Actual source code: klu.c


  2: /*
  3:    Provides an interface to the KLUv1.2 sparse solver

  5:    When build with PETSC_USE_64BIT_INDICES this will use SuiteSparse_long as the
  6:    integer type in KLU, otherwise it will use int. This means
  7:    all integers in this file are simply declared as PetscInt. Also it means
  8:    that KLU SuiteSparse_long version MUST be built with 64-bit integers when used.

 10: */
 11: #include <../src/mat/impls/aij/seq/aij.h>

 13: #if defined(PETSC_USE_64BIT_INDICES)
 14:   #define klu_K_defaults                        klu_l_defaults
 15:   #define klu_K_analyze(a, b, c, d)             klu_l_analyze((SuiteSparse_long)a, (SuiteSparse_long *)b, (SuiteSparse_long *)c, d)
 16:   #define klu_K_analyze_given(a, b, c, d, e, f) klu_l_analyze_given((SuiteSparse_long)a, (SuiteSparse_long *)b, (SuiteSparse_long *)c, (SuiteSparse_long *)d, (SuiteSparse_long *)e, f)
 17:   #define klu_K_free_symbolic                   klu_l_free_symbolic
 18:   #define klu_K_free_numeric                    klu_l_free_numeric
 19:   #define klu_K_common                          klu_l_common
 20:   #define klu_K_symbolic                        klu_l_symbolic
 21:   #define klu_K_numeric                         klu_l_numeric
 22:   #if defined(PETSC_USE_COMPLEX)
 23:     #define klu_K_factor(a, b, c, d, e) klu_zl_factor((SuiteSparse_long *)a, (SuiteSparse_long *)b, c, d, e);
 24:     #define klu_K_solve                 klu_zl_solve
 25:     #define klu_K_tsolve                klu_zl_tsolve
 26:     #define klu_K_refactor              klu_zl_refactor
 27:     #define klu_K_sort                  klu_zl_sort
 28:     #define klu_K_flops                 klu_zl_flops
 29:     #define klu_K_rgrowth               klu_zl_rgrowth
 30:     #define klu_K_condest               klu_zl_condest
 31:     #define klu_K_rcond                 klu_zl_rcond
 32:     #define klu_K_scale                 klu_zl_scale
 33:   #else
 34:     #define klu_K_factor(a, b, c, d, e) klu_l_factor((SuiteSparse_long *)a, (SuiteSparse_long *)b, c, d, e);
 35:     #define klu_K_solve                 klu_l_solve
 36:     #define klu_K_tsolve                klu_l_tsolve
 37:     #define klu_K_refactor              klu_l_refactor
 38:     #define klu_K_sort                  klu_l_sort
 39:     #define klu_K_flops                 klu_l_flops
 40:     #define klu_K_rgrowth               klu_l_rgrowth
 41:     #define klu_K_condest               klu_l_condest
 42:     #define klu_K_rcond                 klu_l_rcond
 43:     #define klu_K_scale                 klu_l_scale
 44:   #endif
 45: #else
 46:   #define klu_K_defaults      klu_defaults
 47:   #define klu_K_analyze       klu_analyze
 48:   #define klu_K_analyze_given klu_analyze_given
 49:   #define klu_K_free_symbolic klu_free_symbolic
 50:   #define klu_K_free_numeric  klu_free_numeric
 51:   #define klu_K_common        klu_common
 52:   #define klu_K_symbolic      klu_symbolic
 53:   #define klu_K_numeric       klu_numeric
 54:   #if defined(PETSC_USE_COMPLEX)
 55:     #define klu_K_factor   klu_z_factor
 56:     #define klu_K_solve    klu_z_solve
 57:     #define klu_K_tsolve   klu_z_tsolve
 58:     #define klu_K_refactor klu_z_refactor
 59:     #define klu_K_sort     klu_z_sort
 60:     #define klu_K_flops    klu_z_flops
 61:     #define klu_K_rgrowth  klu_z_rgrowth
 62:     #define klu_K_condest  klu_z_condest
 63:     #define klu_K_rcond    klu_z_rcond
 64:     #define klu_K_scale    klu_z_scale
 65:   #else
 66:     #define klu_K_factor   klu_factor
 67:     #define klu_K_solve    klu_solve
 68:     #define klu_K_tsolve   klu_tsolve
 69:     #define klu_K_refactor klu_refactor
 70:     #define klu_K_sort     klu_sort
 71:     #define klu_K_flops    klu_flops
 72:     #define klu_K_rgrowth  klu_rgrowth
 73:     #define klu_K_condest  klu_condest
 74:     #define klu_K_rcond    klu_rcond
 75:     #define klu_K_scale    klu_scale
 76:   #endif
 77: #endif

 79: EXTERN_C_BEGIN
 80: #include <klu.h>
 81: EXTERN_C_END

 83: static const char *KluOrderingTypes[] = {"AMD", "COLAMD"};
 84: static const char *scale[]            = {"NONE", "SUM", "MAX"};

 86: typedef struct {
 87:   klu_K_common    Common;
 88:   klu_K_symbolic *Symbolic;
 89:   klu_K_numeric  *Numeric;
 90:   PetscInt       *perm_c, *perm_r;
 91:   MatStructure    flg;
 92:   PetscBool       PetscMatOrdering;
 93:   PetscBool       CleanUpKLU;
 94: } Mat_KLU;

 96: static PetscErrorCode MatDestroy_KLU(Mat A)
 97: {
 98:   Mat_KLU *lu = (Mat_KLU *)A->data;

100:   PetscFunctionBegin;
101:   if (lu->CleanUpKLU) {
102:     klu_K_free_symbolic(&lu->Symbolic, &lu->Common);
103:     klu_K_free_numeric(&lu->Numeric, &lu->Common);
104:     PetscCall(PetscFree2(lu->perm_r, lu->perm_c));
105:   }
106:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorGetSolverType_C", NULL));
107:   PetscCall(PetscFree(A->data));
108:   PetscFunctionReturn(PETSC_SUCCESS);
109: }

111: static PetscErrorCode MatSolveTranspose_KLU(Mat A, Vec b, Vec x)
112: {
113:   Mat_KLU     *lu = (Mat_KLU *)A->data;
114:   PetscScalar *xa;
115:   PetscInt     status;

117:   PetscFunctionBegin;
118:   /* KLU uses a column major format, solve Ax = b by klu_*_solve */
119:   PetscCall(VecCopy(b, x)); /* klu_solve stores the solution in rhs */
120:   PetscCall(VecGetArray(x, &xa));
121:   status = klu_K_solve(lu->Symbolic, lu->Numeric, A->rmap->n, 1, (PetscReal *)xa, &lu->Common);
122:   PetscCheck(status == 1, PETSC_COMM_SELF, PETSC_ERR_LIB, "KLU Solve failed");
123:   PetscCall(VecRestoreArray(x, &xa));
124:   PetscFunctionReturn(PETSC_SUCCESS);
125: }

127: static PetscErrorCode MatSolve_KLU(Mat A, Vec b, Vec x)
128: {
129:   Mat_KLU     *lu = (Mat_KLU *)A->data;
130:   PetscScalar *xa;
131:   PetscInt     status;

133:   PetscFunctionBegin;
134:   /* KLU uses a column major format, solve A^Tx = b by klu_*_tsolve */
135:   PetscCall(VecCopy(b, x)); /* klu_solve stores the solution in rhs */
136:   PetscCall(VecGetArray(x, &xa));
137: #if defined(PETSC_USE_COMPLEX)
138:   PetscInt conj_solve = 1;
139:   status              = klu_K_tsolve(lu->Symbolic, lu->Numeric, A->rmap->n, 1, (PetscReal *)xa, conj_solve, &lu->Common); /* conjugate solve */
140: #else
141:   status = klu_K_tsolve(lu->Symbolic, lu->Numeric, A->rmap->n, 1, xa, &lu->Common);
142: #endif
143:   PetscCheck(status == 1, PETSC_COMM_SELF, PETSC_ERR_LIB, "KLU Solve failed");
144:   PetscCall(VecRestoreArray(x, &xa));
145:   PetscFunctionReturn(PETSC_SUCCESS);
146: }

148: static PetscErrorCode MatLUFactorNumeric_KLU(Mat F, Mat A, const MatFactorInfo *info)
149: {
150:   Mat_KLU     *lu = (Mat_KLU *)(F)->data;
151:   Mat_SeqAIJ  *a  = (Mat_SeqAIJ *)A->data;
152:   PetscInt    *ai = a->i, *aj = a->j;
153:   PetscScalar *av = a->a;

155:   PetscFunctionBegin;
156:   /* numeric factorization of A' */

158:   if (lu->flg == SAME_NONZERO_PATTERN && lu->Numeric) klu_K_free_numeric(&lu->Numeric, &lu->Common);
159:   lu->Numeric = klu_K_factor(ai, aj, (PetscReal *)av, lu->Symbolic, &lu->Common);
160:   PetscCheck(lu->Numeric, PETSC_COMM_SELF, PETSC_ERR_LIB, "KLU Numeric factorization failed");

162:   lu->flg                = SAME_NONZERO_PATTERN;
163:   lu->CleanUpKLU         = PETSC_TRUE;
164:   F->ops->solve          = MatSolve_KLU;
165:   F->ops->solvetranspose = MatSolveTranspose_KLU;
166:   PetscFunctionReturn(PETSC_SUCCESS);
167: }

169: static PetscErrorCode MatLUFactorSymbolic_KLU(Mat F, Mat A, IS r, IS c, const MatFactorInfo *info)
170: {
171:   Mat_SeqAIJ     *a  = (Mat_SeqAIJ *)A->data;
172:   Mat_KLU        *lu = (Mat_KLU *)(F->data);
173:   PetscInt        i, *ai = a->i, *aj = a->j, m = A->rmap->n, n = A->cmap->n;
174:   const PetscInt *ra, *ca;

176:   PetscFunctionBegin;
177:   if (lu->PetscMatOrdering) {
178:     PetscCall(ISGetIndices(r, &ra));
179:     PetscCall(ISGetIndices(c, &ca));
180:     PetscCall(PetscMalloc2(m, &lu->perm_r, n, &lu->perm_c));
181:     /* we cannot simply memcpy on 64-bit archs */
182:     for (i = 0; i < m; i++) lu->perm_r[i] = ra[i];
183:     for (i = 0; i < n; i++) lu->perm_c[i] = ca[i];
184:     PetscCall(ISRestoreIndices(r, &ra));
185:     PetscCall(ISRestoreIndices(c, &ca));
186:   }

188:   /* symbolic factorization of A' */
189:   if (r) {
190:     lu->PetscMatOrdering = PETSC_TRUE;
191:     lu->Symbolic         = klu_K_analyze_given(n, ai, aj, lu->perm_c, lu->perm_r, &lu->Common);
192:   } else { /* use klu internal ordering */
193:     lu->Symbolic = klu_K_analyze(n, ai, aj, &lu->Common);
194:   }
195:   PetscCheck(lu->Symbolic, PETSC_COMM_SELF, PETSC_ERR_LIB, "KLU Symbolic Factorization failed");

197:   lu->flg                   = DIFFERENT_NONZERO_PATTERN;
198:   lu->CleanUpKLU            = PETSC_TRUE;
199:   (F)->ops->lufactornumeric = MatLUFactorNumeric_KLU;
200:   PetscFunctionReturn(PETSC_SUCCESS);
201: }

203: static PetscErrorCode MatView_Info_KLU(Mat A, PetscViewer viewer)
204: {
205:   Mat_KLU       *lu      = (Mat_KLU *)A->data;
206:   klu_K_numeric *Numeric = (klu_K_numeric *)lu->Numeric;

208:   PetscFunctionBegin;
209:   PetscCall(PetscViewerASCIIPrintf(viewer, "KLU stats:\n"));
210:   PetscCall(PetscViewerASCIIPrintf(viewer, "  Number of diagonal blocks: %" PetscInt_FMT "\n", (PetscInt)(Numeric->nblocks)));
211:   PetscCall(PetscViewerASCIIPrintf(viewer, "  Total nonzeros=%" PetscInt_FMT "\n", (PetscInt)(Numeric->lnz + Numeric->unz)));
212:   PetscCall(PetscViewerASCIIPrintf(viewer, "KLU runtime parameters:\n"));
213:   /* Control parameters used by numeric factorization */
214:   PetscCall(PetscViewerASCIIPrintf(viewer, "  Partial pivoting tolerance: %g\n", lu->Common.tol));
215:   /* BTF preordering */
216:   PetscCall(PetscViewerASCIIPrintf(viewer, "  BTF preordering enabled: %" PetscInt_FMT "\n", (PetscInt)(lu->Common.btf)));
217:   /* mat ordering */
218:   if (!lu->PetscMatOrdering) PetscCall(PetscViewerASCIIPrintf(viewer, "  Ordering: %s (not using the PETSc ordering)\n", KluOrderingTypes[(int)lu->Common.ordering]));
219:   /* matrix row scaling */
220:   PetscCall(PetscViewerASCIIPrintf(viewer, "  Matrix row scaling: %s\n", scale[(int)lu->Common.scale]));
221:   PetscFunctionReturn(PETSC_SUCCESS);
222: }

224: static PetscErrorCode MatView_KLU(Mat A, PetscViewer viewer)
225: {
226:   PetscBool         iascii;
227:   PetscViewerFormat format;

229:   PetscFunctionBegin;
230:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
231:   if (iascii) {
232:     PetscCall(PetscViewerGetFormat(viewer, &format));
233:     if (format == PETSC_VIEWER_ASCII_INFO) PetscCall(MatView_Info_KLU(A, viewer));
234:   }
235:   PetscFunctionReturn(PETSC_SUCCESS);
236: }

238: PetscErrorCode MatFactorGetSolverType_seqaij_klu(Mat A, MatSolverType *type)
239: {
240:   PetscFunctionBegin;
241:   *type = MATSOLVERKLU;
242:   PetscFunctionReturn(PETSC_SUCCESS);
243: }

245: /*MC
246:   MATSOLVERKLU = "klu" - A matrix type providing direct solvers, LU, for sequential matrices
247:   via the external package KLU.

249:   `./configure --download-suitesparse` to install PETSc to use KLU

251:   Use `-pc_type lu` `-pc_factor_mat_solver_type klu` to use this direct solver

253:   Consult KLU documentation for more information on the options database keys below.

255:   Options Database Keys:
256: + -mat_klu_pivot_tol <0.001>                  - Partial pivoting tolerance
257: . -mat_klu_use_btf <1>                        - Use BTF preordering
258: . -mat_klu_ordering <AMD>                     - KLU reordering scheme to reduce fill-in (choose one of) `AMD`, `COLAMD`, `PETSC`
259: - -mat_klu_row_scale <NONE>                   - Matrix row scaling (choose one of) `NONE`, `SUM`, `MAX`

261:    Level: beginner

263:    Note:
264:    KLU is part of SuiteSparse http://faculty.cse.tamu.edu/davis/suitesparse.html

266: .seealso: [](ch_matrices), `Mat`, `PCLU`, `MATSOLVERUMFPACK`, `MATSOLVERCHOLMOD`, `PCFactorSetMatSolverType()`, `MatSolverType`
267: M*/

269: PETSC_INTERN PetscErrorCode MatGetFactor_seqaij_klu(Mat A, MatFactorType ftype, Mat *F)
270: {
271:   Mat       B;
272:   Mat_KLU  *lu;
273:   PetscInt  m = A->rmap->n, n = A->cmap->n, idx = 0, status;
274:   PetscBool flg;

276:   PetscFunctionBegin;
277:   /* Create the factorization matrix F */
278:   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
279:   PetscCall(MatSetSizes(B, PETSC_DECIDE, PETSC_DECIDE, m, n));
280:   PetscCall(PetscStrallocpy("klu", &((PetscObject)B)->type_name));
281:   PetscCall(MatSetUp(B));

283:   PetscCall(PetscNew(&lu));

285:   B->data                  = lu;
286:   B->ops->getinfo          = MatGetInfo_External;
287:   B->ops->lufactorsymbolic = MatLUFactorSymbolic_KLU;
288:   B->ops->destroy          = MatDestroy_KLU;
289:   B->ops->view             = MatView_KLU;

291:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_seqaij_klu));

293:   B->factortype   = MAT_FACTOR_LU;
294:   B->assembled    = PETSC_TRUE; /* required by -ksp_view */
295:   B->preallocated = PETSC_TRUE;

297:   PetscCall(PetscFree(B->solvertype));
298:   PetscCall(PetscStrallocpy(MATSOLVERKLU, &B->solvertype));
299:   B->canuseordering = PETSC_TRUE;
300:   PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_LU]));

302:   /* initializations */
303:   /* get the default control parameters */
304:   status = klu_K_defaults(&lu->Common);
305:   PetscCheck(status > 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "KLU Initialization failed");

307:   lu->Common.scale = 0; /* No row scaling */

309:   PetscOptionsBegin(PetscObjectComm((PetscObject)B), ((PetscObject)B)->prefix, "KLU Options", "Mat");
310:   /* Partial pivoting tolerance */
311:   PetscCall(PetscOptionsReal("-mat_klu_pivot_tol", "Partial pivoting tolerance", "None", lu->Common.tol, &lu->Common.tol, NULL));
312:   /* BTF pre-ordering */
313:   PetscCall(PetscOptionsInt("-mat_klu_use_btf", "Enable BTF preordering", "None", (PetscInt)lu->Common.btf, (PetscInt *)&lu->Common.btf, NULL));
314:   /* Matrix reordering */
315:   PetscCall(PetscOptionsEList("-mat_klu_ordering", "Internal ordering method", "None", KluOrderingTypes, PETSC_STATIC_ARRAY_LENGTH(KluOrderingTypes), KluOrderingTypes[0], &idx, &flg));
316:   lu->Common.ordering = (int)idx;
317:   /* Matrix row scaling */
318:   PetscCall(PetscOptionsEList("-mat_klu_row_scale", "Matrix row scaling", "None", scale, 3, scale[0], &idx, &flg));
319:   PetscOptionsEnd();
320:   *F = B;
321:   PetscFunctionReturn(PETSC_SUCCESS);
322: }