Actual source code: mkl_pardiso.c

  1: #include <../src/mat/impls/aij/seq/aij.h>
  2: #include <../src/mat/impls/sbaij/seq/sbaij.h>
  3: #include <../src/mat/impls/dense/seq/dense.h>

  5: #if defined(PETSC_HAVE_MKL_INTEL_ILP64)
  6:   #define MKL_ILP64
  7: #endif
  8: #include <mkl_pardiso.h>

 10: PETSC_EXTERN void PetscSetMKL_PARDISOThreads(int);

 12: /*
 13:  *  Possible mkl_pardiso phases that controls the execution of the solver.
 14:  *  For more information check mkl_pardiso manual.
 15:  */
 16: #define JOB_ANALYSIS                                                    11
 17: #define JOB_ANALYSIS_NUMERICAL_FACTORIZATION                            12
 18: #define JOB_ANALYSIS_NUMERICAL_FACTORIZATION_SOLVE_ITERATIVE_REFINEMENT 13
 19: #define JOB_NUMERICAL_FACTORIZATION                                     22
 20: #define JOB_NUMERICAL_FACTORIZATION_SOLVE_ITERATIVE_REFINEMENT          23
 21: #define JOB_SOLVE_ITERATIVE_REFINEMENT                                  33
 22: #define JOB_SOLVE_FORWARD_SUBSTITUTION                                  331
 23: #define JOB_SOLVE_DIAGONAL_SUBSTITUTION                                 332
 24: #define JOB_SOLVE_BACKWARD_SUBSTITUTION                                 333
 25: #define JOB_RELEASE_OF_LU_MEMORY                                        0
 26: #define JOB_RELEASE_OF_ALL_MEMORY                                       -1

 28: #define IPARM_SIZE 64

 30: #if defined(PETSC_USE_64BIT_INDICES)
 31:   #if defined(PETSC_HAVE_MKL_INTEL_ILP64)
 32:     #define INT_TYPE         long long int
 33:     #define MKL_PARDISO      pardiso
 34:     #define MKL_PARDISO_INIT pardisoinit
 35:   #else
 36:     /* this is the case where the MKL BLAS/LAPACK are 32-bit integers but the 64-bit integer version of
 37:      of Pardiso code is used; hence the need for the 64 below*/
 38:     #define INT_TYPE         long long int
 39:     #define MKL_PARDISO      pardiso_64
 40:     #define MKL_PARDISO_INIT pardiso_64init
 41: void pardiso_64init(void *pt, INT_TYPE *mtype, INT_TYPE iparm[])
 42: {
 43:   int iparm_copy[IPARM_SIZE], mtype_copy, i;

 45:   mtype_copy = *mtype;
 46:   pardisoinit(pt, &mtype_copy, iparm_copy);
 47:   for (i = 0; i < IPARM_SIZE; i++) iparm[i] = iparm_copy[i];
 48: }
 49:   #endif
 50: #else
 51:   #define INT_TYPE         int
 52:   #define MKL_PARDISO      pardiso
 53:   #define MKL_PARDISO_INIT pardisoinit
 54: #endif

 56: /*
 57:  *  Internal data structure.
 58:  *  For more information check mkl_pardiso manual.
 59:  */
 60: typedef struct {
 61:   /* Configuration vector*/
 62:   INT_TYPE iparm[IPARM_SIZE];

 64:   /*
 65:    * Internal mkl_pardiso memory location.
 66:    * After the first call to mkl_pardiso do not modify pt, as that could cause a serious memory leak.
 67:    */
 68:   void *pt[IPARM_SIZE];

 70:   /* Basic mkl_pardiso info*/
 71:   INT_TYPE phase, maxfct, mnum, mtype, n, nrhs, msglvl, err;

 73:   /* Matrix structure*/
 74:   void     *a;
 75:   INT_TYPE *ia, *ja;

 77:   /* Number of non-zero elements*/
 78:   INT_TYPE nz;

 80:   /* Row permutaton vector*/
 81:   INT_TYPE *perm;

 83:   /* Define if matrix preserves sparse structure.*/
 84:   MatStructure matstruc;

 86:   PetscBool needsym;
 87:   PetscBool freeaij;

 89:   /* Schur complement */
 90:   PetscScalar *schur;
 91:   PetscInt     schur_size;
 92:   PetscInt    *schur_idxs;
 93:   PetscScalar *schur_work;
 94:   PetscBLASInt schur_work_size;
 95:   PetscBool    solve_interior;

 97:   /* True if mkl_pardiso function have been used.*/
 98:   PetscBool CleanUp;

100:   /* Conversion to a format suitable for MKL */
101:   PetscErrorCode (*Convert)(Mat, PetscBool, MatReuse, PetscBool *, INT_TYPE *, INT_TYPE **, INT_TYPE **, PetscScalar **);
102: } Mat_MKL_PARDISO;

104: PetscErrorCode MatMKLPardiso_Convert_seqsbaij(Mat A, PetscBool sym, MatReuse reuse, PetscBool *free, INT_TYPE *nnz, INT_TYPE **r, INT_TYPE **c, PetscScalar **v)
105: {
106:   Mat_SeqSBAIJ *aa = (Mat_SeqSBAIJ *)A->data;
107:   PetscInt      bs = A->rmap->bs, i;

109:   PetscFunctionBegin;
110:   PetscCheck(sym, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "This should not happen");
111:   *v = aa->a;
112:   if (bs == 1) { /* already in the correct format */
113:     /* though PetscInt and INT_TYPE are of the same size since they are defined differently the Intel compiler requires a cast */
114:     *r    = (INT_TYPE *)aa->i;
115:     *c    = (INT_TYPE *)aa->j;
116:     *nnz  = (INT_TYPE)aa->nz;
117:     *free = PETSC_FALSE;
118:   } else if (reuse == MAT_INITIAL_MATRIX) {
119:     PetscInt  m = A->rmap->n, nz = aa->nz;
120:     PetscInt *row, *col;
121:     PetscCall(PetscMalloc2(m + 1, &row, nz, &col));
122:     for (i = 0; i < m + 1; i++) row[i] = aa->i[i] + 1;
123:     for (i = 0; i < nz; i++) col[i] = aa->j[i] + 1;
124:     *r    = (INT_TYPE *)row;
125:     *c    = (INT_TYPE *)col;
126:     *nnz  = (INT_TYPE)nz;
127:     *free = PETSC_TRUE;
128:   }
129:   PetscFunctionReturn(PETSC_SUCCESS);
130: }

132: PetscErrorCode MatMKLPardiso_Convert_seqbaij(Mat A, PetscBool sym, MatReuse reuse, PetscBool *free, INT_TYPE *nnz, INT_TYPE **r, INT_TYPE **c, PetscScalar **v)
133: {
134:   Mat_SeqBAIJ *aa = (Mat_SeqBAIJ *)A->data;
135:   PetscInt     bs = A->rmap->bs, i;

137:   PetscFunctionBegin;
138:   if (!sym) {
139:     *v = aa->a;
140:     if (bs == 1) { /* already in the correct format */
141:       /* though PetscInt and INT_TYPE are of the same size since they are defined differently the Intel compiler requires a cast */
142:       *r    = (INT_TYPE *)aa->i;
143:       *c    = (INT_TYPE *)aa->j;
144:       *nnz  = (INT_TYPE)aa->nz;
145:       *free = PETSC_FALSE;
146:       PetscFunctionReturn(PETSC_SUCCESS);
147:     } else if (reuse == MAT_INITIAL_MATRIX) {
148:       PetscInt  m = A->rmap->n, nz = aa->nz;
149:       PetscInt *row, *col;
150:       PetscCall(PetscMalloc2(m + 1, &row, nz, &col));
151:       for (i = 0; i < m + 1; i++) row[i] = aa->i[i] + 1;
152:       for (i = 0; i < nz; i++) col[i] = aa->j[i] + 1;
153:       *r   = (INT_TYPE *)row;
154:       *c   = (INT_TYPE *)col;
155:       *nnz = (INT_TYPE)nz;
156:     }
157:     *free = PETSC_TRUE;
158:   } else {
159:     SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "This should not happen");
160:   }
161:   PetscFunctionReturn(PETSC_SUCCESS);
162: }

164: PetscErrorCode MatMKLPardiso_Convert_seqaij(Mat A, PetscBool sym, MatReuse reuse, PetscBool *free, INT_TYPE *nnz, INT_TYPE **r, INT_TYPE **c, PetscScalar **v)
165: {
166:   Mat_SeqAIJ  *aa = (Mat_SeqAIJ *)A->data;
167:   PetscScalar *aav;

169:   PetscFunctionBegin;
170:   PetscCall(MatSeqAIJGetArrayRead(A, (const PetscScalar **)&aav));
171:   if (!sym) { /* already in the correct format */
172:     *v    = aav;
173:     *r    = (INT_TYPE *)aa->i;
174:     *c    = (INT_TYPE *)aa->j;
175:     *nnz  = (INT_TYPE)aa->nz;
176:     *free = PETSC_FALSE;
177:   } else if (reuse == MAT_INITIAL_MATRIX) { /* need to get the triangular part */
178:     PetscScalar *vals, *vv;
179:     PetscInt    *row, *col, *jj;
180:     PetscInt     m = A->rmap->n, nz, i;

182:     nz = 0;
183:     for (i = 0; i < m; i++) nz += aa->i[i + 1] - aa->diag[i];
184:     PetscCall(PetscMalloc2(m + 1, &row, nz, &col));
185:     PetscCall(PetscMalloc1(nz, &vals));
186:     jj = col;
187:     vv = vals;

189:     row[0] = 0;
190:     for (i = 0; i < m; i++) {
191:       PetscInt    *aj = aa->j + aa->diag[i];
192:       PetscScalar *av = aav + aa->diag[i];
193:       PetscInt     rl = aa->i[i + 1] - aa->diag[i], j;

195:       for (j = 0; j < rl; j++) {
196:         *jj = *aj;
197:         jj++;
198:         aj++;
199:         *vv = *av;
200:         vv++;
201:         av++;
202:       }
203:       row[i + 1] = row[i] + rl;
204:     }
205:     *v    = vals;
206:     *r    = (INT_TYPE *)row;
207:     *c    = (INT_TYPE *)col;
208:     *nnz  = (INT_TYPE)nz;
209:     *free = PETSC_TRUE;
210:   } else {
211:     PetscScalar *vv;
212:     PetscInt     m = A->rmap->n, i;

214:     vv = *v;
215:     for (i = 0; i < m; i++) {
216:       PetscScalar *av = aav + aa->diag[i];
217:       PetscInt     rl = aa->i[i + 1] - aa->diag[i], j;
218:       for (j = 0; j < rl; j++) {
219:         *vv = *av;
220:         vv++;
221:         av++;
222:       }
223:     }
224:     *free = PETSC_TRUE;
225:   }
226:   PetscCall(MatSeqAIJRestoreArrayRead(A, (const PetscScalar **)&aav));
227:   PetscFunctionReturn(PETSC_SUCCESS);
228: }

230: static PetscErrorCode MatMKLPardisoSolveSchur_Private(Mat F, PetscScalar *B, PetscScalar *X)
231: {
232:   Mat_MKL_PARDISO     *mpardiso = (Mat_MKL_PARDISO *)F->data;
233:   Mat                  S, Xmat, Bmat;
234:   MatFactorSchurStatus schurstatus;

236:   PetscFunctionBegin;
237:   PetscCall(MatFactorGetSchurComplement(F, &S, &schurstatus));
238:   PetscCheck(X != B || schurstatus != MAT_FACTOR_SCHUR_INVERTED, PETSC_COMM_SELF, PETSC_ERR_SUP, "X and B cannot point to the same address");
239:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, mpardiso->schur_size, mpardiso->nrhs, B, &Bmat));
240:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, mpardiso->schur_size, mpardiso->nrhs, X, &Xmat));
241:   PetscCall(MatSetType(Bmat, ((PetscObject)S)->type_name));
242:   PetscCall(MatSetType(Xmat, ((PetscObject)S)->type_name));
243: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
244:   PetscCall(MatBindToCPU(Xmat, S->boundtocpu));
245:   PetscCall(MatBindToCPU(Bmat, S->boundtocpu));
246: #endif

248: #if defined(PETSC_USE_COMPLEX)
249:   PetscCheck(mpardiso->iparm[12 - 1] != 1, PetscObjectComm((PetscObject)F), PETSC_ERR_SUP, "Hermitian solve not implemented yet");
250: #endif

252:   switch (schurstatus) {
253:   case MAT_FACTOR_SCHUR_FACTORED:
254:     if (!mpardiso->iparm[12 - 1]) {
255:       PetscCall(MatMatSolve(S, Bmat, Xmat));
256:     } else { /* transpose solve */
257:       PetscCall(MatMatSolveTranspose(S, Bmat, Xmat));
258:     }
259:     break;
260:   case MAT_FACTOR_SCHUR_INVERTED:
261:     PetscCall(MatProductCreateWithMat(S, Bmat, NULL, Xmat));
262:     if (!mpardiso->iparm[12 - 1]) {
263:       PetscCall(MatProductSetType(Xmat, MATPRODUCT_AB));
264:     } else { /* transpose solve */
265:       PetscCall(MatProductSetType(Xmat, MATPRODUCT_AtB));
266:     }
267:     PetscCall(MatProductSetFromOptions(Xmat));
268:     PetscCall(MatProductSymbolic(Xmat));
269:     PetscCall(MatProductNumeric(Xmat));
270:     PetscCall(MatProductClear(Xmat));
271:     break;
272:   default:
273:     SETERRQ(PetscObjectComm((PetscObject)F), PETSC_ERR_SUP, "Unhandled MatFactorSchurStatus %" PetscInt_FMT, F->schur_status);
274:     break;
275:   }
276:   PetscCall(MatFactorRestoreSchurComplement(F, &S, schurstatus));
277:   PetscCall(MatDestroy(&Bmat));
278:   PetscCall(MatDestroy(&Xmat));
279:   PetscFunctionReturn(PETSC_SUCCESS);
280: }

282: PetscErrorCode MatFactorSetSchurIS_MKL_PARDISO(Mat F, IS is)
283: {
284:   Mat_MKL_PARDISO   *mpardiso = (Mat_MKL_PARDISO *)F->data;
285:   const PetscScalar *arr;
286:   const PetscInt    *idxs;
287:   PetscInt           size, i;
288:   PetscMPIInt        csize;
289:   PetscBool          sorted;

291:   PetscFunctionBegin;
292:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)F), &csize));
293:   PetscCheck(csize <= 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "MKL_PARDISO parallel Schur complements not yet supported from PETSc");
294:   PetscCall(ISSorted(is, &sorted));
295:   PetscCheck(sorted, PETSC_COMM_SELF, PETSC_ERR_SUP, "IS for MKL_PARDISO Schur complements needs to be sorted");
296:   PetscCall(ISGetLocalSize(is, &size));
297:   PetscCall(PetscFree(mpardiso->schur_work));
298:   PetscCall(PetscBLASIntCast(PetscMax(mpardiso->n, 2 * size), &mpardiso->schur_work_size));
299:   PetscCall(PetscMalloc1(mpardiso->schur_work_size, &mpardiso->schur_work));
300:   PetscCall(MatDestroy(&F->schur));
301:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, size, size, NULL, &F->schur));
302:   PetscCall(MatDenseGetArrayRead(F->schur, &arr));
303:   mpardiso->schur      = (PetscScalar *)arr;
304:   mpardiso->schur_size = size;
305:   PetscCall(MatDenseRestoreArrayRead(F->schur, &arr));
306:   if (mpardiso->mtype == 2) PetscCall(MatSetOption(F->schur, MAT_SPD, PETSC_TRUE));

308:   PetscCall(PetscFree(mpardiso->schur_idxs));
309:   PetscCall(PetscMalloc1(size, &mpardiso->schur_idxs));
310:   PetscCall(PetscArrayzero(mpardiso->perm, mpardiso->n));
311:   PetscCall(ISGetIndices(is, &idxs));
312:   PetscCall(PetscArraycpy(mpardiso->schur_idxs, idxs, size));
313:   for (i = 0; i < size; i++) mpardiso->perm[idxs[i]] = 1;
314:   PetscCall(ISRestoreIndices(is, &idxs));
315:   if (size) { /* turn on Schur switch if the set of indices is not empty */
316:     mpardiso->iparm[36 - 1] = 2;
317:   }
318:   PetscFunctionReturn(PETSC_SUCCESS);
319: }

321: PetscErrorCode MatDestroy_MKL_PARDISO(Mat A)
322: {
323:   Mat_MKL_PARDISO *mat_mkl_pardiso = (Mat_MKL_PARDISO *)A->data;

325:   PetscFunctionBegin;
326:   if (mat_mkl_pardiso->CleanUp) {
327:     mat_mkl_pardiso->phase = JOB_RELEASE_OF_ALL_MEMORY;

329:     MKL_PARDISO(mat_mkl_pardiso->pt, &mat_mkl_pardiso->maxfct, &mat_mkl_pardiso->mnum, &mat_mkl_pardiso->mtype, &mat_mkl_pardiso->phase, &mat_mkl_pardiso->n, NULL, NULL, NULL, NULL, &mat_mkl_pardiso->nrhs, mat_mkl_pardiso->iparm, &mat_mkl_pardiso->msglvl, NULL, NULL,
330:                 &mat_mkl_pardiso->err);
331:   }
332:   PetscCall(PetscFree(mat_mkl_pardiso->perm));
333:   PetscCall(PetscFree(mat_mkl_pardiso->schur_work));
334:   PetscCall(PetscFree(mat_mkl_pardiso->schur_idxs));
335:   if (mat_mkl_pardiso->freeaij) {
336:     PetscCall(PetscFree2(mat_mkl_pardiso->ia, mat_mkl_pardiso->ja));
337:     if (mat_mkl_pardiso->iparm[34] == 1) PetscCall(PetscFree(mat_mkl_pardiso->a));
338:   }
339:   PetscCall(PetscFree(A->data));

341:   /* clear composed functions */
342:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorGetSolverType_C", NULL));
343:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorSetSchurIS_C", NULL));
344:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMkl_PardisoSetCntl_C", NULL));
345:   PetscFunctionReturn(PETSC_SUCCESS);
346: }

348: static PetscErrorCode MatMKLPardisoScatterSchur_Private(Mat_MKL_PARDISO *mpardiso, PetscScalar *whole, PetscScalar *schur, PetscBool reduce)
349: {
350:   PetscFunctionBegin;
351:   if (reduce) { /* data given for the whole matrix */
352:     PetscInt i, m = 0, p = 0;
353:     for (i = 0; i < mpardiso->nrhs; i++) {
354:       PetscInt j;
355:       for (j = 0; j < mpardiso->schur_size; j++) schur[p + j] = whole[m + mpardiso->schur_idxs[j]];
356:       m += mpardiso->n;
357:       p += mpardiso->schur_size;
358:     }
359:   } else { /* from Schur to whole */
360:     PetscInt i, m = 0, p = 0;
361:     for (i = 0; i < mpardiso->nrhs; i++) {
362:       PetscInt j;
363:       for (j = 0; j < mpardiso->schur_size; j++) whole[m + mpardiso->schur_idxs[j]] = schur[p + j];
364:       m += mpardiso->n;
365:       p += mpardiso->schur_size;
366:     }
367:   }
368:   PetscFunctionReturn(PETSC_SUCCESS);
369: }

371: PetscErrorCode MatSolve_MKL_PARDISO(Mat A, Vec b, Vec x)
372: {
373:   Mat_MKL_PARDISO   *mat_mkl_pardiso = (Mat_MKL_PARDISO *)A->data;
374:   PetscScalar       *xarray;
375:   const PetscScalar *barray;

377:   PetscFunctionBegin;
378:   mat_mkl_pardiso->nrhs = 1;
379:   PetscCall(VecGetArrayWrite(x, &xarray));
380:   PetscCall(VecGetArrayRead(b, &barray));

382:   if (!mat_mkl_pardiso->schur) mat_mkl_pardiso->phase = JOB_SOLVE_ITERATIVE_REFINEMENT;
383:   else mat_mkl_pardiso->phase = JOB_SOLVE_FORWARD_SUBSTITUTION;

385:   if (barray == xarray) { /* if the two vectors share the same memory */
386:     PetscScalar *work;
387:     if (!mat_mkl_pardiso->schur_work) {
388:       PetscCall(PetscMalloc1(mat_mkl_pardiso->n, &work));
389:     } else {
390:       work = mat_mkl_pardiso->schur_work;
391:     }
392:     mat_mkl_pardiso->iparm[6 - 1] = 1;
393:     MKL_PARDISO(mat_mkl_pardiso->pt, &mat_mkl_pardiso->maxfct, &mat_mkl_pardiso->mnum, &mat_mkl_pardiso->mtype, &mat_mkl_pardiso->phase, &mat_mkl_pardiso->n, mat_mkl_pardiso->a, mat_mkl_pardiso->ia, mat_mkl_pardiso->ja, NULL, &mat_mkl_pardiso->nrhs,
394:                 mat_mkl_pardiso->iparm, &mat_mkl_pardiso->msglvl, (void *)xarray, (void *)work, &mat_mkl_pardiso->err);
395:     if (!mat_mkl_pardiso->schur_work) PetscCall(PetscFree(work));
396:   } else {
397:     mat_mkl_pardiso->iparm[6 - 1] = 0;
398:     MKL_PARDISO(mat_mkl_pardiso->pt, &mat_mkl_pardiso->maxfct, &mat_mkl_pardiso->mnum, &mat_mkl_pardiso->mtype, &mat_mkl_pardiso->phase, &mat_mkl_pardiso->n, mat_mkl_pardiso->a, mat_mkl_pardiso->ia, mat_mkl_pardiso->ja, mat_mkl_pardiso->perm,
399:                 &mat_mkl_pardiso->nrhs, mat_mkl_pardiso->iparm, &mat_mkl_pardiso->msglvl, (void *)barray, (void *)xarray, &mat_mkl_pardiso->err);
400:   }
401:   PetscCall(VecRestoreArrayRead(b, &barray));

403:   PetscCheck(mat_mkl_pardiso->err >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error reported by MKL_PARDISO: err=%d. Please check manual", mat_mkl_pardiso->err);

405:   if (mat_mkl_pardiso->schur) { /* solve Schur complement and expand solution */
406:     if (!mat_mkl_pardiso->solve_interior) {
407:       PetscInt shift = mat_mkl_pardiso->schur_size;

409:       PetscCall(MatFactorFactorizeSchurComplement(A));
410:       /* if inverted, uses BLAS *MM subroutines, otherwise LAPACK *TRS */
411:       if (A->schur_status != MAT_FACTOR_SCHUR_INVERTED) shift = 0;

413:       /* solve Schur complement */
414:       PetscCall(MatMKLPardisoScatterSchur_Private(mat_mkl_pardiso, xarray, mat_mkl_pardiso->schur_work, PETSC_TRUE));
415:       PetscCall(MatMKLPardisoSolveSchur_Private(A, mat_mkl_pardiso->schur_work, mat_mkl_pardiso->schur_work + shift));
416:       PetscCall(MatMKLPardisoScatterSchur_Private(mat_mkl_pardiso, xarray, mat_mkl_pardiso->schur_work + shift, PETSC_FALSE));
417:     } else { /* if we are solving for the interior problem, any value in barray[schur] forward-substituted to xarray[schur] will be neglected */
418:       PetscInt i;
419:       for (i = 0; i < mat_mkl_pardiso->schur_size; i++) xarray[mat_mkl_pardiso->schur_idxs[i]] = 0.;
420:     }

422:     /* expansion phase */
423:     mat_mkl_pardiso->iparm[6 - 1] = 1;
424:     mat_mkl_pardiso->phase        = JOB_SOLVE_BACKWARD_SUBSTITUTION;
425:     MKL_PARDISO(mat_mkl_pardiso->pt, &mat_mkl_pardiso->maxfct, &mat_mkl_pardiso->mnum, &mat_mkl_pardiso->mtype, &mat_mkl_pardiso->phase, &mat_mkl_pardiso->n, mat_mkl_pardiso->a, mat_mkl_pardiso->ia, mat_mkl_pardiso->ja, mat_mkl_pardiso->perm,
426:                 &mat_mkl_pardiso->nrhs, mat_mkl_pardiso->iparm, &mat_mkl_pardiso->msglvl, (void *)xarray, (void *)mat_mkl_pardiso->schur_work, /* according to the specs, the solution vector is always used */
427:                 &mat_mkl_pardiso->err);

429:     PetscCheck(mat_mkl_pardiso->err >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error reported by MKL_PARDISO: err=%d. Please check manual", mat_mkl_pardiso->err);
430:     mat_mkl_pardiso->iparm[6 - 1] = 0;
431:   }
432:   PetscCall(VecRestoreArrayWrite(x, &xarray));
433:   mat_mkl_pardiso->CleanUp = PETSC_TRUE;
434:   PetscFunctionReturn(PETSC_SUCCESS);
435: }

437: PetscErrorCode MatSolveTranspose_MKL_PARDISO(Mat A, Vec b, Vec x)
438: {
439:   Mat_MKL_PARDISO *mat_mkl_pardiso = (Mat_MKL_PARDISO *)A->data;
440:   PetscInt         oiparm12;

442:   PetscFunctionBegin;
443:   oiparm12                       = mat_mkl_pardiso->iparm[12 - 1];
444:   mat_mkl_pardiso->iparm[12 - 1] = 2;
445:   PetscCall(MatSolve_MKL_PARDISO(A, b, x));
446:   mat_mkl_pardiso->iparm[12 - 1] = oiparm12;
447:   PetscFunctionReturn(PETSC_SUCCESS);
448: }

450: PetscErrorCode MatMatSolve_MKL_PARDISO(Mat A, Mat B, Mat X)
451: {
452:   Mat_MKL_PARDISO   *mat_mkl_pardiso = (Mat_MKL_PARDISO *)(A)->data;
453:   const PetscScalar *barray;
454:   PetscScalar       *xarray;
455:   PetscBool          flg;

457:   PetscFunctionBegin;
458:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)B, MATSEQDENSE, &flg));
459:   PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Matrix B must be MATSEQDENSE matrix");
460:   if (X != B) {
461:     PetscCall(PetscObjectBaseTypeCompare((PetscObject)X, MATSEQDENSE, &flg));
462:     PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Matrix X must be MATSEQDENSE matrix");
463:   }

465:   PetscCall(MatGetSize(B, NULL, (PetscInt *)&mat_mkl_pardiso->nrhs));

467:   if (mat_mkl_pardiso->nrhs > 0) {
468:     PetscCall(MatDenseGetArrayRead(B, &barray));
469:     PetscCall(MatDenseGetArrayWrite(X, &xarray));

471:     PetscCheck(barray != xarray, PETSC_COMM_SELF, PETSC_ERR_SUP, "B and X cannot share the same memory location");
472:     if (!mat_mkl_pardiso->schur) mat_mkl_pardiso->phase = JOB_SOLVE_ITERATIVE_REFINEMENT;
473:     else mat_mkl_pardiso->phase = JOB_SOLVE_FORWARD_SUBSTITUTION;

475:     MKL_PARDISO(mat_mkl_pardiso->pt, &mat_mkl_pardiso->maxfct, &mat_mkl_pardiso->mnum, &mat_mkl_pardiso->mtype, &mat_mkl_pardiso->phase, &mat_mkl_pardiso->n, mat_mkl_pardiso->a, mat_mkl_pardiso->ia, mat_mkl_pardiso->ja, mat_mkl_pardiso->perm,
476:                 &mat_mkl_pardiso->nrhs, mat_mkl_pardiso->iparm, &mat_mkl_pardiso->msglvl, (void *)barray, (void *)xarray, &mat_mkl_pardiso->err);
477:     PetscCheck(mat_mkl_pardiso->err >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error reported by MKL_PARDISO: err=%d. Please check manual", mat_mkl_pardiso->err);

479:     PetscCall(MatDenseRestoreArrayRead(B, &barray));
480:     if (mat_mkl_pardiso->schur) { /* solve Schur complement and expand solution */
481:       PetscScalar *o_schur_work = NULL;

483:       /* solve Schur complement */
484:       if (!mat_mkl_pardiso->solve_interior) {
485:         PetscInt shift = mat_mkl_pardiso->schur_size * mat_mkl_pardiso->nrhs, scale;
486:         PetscInt mem   = mat_mkl_pardiso->n * mat_mkl_pardiso->nrhs;

488:         PetscCall(MatFactorFactorizeSchurComplement(A));
489:         /* allocate extra memory if it is needed */
490:         scale = 1;
491:         if (A->schur_status == MAT_FACTOR_SCHUR_INVERTED) scale = 2;
492:         mem *= scale;
493:         if (mem > mat_mkl_pardiso->schur_work_size) {
494:           o_schur_work = mat_mkl_pardiso->schur_work;
495:           PetscCall(PetscMalloc1(mem, &mat_mkl_pardiso->schur_work));
496:         }
497:         /* if inverted, uses BLAS *MM subroutines, otherwise LAPACK *TRS */
498:         if (A->schur_status != MAT_FACTOR_SCHUR_INVERTED) shift = 0;
499:         PetscCall(MatMKLPardisoScatterSchur_Private(mat_mkl_pardiso, xarray, mat_mkl_pardiso->schur_work, PETSC_TRUE));
500:         PetscCall(MatMKLPardisoSolveSchur_Private(A, mat_mkl_pardiso->schur_work, mat_mkl_pardiso->schur_work + shift));
501:         PetscCall(MatMKLPardisoScatterSchur_Private(mat_mkl_pardiso, xarray, mat_mkl_pardiso->schur_work + shift, PETSC_FALSE));
502:       } else { /* if we are solving for the interior problem, any value in barray[schur,n] forward-substituted to xarray[schur,n] will be neglected */
503:         PetscInt i, n, m = 0;
504:         for (n = 0; n < mat_mkl_pardiso->nrhs; n++) {
505:           for (i = 0; i < mat_mkl_pardiso->schur_size; i++) xarray[mat_mkl_pardiso->schur_idxs[i] + m] = 0.;
506:           m += mat_mkl_pardiso->n;
507:         }
508:       }

510:       /* expansion phase */
511:       mat_mkl_pardiso->iparm[6 - 1] = 1;
512:       mat_mkl_pardiso->phase        = JOB_SOLVE_BACKWARD_SUBSTITUTION;
513:       MKL_PARDISO(mat_mkl_pardiso->pt, &mat_mkl_pardiso->maxfct, &mat_mkl_pardiso->mnum, &mat_mkl_pardiso->mtype, &mat_mkl_pardiso->phase, &mat_mkl_pardiso->n, mat_mkl_pardiso->a, mat_mkl_pardiso->ia, mat_mkl_pardiso->ja, mat_mkl_pardiso->perm,
514:                   &mat_mkl_pardiso->nrhs, mat_mkl_pardiso->iparm, &mat_mkl_pardiso->msglvl, (void *)xarray, (void *)mat_mkl_pardiso->schur_work, /* according to the specs, the solution vector is always used */
515:                   &mat_mkl_pardiso->err);
516:       if (o_schur_work) { /* restore original schur_work (minimal size) */
517:         PetscCall(PetscFree(mat_mkl_pardiso->schur_work));
518:         mat_mkl_pardiso->schur_work = o_schur_work;
519:       }
520:       PetscCheck(mat_mkl_pardiso->err >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error reported by MKL_PARDISO: err=%d. Please check manual", mat_mkl_pardiso->err);
521:       mat_mkl_pardiso->iparm[6 - 1] = 0;
522:     }
523:     PetscCall(MatDenseRestoreArrayWrite(X, &xarray));
524:   }
525:   mat_mkl_pardiso->CleanUp = PETSC_TRUE;
526:   PetscFunctionReturn(PETSC_SUCCESS);
527: }

529: PetscErrorCode MatFactorNumeric_MKL_PARDISO(Mat F, Mat A, const MatFactorInfo *info)
530: {
531:   Mat_MKL_PARDISO *mat_mkl_pardiso = (Mat_MKL_PARDISO *)(F)->data;

533:   PetscFunctionBegin;
534:   mat_mkl_pardiso->matstruc = SAME_NONZERO_PATTERN;
535:   PetscCall((*mat_mkl_pardiso->Convert)(A, mat_mkl_pardiso->needsym, MAT_REUSE_MATRIX, &mat_mkl_pardiso->freeaij, &mat_mkl_pardiso->nz, &mat_mkl_pardiso->ia, &mat_mkl_pardiso->ja, (PetscScalar **)&mat_mkl_pardiso->a));

537:   mat_mkl_pardiso->phase = JOB_NUMERICAL_FACTORIZATION;
538:   MKL_PARDISO(mat_mkl_pardiso->pt, &mat_mkl_pardiso->maxfct, &mat_mkl_pardiso->mnum, &mat_mkl_pardiso->mtype, &mat_mkl_pardiso->phase, &mat_mkl_pardiso->n, mat_mkl_pardiso->a, mat_mkl_pardiso->ia, mat_mkl_pardiso->ja, mat_mkl_pardiso->perm,
539:               &mat_mkl_pardiso->nrhs, mat_mkl_pardiso->iparm, &mat_mkl_pardiso->msglvl, NULL, (void *)mat_mkl_pardiso->schur, &mat_mkl_pardiso->err);
540:   PetscCheck(mat_mkl_pardiso->err >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error reported by MKL_PARDISO: err=%d. Please check manual", mat_mkl_pardiso->err);

542:   /* report flops */
543:   if (mat_mkl_pardiso->iparm[18] > 0) PetscCall(PetscLogFlops(PetscPowRealInt(10., 6) * mat_mkl_pardiso->iparm[18]));

545:   if (F->schur) { /* schur output from pardiso is in row major format */
546: #if defined(PETSC_HAVE_CUDA)
547:     F->schur->offloadmask = PETSC_OFFLOAD_CPU;
548: #endif
549:     PetscCall(MatFactorRestoreSchurComplement(F, NULL, MAT_FACTOR_SCHUR_UNFACTORED));
550:     PetscCall(MatTranspose(F->schur, MAT_INPLACE_MATRIX, &F->schur));
551:   }
552:   mat_mkl_pardiso->matstruc = SAME_NONZERO_PATTERN;
553:   mat_mkl_pardiso->CleanUp  = PETSC_TRUE;
554:   PetscFunctionReturn(PETSC_SUCCESS);
555: }

557: PetscErrorCode MatSetFromOptions_MKL_PARDISO(Mat F, Mat A)
558: {
559:   Mat_MKL_PARDISO *mat_mkl_pardiso = (Mat_MKL_PARDISO *)F->data;
560:   PetscInt         icntl, bs, threads = 1;
561:   PetscBool        flg;

563:   PetscFunctionBegin;
564:   PetscOptionsBegin(PetscObjectComm((PetscObject)F), ((PetscObject)F)->prefix, "MKL_PARDISO Options", "Mat");

566:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_65", "Suggested number of threads to use within PARDISO", "None", threads, &threads, &flg));
567:   if (flg) PetscSetMKL_PARDISOThreads((int)threads);

569:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_66", "Maximum number of factors with identical sparsity structure that must be kept in memory at the same time", "None", mat_mkl_pardiso->maxfct, &icntl, &flg));
570:   if (flg) mat_mkl_pardiso->maxfct = icntl;

572:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_67", "Indicates the actual matrix for the solution phase", "None", mat_mkl_pardiso->mnum, &icntl, &flg));
573:   if (flg) mat_mkl_pardiso->mnum = icntl;

575:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_68", "Message level information", "None", mat_mkl_pardiso->msglvl, &icntl, &flg));
576:   if (flg) mat_mkl_pardiso->msglvl = icntl;

578:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_69", "Defines the matrix type", "None", mat_mkl_pardiso->mtype, &icntl, &flg));
579:   if (flg) {
580:     void *pt[IPARM_SIZE];
581:     mat_mkl_pardiso->mtype = icntl;
582:     icntl                  = mat_mkl_pardiso->iparm[34];
583:     bs                     = mat_mkl_pardiso->iparm[36];
584:     MKL_PARDISO_INIT(pt, &mat_mkl_pardiso->mtype, mat_mkl_pardiso->iparm);
585: #if defined(PETSC_USE_REAL_SINGLE)
586:     mat_mkl_pardiso->iparm[27] = 1;
587: #else
588:     mat_mkl_pardiso->iparm[27] = 0;
589: #endif
590:     mat_mkl_pardiso->iparm[34] = icntl;
591:     mat_mkl_pardiso->iparm[36] = bs;
592:   }

594:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_1", "Use default values (if 0)", "None", mat_mkl_pardiso->iparm[0], &icntl, &flg));
595:   if (flg) mat_mkl_pardiso->iparm[0] = icntl;

597:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_2", "Fill-in reducing ordering for the input matrix", "None", mat_mkl_pardiso->iparm[1], &icntl, &flg));
598:   if (flg) mat_mkl_pardiso->iparm[1] = icntl;

600:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_4", "Preconditioned CGS/CG", "None", mat_mkl_pardiso->iparm[3], &icntl, &flg));
601:   if (flg) mat_mkl_pardiso->iparm[3] = icntl;

603:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_5", "User permutation", "None", mat_mkl_pardiso->iparm[4], &icntl, &flg));
604:   if (flg) mat_mkl_pardiso->iparm[4] = icntl;

606:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_6", "Write solution on x", "None", mat_mkl_pardiso->iparm[5], &icntl, &flg));
607:   if (flg) mat_mkl_pardiso->iparm[5] = icntl;

609:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_8", "Iterative refinement step", "None", mat_mkl_pardiso->iparm[7], &icntl, &flg));
610:   if (flg) mat_mkl_pardiso->iparm[7] = icntl;

612:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_10", "Pivoting perturbation", "None", mat_mkl_pardiso->iparm[9], &icntl, &flg));
613:   if (flg) mat_mkl_pardiso->iparm[9] = icntl;

615:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_11", "Scaling vectors", "None", mat_mkl_pardiso->iparm[10], &icntl, &flg));
616:   if (flg) mat_mkl_pardiso->iparm[10] = icntl;

618:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_12", "Solve with transposed or conjugate transposed matrix A", "None", mat_mkl_pardiso->iparm[11], &icntl, &flg));
619:   if (flg) mat_mkl_pardiso->iparm[11] = icntl;

621:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_13", "Improved accuracy using (non-) symmetric weighted matching", "None", mat_mkl_pardiso->iparm[12], &icntl, &flg));
622:   if (flg) mat_mkl_pardiso->iparm[12] = icntl;

624:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_18", "Numbers of non-zero elements", "None", mat_mkl_pardiso->iparm[17], &icntl, &flg));
625:   if (flg) mat_mkl_pardiso->iparm[17] = icntl;

627:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_19", "Report number of floating point operations (0 to disable)", "None", mat_mkl_pardiso->iparm[18], &icntl, &flg));
628:   if (flg) mat_mkl_pardiso->iparm[18] = icntl;

630:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_21", "Pivoting for symmetric indefinite matrices", "None", mat_mkl_pardiso->iparm[20], &icntl, &flg));
631:   if (flg) mat_mkl_pardiso->iparm[20] = icntl;

633:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_24", "Parallel factorization control", "None", mat_mkl_pardiso->iparm[23], &icntl, &flg));
634:   if (flg) mat_mkl_pardiso->iparm[23] = icntl;

636:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_25", "Parallel forward/backward solve control", "None", mat_mkl_pardiso->iparm[24], &icntl, &flg));
637:   if (flg) mat_mkl_pardiso->iparm[24] = icntl;

639:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_27", "Matrix checker", "None", mat_mkl_pardiso->iparm[26], &icntl, &flg));
640:   if (flg) mat_mkl_pardiso->iparm[26] = icntl;

642:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_31", "Partial solve and computing selected components of the solution vectors", "None", mat_mkl_pardiso->iparm[30], &icntl, &flg));
643:   if (flg) mat_mkl_pardiso->iparm[30] = icntl;

645:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_34", "Optimal number of threads for conditional numerical reproducibility (CNR) mode", "None", mat_mkl_pardiso->iparm[33], &icntl, &flg));
646:   if (flg) mat_mkl_pardiso->iparm[33] = icntl;

648:   PetscCall(PetscOptionsInt("-mat_mkl_pardiso_60", "Intel MKL_PARDISO mode", "None", mat_mkl_pardiso->iparm[59], &icntl, &flg));
649:   if (flg) mat_mkl_pardiso->iparm[59] = icntl;
650:   PetscOptionsEnd();
651:   PetscFunctionReturn(PETSC_SUCCESS);
652: }

654: PetscErrorCode MatFactorMKL_PARDISOInitialize_Private(Mat A, MatFactorType ftype, Mat_MKL_PARDISO *mat_mkl_pardiso)
655: {
656:   PetscInt  i, bs;
657:   PetscBool match;

659:   PetscFunctionBegin;
660:   for (i = 0; i < IPARM_SIZE; i++) mat_mkl_pardiso->iparm[i] = 0;
661:   for (i = 0; i < IPARM_SIZE; i++) mat_mkl_pardiso->pt[i] = 0;
662: #if defined(PETSC_USE_REAL_SINGLE)
663:   mat_mkl_pardiso->iparm[27] = 1;
664: #else
665:   mat_mkl_pardiso->iparm[27] = 0;
666: #endif
667:   /* Default options for both sym and unsym */
668:   mat_mkl_pardiso->iparm[0]  = 1;  /* Solver default parameters overridden with provided by iparm */
669:   mat_mkl_pardiso->iparm[1]  = 2;  /* Metis reordering */
670:   mat_mkl_pardiso->iparm[5]  = 0;  /* Write solution into x */
671:   mat_mkl_pardiso->iparm[7]  = 0;  /* Max number of iterative refinement steps */
672:   mat_mkl_pardiso->iparm[17] = -1; /* Output: Number of nonzeros in the factor LU */
673:   mat_mkl_pardiso->iparm[18] = -1; /* Output: Mflops for LU factorization */
674: #if 0
675:   mat_mkl_pardiso->iparm[23] =  1; /* Parallel factorization control*/
676: #endif
677:   PetscCall(PetscObjectTypeCompareAny((PetscObject)A, &match, MATSEQBAIJ, MATSEQSBAIJ, ""));
678:   PetscCall(MatGetBlockSize(A, &bs));
679:   if (!match || bs == 1) {
680:     mat_mkl_pardiso->iparm[34] = 1; /* Cluster Sparse Solver use C-style indexing for ia and ja arrays */
681:     mat_mkl_pardiso->n         = A->rmap->N;
682:   } else {
683:     mat_mkl_pardiso->iparm[34] = 0; /* Cluster Sparse Solver use Fortran-style indexing for ia and ja arrays */
684:     mat_mkl_pardiso->iparm[36] = bs;
685:     mat_mkl_pardiso->n         = A->rmap->N / bs;
686:   }
687:   mat_mkl_pardiso->iparm[39] = 0; /* Input: matrix/rhs/solution stored on rank-0 */

689:   mat_mkl_pardiso->CleanUp = PETSC_FALSE;
690:   mat_mkl_pardiso->maxfct  = 1; /* Maximum number of numerical factorizations. */
691:   mat_mkl_pardiso->mnum    = 1; /* Which factorization to use. */
692:   mat_mkl_pardiso->msglvl  = 0; /* 0: do not print 1: Print statistical information in file */
693:   mat_mkl_pardiso->phase   = -1;
694:   mat_mkl_pardiso->err     = 0;

696:   mat_mkl_pardiso->nrhs  = 1;
697:   mat_mkl_pardiso->err   = 0;
698:   mat_mkl_pardiso->phase = -1;

700:   if (ftype == MAT_FACTOR_LU) {
701:     mat_mkl_pardiso->iparm[9]  = 13; /* Perturb the pivot elements with 1E-13 */
702:     mat_mkl_pardiso->iparm[10] = 1;  /* Use nonsymmetric permutation and scaling MPS */
703:     mat_mkl_pardiso->iparm[12] = 1;  /* Switch on Maximum Weighted Matching algorithm (default for non-symmetric) */
704:   } else {
705:     mat_mkl_pardiso->iparm[9]  = 8; /* Perturb the pivot elements with 1E-8 */
706:     mat_mkl_pardiso->iparm[10] = 0; /* Use nonsymmetric permutation and scaling MPS */
707:     mat_mkl_pardiso->iparm[12] = 1; /* Switch on Maximum Weighted Matching algorithm (default for non-symmetric) */
708: #if defined(PETSC_USE_DEBUG)
709:     mat_mkl_pardiso->iparm[26] = 1; /* Matrix checker */
710: #endif
711:   }
712:   PetscCall(PetscCalloc1(A->rmap->N * sizeof(INT_TYPE), &mat_mkl_pardiso->perm));
713:   mat_mkl_pardiso->schur_size = 0;
714:   PetscFunctionReturn(PETSC_SUCCESS);
715: }

717: PetscErrorCode MatFactorSymbolic_AIJMKL_PARDISO_Private(Mat F, Mat A, const MatFactorInfo *info)
718: {
719:   Mat_MKL_PARDISO *mat_mkl_pardiso = (Mat_MKL_PARDISO *)F->data;

721:   PetscFunctionBegin;
722:   mat_mkl_pardiso->matstruc = DIFFERENT_NONZERO_PATTERN;
723:   PetscCall(MatSetFromOptions_MKL_PARDISO(F, A));
724:   /* throw away any previously computed structure */
725:   if (mat_mkl_pardiso->freeaij) {
726:     PetscCall(PetscFree2(mat_mkl_pardiso->ia, mat_mkl_pardiso->ja));
727:     if (mat_mkl_pardiso->iparm[34] == 1) PetscCall(PetscFree(mat_mkl_pardiso->a));
728:   }
729:   PetscCall((*mat_mkl_pardiso->Convert)(A, mat_mkl_pardiso->needsym, MAT_INITIAL_MATRIX, &mat_mkl_pardiso->freeaij, &mat_mkl_pardiso->nz, &mat_mkl_pardiso->ia, &mat_mkl_pardiso->ja, (PetscScalar **)&mat_mkl_pardiso->a));
730:   if (mat_mkl_pardiso->iparm[34] == 1) mat_mkl_pardiso->n = A->rmap->N;
731:   else mat_mkl_pardiso->n = A->rmap->N / A->rmap->bs;

733:   mat_mkl_pardiso->phase = JOB_ANALYSIS;

735:   /* reset flops counting if requested */
736:   if (mat_mkl_pardiso->iparm[18]) mat_mkl_pardiso->iparm[18] = -1;

738:   MKL_PARDISO(mat_mkl_pardiso->pt, &mat_mkl_pardiso->maxfct, &mat_mkl_pardiso->mnum, &mat_mkl_pardiso->mtype, &mat_mkl_pardiso->phase, &mat_mkl_pardiso->n, mat_mkl_pardiso->a, mat_mkl_pardiso->ia, mat_mkl_pardiso->ja, mat_mkl_pardiso->perm,
739:               &mat_mkl_pardiso->nrhs, mat_mkl_pardiso->iparm, &mat_mkl_pardiso->msglvl, NULL, NULL, &mat_mkl_pardiso->err);
740:   PetscCheck(mat_mkl_pardiso->err >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error reported by MKL_PARDISO: err=%d. Please check manual", mat_mkl_pardiso->err);

742:   mat_mkl_pardiso->CleanUp = PETSC_TRUE;

744:   if (F->factortype == MAT_FACTOR_LU) F->ops->lufactornumeric = MatFactorNumeric_MKL_PARDISO;
745:   else F->ops->choleskyfactornumeric = MatFactorNumeric_MKL_PARDISO;

747:   F->ops->solve          = MatSolve_MKL_PARDISO;
748:   F->ops->solvetranspose = MatSolveTranspose_MKL_PARDISO;
749:   F->ops->matsolve       = MatMatSolve_MKL_PARDISO;
750:   PetscFunctionReturn(PETSC_SUCCESS);
751: }

753: PetscErrorCode MatLUFactorSymbolic_AIJMKL_PARDISO(Mat F, Mat A, IS r, IS c, const MatFactorInfo *info)
754: {
755:   PetscFunctionBegin;
756:   PetscCall(MatFactorSymbolic_AIJMKL_PARDISO_Private(F, A, info));
757:   PetscFunctionReturn(PETSC_SUCCESS);
758: }

760: #if !defined(PETSC_USE_COMPLEX)
761: PetscErrorCode MatGetInertia_MKL_PARDISO(Mat F, PetscInt *nneg, PetscInt *nzero, PetscInt *npos)
762: {
763:   Mat_MKL_PARDISO *mat_mkl_pardiso = (Mat_MKL_PARDISO *)F->data;

765:   PetscFunctionBegin;
766:   if (nneg) *nneg = mat_mkl_pardiso->iparm[22];
767:   if (npos) *npos = mat_mkl_pardiso->iparm[21];
768:   if (nzero) *nzero = F->rmap->N - (mat_mkl_pardiso->iparm[22] + mat_mkl_pardiso->iparm[21]);
769:   PetscFunctionReturn(PETSC_SUCCESS);
770: }
771: #endif

773: PetscErrorCode MatCholeskyFactorSymbolic_AIJMKL_PARDISO(Mat F, Mat A, IS r, const MatFactorInfo *info)
774: {
775:   PetscFunctionBegin;
776:   PetscCall(MatFactorSymbolic_AIJMKL_PARDISO_Private(F, A, info));
777:   F->ops->getinertia = NULL;
778: #if !defined(PETSC_USE_COMPLEX)
779:   F->ops->getinertia = MatGetInertia_MKL_PARDISO;
780: #endif
781:   PetscFunctionReturn(PETSC_SUCCESS);
782: }

784: PetscErrorCode MatView_MKL_PARDISO(Mat A, PetscViewer viewer)
785: {
786:   PetscBool         iascii;
787:   PetscViewerFormat format;
788:   Mat_MKL_PARDISO  *mat_mkl_pardiso = (Mat_MKL_PARDISO *)A->data;
789:   PetscInt          i;

791:   PetscFunctionBegin;
792:   if (A->ops->solve != MatSolve_MKL_PARDISO) PetscFunctionReturn(PETSC_SUCCESS);

794:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
795:   if (iascii) {
796:     PetscCall(PetscViewerGetFormat(viewer, &format));
797:     if (format == PETSC_VIEWER_ASCII_INFO) {
798:       PetscCall(PetscViewerASCIIPrintf(viewer, "MKL_PARDISO run parameters:\n"));
799:       PetscCall(PetscViewerASCIIPrintf(viewer, "MKL_PARDISO phase:             %d \n", mat_mkl_pardiso->phase));
800:       for (i = 1; i <= 64; i++) PetscCall(PetscViewerASCIIPrintf(viewer, "MKL_PARDISO iparm[%d]:     %d \n", i, mat_mkl_pardiso->iparm[i - 1]));
801:       PetscCall(PetscViewerASCIIPrintf(viewer, "MKL_PARDISO maxfct:     %d \n", mat_mkl_pardiso->maxfct));
802:       PetscCall(PetscViewerASCIIPrintf(viewer, "MKL_PARDISO mnum:     %d \n", mat_mkl_pardiso->mnum));
803:       PetscCall(PetscViewerASCIIPrintf(viewer, "MKL_PARDISO mtype:     %d \n", mat_mkl_pardiso->mtype));
804:       PetscCall(PetscViewerASCIIPrintf(viewer, "MKL_PARDISO n:     %d \n", mat_mkl_pardiso->n));
805:       PetscCall(PetscViewerASCIIPrintf(viewer, "MKL_PARDISO nrhs:     %d \n", mat_mkl_pardiso->nrhs));
806:       PetscCall(PetscViewerASCIIPrintf(viewer, "MKL_PARDISO msglvl:     %d \n", mat_mkl_pardiso->msglvl));
807:     }
808:   }
809:   PetscFunctionReturn(PETSC_SUCCESS);
810: }

812: PetscErrorCode MatGetInfo_MKL_PARDISO(Mat A, MatInfoType flag, MatInfo *info)
813: {
814:   Mat_MKL_PARDISO *mat_mkl_pardiso = (Mat_MKL_PARDISO *)A->data;

816:   PetscFunctionBegin;
817:   info->block_size        = 1.0;
818:   info->nz_used           = mat_mkl_pardiso->iparm[17];
819:   info->nz_allocated      = mat_mkl_pardiso->iparm[17];
820:   info->nz_unneeded       = 0.0;
821:   info->assemblies        = 0.0;
822:   info->mallocs           = 0.0;
823:   info->memory            = 0.0;
824:   info->fill_ratio_given  = 0;
825:   info->fill_ratio_needed = 0;
826:   info->factor_mallocs    = 0;
827:   PetscFunctionReturn(PETSC_SUCCESS);
828: }

830: PetscErrorCode MatMkl_PardisoSetCntl_MKL_PARDISO(Mat F, PetscInt icntl, PetscInt ival)
831: {
832:   PetscInt         backup, bs;
833:   Mat_MKL_PARDISO *mat_mkl_pardiso = (Mat_MKL_PARDISO *)F->data;

835:   PetscFunctionBegin;
836:   if (icntl <= 64) {
837:     mat_mkl_pardiso->iparm[icntl - 1] = ival;
838:   } else {
839:     if (icntl == 65) PetscSetMKL_PARDISOThreads(ival);
840:     else if (icntl == 66) mat_mkl_pardiso->maxfct = ival;
841:     else if (icntl == 67) mat_mkl_pardiso->mnum = ival;
842:     else if (icntl == 68) mat_mkl_pardiso->msglvl = ival;
843:     else if (icntl == 69) {
844:       void *pt[IPARM_SIZE];
845:       backup                 = mat_mkl_pardiso->iparm[34];
846:       bs                     = mat_mkl_pardiso->iparm[36];
847:       mat_mkl_pardiso->mtype = ival;
848:       MKL_PARDISO_INIT(pt, &mat_mkl_pardiso->mtype, mat_mkl_pardiso->iparm);
849: #if defined(PETSC_USE_REAL_SINGLE)
850:       mat_mkl_pardiso->iparm[27] = 1;
851: #else
852:       mat_mkl_pardiso->iparm[27] = 0;
853: #endif
854:       mat_mkl_pardiso->iparm[34] = backup;
855:       mat_mkl_pardiso->iparm[36] = bs;
856:     } else if (icntl == 70) mat_mkl_pardiso->solve_interior = (PetscBool) !!ival;
857:   }
858:   PetscFunctionReturn(PETSC_SUCCESS);
859: }

861: /*@
862:   MatMkl_PardisoSetCntl - Set Mkl_Pardiso parameters

864:    Logically Collective

866:    Input Parameters:
867: +  F - the factored matrix obtained by calling `MatGetFactor()`
868: .  icntl - index of Mkl_Pardiso parameter
869: -  ival - value of Mkl_Pardiso parameter

871:   Options Database Key:
872: .   -mat_mkl_pardiso_<icntl> <ival> - change the option numbered icntl to the value ival

874:    Level: beginner

876:    References:
877: .  * - Mkl_Pardiso Users' Guide

879: .seealso: [](ch_matrices), `Mat`, `MATSOLVERMKL_PARDISO`, `MatGetFactor()`
880: @*/
881: PetscErrorCode MatMkl_PardisoSetCntl(Mat F, PetscInt icntl, PetscInt ival)
882: {
883:   PetscFunctionBegin;
884:   PetscTryMethod(F, "MatMkl_PardisoSetCntl_C", (Mat, PetscInt, PetscInt), (F, icntl, ival));
885:   PetscFunctionReturn(PETSC_SUCCESS);
886: }

888: /*MC
889:   MATSOLVERMKL_PARDISO -  A matrix type providing direct solvers, LU, for
890:   `MATSEQAIJ` matrices via the external package MKL_PARDISO.

892:   Use `-pc_type lu` `-pc_factor_mat_solver_type mkl_pardiso` to use this direct solver

894:   Options Database Keys:
895: + -mat_mkl_pardiso_65 - Suggested number of threads to use within MKL_PARDISO
896: . -mat_mkl_pardiso_66 - Maximum number of factors with identical sparsity structure that must be kept in memory at the same time
897: . -mat_mkl_pardiso_67 - Indicates the actual matrix for the solution phase
898: . -mat_mkl_pardiso_68 - Message level information, use 1 to get detailed information on the solver options
899: . -mat_mkl_pardiso_69 - Defines the matrix type. IMPORTANT: When you set this flag, iparm parameters are going to be set to the default ones for the matrix type
900: . -mat_mkl_pardiso_1  - Use default values
901: . -mat_mkl_pardiso_2  - Fill-in reducing ordering for the input matrix
902: . -mat_mkl_pardiso_4  - Preconditioned CGS/CG
903: . -mat_mkl_pardiso_5  - User permutation
904: . -mat_mkl_pardiso_6  - Write solution on x
905: . -mat_mkl_pardiso_8  - Iterative refinement step
906: . -mat_mkl_pardiso_10 - Pivoting perturbation
907: . -mat_mkl_pardiso_11 - Scaling vectors
908: . -mat_mkl_pardiso_12 - Solve with transposed or conjugate transposed matrix A
909: . -mat_mkl_pardiso_13 - Improved accuracy using (non-) symmetric weighted matching
910: . -mat_mkl_pardiso_18 - Numbers of non-zero elements
911: . -mat_mkl_pardiso_19 - Report number of floating point operations
912: . -mat_mkl_pardiso_21 - Pivoting for symmetric indefinite matrices
913: . -mat_mkl_pardiso_24 - Parallel factorization control
914: . -mat_mkl_pardiso_25 - Parallel forward/backward solve control
915: . -mat_mkl_pardiso_27 - Matrix checker
916: . -mat_mkl_pardiso_31 - Partial solve and computing selected components of the solution vectors
917: . -mat_mkl_pardiso_34 - Optimal number of threads for conditional numerical reproducibility (CNR) mode
918: - -mat_mkl_pardiso_60 - Intel MKL_PARDISO mode

920:   Level: beginner

922:   Notes:
923:     Use `-mat_mkl_pardiso_68 1` to display the number of threads the solver is using. MKL does not provide a way to directly access this
924:     information.

926:     For more information on the options check the MKL_Pardiso manual

928: .seealso: [](ch_matrices), `Mat`, `MATSEQAIJ`, `PCFactorSetMatSolverType()`, `MatSolverType`, `MatMkl_PardisoSetCntl()`
929: M*/
930: static PetscErrorCode MatFactorGetSolverType_mkl_pardiso(Mat A, MatSolverType *type)
931: {
932:   PetscFunctionBegin;
933:   *type = MATSOLVERMKL_PARDISO;
934:   PetscFunctionReturn(PETSC_SUCCESS);
935: }

937: PETSC_EXTERN PetscErrorCode MatGetFactor_aij_mkl_pardiso(Mat A, MatFactorType ftype, Mat *F)
938: {
939:   Mat              B;
940:   Mat_MKL_PARDISO *mat_mkl_pardiso;
941:   PetscBool        isSeqAIJ, isSeqBAIJ, isSeqSBAIJ;

943:   PetscFunctionBegin;
944:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATSEQAIJ, &isSeqAIJ));
945:   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQBAIJ, &isSeqBAIJ));
946:   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQSBAIJ, &isSeqSBAIJ));
947:   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
948:   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
949:   PetscCall(PetscStrallocpy("mkl_pardiso", &((PetscObject)B)->type_name));
950:   PetscCall(MatSetUp(B));

952:   PetscCall(PetscNew(&mat_mkl_pardiso));
953:   B->data = mat_mkl_pardiso;

955:   PetscCall(MatFactorMKL_PARDISOInitialize_Private(A, ftype, mat_mkl_pardiso));
956:   if (ftype == MAT_FACTOR_LU) {
957:     B->ops->lufactorsymbolic = MatLUFactorSymbolic_AIJMKL_PARDISO;
958:     B->factortype            = MAT_FACTOR_LU;
959:     mat_mkl_pardiso->needsym = PETSC_FALSE;
960:     if (isSeqAIJ) mat_mkl_pardiso->Convert = MatMKLPardiso_Convert_seqaij;
961:     else if (isSeqBAIJ) mat_mkl_pardiso->Convert = MatMKLPardiso_Convert_seqbaij;
962:     else {
963:       PetscCheck(!isSeqSBAIJ, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "No support for PARDISO LU factor with SEQSBAIJ format! Use MAT_FACTOR_CHOLESKY instead");
964:       SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "No support for PARDISO LU with %s format", ((PetscObject)A)->type_name);
965:     }
966: #if defined(PETSC_USE_COMPLEX)
967:     mat_mkl_pardiso->mtype = 13;
968: #else
969:     mat_mkl_pardiso->mtype = 11;
970: #endif
971:   } else {
972:     B->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_AIJMKL_PARDISO;
973:     B->factortype                  = MAT_FACTOR_CHOLESKY;
974:     if (isSeqAIJ) mat_mkl_pardiso->Convert = MatMKLPardiso_Convert_seqaij;
975:     else if (isSeqBAIJ) mat_mkl_pardiso->Convert = MatMKLPardiso_Convert_seqbaij;
976:     else if (isSeqSBAIJ) mat_mkl_pardiso->Convert = MatMKLPardiso_Convert_seqsbaij;
977:     else SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "No support for PARDISO CHOLESKY with %s format", ((PetscObject)A)->type_name);

979:     mat_mkl_pardiso->needsym = PETSC_TRUE;
980: #if !defined(PETSC_USE_COMPLEX)
981:     if (A->spd == PETSC_BOOL3_TRUE) mat_mkl_pardiso->mtype = 2;
982:     else mat_mkl_pardiso->mtype = -2;
983: #else
984:     mat_mkl_pardiso->mtype = 6;
985:     PetscCheck(A->hermitian != PETSC_BOOL3_TRUE, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "No support for PARDISO CHOLESKY with Hermitian matrices! Use MAT_FACTOR_LU instead");
986: #endif
987:   }
988:   B->ops->destroy = MatDestroy_MKL_PARDISO;
989:   B->ops->view    = MatView_MKL_PARDISO;
990:   B->ops->getinfo = MatGetInfo_MKL_PARDISO;
991:   B->factortype   = ftype;
992:   B->assembled    = PETSC_TRUE;

994:   PetscCall(PetscFree(B->solvertype));
995:   PetscCall(PetscStrallocpy(MATSOLVERMKL_PARDISO, &B->solvertype));

997:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mkl_pardiso));
998:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MKL_PARDISO));
999:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMkl_PardisoSetCntl_C", MatMkl_PardisoSetCntl_MKL_PARDISO));

1001:   *F = B;
1002:   PetscFunctionReturn(PETSC_SUCCESS);
1003: }

1005: PETSC_EXTERN PetscErrorCode MatSolverTypeRegister_MKL_Pardiso(void)
1006: {
1007:   PetscFunctionBegin;
1008:   PetscCall(MatSolverTypeRegister(MATSOLVERMKL_PARDISO, MATSEQAIJ, MAT_FACTOR_LU, MatGetFactor_aij_mkl_pardiso));
1009:   PetscCall(MatSolverTypeRegister(MATSOLVERMKL_PARDISO, MATSEQAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mkl_pardiso));
1010:   PetscCall(MatSolverTypeRegister(MATSOLVERMKL_PARDISO, MATSEQBAIJ, MAT_FACTOR_LU, MatGetFactor_aij_mkl_pardiso));
1011:   PetscCall(MatSolverTypeRegister(MATSOLVERMKL_PARDISO, MATSEQSBAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mkl_pardiso));
1012:   PetscFunctionReturn(PETSC_SUCCESS);
1013: }