xref: /petsc/src/mat/impls/aij/seq/mkl_pardiso/mkl_pardiso.c (revision bcee047adeeb73090d7e36cc71e39fc287cdbb97)
1 #include <../src/mat/impls/aij/seq/aij.h> /*I "petscmat.h" I*/
2 #include <../src/mat/impls/sbaij/seq/sbaij.h>
3 #include <../src/mat/impls/dense/seq/dense.h>
4 
5 #if defined(PETSC_HAVE_MKL_INTEL_ILP64)
6   #define MKL_ILP64
7 #endif
8 #include <mkl_pardiso.h>
9 
10 PETSC_EXTERN void PetscSetMKL_PARDISOThreads(int);
11 
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
27 
28 #define IPARM_SIZE 64
29 
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;
44 
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
55 
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];
63 
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];
69 
70   /* Basic mkl_pardiso info*/
71   INT_TYPE phase, maxfct, mnum, mtype, n, nrhs, msglvl, err;
72 
73   /* Matrix structure*/
74   void     *a;
75   INT_TYPE *ia, *ja;
76 
77   /* Number of non-zero elements*/
78   INT_TYPE nz;
79 
80   /* Row permutaton vector*/
81   INT_TYPE *perm;
82 
83   /* Define if matrix preserves sparse structure.*/
84   MatStructure matstruc;
85 
86   PetscBool needsym;
87   PetscBool freeaij;
88 
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;
96 
97   /* True if mkl_pardiso function have been used.*/
98   PetscBool CleanUp;
99 
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;
103 
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;
108 
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 }
131 
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;
136 
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 }
163 
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;
168 
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;
181 
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;
188 
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;
194 
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;
213 
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 }
229 
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;
235 
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
247 
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
251 
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 }
281 
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;
290 
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));
307 
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 }
320 
321 PetscErrorCode MatDestroy_MKL_PARDISO(Mat A)
322 {
323   Mat_MKL_PARDISO *mat_mkl_pardiso = (Mat_MKL_PARDISO *)A->data;
324 
325   PetscFunctionBegin;
326   if (mat_mkl_pardiso->CleanUp) {
327     mat_mkl_pardiso->phase = JOB_RELEASE_OF_ALL_MEMORY;
328 
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));
340 
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 }
347 
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 }
370 
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;
376 
377   PetscFunctionBegin;
378   mat_mkl_pardiso->nrhs = 1;
379   PetscCall(VecGetArrayWrite(x, &xarray));
380   PetscCall(VecGetArrayRead(b, &barray));
381 
382   if (!mat_mkl_pardiso->schur) mat_mkl_pardiso->phase = JOB_SOLVE_ITERATIVE_REFINEMENT;
383   else mat_mkl_pardiso->phase = JOB_SOLVE_FORWARD_SUBSTITUTION;
384 
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));
402 
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);
404 
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;
408 
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;
412 
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     }
421 
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);
428 
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 }
436 
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;
441 
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 }
449 
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;
456 
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   }
464 
465   PetscCall(MatGetSize(B, NULL, (PetscInt *)&mat_mkl_pardiso->nrhs));
466 
467   if (mat_mkl_pardiso->nrhs > 0) {
468     PetscCall(MatDenseGetArrayRead(B, &barray));
469     PetscCall(MatDenseGetArrayWrite(X, &xarray));
470 
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;
474 
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);
478 
479     PetscCall(MatDenseRestoreArrayRead(B, &barray));
480     if (mat_mkl_pardiso->schur) { /* solve Schur complement and expand solution */
481       PetscScalar *o_schur_work = NULL;
482 
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;
487 
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       }
509 
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 }
528 
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;
532 
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));
536 
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);
541 
542   /* report flops */
543   if (mat_mkl_pardiso->iparm[18] > 0) PetscCall(PetscLogFlops(PetscPowRealInt(10., 6) * mat_mkl_pardiso->iparm[18]));
544 
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 }
556 
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;
562 
563   PetscFunctionBegin;
564   PetscOptionsBegin(PetscObjectComm((PetscObject)F), ((PetscObject)F)->prefix, "MKL_PARDISO Options", "Mat");
565 
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);
568 
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;
571 
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;
574 
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;
577 
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   }
593 
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;
596 
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;
599 
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;
602 
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;
605 
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;
608 
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;
611 
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;
614 
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;
617 
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;
620 
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;
623 
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;
626 
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;
629 
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;
632 
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;
635 
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;
638 
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;
641 
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;
644 
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;
647 
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 }
653 
654 PetscErrorCode MatFactorMKL_PARDISOInitialize_Private(Mat A, MatFactorType ftype, Mat_MKL_PARDISO *mat_mkl_pardiso)
655 {
656   PetscInt  i, bs;
657   PetscBool match;
658 
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 */
688 
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;
695 
696   mat_mkl_pardiso->nrhs  = 1;
697   mat_mkl_pardiso->err   = 0;
698   mat_mkl_pardiso->phase = -1;
699 
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 }
716 
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;
720 
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;
732 
733   mat_mkl_pardiso->phase = JOB_ANALYSIS;
734 
735   /* reset flops counting if requested */
736   if (mat_mkl_pardiso->iparm[18]) mat_mkl_pardiso->iparm[18] = -1;
737 
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);
741 
742   mat_mkl_pardiso->CleanUp = PETSC_TRUE;
743 
744   if (F->factortype == MAT_FACTOR_LU) F->ops->lufactornumeric = MatFactorNumeric_MKL_PARDISO;
745   else F->ops->choleskyfactornumeric = MatFactorNumeric_MKL_PARDISO;
746 
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 }
752 
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 }
759 
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;
764 
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
772 
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 }
783 
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;
790 
791   PetscFunctionBegin;
792   if (A->ops->solve != MatSolve_MKL_PARDISO) PetscFunctionReturn(PETSC_SUCCESS);
793 
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 }
811 
812 PetscErrorCode MatGetInfo_MKL_PARDISO(Mat A, MatInfoType flag, MatInfo *info)
813 {
814   Mat_MKL_PARDISO *mat_mkl_pardiso = (Mat_MKL_PARDISO *)A->data;
815 
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 }
829 
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;
834 
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 }
860 
861 /*@
862   MatMkl_PardisoSetCntl - Set Mkl_Pardiso parameters
863 
864    Logically Collective
865 
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
870 
871   Options Database Key:
872 .   -mat_mkl_pardiso_<icntl> <ival> - change the option numbered icntl to the value ival
873 
874    Level: beginner
875 
876    References:
877 .  * - Mkl_Pardiso Users' Guide
878 
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 }
887 
888 /*MC
889   MATSOLVERMKL_PARDISO -  A matrix type providing direct solvers, LU, for
890   `MATSEQAIJ` matrices via the external package MKL_PARDISO.
891 
892   Use `-pc_type lu` `-pc_factor_mat_solver_type mkl_pardiso` to use this direct solver
893 
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
919 
920   Level: beginner
921 
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.
925 
926     For more information on the options check the MKL_Pardiso manual
927 
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 }
936 
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;
942 
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));
951 
952   PetscCall(PetscNew(&mat_mkl_pardiso));
953   B->data = mat_mkl_pardiso;
954 
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);
978 
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;
993 
994   PetscCall(PetscFree(B->solvertype));
995   PetscCall(PetscStrallocpy(MATSOLVERMKL_PARDISO, &B->solvertype));
996 
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));
1000 
1001   *F = B;
1002   PetscFunctionReturn(PETSC_SUCCESS);
1003 }
1004 
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 }
1014