtmp = aj + ai[r[i]]; 52 v = aa + bs2*ai[r[i]]; 53 for (j=0; j<nz; j++) { 54 ierr = PetscArraycpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2);CHKERRQ(ierr); 55 } 56 57 /* elimination */ 58 bjtmp = bj + bi[i]; 59 nzL = bi[i+1] - bi[i]; 60 for (k=0; k < nzL; k++) { 61 row = bjtmp[k]; 62 pc = rtmp + bs2*row; 63 for (flg=0,j=0; j<bs2; j++) { 64 if (pc[j] != (PetscScalar)0.0) { 65 flg = 1; 66 break; 67 } 68 } 69 if (flg) { 70 pv = b->a + bs2*bdiag[row]; 71 /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */ 72 ierr = PetscKernel_A_gets_A_times_B_2(pc,pv,mwork);CHKERRQ(ierr); 73 74 pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */ 75 pv = b->a + bs2*(bdiag[row+1]+1); 76 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */ 77 for (j=0; j<nz; j++) { 78 /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */ 79 /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */ 80 v = rtmp + 4*pj[j]; 81 ierr = PetscKernel_A_gets_A_minus_B_times_C_2(v,pc,pv);CHKERRQ(ierr); 82 pv += 4; 83 } 84 ierr = PetscLogFlops(16*nz+12);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */ 85 } 86 } 87 88 /* finished row so stick it into b->a */ 89 /* L part */ 90 pv = b->a + bs2*bi[i]; 91 pj = b->j + bi[i]; 92 nz = bi[i+1] - bi[i]; 93 for (j=0; j<nz; j++) { 94 ierr = PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);CHKERRQ(ierr); 95 } 96 97 /* Mark diagonal and invert diagonal for simplier triangular solves */ 98 pv = b->a + bs2*bdiag[i]; 99 pj = b->j + bdiag[i]; 100 ierr = PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);CHKERRQ(ierr); 101 ierr = PetscKernel_A_gets_inverse_A_2(pv,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr); 102 if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 103 104 /* U part */ 105 pv = b->a + bs2*(bdiag[i+1]+1); 106 pj = b->j + bdiag[i+1]+1; 107 nz = bdiag[i] - bdiag[i+1] - 1; 108 for (j=0; j<nz; j++) { 109 ierr = PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);CHKERRQ(ierr); 110 } 111 } 112 113 ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr); 114 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 115 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 116 117 C->ops->solve = MatSolve_SeqBAIJ_2; 118 C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2; 119 C->assembled = PETSC_TRUE; 120 121 ierr = PetscLogFlops(1.333333333333*2*2*2*n);CHKERRQ(ierr); /* from inverting diagonal blocks */ 122 PetscFunctionReturn(0); 123 } 124 125 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info) 126 { 127 Mat C =B; 128 Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data; 129 PetscErrorCode ierr; 130 PetscInt i,j,k,nz,nzL,row,*pj; 131 const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,bs2=a->bs2; 132 const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag; 133 MatScalar *rtmp,*pc,*mwork,*pv; 134 MatScalar *aa=a->a,*v; 135 PetscInt flg; 136 PetscReal shift = info->shiftamount; 137 PetscBool allowzeropivot,zeropivotdetected; 138 139 PetscFunctionBegin; 140 allowzeropivot = PetscNot(A->erroriffailure); 141 142 /* generate work space needed by the factorization */ 143 ierr = PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);CHKERRQ(ierr); 144 ierr = PetscArrayzero(rtmp,bs2*n);CHKERRQ(ierr); 145 146 for (i=0; i<n; i++) { 147 /* zero rtmp */ 148 /* L part */ 149 nz = bi[i+1] - bi[i]; 150 bjtmp = bj + bi[i]; 151 for (j=0; j<nz; j++) { 152 ierr = PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);CHKERRQ(ierr); 153 } 154 155 /* U part */ 156 nz = bdiag[i] - bdiag[i+1]; 157 bjtmp = bj + bdiag[i+1]+1; 158 for (j=0; j<nz; j++) { 159 ierr = PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);CHKERRQ(ierr); 160 } 161 162 /* load in initial (unfactored row) */ 163 nz = ai[i+1] - ai[i]; 164 ajtmp = aj + ai[i]; 165 v = aa + bs2*ai[i]; 166 for (j=0; j<nz; j++) { 167 ierr = PetscArraycpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2);CHKERRQ(ierr); 168 } 169 170 /* elimination */ 171 bjtmp = bj + bi[i]; 172 nzL = bi[i+1] - bi[i]; 173 for (k=0; k < nzL; k++) { 174 row = bjtmp[k]; 175 pc = rtmp + bs2*row; 176 for (flg=0,j=0; j<bs2; j++) { 177 if (pc[j]!=(PetscScalar)0.0) { 178 flg = 1; 179 break; 180 } 181 } 182 if (flg) { 183 pv = b->a + bs2*bdiag[row]; 184 /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */ 185 ierr = PetscKernel_A_gets_A_times_B_2(pc,pv,mwork);CHKERRQ(ierr); 186 187 pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */ 188 pv = b->a + bs2*(bdiag[row+1]+1); 189 nz = bdiag[row]-bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */ 190 for (j=0; j<nz; j++) { 191 /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */ 192 /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */ 193 v = rtmp + 4*pj[j]; 194 ierr = PetscKernel_A_gets_A_minus_B_times_C_2(v,pc,pv);CHKERRQ(ierr); 195 pv += 4; 196 } 197 ierr = PetscLogFlops(16*nz+12);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */ 198 } 199 } 200 201 /* finished row so stick it into b->a */ 202 /* L part */ 203 pv = b->a + bs2*bi[i]; 204 pj = b->j + bi[i]; 205 nz = bi[i+1] - bi[i]; 206 for (j=0; j<nz; j++) { 207 ierr = PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);CHKERRQ(ierr); 208 } 209 210 /* Mark diagonal and invert diagonal for simplier triangular solves */ 211 pv = b->a + bs2*bdiag[i]; 212 pj = b->j + bdiag[i]; 213 ierr = PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);CHKERRQ(ierr); 214 ierr = PetscKernel_A_gets_inverse_A_2(pv,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr); 215 if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 216 217 /* U part */ 218 /* 219 pv = b->a + bs2*bi[2*n-i]; 220 pj = b->j + bi[2*n-i]; 221 nz = bi[2*n-i+1] - bi[2*n-i] - 1; 222 */ 223 pv = b->a + bs2*(bdiag[i+1]+1); 224 pj = b->j + bdiag[i+1]+1; 225 nz = bdiag[i] - bdiag[i+1] - 1; 226 for (j=0; j<nz; j++) { 227 ierr = PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);CHKERRQ(ierr); 228 } 229 } 230 ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr); 231 232 C->ops->solve = MatSolve_SeqBAIJ_2_NaturalOrdering; 233 C->ops->forwardsolve = MatForwardSolve_SeqBAIJ_2_NaturalOrdering; 234 C->ops->backwardsolve = MatBackwardSolve_SeqBAIJ_2_NaturalOrdering; 235 C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2_NaturalOrdering; 236 C->assembled = PETSC_TRUE; 237 238 ierr = PetscLogFlops(1.333333333333*2*2*2*n);CHKERRQ(ierr); /* from inverting diagonal blocks */ 239 PetscFunctionReturn(0); 240 } 241 242 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2_inplace(Mat B,Mat A,const MatFactorInfo *info) 243 { 244 Mat C = B; 245 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data; 246 IS isrow = b->row,isicol = b->icol; 247 PetscErrorCode ierr; 248 const PetscInt *r,*ic; 249 PetscInt i,j,n = a->mbs,*bi = b->i,*bj = b->j; 250 PetscInt *ajtmpold,*ajtmp,nz,row; 251 PetscInt *diag_offset=b->diag,idx,*ai=a->i,*aj=a->j,*pj; 252 MatScalar *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4; 253 MatScalar p1,p2,p3,p4; 254 MatScalar *ba = b->a,*aa = a->a; 255 PetscReal shift = info->shiftamount; 256 PetscBool allowzeropivot,zeropivotdetected; 257 258 PetscFunctionBegin; 259 allowzeropivot = PetscNot(A->erroriffailure); 260 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 261 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 262 ierr = PetscMalloc1(4*(n+1),&rtmp);CHKERRQ(ierr); 263 264 for (i=0; i<n; i++) { 265 nz = bi[i+1] - bi[i]; 266 ajtmp = bj + bi[i]; 267 for (j=0; j<nz; j++) { 268 x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0; 269 } 270 /* load in initial (unfactored row) */ 271 idx = r[i]; 272 nz = ai[idx+1] - ai[idx]; 273 ajtmpold = aj + ai[idx]; 274 v = aa + 4*ai[idx]; 275 for (j=0; j<nz; j++) { 276 x = rtmp+4*ic[ajtmpold[j]]; 277 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 278 v += 4; 279 } 280 row = *ajtmp++; 281 while (row < i) { 282 pc = rtmp + 4*row; 283 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 284 if (p1 != (PetscScalar)0.0 || p2 != (PetscScalar)0.0 || p3 != (PetscScalar)0.0 || p4 != (PetscScalar)0.0) { 285 pv = ba + 4*diag_offset[row]; 286 pj = bj + diag_offset[row] + 1; 287 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 288 pc[0] = m1 = p1*x1 + p3*x2; 289 pc[1] = m2 = p2*x1 + p4*x2; 290 pc[2] = m3 = p1*x3 + p3*x4; 291 pc[3] = m4 = p2*x3 + p4*x4; 292 nz = bi[row+1] - diag_offset[row] - 1; 293 pv += 4; 294 for (j=0; j<nz; j++) { 295 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 296 x = rtmp + 4*pj[j]; 297 x[0] -= m1*x1 + m3*x2; 298 x[1] -= m2*x1 + m4*x2; 299 x[2] -= m1*x3 + m3*x4; 300 x[3] -= m2*x3 + m4*x4; 301 pv += 4; 302 } 303 ierr = PetscLogFlops(16.0*nz+12.0);CHKERRQ(ierr); 304 } 305 row = *ajtmp++; 306 } 307 /* finished row so stick it into b->a */ 308 pv = ba + 4*bi[i]; 309 pj = bj + bi[i]; 310 nz = bi[i+1] - bi[i]; 311 for (j=0; j<nz; j++) { 312 x = rtmp+4*pj[j]; 313 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 314 pv += 4; 315 } 316 /* invert diagonal block */ 317 w = ba + 4*diag_offset[i]; 318 ierr = PetscKernel_A_gets_inverse_A_2(w,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr); 319 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 320 } 321 322 ierr = PetscFree(rtmp);CHKERRQ(ierr); 323 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 324 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 325 326 C->ops->solve = MatSolve_SeqBAIJ_2_inplace; 327 C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2_inplace; 328 C->assembled = PETSC_TRUE; 329 330 ierr = PetscLogFlops(1.333333333333*8*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */ 331 PetscFunctionReturn(0); 332 } 333 /* 334 Version for when blocks are 2 by 2 Using natural ordering 335 */ 336 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info) 337 { 338 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data; 339 PetscErrorCode ierr; 340 PetscInt i,j,n = a->mbs,*bi = b->i,*bj = b->j; 341 PetscInt *ajtmpold,*ajtmp,nz,row; 342 PetscInt *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 343 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 344 MatScalar p1,p2,p3,p4,m1,m2,m3,m4,x1,x2,x3,x4; 345 MatScalar *ba = b->a,*aa = a->a; 346 PetscReal shift = info->shiftamount; 347 PetscBool allowzeropivot,zeropivotdetected; 348 349 PetscFunctionBegin; 350 allowzeropivot = PetscNot(A->erroriffailure); 351 ierr = PetscMalloc1(4*(n+1),&rtmp);CHKERRQ(ierr); 352 for (i=0; i<n; i++) { 353 nz = bi[i+1] - bi[i]; 354 ajtmp = bj + bi[i]; 355 for (j=0; j<nz; j++) { 356 x = rtmp+4*ajtmp[j]; 357 x[0] = x[1] = x[2] = x[3] = 0.0; 358 } 359 /* load in initial (unfactored row) */ 360 nz = ai[i+1] - ai[i]; 361 ajtmpold = aj + ai[i]; 362 v = aa + 4*ai[i]; 363 for (j=0; j<nz; j++) { 364 x = rtmp+4*ajtmpold[j]; 365 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 366 v += 4; 367 } 368 row = *ajtmp++; 369 while (row < i) { 370 pc = rtmp + 4*row; 371 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 372 if (p1 != (PetscScalar)0.0 || p2 != (PetscScalar)0.0 || p3 != (PetscScalar)0.0 || p4 != (PetscScalar)0.0) { 373 pv = ba + 4*diag_offset[row]; 374 pj = bj + diag_offset[row] + 1; 375 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 376 pc[0] = m1 = p1*x1 + p3*x2; 377 pc[1] = m2 = p2*x1 + p4*x2; 378 pc[2] = m3 = p1*x3 + p3*x4; 379 pc[3] = m4 = p2*x3 + p4*x4; 380 nz = bi[row+1] - diag_offset[row] - 1; 381 pv += 4; 382 for (j=0; j<nz; j++) { 383 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 384 x = rtmp + 4*pj[j]; 385 x[0] -= m1*x1 + m3*x2; 386 x[1] -= m2*x1 + m4*x2; 387 x[2] -= m1*x3 + m3*x4; 388 x[3] -= m2*x3 + m4*x4; 389 pv += 4; 390 } 391 ierr = PetscLogFlops(16.0*nz+12.0);CHKERRQ(ierr); 392 } 393 row = *ajtmp++; 394 } 395 /* finished row so stick it into b->a */ 396 pv = ba + 4*bi[i]; 397 pj = bj + bi[i]; 398 nz = bi[i+1] - bi[i]; 399 for (j=0; j<nz; j++) { 400 x = rtmp+4*pj[j]; 401 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 402 /* 403 printf(" col %d:",pj[j]); 404 PetscInt j1; 405 for (j1=0; j1<4; j1++) printf(" %g,",*(pv+j1)); 406 printf("\n"); 407 */ 408 pv += 4; 409 } 410 /* invert diagonal block */ 411 w = ba + 4*diag_offset[i]; 412 ierr = PetscKernel_A_gets_inverse_A_2(w,shift, allowzeropivot,&zeropivotdetected);CHKERRQ(ierr); 413 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 414 } 415 416 ierr = PetscFree(rtmp);CHKERRQ(ierr); 417 418 C->ops->solve = MatSolve_SeqBAIJ_2_NaturalOrdering_inplace; 419 C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2_NaturalOrdering_inplace; 420 C->assembled = PETSC_TRUE; 421 422 ierr = PetscLogFlops(1.333333333333*8*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */ 423 PetscFunctionReturn(0); 424 } 425 426 /* ----------------------------------------------------------- */ 427 /* 428 Version for when blocks are 1 by 1. 429 */ 430 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_1(Mat B,Mat A,const MatFactorInfo *info) 431 { 432 Mat C =B; 433 Mat_SeqBAIJ *a =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data; 434 IS isrow = b->row,isicol = b->icol; 435 PetscErrorCode ierr; 436 const PetscInt *r,*ic,*ics; 437 const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bdiag=b->diag; 438 PetscInt i,j,k,nz,nzL,row,*pj; 439 const PetscInt *ajtmp,*bjtmp; 440 MatScalar *rtmp,*pc,multiplier,*pv; 441 const MatScalar *aa=a->a,*v; 442 PetscBool row_identity,col_identity; 443 FactorShiftCtx sctx; 444 const PetscInt *ddiag; 445 PetscReal rs; 446 MatScalar d; 447 448 PetscFunctionBegin; 449 /* MatPivotSetUp(): initialize shift context sctx */ 450 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 451 452 if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 453 ddiag = a->diag; 454 sctx.shift_top = info->zeropivot; 455 for (i=0; i<n; i++) { 456 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 457 d = (aa)[ddiag[i]]; 458 rs = -PetscAbsScalar(d) - PetscRealPart(d); 459 v = aa+ai[i]; 460 nz = ai[i+1] - ai[i]; 461 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 462 if (rs>sctx.shift_top) sctx.shift_top = rs; 463 } 464 sctx.shift_top *= 1.1; 465 sctx.nshift_max = 5; 466 sctx.shift_lo = 0.; 467 sctx.shift_hi = 1.; 468 } 469 470 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 471 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 472 ierr = PetscMalloc1(n+1,&rtmp);CHKERRQ(ierr); 473 ics = ic; 474 475 do { 476 sctx.newshift = PETSC_FALSE; 477 for (i=0; i<n; i++) { 478 /* zero rtmp */ 479 /* L part */ 480 nz = bi[i+1] - bi[i]; 481 bjtmp = bj + bi[i]; 482 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 483 484 /* U part */ 485 nz = bdiag[i]-bdiag[i+1]; 486 bjtmp = bj + bdiag[i+1]+1; 487 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 488 489 /* load in initial (unfactored row) */ 490 nz = ai[r[i]+1] - ai[r[i]]; 491 ajtmp = aj + ai[r[i]]; 492 v = aa + ai[r[i]]; 493 for (j=0; j<nz; j++) rtmp[ics[ajtmp[j]]] = v[j]; 494 495 /* ZeropivotApply() */ 496 rtmp[i] += sctx.shift_amount; /* shift the diagonal of the matrix */ 497 498 /* elimination */ 499 bjtmp = bj + bi[i]; 500 row = *bjtmp++; 501 nzL = bi[i+1] - bi[i]; 502 for (k=0; k < nzL; k++) { 503 pc = rtmp + row; 504 if (*pc != (PetscScalar)0.0) { 505 pv = b->a + bdiag[row]; 506 multiplier = *pc * (*pv); 507 *pc = multiplier; 508 509 pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */ 510 pv = b->a + bdiag[row+1]+1; 511 nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */ 512 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 513 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 514 } 515 row = *bjtmp++; 516 } 517 518 /* finished row so stick it into b->a */ 519 rs = 0.0; 520 /* L part */ 521 pv = b->a + bi[i]; 522 pj = b->j + bi[i]; 523 nz = bi[i+1] - bi[i]; 524 for (j=0; j<nz; j++) { 525 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 526 } 527 528 /* U part */ 529 pv = b->a + bdiag[i+1]+1; 530 pj = b->j + bdiag[i+1]+1; 531 nz = bdiag[i] - bdiag[i+1]-1; 532 for (j=0; j<nz; j++) { 533 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 534 } 535 536 sctx.rs = rs; 537 sctx.pv = rtmp[i]; 538 ierr = MatPivotCheck(B,A,info,&sctx,i);CHKERRQ(ierr); 539 if (sctx.newshift) break; /* break for-loop */ 540 rtmp[i] = sctx.pv; /* sctx.pv might be updated in the case of MAT_SHIFT_INBLOCKS */ 541 542 /* Mark diagonal and invert diagonal for simplier triangular solves */ 543 pv = b->a + bdiag[i]; 544 *pv = (PetscScalar)1.0/rtmp[i]; 545 546 } /* endof for (i=0; i<n; i++) { */ 547 548 /* MatPivotRefine() */ 549 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 550 /* 551 * if no shift in this attempt & shifting & started shifting & can refine, 552 * then try lower shift 553 */ 554 sctx.shift_hi = sctx.shift_fraction; 555 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 556 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 557 sctx.newshift = PETSC_TRUE; 558 sctx.nshift++; 559 } 560 } while (sctx.newshift); 561 562 ierr = PetscFree(rtmp);CHKERRQ(ierr); 563 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 564 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 565 566 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 567 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 568 if (row_identity && col_identity) { 569 C->ops->solve = MatSolve_SeqBAIJ_1_NaturalOrdering; 570 C->ops->forwardsolve = MatForwardSolve_SeqBAIJ_1_NaturalOrdering; 571 C->ops->backwardsolve = MatBackwardSolve_SeqBAIJ_1_NaturalOrdering; 572 C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_1_NaturalOrdering; 573 } else { 574 C->ops->solve = MatSolve_SeqBAIJ_1; 575 C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_1; 576 } 577 C->assembled = PETSC_TRUE; 578 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 579 580 /* MatShiftView(A,info,&sctx) */ 581 if (sctx.nshift) { 582 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 583 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %g, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,(double)sctx.shift_amount,(double)sctx.shift_fraction,(double)sctx.shift_top);CHKERRQ(ierr); 584 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 585 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 586 } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) { 587 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);CHKERRQ(ierr); 588 } 589 } 590 PetscFunctionReturn(0); 591 } 592 593 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_1_inplace(Mat C,Mat A,const MatFactorInfo *info) 594 { 595 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data; 596 IS isrow = b->row,isicol = b->icol; 597 PetscErrorCode ierr; 598 const PetscInt *r,*ic; 599 PetscInt i,j,n = a->mbs,*bi = b->i,*bj = b->j; 600 PetscInt *ajtmpold,*ajtmp,nz,row,*ai = a->i,*aj = a->j; 601 PetscInt *diag_offset = b->diag,diag,*pj; 602 MatScalar *pv,*v,*rtmp,multiplier,*pc; 603 MatScalar *ba = b->a,*aa = a->a; 604 PetscBool row_identity, col_identity; 605 606 PetscFunctionBegin; 607 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 608 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 609 ierr = PetscMalloc1(n+1,&rtmp);CHKERRQ(ierr); 610 611 for (i=0; i<n; i++) { 612 nz = bi[i+1] - bi[i]; 613 ajtmp = bj + bi[i]; 614 for (j=0; j<nz; j++) rtmp[ajtmp[j]] = 0.0; 615 616 /* load in initial (unfactored row) */ 617 nz = ai[r[i]+1] - ai[r[i]]; 618 ajtmpold = aj + ai[r[i]]; 619 v = aa + ai[r[i]]; 620 for (j=0; j<nz; j++) rtmp[ic[ajtmpold[j]]] = v[j]; 621 622 row = *ajtmp++; 623 while (row < i) { 624 pc = rtmp + row; 625 if (*pc != 0.0) { 626 pv = ba + diag_offset[row]; 627 pj = bj + diag_offset[row] + 1; 628 multiplier = *pc * *pv++; 629 *pc = multiplier; 630 nz = bi[row+1] - diag_offset[row] - 1; 631 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 632 ierr = PetscLogFlops(1.0+2.0*nz);CHKERRQ(ierr); 633 } 634 row = *ajtmp++; 635 } 636 /* finished row so stick it into b->a */ 637 pv = ba + bi[i]; 638 pj = bj + bi[i]; 639 nz = bi[i+1] - bi[i]; 640 for (j=0; j<nz; j++) pv[j] = rtmp[pj[j]]; 641 diag = diag_offset[i] - bi[i]; 642 /* check pivot entry for current row */ 643 if (pv[diag] == 0.0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot: row in original ordering %D in permuted ordering %D",r[i],i); 644 pv[diag] = 1.0/pv[diag]; 645 } 646 647 ierr = PetscFree(rtmp);CHKERRQ(ierr); 648 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 649 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 650 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 651 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 652 if (row_identity && col_identity) { 653 C->ops->solve = MatSolve_SeqBAIJ_1_NaturalOrdering_inplace; 654 C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_1_NaturalOrdering_inplace; 655 } else { 656 C->ops->solve = MatSolve_SeqBAIJ_1_inplace; 657 C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_1_inplace; 658 } 659 C->assembled = PETSC_TRUE; 660 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 661 PetscFunctionReturn(0); 662 } 663 664 PETSC_INTERN PetscErrorCode MatGetFactor_seqbaij_petsc(Mat A,MatFactorType ftype,Mat *B) 665 { 666 PetscInt n = A->rmap->n; 667 PetscErrorCode ierr; 668 669 PetscFunctionBegin; 670 #if defined(PETSC_USE_COMPLEX) 671 if (A->hermitian && (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Hermitian Factor is not supported"); 672 #endif 673 ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr); 674 ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr); 675 if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT) { 676 ierr = MatSetType(*B,MATSEQBAIJ);CHKERRQ(ierr); 677 678 (*B)->ops->lufactorsymbolic = MatLUFactorSymbolic_SeqBAIJ; 679 (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqBAIJ; 680 } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) { 681 ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr); 682 ierr = MatSeqSBAIJSetPreallocation(*B,A->rmap->bs,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 683 684 (*B)->ops->iccfactorsymbolic = MatICCFactorSymbolic_SeqBAIJ; 685 (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqBAIJ; 686 } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported"); 687 (*B)->factortype = ftype; 688 689 ierr = PetscFree((*B)->solvertype);CHKERRQ(ierr); 690 ierr = PetscStrallocpy(MATSOLVERPETSC,&(*B)->solvertype);CHKERRQ(ierr); 691 PetscFunctionReturn(0); 692 } 693 694 /* ----------------------------------------------------------- */ 695 PetscErrorCode MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,const MatFactorInfo *info) 696 { 697 PetscErrorCode ierr; 698 Mat C; 699 700 PetscFunctionBegin; 701 ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr); 702 ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr); 703 ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr); 704 705 A->ops->solve = C->ops->solve; 706 A->ops->solvetranspose = C->ops->solvetranspose; 707 708 ierr = MatHeaderMerge(A,&C);CHKERRQ(ierr); 709 ierr = PetscLogObjectParent((PetscObject)A,(PetscObject)((Mat_SeqBAIJ*)(A->data))->icol);CHKERRQ(ierr); 710 PetscFunctionReturn(0); 711 } 712 713 #include <../src/mat/impls/sbaij/seq/sbaij.h> 714 PetscErrorCode MatCholeskyFactorNumeric_SeqBAIJ_N(Mat C,Mat A,const MatFactorInfo *info) 715 { 716 PetscErrorCode ierr; 717 Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data; 718 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 719 IS ip=b->row; 720 const PetscInt *rip; 721 PetscInt i,j,mbs=a->mbs,bs=A->rmap->bs,*bi=b->i,*bj=b->j,*bcol; 722 PetscInt *ai=a->i,*aj=a->j; 723 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 724 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 725 PetscReal rs; 726 FactorShiftCtx sctx; 727 728 PetscFunctionBegin; 729 if (bs > 1) { /* convert A to a SBAIJ matrix and apply Cholesky factorization from it */ 730 if (!a->sbaijMat) { 731 ierr = MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&a->sbaijMat);CHKERRQ(ierr); 732 } 733 ierr = (a->sbaijMat)->ops->choleskyfactornumeric(C,a->sbaijMat,info);CHKERRQ(ierr); 734 ierr = MatDestroy(&a->sbaijMat);CHKERRQ(ierr); 735 PetscFunctionReturn(0); 736 } 737 738 /* MatPivotSetUp(): initialize shift context sctx */ 739 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 740 741 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 742 ierr = PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&jl);CHKERRQ(ierr); 743 744 sctx.shift_amount = 0.; 745 sctx.nshift = 0; 746 do { 747 sctx.newshift = PETSC_FALSE; 748 for (i=0; i<mbs; i++) { 749 rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0; 750 } 751 752 for (k = 0; k<mbs; k++) { 753 bval = ba + bi[k]; 754 /* initialize k-th row by the perm[k]-th row of A */ 755 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 756 for (j = jmin; j < jmax; j++) { 757 col = rip[aj[j]]; 758 if (col >= k) { /* only take upper triangular entry */ 759 rtmp[col] = aa[j]; 760 *bval++ = 0.0; /* for in-place factorization */ 761 } 762 } 763 764 /* shift the diagonal of the matrix */ 765 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 766 767 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 768 dk = rtmp[k]; 769 i = jl[k]; /* first row to be added to k_th row */ 770 771 while (i < k) { 772 nexti = jl[i]; /* next row to be added to k_th row */ 773 774 /* compute multiplier, update diag(k) and U(i,k) */ 775 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 776 uikdi = -ba[ili]*ba[bi[i]]; /* diagonal(k) */ 777 dk += uikdi*ba[ili]; 778 ba[ili] = uikdi; /* -U(i,k) */ 779 780 /* add multiple of row i to k-th row */ 781 jmin = ili + 1; jmax = bi[i+1]; 782 if (jmin < jmax) { 783 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 784 /* update il and jl for row i */ 785 il[i] = jmin; 786 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 787 } 788 i = nexti; 789 } 790 791 /* shift the diagonals when zero pivot is detected */ 792 /* compute rs=sum of abs(off-diagonal) */ 793 rs = 0.0; 794 jmin = bi[k]+1; 795 nz = bi[k+1] - jmin; 796 if (nz) { 797 bcol = bj + jmin; 798 while (nz--) { 799 rs += PetscAbsScalar(rtmp[*bcol]); 800 bcol++; 801 } 802 } 803 804 sctx.rs = rs; 805 sctx.pv = dk; 806 ierr = MatPivotCheck(C,A,info,&sctx,k);CHKERRQ(ierr); 807 if (sctx.newshift) break; 808 dk = sctx.pv; 809 810 /* copy data into U(k,:) */ 811 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 812 jmin = bi[k]+1; jmax = bi[k+1]; 813 if (jmin < jmax) { 814 for (j=jmin; j<jmax; j++) { 815 col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0; 816 } 817 /* add the k-th row into il and jl */ 818 il[k] = jmin; 819 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 820 } 821 } 822 } while (sctx.newshift); 823 ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr); 824 825 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 826 827 C->assembled = PETSC_TRUE; 828 C->preallocated = PETSC_TRUE; 829 830 ierr = PetscLogFlops(C->rmap->N);CHKERRQ(ierr); 831 if (sctx.nshift) { 832 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 833 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 834 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 835 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 836 } 837 } 838 PetscFunctionReturn(0); 839 } 840 841 PetscErrorCode MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info) 842 { 843 Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data; 844 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 845 PetscErrorCode ierr; 846 PetscInt i,j,am=a->mbs; 847 PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 848 PetscInt k,jmin,*jl,*il,nexti,ili,*acol,*bcol,nz; 849 MatScalar *rtmp,*ba=b->a,*aa=a->a,dk,uikdi,*aval,*bval; 850 PetscReal rs; 851 FactorShiftCtx sctx; 852 853 PetscFunctionBegin; 854 /* MatPivotSetUp(): initialize shift context sctx */ 855 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 856 857 ierr = PetscMalloc3(am,&rtmp,am,&il,am,&jl);CHKERRQ(ierr); 858 859 do { 860 sctx.newshift = PETSC_FALSE; 861 for (i=0; i<am; i++) { 862 rtmp[i] = 0.0; jl[i] = am; il[0] = 0; 863 } 864 865 for (k = 0; k<am; k++) { 866 /* initialize k-th row with elements nonzero in row perm(k) of A */ 867 nz = ai[k+1] - ai[k]; 868 acol = aj + ai[k]; 869 aval = aa + ai[k]; 870 bval = ba + bi[k]; 871 while (nz--) { 872 if (*acol < k) { /* skip lower triangular entries */ 873 acol++; aval++; 874 } else { 875 rtmp[*acol++] = *aval++; 876 *bval++ = 0.0; /* for in-place factorization */ 877 } 878 } 879 880 /* shift the diagonal of the matrix */ 881 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 882 883 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 884 dk = rtmp[k]; 885 i = jl[k]; /* first row to be added to k_th row */ 886 887 while (i < k) { 888 nexti = jl[i]; /* next row to be added to k_th row */ 889 /* compute multiplier, update D(k) and U(i,k) */ 890 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 891 uikdi = -ba[ili]*ba[bi[i]]; 892 dk += uikdi*ba[ili]; 893 ba[ili] = uikdi; /* -U(i,k) */ 894 895 /* add multiple of row i to k-th row ... */ 896 jmin = ili + 1; 897 nz = bi[i+1] - jmin; 898 if (nz > 0) { 899 bcol = bj + jmin; 900 bval = ba + jmin; 901 while (nz--) rtmp[*bcol++] += uikdi*(*bval++); 902 /* update il and jl for i-th row */ 903 il[i] = jmin; 904 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 905 } 906 i = nexti; 907 } 908 909 /* shift the diagonals when zero pivot is detected */ 910 /* compute rs=sum of abs(off-diagonal) */ 911 rs = 0.0; 912 jmin = bi[k]+1; 913 nz = bi[k+1] - jmin; 914 if (nz) { 915 bcol = bj + jmin; 916 while (nz--) { 917 rs += PetscAbsScalar(rtmp[*bcol]); 918 bcol++; 919 } 920 } 921 922 sctx.rs = rs; 923 sctx.pv = dk; 924 ierr = MatPivotCheck(C,A,info,&sctx,k);CHKERRQ(ierr); 925 if (sctx.newshift) break; /* sctx.shift_amount is updated */ 926 dk = sctx.pv; 927 928 /* copy data into U(k,:) */ 929 ba[bi[k]] = 1.0/dk; 930 jmin = bi[k]+1; 931 nz = bi[k+1] - jmin; 932 if (nz) { 933 bcol = bj + jmin; 934 bval = ba + jmin; 935 while (nz--) { 936 *bval++ = rtmp[*bcol]; 937 rtmp[*bcol++] = 0.0; 938 } 939 /* add k-th row into il and jl */ 940 il[k] = jmin; 941 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 942 } 943 } 944 } while (sctx.newshift); 945 ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr); 946 947 C->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 948 C->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 949 C->assembled = PETSC_TRUE; 950 C->preallocated = PETSC_TRUE; 951 952 ierr = PetscLogFlops(C->rmap->N);CHKERRQ(ierr); 953 if (sctx.nshift) { 954 if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 955 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 956 } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 957 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 958 } 959 } 960 PetscFunctionReturn(0); 961 } 962 963 #include <petscbt.h> 964 #include <../src/mat/utils/freespace.h> 965 PetscErrorCode MatICCFactorSymbolic_SeqBAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 966 { 967 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data; 968 Mat_SeqSBAIJ *b; 969 Mat B; 970 PetscErrorCode ierr; 971 PetscBool perm_identity,missing; 972 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=a->mbs,bs=A->rmap->bs,*ui; 973 const PetscInt *rip; 974 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 975 PetscInt nlnk,*lnk,*lnk_lvl=NULL,ncols,ncols_upper,*cols,*cols_lvl,*uj,**uj_ptr,**uj_lvl_ptr; 976 PetscReal fill =info->fill,levels=info->levels; 977 PetscFreeSpaceList free_space =NULL,current_space=NULL; 978 PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL; 979 PetscBT lnkbt; 980 981 PetscFunctionBegin; 982 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 983 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 984 985 if (bs > 1) { 986 if (!a->sbaijMat) { 987 ierr = MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&a->sbaijMat);CHKERRQ(ierr); 988 } 989 (fact)->ops->iccfactorsymbolic = MatICCFactorSymbolic_SeqSBAIJ; /* undue the change made in MatGetFactor_seqbaij_petsc */ 990 991 ierr = MatICCFactorSymbolic(fact,a->sbaijMat,perm,info);CHKERRQ(ierr); 992 PetscFunctionReturn(0); 993 } 994 995 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 996 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 997 998 /* special case that simply copies fill pattern */ 999 if (!levels && perm_identity) { 1000 ierr = PetscMalloc1(am+1,&ui);CHKERRQ(ierr); 1001 for (i=0; i<am; i++) ui[i] = ai[i+1] - a->diag[i]; /* ui: rowlengths - changes when !perm_identity */ 1002 B = fact; 1003 ierr = MatSeqSBAIJSetPreallocation(B,1,0,ui);CHKERRQ(ierr); 1004 1005 1006 b = (Mat_SeqSBAIJ*)B->data; 1007 uj = b->j; 1008 for (i=0; i<am; i++) { 1009 aj = a->j + a->diag[i]; 1010 for (j=0; j<ui[i]; j++) *uj++ = *aj++; 1011 b->ilen[i] = ui[i]; 1012 } 1013 ierr = PetscFree(ui);CHKERRQ(ierr); 1014 1015 B->factortype = MAT_FACTOR_NONE; 1016 1017 ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1018 ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1019 B->factortype = MAT_FACTOR_ICC; 1020 1021 B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering; 1022 PetscFunctionReturn(0); 1023 } 1024 1025 /* initialization */ 1026 ierr = PetscMalloc1(am+1,&ui);CHKERRQ(ierr); 1027 ui[0] = 0; 1028 ierr = PetscMalloc1(2*am+1,&cols_lvl);CHKERRQ(ierr); 1029 1030 /* jl: linked list for storing indices of the pivot rows 1031 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 1032 ierr = PetscMalloc4(am,&uj_ptr,am,&uj_lvl_ptr,am,&il,am,&jl);CHKERRQ(ierr); 1033 for (i=0; i<am; i++) { 1034 jl[i] = am; il[i] = 0; 1035 } 1036 1037 /* create and initialize a linked list for storing column indices of the active row k */ 1038 nlnk = am + 1; 1039 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1040 1041 /* initial FreeSpace size is fill*(ai[am]+am)/2 */ 1042 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am]/2,am/2)),&free_space);CHKERRQ(ierr); 1043 1044 current_space = free_space; 1045 1046 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am]/2,am/2)),&free_space_lvl);CHKERRQ(ierr); 1047 current_space_lvl = free_space_lvl; 1048 1049 for (k=0; k<am; k++) { /* for each active row k */ 1050 /* initialize lnk by the column indices of row rip[k] of A */ 1051 nzk = 0; 1052 ncols = ai[rip[k]+1] - ai[rip[k]]; 1053 ncols_upper = 0; 1054 cols = cols_lvl + am; 1055 for (j=0; j<ncols; j++) { 1056 i = rip[*(aj + ai[rip[k]] + j)]; 1057 if (i >= k) { /* only take upper triangular entry */ 1058 cols[ncols_upper] = i; 1059 cols_lvl[ncols_upper] = -1; /* initialize level for nonzero entries */ 1060 ncols_upper++; 1061 } 1062 } 1063 ierr = PetscIncompleteLLAdd(ncols_upper,cols,levels,cols_lvl,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1064 nzk += nlnk; 1065 1066 /* update lnk by computing fill-in for each pivot row to be merged in */ 1067 prow = jl[k]; /* 1st pivot row */ 1068 1069 while (prow < k) { 1070 nextprow = jl[prow]; 1071 1072 /* merge prow into k-th row */ 1073 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 1074 jmax = ui[prow+1]; 1075 ncols = jmax-jmin; 1076 i = jmin - ui[prow]; 1077 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 1078 for (j=0; j<ncols; j++) cols_lvl[j] = *(uj_lvl_ptr[prow] + i + j); 1079 ierr = PetscIncompleteLLAddSorted(ncols,cols,levels,cols_lvl,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1080 nzk += nlnk; 1081 1082 /* update il and jl for prow */ 1083 if (jmin < jmax) { 1084 il[prow] = jmin; 1085 1086 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 1087 } 1088 prow = nextprow; 1089 } 1090 1091 /* if free space is not available, make more free space */ 1092 if (current_space->local_remaining<nzk) { 1093 i = am - k + 1; /* num of unfactored rows */ 1094 i = PetscMin(PetscIntMultTruncate(i,nzk), PetscIntMultTruncate(i,i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 1095 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 1096 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 1097 reallocs++; 1098 } 1099 1100 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1101 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1102 1103 /* add the k-th row into il and jl */ 1104 if (nzk-1 > 0) { 1105 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 1106 jl[k] = jl[i]; jl[i] = k; 1107 il[k] = ui[k] + 1; 1108 } 1109 uj_ptr[k] = current_space->array; 1110 uj_lvl_ptr[k] = current_space_lvl->array; 1111 1112 current_space->array += nzk; 1113 current_space->local_used += nzk; 1114 current_space->local_remaining -= nzk; 1115 1116 current_space_lvl->array += nzk; 1117 current_space_lvl->local_used += nzk; 1118 current_space_lvl->local_remaining -= nzk; 1119 1120 ui[k+1] = ui[k] + nzk; 1121 } 1122 1123 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 1124 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,il,jl);CHKERRQ(ierr); 1125 ierr = PetscFree(cols_lvl);CHKERRQ(ierr); 1126 1127 /* copy free_space into uj and free free_space; set uj in new datastructure; */ 1128 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 1129 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 1130 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1131 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1132 1133 /* put together the new matrix in MATSEQSBAIJ format */ 1134 B = fact; 1135 ierr = MatSeqSBAIJSetPreallocation(B,1,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 1136 1137 b = (Mat_SeqSBAIJ*)B->data; 1138 b->singlemalloc = PETSC_FALSE; 1139 b->free_a = PETSC_TRUE; 1140 b->free_ij = PETSC_TRUE; 1141 1142 ierr = PetscMalloc1(ui[am]+1,&b->a);CHKERRQ(ierr); 1143 1144 b->j = uj; 1145 b->i = ui; 1146 b->diag = 0; 1147 b->ilen = 0; 1148 b->imax = 0; 1149 b->row = perm; 1150 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 1151 1152 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 1153 1154 b->icol = perm; 1155 1156 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 1157 ierr = PetscMalloc1(am+1,&b->solve_work);CHKERRQ(ierr); 1158 ierr = PetscLogObjectMemory((PetscObject)B,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 1159 1160 b->maxnz = b->nz = ui[am]; 1161 1162 B->info.factor_mallocs = reallocs; 1163 B->info.fill_ratio_given = fill; 1164 if (ai[am] != 0.) { 1165 /* nonzeros in lower triangular part of A (includign diagonals)= (ai[am]+am)/2 */ 1166 B->info.fill_ratio_needed = ((PetscReal)2*ui[am])/(ai[am]+am); 1167 } else { 1168 B->info.fill_ratio_needed = 0.0; 1169 } 1170 #if defined(PETSC_USE_INFO) 1171 if (ai[am] != 0) { 1172 PetscReal af = B->info.fill_ratio_needed; 1173 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);CHKERRQ(ierr); 1174 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 1175 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);CHKERRQ(ierr); 1176 } else { 1177 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 1178 } 1179 #endif 1180 if (perm_identity) { 1181 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 1182 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 1183 B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering; 1184 } else { 1185 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N; 1186 } 1187 PetscFunctionReturn(0); 1188 } 1189 1190 PetscErrorCode MatCholeskyFactorSymbolic_SeqBAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 1191 { 1192 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data; 1193 Mat_SeqSBAIJ *b; 1194 Mat B; 1195 PetscErrorCode ierr; 1196 PetscBool perm_identity,missing; 1197 PetscReal fill = info->fill; 1198 const PetscInt *rip; 1199 PetscInt i,mbs=a->mbs,bs=A->rmap->bs,*ai=a->i,*aj=a->j,reallocs=0,prow; 1200 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 1201 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 1202 PetscFreeSpaceList free_space=NULL,current_space=NULL; 1203 PetscBT lnkbt; 1204 1205 PetscFunctionBegin; 1206 if (bs > 1) { /* convert to seqsbaij */ 1207 if (!a->sbaijMat) { 1208 ierr = MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&a->sbaijMat);CHKERRQ(ierr); 1209 } 1210 (fact)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqSBAIJ; /* undue the change made in MatGetFactor_seqbaij_petsc */ 1211 1212 ierr = MatCholeskyFactorSymbolic(fact,a->sbaijMat,perm,info);CHKERRQ(ierr); 1213 PetscFunctionReturn(0); 1214 } 1215 1216 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 1217 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 1218 1219 /* check whether perm is the identity mapping */ 1220 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 1221 if (!perm_identity) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix reordering is not supported"); 1222 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 1223 1224 /* initialization */ 1225 ierr = PetscMalloc1(mbs+1,&ui);CHKERRQ(ierr); 1226 ui[0] = 0; 1227 1228 /* jl: linked list for storing indices of the pivot rows 1229 il: il[i] points to the 1st nonzero entry of U(i,k:mbs-1) */ 1230 ierr = PetscMalloc4(mbs,&ui_ptr,mbs,&il,mbs,&jl,mbs,&cols);CHKERRQ(ierr); 1231 for (i=0; i<mbs; i++) { 1232 jl[i] = mbs; il[i] = 0; 1233 } 1234 1235 /* create and initialize a linked list for storing column indices of the active row k */ 1236 nlnk = mbs + 1; 1237 ierr = PetscLLCreate(mbs,mbs,nlnk,lnk,lnkbt);CHKERRQ(ierr); 1238 1239 /* initial FreeSpace size is fill* (ai[mbs]+mbs)/2 */ 1240 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[mbs]/2,mbs/2)),&free_space);CHKERRQ(ierr); 1241 1242 current_space = free_space; 1243 1244 for (k=0; k<mbs; k++) { /* for each active row k */ 1245 /* initialize lnk by the column indices of row rip[k] of A */ 1246 nzk = 0; 1247 ncols = ai[rip[k]+1] - ai[rip[k]]; 1248 ncols_upper = 0; 1249 for (j=0; j<ncols; j++) { 1250 i = rip[*(aj + ai[rip[k]] + j)]; 1251 if (i >= k) { /* only take upper triangular entry */ 1252 cols[ncols_upper] = i; 1253 ncols_upper++; 1254 } 1255 } 1256 ierr = PetscLLAdd(ncols_upper,cols,mbs,nlnk,lnk,lnkbt);CHKERRQ(ierr); 1257 nzk += nlnk; 1258 1259 /* update lnk by computing fill-in for each pivot row to be merged in */ 1260 prow = jl[k]; /* 1st pivot row */ 1261 1262 while (prow < k) { 1263 nextprow = jl[prow]; 1264 /* merge prow into k-th row */ 1265 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:mbs-1) */ 1266 jmax = ui[prow+1]; 1267 ncols = jmax-jmin; 1268 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:mbs-1) */ 1269 ierr = PetscLLAddSorted(ncols,uj_ptr,mbs,nlnk,lnk,lnkbt);CHKERRQ(ierr); 1270 nzk += nlnk; 1271 1272 /* update il and jl for prow */ 1273 if (jmin < jmax) { 1274 il[prow] = jmin; 1275 j = *uj_ptr; 1276 jl[prow] = jl[j]; 1277 jl[j] = prow; 1278 } 1279 prow = nextprow; 1280 } 1281 1282 /* if free space is not available, make more free space */ 1283 if (current_space->local_remaining<nzk) { 1284 i = mbs - k + 1; /* num of unfactored rows */ 1285 i = PetscMin(PetscIntMultTruncate(i,nzk), PetscIntMultTruncate(i,i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 1286 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 1287 reallocs++; 1288 } 1289 1290 /* copy data into free space, then initialize lnk */ 1291 ierr = PetscLLClean(mbs,mbs,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 1292 1293 /* add the k-th row into il and jl */ 1294 if (nzk-1 > 0) { 1295 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:mbs-1) */ 1296 jl[k] = jl[i]; jl[i] = k; 1297 il[k] = ui[k] + 1; 1298 } 1299 ui_ptr[k] = current_space->array; 1300 current_space->array += nzk; 1301 current_space->local_used += nzk; 1302 current_space->local_remaining -= nzk; 1303 1304 ui[k+1] = ui[k] + nzk; 1305 } 1306 1307 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 1308 ierr = PetscFree4(ui_ptr,il,jl,cols);CHKERRQ(ierr); 1309 1310 /* copy free_space into uj and free free_space; set uj in new datastructure; */ 1311 ierr = PetscMalloc1(ui[mbs]+1,&uj);CHKERRQ(ierr); 1312 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 1313 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1314 1315 /* put together the new matrix in MATSEQSBAIJ format */ 1316 B = fact; 1317 ierr = MatSeqSBAIJSetPreallocation(B,bs,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 1318 1319 b = (Mat_SeqSBAIJ*)B->data; 1320 b->singlemalloc = PETSC_FALSE; 1321 b->free_a = PETSC_TRUE; 1322 b->free_ij = PETSC_TRUE; 1323 1324 ierr = PetscMalloc1(ui[mbs]+1,&b->a);CHKERRQ(ierr); 1325 1326 b->j = uj; 1327 b->i = ui; 1328 b->diag = 0; 1329 b->ilen = 0; 1330 b->imax = 0; 1331 b->row = perm; 1332 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 1333 1334 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 1335 b->icol = perm; 1336 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 1337 ierr = PetscMalloc1(mbs+1,&b->solve_work);CHKERRQ(ierr); 1338 ierr = PetscLogObjectMemory((PetscObject)B,(ui[mbs]-mbs)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 1339 b->maxnz = b->nz = ui[mbs]; 1340 1341 B->info.factor_mallocs = reallocs; 1342 B->info.fill_ratio_given = fill; 1343 if (ai[mbs] != 0.) { 1344 /* nonzeros in lower triangular part of A = (ai[mbs]+mbs)/2 */ 1345 B->info.fill_ratio_needed = ((PetscReal)2*ui[mbs])/(ai[mbs]+mbs); 1346 } else { 1347 B->info.fill_ratio_needed = 0.0; 1348 } 1349 #if defined(PETSC_USE_INFO) 1350 if (ai[mbs] != 0.) { 1351 PetscReal af = B->info.fill_ratio_needed; 1352 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);CHKERRQ(ierr); 1353 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 1354 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);CHKERRQ(ierr); 1355 } else { 1356 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 1357 } 1358 #endif 1359 if (perm_identity) { 1360 B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering; 1361 } else { 1362 B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N; 1363 } 1364 PetscFunctionReturn(0); 1365 } 1366 1367 PetscErrorCode MatSolve_SeqBAIJ_N_NaturalOrdering(Mat A,Vec bb,Vec xx) 1368 { 1369 Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data; 1370 PetscErrorCode ierr; 1371 const PetscInt *ai=a->i,*aj=a->j,*adiag=a->diag,*vi; 1372 PetscInt i,k,n=a->mbs; 1373 PetscInt nz,bs=A->rmap->bs,bs2=a->bs2; 1374 const MatScalar *aa=a->a,*v; 1375 PetscScalar *x,*s,*t,*ls; 1376 const PetscScalar *b; 1377 1378 PetscFunctionBegin; 1379 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1380 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1381 t = a->solve_work; 1382 1383 /* forward solve the lower triangular */ 1384 ierr = PetscArraycpy(t,b,bs);CHKERRQ(ierr); /* copy 1st block of b to t */ 1385 1386 for (i=1; i<n; i++) { 1387 v = aa + bs2*ai[i]; 1388 vi = aj + ai[i]; 1389 nz = ai[i+1] - ai[i]; 1390 s = t + bs*i; 1391 ierr = PetscArraycpy(s,b+bs*i,bs);CHKERRQ(ierr); /* copy i_th block of b to t */ 1392 for (k=0;k<nz;k++) { 1393 PetscKernel_v_gets_v_minus_A_times_w(bs,s,v,t+bs*vi[k]); 1394 v += bs2; 1395 } 1396 } 1397 1398 /* backward solve the upper triangular */ 1399 ls = a->solve_work + A->cmap->n; 1400 for (i=n-1; i>=0; i--) { 1401 v = aa + bs2*(adiag[i+1]+1); 1402 vi = aj + adiag[i+1]+1; 1403 nz = adiag[i] - adiag[i+1]-1; 1404 ierr = PetscArraycpy(ls,t+i*bs,bs);CHKERRQ(ierr); 1405 for (k=0; k<nz; k++) { 1406 PetscKernel_v_gets_v_minus_A_times_w(bs,ls,v,t+bs*vi[k]); 1407 v += bs2; 1408 } 1409 PetscKernel_w_gets_A_times_v(bs,ls,aa+bs2*adiag[i],t+i*bs); /* *inv(diagonal[i]) */ 1410 ierr = PetscArraycpy(x+i*bs,t+i*bs,bs);CHKERRQ(ierr); 1411 } 1412 1413 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1414 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1415 ierr = PetscLogFlops(2.0*(a->bs2)*(a->nz) - A->rmap->bs*A->cmap->n);CHKERRQ(ierr); 1416 PetscFunctionReturn(0); 1417 } 1418 1419 PetscErrorCode MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx) 1420 { 1421 Mat_SeqBAIJ *a =(Mat_SeqBAIJ*)A->data; 1422 IS iscol=a->col,isrow=a->row; 1423 PetscErrorCode ierr; 1424 const PetscInt *r,*c,*rout,*cout,*ai=a->i,*aj=a->j,*adiag=a->diag,*vi; 1425 PetscInt i,m,n=a->mbs; 1426 PetscInt nz,bs=A->rmap->bs,bs2=a->bs2; 1427 const MatScalar *aa=a->a,*v; 1428 PetscScalar *x,*s,*t,*ls; 1429 const PetscScalar *b; 1430 1431 PetscFunctionBegin; 1432 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1433 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1434 t = a->solve_work; 1435 1436 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1437 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1438 1439 /* forward solve the lower triangular */ 1440 ierr = PetscArraycpy(t,b+bs*r[0],bs);CHKERRQ(ierr); 1441 for (i=1; i<n; i++) { 1442 v = aa + bs2*ai[i]; 1443 vi = aj + ai[i]; 1444 nz = ai[i+1] - ai[i]; 1445 s = t + bs*i; 1446 ierr = PetscArraycpy(s,b+bs*r[i],bs);CHKERRQ(ierr); 1447 for (m=0; m<nz; m++) { 1448 PetscKernel_v_gets_v_minus_A_times_w(bs,s,v,t+bs*vi[m]); 1449 v += bs2; 1450 } 1451 } 1452 1453 /* backward solve the upper triangular */ 1454 ls = a->solve_work + A->cmap->n; 1455 for (i=n-1; i>=0; i--) { 1456 v = aa + bs2*(adiag[i+1]+1); 1457 vi = aj + adiag[i+1]+1; 1458 nz = adiag[i] - adiag[i+1] - 1; 1459 ierr = PetscArraycpy(ls,t+i*bs,bs);CHKERRQ(ierr); 1460 for (m=0; m<nz; m++) { 1461 PetscKernel_v_gets_v_minus_A_times_w(bs,ls,v,t+bs*vi[m]); 1462 v += bs2; 1463 } 1464 PetscKernel_w_gets_A_times_v(bs,ls,v,t+i*bs); /* *inv(diagonal[i]) */ 1465 ierr = PetscArraycpy(x + bs*c[i],t+i*bs,bs);CHKERRQ(ierr); 1466 } 1467 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1468 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1469 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1470 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1471 ierr = PetscLogFlops(2.0*(a->bs2)*(a->nz) - A->rmap->bs*A->cmap->n);CHKERRQ(ierr); 1472 PetscFunctionReturn(0); 1473 } 1474 1475 /* 1476 For each block in an block array saves the largest absolute value in the block into another array 1477 */ 1478 static PetscErrorCode MatBlockAbs_private(PetscInt nbs,PetscInt bs2,PetscScalar *blockarray,PetscReal *absarray) 1479 { 1480 PetscErrorCode ierr; 1481 PetscInt i,j; 1482 1483 PetscFunctionBegin; 1484 ierr = PetscArrayzero(absarray,nbs+1);CHKERRQ(ierr); 1485 for (i=0; i<nbs; i++) { 1486 for (j=0; j<bs2; j++) { 1487 if (absarray[i] < PetscAbsScalar(blockarray[i*nbs+j])) absarray[i] = PetscAbsScalar(blockarray[i*nbs+j]); 1488 } 1489 } 1490 PetscFunctionReturn(0); 1491 } 1492 1493 /* 1494 This needs to be renamed and called by the regular MatILUFactor_SeqBAIJ when drop tolerance is used 1495 */ 1496 PetscErrorCode MatILUDTFactor_SeqBAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 1497 { 1498 Mat B = *fact; 1499 Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data,*b; 1500 IS isicol; 1501 PetscErrorCode ierr; 1502 const PetscInt *r,*ic; 1503 PetscInt i,mbs=a->mbs,bs=A->rmap->bs,bs2=a->bs2,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 1504 PetscInt *bi,*bj,*bdiag; 1505 1506 PetscInt row,nzi,nzi_bl,nzi_bu,*im,dtcount,nzi_al,nzi_au; 1507 PetscInt nlnk,*lnk; 1508 PetscBT lnkbt; 1509 PetscBool row_identity,icol_identity; 1510 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,*multiplier,*vtmp; 1511 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 1512 1513 PetscReal dt=info->dt; /* shift=info->shiftamount; */ 1514 PetscInt nnz_max; 1515 PetscBool missing; 1516 PetscReal *vtmp_abs; 1517 MatScalar *v_work; 1518 PetscInt *v_pivots; 1519 PetscBool allowzeropivot,zeropivotdetected=PETSC_FALSE; 1520 1521 PetscFunctionBegin; 1522 /* ------- symbolic factorization, can be reused ---------*/ 1523 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 1524 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 1525 adiag=a->diag; 1526 1527 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1528 1529 /* bdiag is location of diagonal in factor */ 1530 ierr = PetscMalloc1(mbs+1,&bdiag);CHKERRQ(ierr); 1531 1532 /* allocate row pointers bi */ 1533 ierr = PetscMalloc1(2*mbs+2,&bi);CHKERRQ(ierr); 1534 1535 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 1536 dtcount = (PetscInt)info->dtcount; 1537 if (dtcount > mbs-1) dtcount = mbs-1; 1538 nnz_max = ai[mbs]+2*mbs*dtcount +2; 1539 /* printf("MatILUDTFactor_SeqBAIJ, bs %d, ai[mbs] %d, nnz_max %d, dtcount %d\n",bs,ai[mbs],nnz_max,dtcount); */ 1540 ierr = PetscMalloc1(nnz_max,&bj);CHKERRQ(ierr); 1541 nnz_max = nnz_max*bs2; 1542 ierr = PetscMalloc1(nnz_max,&ba);CHKERRQ(ierr); 1543 1544 /* put together the new matrix */ 1545 ierr = MatSeqBAIJSetPreallocation(B,bs,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 1546 ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);CHKERRQ(ierr); 1547 1548 b = (Mat_SeqBAIJ*)(B)->data; 1549 b->free_a = PETSC_TRUE; 1550 b->free_ij = PETSC_TRUE; 1551 b->singlemalloc = PETSC_FALSE; 1552 1553 b->a = ba; 1554 b->j = bj; 1555 b->i = bi; 1556 b->diag = bdiag; 1557 b->ilen = 0; 1558 b->imax = 0; 1559 b->row = isrow; 1560 b->col = iscol; 1561 1562 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1563 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1564 1565 b->icol = isicol; 1566 ierr = PetscMalloc1(bs*(mbs+1),&b->solve_work);CHKERRQ(ierr); 1567 ierr = PetscLogObjectMemory((PetscObject)B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 1568 b->maxnz = nnz_max/bs2; 1569 1570 (B)->factortype = MAT_FACTOR_ILUDT; 1571 (B)->info.factor_mallocs = 0; 1572 (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)(ai[mbs]*bs2)); 1573 /* ------- end of symbolic factorization ---------*/ 1574 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1575 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1576 1577 /* linked list for storing column indices of the active row */ 1578 nlnk = mbs + 1; 1579 ierr = PetscLLCreate(mbs,mbs,nlnk,lnk,lnkbt);CHKERRQ(ierr); 1580 1581 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 1582 ierr = PetscMalloc2(mbs,&im,mbs,&jtmp);CHKERRQ(ierr); 1583 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 1584 ierr = PetscMalloc2(mbs*bs2,&rtmp,mbs*bs2,&vtmp);CHKERRQ(ierr); 1585 ierr = PetscMalloc1(mbs+1,&vtmp_abs);CHKERRQ(ierr); 1586 ierr = PetscMalloc3(bs,&v_work,bs2,&multiplier,bs,&v_pivots);CHKERRQ(ierr); 1587 1588 allowzeropivot = PetscNot(A->erroriffailure); 1589 bi[0] = 0; 1590 bdiag[0] = (nnz_max/bs2)-1; /* location of diagonal in factor B */ 1591 bi[2*mbs+1] = bdiag[0]+1; /* endof bj and ba array */ 1592 for (i=0; i<mbs; i++) { 1593 /* copy initial fill into linked list */ 1594 nzi = ai[r[i]+1] - ai[r[i]]; 1595 if (!nzi) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1596 nzi_al = adiag[r[i]] - ai[r[i]]; 1597 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 1598 1599 /* load in initial unfactored row */ 1600 ajtmp = aj + ai[r[i]]; 1601 ierr = PetscLLAddPerm(nzi,ajtmp,ic,mbs,nlnk,lnk,lnkbt);CHKERRQ(ierr); 1602 ierr = PetscArrayzero(rtmp,mbs*bs2);CHKERRQ(ierr); 1603 aatmp = a->a + bs2*ai[r[i]]; 1604 for (j=0; j<nzi; j++) { 1605 ierr = PetscArraycpy(rtmp+bs2*ic[ajtmp[j]],aatmp+bs2*j,bs2);CHKERRQ(ierr); 1606 } 1607 1608 /* add pivot rows into linked list */ 1609 row = lnk[mbs]; 1610 while (row < i) { 1611 nzi_bl = bi[row+1] - bi[row] + 1; 1612 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 1613 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 1614 nzi += nlnk; 1615 row = lnk[row]; 1616 } 1617 1618 /* copy data from lnk into jtmp, then initialize lnk */ 1619 ierr = PetscLLClean(mbs,mbs,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 1620 1621 /* numerical factorization */ 1622 bjtmp = jtmp; 1623 row = *bjtmp++; /* 1st pivot row */ 1624 1625 while (row < i) { 1626 pc = rtmp + bs2*row; 1627 pv = ba + bs2*bdiag[row]; /* inv(diag) of the pivot row */ 1628 PetscKernel_A_gets_A_times_B(bs,pc,pv,multiplier); /* pc= multiplier = pc*inv(diag[row]) */ 1629 ierr = MatBlockAbs_private(1,bs2,pc,vtmp_abs);CHKERRQ(ierr); 1630 if (vtmp_abs[0] > dt) { /* apply tolerance dropping rule */ 1631 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 1632 pv = ba + bs2*(bdiag[row+1] + 1); 1633 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 1634 for (j=0; j<nz; j++) { 1635 PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); 1636 } 1637 /* ierr = PetscLogFlops(bslog*(nz+1.0)-bs);CHKERRQ(ierr); */ 1638 } 1639 row = *bjtmp++; 1640 } 1641 1642 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 1643 nzi_bl = 0; j = 0; 1644 while (jtmp[j] < i) { /* L-part. Note: jtmp is sorted */ 1645 ierr = PetscArraycpy(vtmp+bs2*j,rtmp+bs2*jtmp[j],bs2);CHKERRQ(ierr); 1646 nzi_bl++; j++; 1647 } 1648 nzi_bu = nzi - nzi_bl -1; 1649 1650 while (j < nzi) { /* U-part */ 1651 ierr = PetscArraycpy(vtmp+bs2*j,rtmp+bs2*jtmp[j],bs2);CHKERRQ(ierr); 1652 j++; 1653 } 1654 1655 ierr = MatBlockAbs_private(nzi,bs2,vtmp,vtmp_abs);CHKERRQ(ierr); 1656 1657 bjtmp = bj + bi[i]; 1658 batmp = ba + bs2*bi[i]; 1659 /* apply level dropping rule to L part */ 1660 ncut = nzi_al + dtcount; 1661 if (ncut < nzi_bl) { 1662 ierr = PetscSortSplitReal(ncut,nzi_bl,vtmp_abs,jtmp);CHKERRQ(ierr); 1663 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 1664 } else { 1665 ncut = nzi_bl; 1666 } 1667 for (j=0; j<ncut; j++) { 1668 bjtmp[j] = jtmp[j]; 1669 ierr = PetscArraycpy(batmp+bs2*j,rtmp+bs2*bjtmp[j],bs2);CHKERRQ(ierr); 1670 } 1671 bi[i+1] = bi[i] + ncut; 1672 nzi = ncut + 1; 1673 1674 /* apply level dropping rule to U part */ 1675 ncut = nzi_au + dtcount; 1676 if (ncut < nzi_bu) { 1677 ierr = PetscSortSplitReal(ncut,nzi_bu,vtmp_abs+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 1678 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 1679 } else { 1680 ncut = nzi_bu; 1681 } 1682 nzi += ncut; 1683 1684 /* mark bdiagonal */ 1685 bdiag[i+1] = bdiag[i] - (ncut + 1); 1686 bi[2*mbs - i] = bi[2*mbs - i +1] - (ncut + 1); 1687 1688 bjtmp = bj + bdiag[i]; 1689 batmp = ba + bs2*bdiag[i]; 1690 ierr = PetscArraycpy(batmp,rtmp+bs2*i,bs2);CHKERRQ(ierr); 1691 *bjtmp = i; 1692 1693 bjtmp = bj + bdiag[i+1]+1; 1694 batmp = ba + (bdiag[i+1]+1)*bs2; 1695 1696 for (k=0; k<ncut; k++) { 1697 bjtmp[k] = jtmp[nzi_bl+1+k]; 1698 ierr = PetscArraycpy(batmp+bs2*k,rtmp+bs2*bjtmp[k],bs2);CHKERRQ(ierr); 1699 } 1700 1701 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 1702 1703 /* invert diagonal block for simplier triangular solves - add shift??? */ 1704 batmp = ba + bs2*bdiag[i]; 1705 1706 ierr = PetscKernel_A_gets_inverse_A(bs,batmp,v_pivots,v_work,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr); 1707 if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 1708 } /* for (i=0; i<mbs; i++) */ 1709 ierr = PetscFree3(v_work,multiplier,v_pivots);CHKERRQ(ierr); 1710 1711 /* printf("end of L %d, beginning of U %d\n",bi[mbs],bdiag[mbs]); */ 1712 if (bi[mbs] >= bdiag[mbs]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"end of L array %d cannot >= the beginning of U array %d",bi[mbs],bdiag[mbs]); 1713 1714 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1715 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1716 1717 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1718 1719 ierr = PetscFree2(im,jtmp);CHKERRQ(ierr); 1720 ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr); 1721 1722 ierr = PetscLogFlops(bs2*B->cmap->n);CHKERRQ(ierr); 1723 b->maxnz = b->nz = bi[mbs] + bdiag[0] - bdiag[mbs]; 1724 1725 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1726 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 1727 if (row_identity && icol_identity) { 1728 B->ops->solve = MatSolve_SeqBAIJ_N_NaturalOrdering; 1729 } else { 1730 B->ops->solve = MatSolve_SeqBAIJ_N; 1731 } 1732 1733 B->ops->solveadd = 0; 1734 B->ops->solvetranspose = 0; 1735 B->ops->solvetransposeadd = 0; 1736 B->ops->matsolve = 0; 1737 B->assembled = PETSC_TRUE; 1738 B->preallocated = PETSC_TRUE; 1739 PetscFunctionReturn(0); 1740 } 1741