Actual source code: schurm.c
1: #include <../src/ksp/ksp/utils/schurm/schurm.h>
3: const char *const MatSchurComplementAinvTypes[] = {"DIAG", "LUMP", "BLOCKDIAG", "FULL", "MatSchurComplementAinvType", "MAT_SCHUR_COMPLEMENT_AINV_", NULL};
5: PetscErrorCode MatCreateVecs_SchurComplement(Mat N, Vec *right, Vec *left)
6: {
7: Mat_SchurComplement *Na = (Mat_SchurComplement *)N->data;
9: PetscFunctionBegin;
10: if (Na->D) {
11: PetscCall(MatCreateVecs(Na->D, right, left));
12: PetscFunctionReturn(PETSC_SUCCESS);
13: }
14: if (right) PetscCall(MatCreateVecs(Na->B, right, NULL));
15: if (left) PetscCall(MatCreateVecs(Na->C, NULL, left));
16: PetscFunctionReturn(PETSC_SUCCESS);
17: }
19: PetscErrorCode MatView_SchurComplement(Mat N, PetscViewer viewer)
20: {
21: Mat_SchurComplement *Na = (Mat_SchurComplement *)N->data;
23: PetscFunctionBegin;
24: PetscCall(PetscViewerASCIIPrintf(viewer, "Schur complement A11 - A10 inv(A00) A01\n"));
25: if (Na->D) {
26: PetscCall(PetscViewerASCIIPrintf(viewer, "A11\n"));
27: PetscCall(PetscViewerASCIIPushTab(viewer));
28: PetscCall(MatView(Na->D, viewer));
29: PetscCall(PetscViewerASCIIPopTab(viewer));
30: } else {
31: PetscCall(PetscViewerASCIIPrintf(viewer, "A11 = 0\n"));
32: }
33: PetscCall(PetscViewerASCIIPrintf(viewer, "A10\n"));
34: PetscCall(PetscViewerASCIIPushTab(viewer));
35: PetscCall(MatView(Na->C, viewer));
36: PetscCall(PetscViewerASCIIPopTab(viewer));
37: PetscCall(PetscViewerASCIIPrintf(viewer, "KSP solver for A00 block viewable with the additional option -%sksp_view\n", ((PetscObject)Na->ksp)->prefix ? ((PetscObject)Na->ksp)->prefix : NULL));
38: PetscCall(PetscViewerASCIIPrintf(viewer, "A01\n"));
39: PetscCall(PetscViewerASCIIPushTab(viewer));
40: PetscCall(MatView(Na->B, viewer));
41: PetscCall(PetscViewerASCIIPopTab(viewer));
42: PetscFunctionReturn(PETSC_SUCCESS);
43: }
45: /*
46: A11^T - A01^T ksptrans(A00,Ap00) A10^T
47: */
48: PetscErrorCode MatMultTranspose_SchurComplement(Mat N, Vec x, Vec y)
49: {
50: Mat_SchurComplement *Na = (Mat_SchurComplement *)N->data;
52: PetscFunctionBegin;
53: if (!Na->work1) PetscCall(MatCreateVecs(Na->A, &Na->work1, NULL));
54: if (!Na->work2) PetscCall(MatCreateVecs(Na->A, &Na->work2, NULL));
55: PetscCall(MatMultTranspose(Na->C, x, Na->work1));
56: PetscCall(KSPSolveTranspose(Na->ksp, Na->work1, Na->work2));
57: PetscCall(MatMultTranspose(Na->B, Na->work2, y));
58: PetscCall(VecScale(y, -1.0));
59: if (Na->D) PetscCall(MatMultTransposeAdd(Na->D, x, y, y));
60: PetscFunctionReturn(PETSC_SUCCESS);
61: }
63: /*
64: A11 - A10 ksp(A00,Ap00) A01
65: */
66: PetscErrorCode MatMult_SchurComplement(Mat N, Vec x, Vec y)
67: {
68: Mat_SchurComplement *Na = (Mat_SchurComplement *)N->data;
70: PetscFunctionBegin;
71: if (!Na->work1) PetscCall(MatCreateVecs(Na->A, &Na->work1, NULL));
72: if (!Na->work2) PetscCall(MatCreateVecs(Na->A, &Na->work2, NULL));
73: PetscCall(MatMult(Na->B, x, Na->work1));
74: PetscCall(KSPSolve(Na->ksp, Na->work1, Na->work2));
75: PetscCall(MatMult(Na->C, Na->work2, y));
76: PetscCall(VecScale(y, -1.0));
77: if (Na->D) PetscCall(MatMultAdd(Na->D, x, y, y));
78: PetscFunctionReturn(PETSC_SUCCESS);
79: }
81: /*
82: A11 - A10 ksp(A00,Ap00) A01
83: */
84: PetscErrorCode MatMultAdd_SchurComplement(Mat N, Vec x, Vec y, Vec z)
85: {
86: Mat_SchurComplement *Na = (Mat_SchurComplement *)N->data;
88: PetscFunctionBegin;
89: if (!Na->work1) PetscCall(MatCreateVecs(Na->A, &Na->work1, NULL));
90: if (!Na->work2) PetscCall(MatCreateVecs(Na->A, &Na->work2, NULL));
91: PetscCall(MatMult(Na->B, x, Na->work1));
92: PetscCall(KSPSolve(Na->ksp, Na->work1, Na->work2));
93: if (y == z) {
94: PetscCall(VecScale(Na->work2, -1.0));
95: PetscCall(MatMultAdd(Na->C, Na->work2, z, z));
96: } else {
97: PetscCall(MatMult(Na->C, Na->work2, z));
98: PetscCall(VecAYPX(z, -1.0, y));
99: }
100: if (Na->D) PetscCall(MatMultAdd(Na->D, x, z, z));
101: PetscFunctionReturn(PETSC_SUCCESS);
102: }
104: PetscErrorCode MatSetFromOptions_SchurComplement(Mat N, PetscOptionItems *PetscOptionsObject)
105: {
106: Mat_SchurComplement *Na = (Mat_SchurComplement *)N->data;
108: PetscFunctionBegin;
109: PetscOptionsHeadBegin(PetscOptionsObject, "MatSchurComplementOptions");
110: Na->ainvtype = MAT_SCHUR_COMPLEMENT_AINV_DIAG;
111: PetscCall(PetscOptionsEnum("-mat_schur_complement_ainv_type", "Type of approximation for DIAGFORM(A00) used when assembling Sp = A11 - A10 inv(DIAGFORM(A00)) A01", "MatSchurComplementSetAinvType", MatSchurComplementAinvTypes, (PetscEnum)Na->ainvtype,
112: (PetscEnum *)&Na->ainvtype, NULL));
113: PetscOptionsHeadEnd();
114: PetscCall(KSPSetFromOptions(Na->ksp));
115: PetscFunctionReturn(PETSC_SUCCESS);
116: }
118: PetscErrorCode MatDestroy_SchurComplement(Mat N)
119: {
120: Mat_SchurComplement *Na = (Mat_SchurComplement *)N->data;
122: PetscFunctionBegin;
123: PetscCall(MatDestroy(&Na->A));
124: PetscCall(MatDestroy(&Na->Ap));
125: PetscCall(MatDestroy(&Na->B));
126: PetscCall(MatDestroy(&Na->C));
127: PetscCall(MatDestroy(&Na->D));
128: PetscCall(VecDestroy(&Na->work1));
129: PetscCall(VecDestroy(&Na->work2));
130: PetscCall(KSPDestroy(&Na->ksp));
131: PetscCall(PetscFree(N->data));
132: PetscCall(PetscObjectComposeFunction((PetscObject)N, "MatProductSetFromOptions_schurcomplement_seqdense_C", NULL));
133: PetscCall(PetscObjectComposeFunction((PetscObject)N, "MatProductSetFromOptions_schurcomplement_mpidense_C", NULL));
134: PetscFunctionReturn(PETSC_SUCCESS);
135: }
137: /*@
138: MatCreateSchurComplement - Creates a new `Mat` that behaves like the Schur complement of a matrix
140: Collective
142: Input Parameters:
143: + A00 - the upper-left block of the original matrix A = [A00 A01; A10 A11]
144: . Ap00 - preconditioning matrix for use in ksp(A00,Ap00) to approximate the action of A00^{-1}
145: . A01 - the upper-right block of the original matrix A = [A00 A01; A10 A11]
146: . A10 - the lower-left block of the original matrix A = [A00 A01; A10 A11]
147: - A11 - (optional) the lower-right block of the original matrix A = [A00 A01; A10 A11]
149: Output Parameter:
150: . S - the matrix that behaves as the Schur complement S = A11 - A10 ksp(A00,Ap00) A01
152: Level: intermediate
154: Notes:
155: The Schur complement is NOT explicitly formed! Rather, this function returns a virtual Schur complement
156: that can compute the matrix-vector product by using formula S = A11 - A10 A^{-1} A01
157: for Schur complement S and a `KSP` solver to approximate the action of A^{-1}.
159: All four matrices must have the same MPI communicator.
161: `A00` and `A11` must be square matrices.
163: `MatGetSchurComplement()` takes as arguments the index sets for the submatrices and returns both the virtual Schur complement (what this returns) plus
164: a sparse approximation to the Schur complement (useful for building a preconditioner for the Schur complement) which can be obtained from this
165: matrix with `MatSchurComplementGetPmat()`
167: Developer Notes:
168: The API that includes `MatGetSchurComplement()`, `MatCreateSchurComplement()`, `MatSchurComplementGetPmat()` should be refactored to
169: remove redundancy and be clearer and simpler.
171: .seealso: [](ch_ksp), `MatCreateNormal()`, `MatMult()`, `MatCreate()`, `MatSchurComplementGetKSP()`, `MatSchurComplementUpdateSubMatrices()`, `MatCreateTranspose()`, `MatGetSchurComplement()`,
172: `MatSchurComplementGetPmat()`, `MatSchurComplementSetSubMatrices()`
173: @*/
174: PetscErrorCode MatCreateSchurComplement(Mat A00, Mat Ap00, Mat A01, Mat A10, Mat A11, Mat *S)
175: {
176: PetscFunctionBegin;
177: PetscCall(KSPInitializePackage());
178: PetscCall(MatCreate(PetscObjectComm((PetscObject)A00), S));
179: PetscCall(MatSetType(*S, MATSCHURCOMPLEMENT));
180: PetscCall(MatSchurComplementSetSubMatrices(*S, A00, Ap00, A01, A10, A11));
181: PetscFunctionReturn(PETSC_SUCCESS);
182: }
184: /*@
185: MatSchurComplementSetSubMatrices - Sets the matrices that define the Schur complement
187: Collective
189: Input Parameters:
190: + S - matrix obtained with `MatSetType`(S,`MATSCHURCOMPLEMENT`)
191: . A00 - the upper-left block of the original matrix A = [A00 A01; A10 A11]
192: . Ap00 - preconditioning matrix for use in ksp(A00,Ap00) to approximate the action of A00^{-1}
193: . A01 - the upper-right block of the original matrix A = [A00 A01; A10 A11]
194: . A10 - the lower-left block of the original matrix A = [A00 A01; A10 A11]
195: - A11 - (optional) the lower-right block of the original matrix A = [A00 A01; A10 A11]
197: Level: intermediate
199: Notes:
200: The Schur complement is NOT explicitly formed! Rather, this
201: object performs the matrix-vector product of the Schur complement by using formula S = A11 - A10 ksp(A00,Ap00) A01
203: All four matrices must have the same MPI communicator.
205: `A00` and `A11` must be square matrices.
207: This is to be used in the context of code such as
208: .vb
209: MatSetType(S,MATSCHURCOMPLEMENT);
210: MatSchurComplementSetSubMatrices(S,...);
211: .ve
212: while `MatSchurComplementUpdateSubMatrices()` should only be called after `MatCreateSchurComplement()` or `MatSchurComplementSetSubMatrices()`
214: .seealso: [](ch_ksp), `Mat`, `MatCreateNormal()`, `MatMult()`, `MatCreate()`, `MatSchurComplementGetKSP()`, `MatSchurComplementUpdateSubMatrices()`, `MatCreateTranspose()`, `MatCreateSchurComplement()`, `MatGetSchurComplement()`
215: @*/
216: PetscErrorCode MatSchurComplementSetSubMatrices(Mat S, Mat A00, Mat Ap00, Mat A01, Mat A10, Mat A11)
217: {
218: Mat_SchurComplement *Na = (Mat_SchurComplement *)S->data;
219: PetscBool isschur;
221: PetscFunctionBegin;
222: PetscCall(PetscObjectTypeCompare((PetscObject)S, MATSCHURCOMPLEMENT, &isschur));
223: if (!isschur) PetscFunctionReturn(PETSC_SUCCESS);
224: PetscCheck(!S->assembled, PetscObjectComm((PetscObject)S), PETSC_ERR_ARG_WRONGSTATE, "Use MatSchurComplementUpdateSubMatrices() for already used matrix");
229: PetscCheckSameComm(A00, 2, Ap00, 3);
230: PetscCheckSameComm(A00, 2, A01, 4);
231: PetscCheckSameComm(A00, 2, A10, 5);
232: PetscCheck(A00->rmap->n == A00->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Local rows of A00 %" PetscInt_FMT " do not equal local columns %" PetscInt_FMT, A00->rmap->n, A00->cmap->n);
233: PetscCheck(A00->rmap->n == Ap00->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Local rows of A00 %" PetscInt_FMT " do not equal local rows of Ap00 %" PetscInt_FMT, A00->rmap->n, Ap00->rmap->n);
234: PetscCheck(Ap00->rmap->n == Ap00->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Local rows of Ap00 %" PetscInt_FMT " do not equal local columns %" PetscInt_FMT, Ap00->rmap->n, Ap00->cmap->n);
235: PetscCheck(A00->cmap->n == A01->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Local columns of A00 %" PetscInt_FMT " do not equal local rows of A01 %" PetscInt_FMT, A00->cmap->n, A01->rmap->n);
236: PetscCheck(A10->cmap->n == A00->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Local columns of A10 %" PetscInt_FMT " do not equal local rows of A00 %" PetscInt_FMT, A10->cmap->n, A00->rmap->n);
237: if (A11) {
239: PetscCheckSameComm(A00, 2, A11, 6);
240: PetscCheck(A10->rmap->n == A11->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Local rows of A10 %" PetscInt_FMT " do not equal local rows A11 %" PetscInt_FMT, A10->rmap->n, A11->rmap->n);
241: }
243: PetscCall(MatSetSizes(S, A10->rmap->n, A01->cmap->n, A10->rmap->N, A01->cmap->N));
244: PetscCall(PetscObjectReference((PetscObject)A00));
245: PetscCall(PetscObjectReference((PetscObject)Ap00));
246: PetscCall(PetscObjectReference((PetscObject)A01));
247: PetscCall(PetscObjectReference((PetscObject)A10));
248: Na->A = A00;
249: Na->Ap = Ap00;
250: Na->B = A01;
251: Na->C = A10;
252: Na->D = A11;
253: if (A11) PetscCall(PetscObjectReference((PetscObject)A11));
254: PetscCall(MatSetUp(S));
255: PetscCall(KSPSetOperators(Na->ksp, A00, Ap00));
256: S->assembled = PETSC_TRUE;
257: PetscFunctionReturn(PETSC_SUCCESS);
258: }
260: /*@
261: MatSchurComplementGetKSP - Gets the `KSP` object that is used to solve with A00 in the Schur complement matrix S = A11 - A10 ksp(A00,Ap00) A01
263: Not Collective
265: Input Parameter:
266: . S - matrix obtained with `MatCreateSchurComplement()` (or equivalent) and implementing the action of A11 - A10 ksp(A00,Ap00) A01
268: Output Parameter:
269: . ksp - the linear solver object
271: Options Database Key:
272: . -fieldsplit_<splitname_0>_XXX - sets KSP and PC options for the 0-split solver inside the Schur complement used in `PCFIELDSPLIT`; default <splitname_0> is 0.
274: Level: intermediate
276: .seealso: [](ch_ksp), `Mat`, `MatSchurComplementSetKSP()`, `MatCreateSchurComplement()`, `MatCreateNormal()`, `MatMult()`, `MatCreate()`
277: @*/
278: PetscErrorCode MatSchurComplementGetKSP(Mat S, KSP *ksp)
279: {
280: Mat_SchurComplement *Na;
281: PetscBool isschur;
283: PetscFunctionBegin;
285: PetscCall(PetscObjectTypeCompare((PetscObject)S, MATSCHURCOMPLEMENT, &isschur));
286: PetscCheck(isschur, PetscObjectComm((PetscObject)S), PETSC_ERR_ARG_WRONG, "Not for type %s", ((PetscObject)S)->type_name);
287: PetscAssertPointer(ksp, 2);
288: Na = (Mat_SchurComplement *)S->data;
289: *ksp = Na->ksp;
290: PetscFunctionReturn(PETSC_SUCCESS);
291: }
293: /*@
294: MatSchurComplementSetKSP - Sets the `KSP` object that is used to solve with A00 in the Schur complement matrix S = A11 - A10 ksp(A00,Ap00) A01
296: Not Collective
298: Input Parameters:
299: + S - matrix created with `MatCreateSchurComplement()`
300: - ksp - the linear solver object
302: Level: developer
304: Developer Notes:
305: This is used in `PCFIELDSPLIT` to reuse the 0-split `KSP` to implement ksp(A00,Ap00) in S.
306: The `KSP` operators are overwritten with A00 and Ap00 currently set in S.
308: .seealso: [](ch_ksp), `Mat`, `MatSchurComplementGetKSP()`, `MatCreateSchurComplement()`, `MatCreateNormal()`, `MatMult()`, `MatCreate()`, `MATSCHURCOMPLEMENT`
309: @*/
310: PetscErrorCode MatSchurComplementSetKSP(Mat S, KSP ksp)
311: {
312: Mat_SchurComplement *Na;
313: PetscBool isschur;
315: PetscFunctionBegin;
317: PetscCall(PetscObjectTypeCompare((PetscObject)S, MATSCHURCOMPLEMENT, &isschur));
318: if (!isschur) PetscFunctionReturn(PETSC_SUCCESS);
320: Na = (Mat_SchurComplement *)S->data;
321: PetscCall(PetscObjectReference((PetscObject)ksp));
322: PetscCall(KSPDestroy(&Na->ksp));
323: Na->ksp = ksp;
324: PetscCall(KSPSetOperators(Na->ksp, Na->A, Na->Ap));
325: PetscFunctionReturn(PETSC_SUCCESS);
326: }
328: /*@
329: MatSchurComplementUpdateSubMatrices - Updates the Schur complement matrix object with new submatrices
331: Collective
333: Input Parameters:
334: + S - matrix obtained with `MatCreateSchurComplement()` (or `MatSchurSetSubMatrices()`) and implementing the action of A11 - A10 ksp(A00,Ap00) A01
335: . A00 - the upper-left block of the original matrix A = [A00 A01; A10 A11]
336: . Ap00 - preconditioning matrix for use in ksp(A00,Ap00) to approximate the action of A00^{-1}
337: . A01 - the upper-right block of the original matrix A = [A00 A01; A10 A11]
338: . A10 - the lower-left block of the original matrix A = [A00 A01; A10 A11]
339: - A11 - (optional) the lower-right block of the original matrix A = [A00 A01; A10 A11]
341: Level: intermediate
343: Notes:
344: All four matrices must have the same MPI communicator
346: `A00` and `A11` must be square matrices
348: All of the matrices provided must have the same sizes as was used with `MatCreateSchurComplement()` or `MatSchurComplementSetSubMatrices()`
349: though they need not be the same matrices.
351: This can only be called after `MatCreateSchurComplement()` or `MatSchurComplementSetSubMatrices()`, it cannot be called immediately after `MatSetType`(S,`MATSCHURCOMPLEMENT`);
353: Developer Notes:
354: This code is almost identical to `MatSchurComplementSetSubMatrices()`. The API should be refactored.
356: .seealso: [](ch_ksp), `Mat`, `MatCreateNormal()`, `MatMult()`, `MatCreate()`, `MatSchurComplementGetKSP()`, `MatCreateSchurComplement()`
357: @*/
358: PetscErrorCode MatSchurComplementUpdateSubMatrices(Mat S, Mat A00, Mat Ap00, Mat A01, Mat A10, Mat A11)
359: {
360: Mat_SchurComplement *Na = (Mat_SchurComplement *)S->data;
361: PetscBool isschur;
363: PetscFunctionBegin;
365: PetscCall(PetscObjectTypeCompare((PetscObject)S, MATSCHURCOMPLEMENT, &isschur));
366: if (!isschur) PetscFunctionReturn(PETSC_SUCCESS);
367: PetscCheck(S->assembled, PetscObjectComm((PetscObject)S), PETSC_ERR_ARG_WRONGSTATE, "Use MatSchurComplementSetSubMatrices() for a new matrix");
372: PetscCheckSameComm(A00, 2, Ap00, 3);
373: PetscCheckSameComm(A00, 2, A01, 4);
374: PetscCheckSameComm(A00, 2, A10, 5);
375: PetscCheck(A00->rmap->n == A00->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Local rows of A00 %" PetscInt_FMT " do not equal local columns %" PetscInt_FMT, A00->rmap->n, A00->cmap->n);
376: PetscCheck(A00->rmap->n == Ap00->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Local rows of A00 %" PetscInt_FMT " do not equal local rows of Ap00 %" PetscInt_FMT, A00->rmap->n, Ap00->rmap->n);
377: PetscCheck(Ap00->rmap->n == Ap00->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Local rows of Ap00 %" PetscInt_FMT " do not equal local columns %" PetscInt_FMT, Ap00->rmap->n, Ap00->cmap->n);
378: PetscCheck(A00->cmap->n == A01->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Local columns of A00 %" PetscInt_FMT " do not equal local rows of A01 %" PetscInt_FMT, A00->cmap->n, A01->rmap->n);
379: PetscCheck(A10->cmap->n == A00->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Local columns of A10 %" PetscInt_FMT " do not equal local rows of A00 %" PetscInt_FMT, A10->cmap->n, A00->rmap->n);
380: if (A11) {
382: PetscCheckSameComm(A00, 2, A11, 6);
383: PetscCheck(A10->rmap->n == A11->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Local rows of A10 %" PetscInt_FMT " do not equal local rows A11 %" PetscInt_FMT, A10->rmap->n, A11->rmap->n);
384: }
386: PetscCall(PetscObjectReference((PetscObject)A00));
387: PetscCall(PetscObjectReference((PetscObject)Ap00));
388: PetscCall(PetscObjectReference((PetscObject)A01));
389: PetscCall(PetscObjectReference((PetscObject)A10));
390: if (A11) PetscCall(PetscObjectReference((PetscObject)A11));
392: PetscCall(MatDestroy(&Na->A));
393: PetscCall(MatDestroy(&Na->Ap));
394: PetscCall(MatDestroy(&Na->B));
395: PetscCall(MatDestroy(&Na->C));
396: PetscCall(MatDestroy(&Na->D));
398: Na->A = A00;
399: Na->Ap = Ap00;
400: Na->B = A01;
401: Na->C = A10;
402: Na->D = A11;
404: PetscCall(KSPSetOperators(Na->ksp, A00, Ap00));
405: PetscFunctionReturn(PETSC_SUCCESS);
406: }
408: /*@C
409: MatSchurComplementGetSubMatrices - Get the individual submatrices in the Schur complement
411: Collective
413: Input Parameter:
414: . S - matrix obtained with `MatCreateSchurComplement()` (or equivalent) and implementing the action of A11 - A10 ksp(A00,Ap00) A01
416: Output Parameters:
417: + A00 - the upper-left block of the original matrix A = [A00 A01; A10 A11]
418: . Ap00 - preconditioning matrix for use in ksp(A00,Ap00) to approximate the action of A^{-1}
419: . A01 - the upper-right block of the original matrix A = [A00 A01; A10 A11]
420: . A10 - the lower-left block of the original matrix A = [A00 A01; A10 A11]
421: - A11 - (optional) the lower-right block of the original matrix A = [A00 A01; A10 A11]
423: Level: intermediate
425: Note:
426: `A11` is optional, and thus can be `NULL`.
428: The reference counts of the submatrices are not increased before they are returned and the matrices should not be modified or destroyed.
430: .seealso: [](ch_ksp), `MatCreateNormal()`, `MatMult()`, `MatCreate()`, `MatSchurComplementGetKSP()`, `MatCreateSchurComplement()`, `MatSchurComplementUpdateSubMatrices()`
431: @*/
432: PetscErrorCode MatSchurComplementGetSubMatrices(Mat S, Mat *A00, Mat *Ap00, Mat *A01, Mat *A10, Mat *A11)
433: {
434: Mat_SchurComplement *Na = (Mat_SchurComplement *)S->data;
435: PetscBool flg;
437: PetscFunctionBegin;
439: PetscCall(PetscObjectTypeCompare((PetscObject)S, MATSCHURCOMPLEMENT, &flg));
440: PetscCheck(flg, PetscObjectComm((PetscObject)S), PETSC_ERR_ARG_WRONG, "Not for type %s", ((PetscObject)S)->type_name);
441: if (A00) *A00 = Na->A;
442: if (Ap00) *Ap00 = Na->Ap;
443: if (A01) *A01 = Na->B;
444: if (A10) *A10 = Na->C;
445: if (A11) *A11 = Na->D;
446: PetscFunctionReturn(PETSC_SUCCESS);
447: }
449: #include <petsc/private/kspimpl.h>
451: /*@
452: MatSchurComplementComputeExplicitOperator - Compute the Schur complement matrix explicitly
454: Collective
456: Input Parameter:
457: . A - the matrix obtained with `MatCreateSchurComplement()`
459: Output Parameter:
460: . S - the Schur complement matrix
462: Notes:
463: This can be expensive, so it is mainly for testing
465: Use `MatSchurComplementGetPmat()` to get a sparse approximation for the Schur complement suitable for use in building a preconditioner
467: Level: advanced
469: .seealso: [](ch_ksp), `MatCreateSchurComplement()`, `MatSchurComplementUpdate()`, `MatSchurComplementGetPmat()`
470: @*/
471: PetscErrorCode MatSchurComplementComputeExplicitOperator(Mat A, Mat *S)
472: {
473: Mat B, C, D, E = NULL, Bd, AinvBd;
474: KSP ksp;
475: PetscInt n, N, m, M;
476: PetscBool flg = PETSC_FALSE, set, symm;
478: PetscFunctionBegin;
479: PetscCall(MatSchurComplementGetSubMatrices(A, NULL, NULL, &B, &C, &D));
480: PetscCall(MatSchurComplementGetKSP(A, &ksp));
481: PetscCall(KSPSetUp(ksp));
482: PetscCall(MatConvert(B, MATDENSE, MAT_INITIAL_MATRIX, &Bd));
483: PetscCall(MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd));
484: PetscCall(KSPMatSolve(ksp, Bd, AinvBd));
485: PetscCall(MatDestroy(&Bd));
486: PetscCall(MatFilter(AinvBd, PETSC_SMALL, PETSC_FALSE, PETSC_FALSE));
487: if (D) {
488: PetscCall(MatGetLocalSize(D, &m, &n));
489: PetscCall(MatGetSize(D, &M, &N));
490: PetscCall(MatCreateDense(PetscObjectComm((PetscObject)A), m, n, M, N, NULL, S));
491: }
492: PetscCall(MatMatMult(C, AinvBd, D ? MAT_REUSE_MATRIX : MAT_INITIAL_MATRIX, PETSC_DEFAULT, S));
493: PetscCall(MatDestroy(&AinvBd));
494: if (D) {
495: PetscCall(PetscObjectTypeCompareAny((PetscObject)D, &flg, MATSEQSBAIJ, MATMPISBAIJ, ""));
496: if (flg) {
497: PetscCall(MatIsSymmetricKnown(A, &set, &symm));
498: if (!set || !symm) PetscCall(MatConvert(D, MATBAIJ, MAT_INITIAL_MATRIX, &E)); /* convert the (1,1) block to nonsymmetric storage for MatAXPY() */
499: }
500: PetscCall(MatAXPY(*S, -1.0, E ? E : D, DIFFERENT_NONZERO_PATTERN)); /* calls Mat[Get|Restore]RowUpperTriangular(), so only the upper triangular part is valid with symmetric storage */
501: }
502: PetscCall(MatConvert(*S, !E && flg ? MATSBAIJ : MATAIJ, MAT_INPLACE_MATRIX, S)); /* if A is symmetric and the (1,1) block is a MatSBAIJ, return S as a MatSBAIJ */
503: PetscCall(MatScale(*S, -1.0));
504: PetscCall(MatDestroy(&E));
505: PetscFunctionReturn(PETSC_SUCCESS);
506: }
508: /* Developer Notes:
509: This should be implemented with a MatCreate_SchurComplement() as that is the standard design for new Mat classes. */
510: PetscErrorCode MatGetSchurComplement_Basic(Mat mat, IS isrow0, IS iscol0, IS isrow1, IS iscol1, MatReuse mreuse, Mat *S, MatSchurComplementAinvType ainvtype, MatReuse preuse, Mat *Sp)
511: {
512: Mat A = NULL, Ap = NULL, B = NULL, C = NULL, D = NULL;
513: MatReuse reuse;
515: PetscFunctionBegin;
525: if (mreuse == MAT_IGNORE_MATRIX && preuse == MAT_IGNORE_MATRIX) PetscFunctionReturn(PETSC_SUCCESS);
529: PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
531: reuse = MAT_INITIAL_MATRIX;
532: if (mreuse == MAT_REUSE_MATRIX) {
533: PetscCall(MatSchurComplementGetSubMatrices(*S, &A, &Ap, &B, &C, &D));
534: PetscCheck(A && Ap && B && C, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Attempting to reuse matrix but Schur complement matrices unset");
535: PetscCheck(A == Ap, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Preconditioning matrix does not match operator");
536: PetscCall(MatDestroy(&Ap)); /* get rid of extra reference */
537: reuse = MAT_REUSE_MATRIX;
538: }
539: PetscCall(MatCreateSubMatrix(mat, isrow0, iscol0, reuse, &A));
540: PetscCall(MatCreateSubMatrix(mat, isrow0, iscol1, reuse, &B));
541: PetscCall(MatCreateSubMatrix(mat, isrow1, iscol0, reuse, &C));
542: PetscCall(MatCreateSubMatrix(mat, isrow1, iscol1, reuse, &D));
543: switch (mreuse) {
544: case MAT_INITIAL_MATRIX:
545: PetscCall(MatCreateSchurComplement(A, A, B, C, D, S));
546: break;
547: case MAT_REUSE_MATRIX:
548: PetscCall(MatSchurComplementUpdateSubMatrices(*S, A, A, B, C, D));
549: break;
550: default:
551: PetscCheck(mreuse == MAT_IGNORE_MATRIX, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Unrecognized value of mreuse %d", (int)mreuse);
552: }
553: if (preuse != MAT_IGNORE_MATRIX) PetscCall(MatCreateSchurComplementPmat(A, B, C, D, ainvtype, preuse, Sp));
554: PetscCall(MatDestroy(&A));
555: PetscCall(MatDestroy(&B));
556: PetscCall(MatDestroy(&C));
557: PetscCall(MatDestroy(&D));
558: PetscFunctionReturn(PETSC_SUCCESS);
559: }
561: /*@
562: MatGetSchurComplement - Obtain the Schur complement from eliminating part of the matrix in another part.
564: Collective
566: Input Parameters:
567: + A - matrix in which the complement is to be taken
568: . isrow0 - rows to eliminate
569: . iscol0 - columns to eliminate, (isrow0,iscol0) should be square and nonsingular
570: . isrow1 - rows in which the Schur complement is formed
571: . iscol1 - columns in which the Schur complement is formed
572: . mreuse - `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`, use `MAT_IGNORE_MATRIX` to put nothing in S
573: . ainvtype - the type of approximation used for the inverse of the (0,0) block used in forming Sp:
574: `MAT_SCHUR_COMPLEMENT_AINV_DIAG`, `MAT_SCHUR_COMPLEMENT_AINV_LUMP`, `MAT_SCHUR_COMPLEMENT_AINV_BLOCK_DIAG`, or `MAT_SCHUR_COMPLEMENT_AINV_FULL`
575: - preuse - `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`, use `MAT_IGNORE_MATRIX` to put nothing in Sp
577: Output Parameters:
578: + S - exact Schur complement, often of type `MATSCHURCOMPLEMENT` which is difficult to use for preconditioning
579: - Sp - approximate Schur complement from which a preconditioner can be built A11 - A10 inv(DIAGFORM(A00)) A01
581: Level: advanced
583: Notes:
584: Since the real Schur complement is usually dense, providing a good approximation to Sp usually requires
585: application-specific information.
587: Sometimes users would like to provide problem-specific data in the Schur complement, usually only for special row
588: and column index sets. In that case, the user should call `PetscObjectComposeFunction()` on the *S matrix and pass mreuse of `MAT_REUSE_MATRIX` to set
589: "MatGetSchurComplement_C" to their function. If their function needs to fall back to the default implementation, it
590: should call `MatGetSchurComplement_Basic()`.
592: `MatCreateSchurComplement()` takes as arguments the four submatrices and returns the virtual Schur complement (what this function returns in S).
594: `MatSchurComplementGetPmat()` takes the virtual Schur complement and returns an explicit approximate Schur complement (what this returns in Sp).
596: In other words calling `MatCreateSchurComplement()` followed by `MatSchurComplementGetPmat()` produces the same output as this function but with slightly different
597: inputs. The actually submatrices of the original block matrix instead of index sets to the submatrices.
599: Developer Notes:
600: The API that includes `MatGetSchurComplement()`, `MatCreateSchurComplement()`, `MatSchurComplementGetPmat()` should be refactored to
601: remove redundancy and be clearer and simpler.
603: .seealso: [](ch_ksp), `MatCreateSubMatrix()`, `PCFIELDSPLIT`, `MatCreateSchurComplement()`, `MatSchurComplementAinvType`
604: @*/
605: PetscErrorCode MatGetSchurComplement(Mat A, IS isrow0, IS iscol0, IS isrow1, IS iscol1, MatReuse mreuse, Mat *S, MatSchurComplementAinvType ainvtype, MatReuse preuse, Mat *Sp)
606: {
607: PetscErrorCode (*f)(Mat, IS, IS, IS, IS, MatReuse, Mat *, MatReuse, Mat *) = NULL;
609: PetscFunctionBegin;
621: PetscCheck(!A->factortype, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
622: if (mreuse == MAT_REUSE_MATRIX) { /* This is the only situation, in which we can demand that the user pass a non-NULL pointer to non-garbage in S. */
623: PetscCall(PetscObjectQueryFunction((PetscObject)*S, "MatGetSchurComplement_C", &f));
624: }
625: if (f) PetscCall((*f)(A, isrow0, iscol0, isrow1, iscol1, mreuse, S, preuse, Sp));
626: else PetscCall(MatGetSchurComplement_Basic(A, isrow0, iscol0, isrow1, iscol1, mreuse, S, ainvtype, preuse, Sp));
627: PetscFunctionReturn(PETSC_SUCCESS);
628: }
630: /*@
631: MatSchurComplementSetAinvType - set the type of approximation used for the inverse of the (0,0) block used in forming Sp in `MatSchurComplementGetPmat()`
633: Not Collective
635: Input Parameters:
636: + S - matrix obtained with `MatCreateSchurComplement()` (or equivalent) and implementing the action of A11 - A10 ksp(A00,Ap00) A01
637: - ainvtype - type of approximation to be used to form approximate Schur complement Sp = A11 - A10 inv(DIAGFORM(A00)) A01:
638: `MAT_SCHUR_COMPLEMENT_AINV_DIAG`, `MAT_SCHUR_COMPLEMENT_AINV_LUMP`, `MAT_SCHUR_COMPLEMENT_AINV_BLOCK_DIAG`, or `MAT_SCHUR_COMPLEMENT_AINV_FULL`
640: Options Database Key:
641: . -mat_schur_complement_ainv_type diag | lump | blockdiag | full - set schur complement type
643: Level: advanced
645: .seealso: [](ch_ksp), `MatSchurComplementAinvType`, `MatCreateSchurComplement()`, `MatGetSchurComplement()`, `MatSchurComplementGetPmat()`, `MatSchurComplementGetAinvType()`
646: @*/
647: PetscErrorCode MatSchurComplementSetAinvType(Mat S, MatSchurComplementAinvType ainvtype)
648: {
649: PetscBool isschur;
650: Mat_SchurComplement *schur;
652: PetscFunctionBegin;
654: PetscCall(PetscObjectTypeCompare((PetscObject)S, MATSCHURCOMPLEMENT, &isschur));
655: if (!isschur) PetscFunctionReturn(PETSC_SUCCESS);
657: schur = (Mat_SchurComplement *)S->data;
658: PetscCheck(ainvtype == MAT_SCHUR_COMPLEMENT_AINV_DIAG || ainvtype == MAT_SCHUR_COMPLEMENT_AINV_LUMP || ainvtype == MAT_SCHUR_COMPLEMENT_AINV_BLOCK_DIAG || ainvtype == MAT_SCHUR_COMPLEMENT_AINV_FULL, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unknown MatSchurComplementAinvType: %d", (int)ainvtype);
659: schur->ainvtype = ainvtype;
660: PetscFunctionReturn(PETSC_SUCCESS);
661: }
663: /*@
664: MatSchurComplementGetAinvType - get the type of approximation for the inverse of the (0,0) block used in forming Sp in `MatSchurComplementGetPmat()`
666: Not Collective
668: Input Parameter:
669: . S - matrix obtained with `MatCreateSchurComplement()` (or equivalent) and implementing the action of A11 - A10 ksp(A00,Ap00) A01
671: Output Parameter:
672: . ainvtype - type of approximation used to form approximate Schur complement Sp = A11 - A10 inv(DIAGFORM(A00)) A01:
673: `MAT_SCHUR_COMPLEMENT_AINV_DIAG`, `MAT_SCHUR_COMPLEMENT_AINV_LUMP`, `MAT_SCHUR_COMPLEMENT_AINV_BLOCK_DIAG`, or `MAT_SCHUR_COMPLEMENT_AINV_FULL`
675: Level: advanced
677: .seealso: [](ch_ksp), `MatSchurComplementAinvType`, `MatCreateSchurComplement()`, `MatGetSchurComplement()`, `MatSchurComplementGetPmat()`, `MatSchurComplementSetAinvType()`
678: @*/
679: PetscErrorCode MatSchurComplementGetAinvType(Mat S, MatSchurComplementAinvType *ainvtype)
680: {
681: PetscBool isschur;
682: Mat_SchurComplement *schur;
684: PetscFunctionBegin;
686: PetscCall(PetscObjectTypeCompare((PetscObject)S, MATSCHURCOMPLEMENT, &isschur));
687: PetscCheck(isschur, PetscObjectComm((PetscObject)S), PETSC_ERR_ARG_WRONG, "Not for type %s", ((PetscObject)S)->type_name);
688: schur = (Mat_SchurComplement *)S->data;
689: if (ainvtype) *ainvtype = schur->ainvtype;
690: PetscFunctionReturn(PETSC_SUCCESS);
691: }
693: /*@
694: MatCreateSchurComplementPmat - create a preconditioning matrix for the Schur complement by explicitly assembling the sparse matrix
695: Sp = A11 - A10 inv(DIAGFORM(A00)) A01
697: Collective
699: Input Parameters:
700: + A00 - the upper-left part of the original matrix A = [A00 A01; A10 A11]
701: . A01 - (optional) the upper-right part of the original matrix A = [A00 A01; A10 A11]
702: . A10 - (optional) the lower-left part of the original matrix A = [A00 A01; A10 A11]
703: . A11 - (optional) the lower-right part of the original matrix A = [A00 A01; A10 A11]
704: . ainvtype - type of approximation for DIAGFORM(A00) used when forming Sp = A11 - A10 inv(DIAGFORM(A00)) A01. See MatSchurComplementAinvType.
705: - preuse - `MAT_INITIAL_MATRIX` for a new Sp, or `MAT_REUSE_MATRIX` to reuse an existing Sp, or `MAT_IGNORE_MATRIX` to put nothing in Sp
707: Output Parameter:
708: . Sp - approximate Schur complement suitable for preconditioning the true Schur complement S = A11 - A10 inv(A00) A01
710: Level: advanced
712: .seealso: [](ch_ksp), `MatCreateSchurComplement()`, `MatGetSchurComplement()`, `MatSchurComplementGetPmat()`, `MatSchurComplementAinvType`
713: @*/
714: PetscErrorCode MatCreateSchurComplementPmat(Mat A00, Mat A01, Mat A10, Mat A11, MatSchurComplementAinvType ainvtype, MatReuse preuse, Mat *Sp)
715: {
716: PetscInt N00;
718: PetscFunctionBegin;
719: /* Use an appropriate approximate inverse of A00 to form A11 - A10 inv(DIAGFORM(A00)) A01; a NULL A01, A10 or A11 indicates a zero matrix. */
720: /* TODO: Perhaps should create an appropriately-sized zero matrix of the same type as A00? */
722: if (preuse == MAT_IGNORE_MATRIX) PetscFunctionReturn(PETSC_SUCCESS);
724: /* A zero size A00 or empty A01 or A10 imply S = A11. */
725: PetscCall(MatGetSize(A00, &N00, NULL));
726: if (!A01 || !A10 || !N00) {
727: if (preuse == MAT_INITIAL_MATRIX) {
728: PetscCall(MatDuplicate(A11, MAT_COPY_VALUES, Sp));
729: } else { /* MAT_REUSE_MATRIX */
730: /* TODO: when can we pass SAME_NONZERO_PATTERN? */
731: PetscCall(MatCopy(A11, *Sp, DIFFERENT_NONZERO_PATTERN));
732: }
733: } else {
734: Mat AdB;
735: Vec diag;
737: if (ainvtype == MAT_SCHUR_COMPLEMENT_AINV_LUMP || ainvtype == MAT_SCHUR_COMPLEMENT_AINV_DIAG) {
738: PetscCall(MatDuplicate(A01, MAT_COPY_VALUES, &AdB));
739: PetscCall(MatCreateVecs(A00, &diag, NULL));
740: if (ainvtype == MAT_SCHUR_COMPLEMENT_AINV_LUMP) {
741: PetscCall(MatGetRowSum(A00, diag));
742: } else {
743: PetscCall(MatGetDiagonal(A00, diag));
744: }
745: PetscCall(VecReciprocal(diag));
746: PetscCall(MatDiagonalScale(AdB, diag, NULL));
747: PetscCall(VecDestroy(&diag));
748: } else if (ainvtype == MAT_SCHUR_COMPLEMENT_AINV_BLOCK_DIAG) {
749: Mat A00_inv;
750: MatType type;
751: MPI_Comm comm;
753: PetscCall(PetscObjectGetComm((PetscObject)A00, &comm));
754: PetscCall(MatGetType(A00, &type));
755: PetscCall(MatCreate(comm, &A00_inv));
756: PetscCall(MatSetType(A00_inv, type));
757: PetscCall(MatInvertBlockDiagonalMat(A00, A00_inv));
758: PetscCall(MatMatMult(A00_inv, A01, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &AdB));
759: PetscCall(MatDestroy(&A00_inv));
760: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unknown MatSchurComplementAinvType: %d", ainvtype);
761: /* Cannot really reuse Sp in MatMatMult() because of MatAYPX() -->
762: MatAXPY() --> MatHeaderReplace() --> MatDestroy_XXX_MatMatMult() */
763: if (preuse == MAT_REUSE_MATRIX) PetscCall(MatDestroy(Sp));
764: PetscCall(MatMatMult(A10, AdB, MAT_INITIAL_MATRIX, PETSC_DEFAULT, Sp));
765: if (!A11) {
766: PetscCall(MatScale(*Sp, -1.0));
767: } else {
768: /* TODO: when can we pass SAME_NONZERO_PATTERN? */
769: PetscCall(MatAYPX(*Sp, -1, A11, DIFFERENT_NONZERO_PATTERN));
770: }
771: PetscCall(MatDestroy(&AdB));
772: }
773: PetscFunctionReturn(PETSC_SUCCESS);
774: }
776: static PetscErrorCode MatSchurComplementGetPmat_Basic(Mat S, MatReuse preuse, Mat *Sp)
777: {
778: Mat A, B, C, D;
779: Mat_SchurComplement *schur = (Mat_SchurComplement *)S->data;
781: PetscFunctionBegin;
782: if (preuse == MAT_IGNORE_MATRIX) PetscFunctionReturn(PETSC_SUCCESS);
783: PetscCall(MatSchurComplementGetSubMatrices(S, &A, NULL, &B, &C, &D));
784: PetscCheck(A, PetscObjectComm((PetscObject)S), PETSC_ERR_ARG_WRONGSTATE, "Schur complement component matrices unset");
785: if (schur->ainvtype != MAT_SCHUR_COMPLEMENT_AINV_FULL) PetscCall(MatCreateSchurComplementPmat(A, B, C, D, schur->ainvtype, preuse, Sp));
786: else {
787: if (preuse == MAT_REUSE_MATRIX) PetscCall(MatDestroy(Sp));
788: PetscCall(MatSchurComplementComputeExplicitOperator(S, Sp));
789: }
790: PetscFunctionReturn(PETSC_SUCCESS);
791: }
793: /*@
794: MatSchurComplementGetPmat - Obtain a preconditioning matrix for the Schur complement by assembling Sp = A11 - A10 inv(DIAGFORM(A00)) A01
796: Collective
798: Input Parameters:
799: + S - matrix obtained with MatCreateSchurComplement() (or equivalent) that implements the action of A11 - A10 ksp(A00,Ap00) A01
800: - preuse - `MAT_INITIAL_MATRIX` for a new Sp, or `MAT_REUSE_MATRIX` to reuse an existing Sp, or `MAT_IGNORE_MATRIX` to put nothing in Sp
802: Output Parameter:
803: . Sp - approximate Schur complement suitable for preconditioning the exact Schur complement S = A11 - A10 inv(A00) A01
805: Level: advanced
807: Notes:
808: The approximation of Sp depends on the the argument passed to to `MatSchurComplementSetAinvType()`
809: `MAT_SCHUR_COMPLEMENT_AINV_DIAG`, `MAT_SCHUR_COMPLEMENT_AINV_LUMP`, `MAT_SCHUR_COMPLEMENT_AINV_BLOCK_DIAG`, or `MAT_SCHUR_COMPLEMENT_AINV_FULL`
810: -mat_schur_complement_ainv_type <diag,lump,blockdiag,full>
812: Sometimes users would like to provide problem-specific data in the Schur complement, usually only
813: for special row and column index sets. In that case, the user should call `PetscObjectComposeFunction()` to set
814: "MatSchurComplementGetPmat_C" to their function. If their function needs to fall back to the default implementation,
815: it should call `MatSchurComplementGetPmat_Basic()`.
817: Developer Notes:
818: The API that includes `MatGetSchurComplement()`, `MatCreateSchurComplement()`, `MatSchurComplementGetPmat()` should be refactored to
819: remove redundancy and be clearer and simpler.
821: This routine should be called `MatSchurComplementCreatePmat()`
823: .seealso: [](ch_ksp), `MatCreateSubMatrix()`, `PCFIELDSPLIT`, `MatGetSchurComplement()`, `MatCreateSchurComplement()`, `MatSchurComplementSetAinvType()`
824: @*/
825: PetscErrorCode MatSchurComplementGetPmat(Mat S, MatReuse preuse, Mat *Sp)
826: {
827: PetscErrorCode (*f)(Mat, MatReuse, Mat *);
829: PetscFunctionBegin;
833: if (preuse != MAT_IGNORE_MATRIX) {
834: PetscAssertPointer(Sp, 3);
835: if (preuse == MAT_INITIAL_MATRIX) *Sp = NULL;
837: }
838: PetscCheck(!S->factortype, PetscObjectComm((PetscObject)S), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
840: PetscCall(PetscObjectQueryFunction((PetscObject)S, "MatSchurComplementGetPmat_C", &f));
841: if (f) PetscCall((*f)(S, preuse, Sp));
842: else PetscCall(MatSchurComplementGetPmat_Basic(S, preuse, Sp));
843: PetscFunctionReturn(PETSC_SUCCESS);
844: }
846: static PetscErrorCode MatProductNumeric_SchurComplement_Dense(Mat C)
847: {
848: Mat_Product *product = C->product;
849: Mat_SchurComplement *Na = (Mat_SchurComplement *)product->A->data;
850: Mat work1, work2;
851: PetscScalar *v;
852: PetscInt lda;
854: PetscFunctionBegin;
855: PetscCall(MatMatMult(Na->B, product->B, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &work1));
856: PetscCall(MatDuplicate(work1, MAT_DO_NOT_COPY_VALUES, &work2));
857: PetscCall(KSPMatSolve(Na->ksp, work1, work2));
858: PetscCall(MatDestroy(&work1));
859: PetscCall(MatDenseGetArrayWrite(C, &v));
860: PetscCall(MatDenseGetLDA(C, &lda));
861: PetscCall(MatCreateDense(PetscObjectComm((PetscObject)C), C->rmap->n, C->cmap->n, C->rmap->N, C->cmap->N, v, &work1));
862: PetscCall(MatDenseSetLDA(work1, lda));
863: PetscCall(MatMatMult(Na->C, work2, MAT_REUSE_MATRIX, PETSC_DEFAULT, &work1));
864: PetscCall(MatDenseRestoreArrayWrite(C, &v));
865: PetscCall(MatDestroy(&work2));
866: PetscCall(MatDestroy(&work1));
867: if (Na->D) {
868: PetscCall(MatMatMult(Na->D, product->B, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &work1));
869: PetscCall(MatAYPX(C, -1.0, work1, SAME_NONZERO_PATTERN));
870: PetscCall(MatDestroy(&work1));
871: } else PetscCall(MatScale(C, -1.0));
872: PetscFunctionReturn(PETSC_SUCCESS);
873: }
875: static PetscErrorCode MatProductSymbolic_SchurComplement_Dense(Mat C)
876: {
877: Mat_Product *product = C->product;
878: Mat A = product->A, B = product->B;
879: PetscInt m = A->rmap->n, n = B->cmap->n, M = A->rmap->N, N = B->cmap->N;
880: PetscBool flg;
882: PetscFunctionBegin;
883: PetscCall(MatSetSizes(C, m, n, M, N));
884: PetscCall(PetscObjectBaseTypeCompareAny((PetscObject)C, &flg, MATSEQDENSE, MATMPIDENSE, ""));
885: if (!flg) {
886: PetscCall(MatSetType(C, ((PetscObject)B)->type_name));
887: C->ops->productsymbolic = MatProductSymbolic_SchurComplement_Dense;
888: }
889: PetscCall(MatSetUp(C));
890: C->ops->productnumeric = MatProductNumeric_SchurComplement_Dense;
891: PetscFunctionReturn(PETSC_SUCCESS);
892: }
894: static PetscErrorCode MatProductSetFromOptions_Dense_AB(Mat C)
895: {
896: PetscFunctionBegin;
897: C->ops->productsymbolic = MatProductSymbolic_SchurComplement_Dense;
898: PetscFunctionReturn(PETSC_SUCCESS);
899: }
901: static PetscErrorCode MatProductSetFromOptions_SchurComplement_Dense(Mat C)
902: {
903: Mat_Product *product = C->product;
905: PetscFunctionBegin;
906: PetscCheck(product->type == MATPRODUCT_AB, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Not for product type %s", MatProductTypes[product->type]);
907: PetscCall(MatProductSetFromOptions_Dense_AB(C));
908: PetscFunctionReturn(PETSC_SUCCESS);
909: }
911: /*MC
912: MATSCHURCOMPLEMENT - "schurcomplement" - Matrix type that behaves like the Schur complement of a matrix.
914: Level: intermediate
916: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatType`, `MatCreateSchurComplement()`, `MatSchurComplementComputeExplicitOperator()`,
917: `MatSchurComplementGetSubMatrices()`, `MatSchurComplementGetKSP()`
918: M*/
919: PETSC_EXTERN PetscErrorCode MatCreate_SchurComplement(Mat N)
920: {
921: Mat_SchurComplement *Na;
923: PetscFunctionBegin;
924: PetscCall(PetscNew(&Na));
925: N->data = (void *)Na;
927: N->ops->destroy = MatDestroy_SchurComplement;
928: N->ops->getvecs = MatCreateVecs_SchurComplement;
929: N->ops->view = MatView_SchurComplement;
930: N->ops->mult = MatMult_SchurComplement;
931: N->ops->multtranspose = MatMultTranspose_SchurComplement;
932: N->ops->multadd = MatMultAdd_SchurComplement;
933: N->ops->setfromoptions = MatSetFromOptions_SchurComplement;
934: N->assembled = PETSC_FALSE;
935: N->preallocated = PETSC_FALSE;
937: PetscCall(KSPCreate(PetscObjectComm((PetscObject)N), &Na->ksp));
938: PetscCall(PetscObjectChangeTypeName((PetscObject)N, MATSCHURCOMPLEMENT));
939: PetscCall(PetscObjectComposeFunction((PetscObject)N, "MatProductSetFromOptions_schurcomplement_seqdense_C", MatProductSetFromOptions_SchurComplement_Dense));
940: PetscCall(PetscObjectComposeFunction((PetscObject)N, "MatProductSetFromOptions_schurcomplement_mpidense_C", MatProductSetFromOptions_SchurComplement_Dense));
941: PetscFunctionReturn(PETSC_SUCCESS);
942: }