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: PetscCall(PetscObjectComposeFunction((PetscObject)N, "MatProductSetFromOptions_anytype_C", NULL));
135: PetscFunctionReturn(PETSC_SUCCESS);
136: }
138: /*@
139: MatCreateSchurComplement - Creates a new `Mat` that behaves like the Schur complement of a matrix
141: Collective
143: Input Parameters:
144: + A00 - the upper-left block of the original matrix $A = [A00 A01; A10 A11]$
145: . Ap00 - matrix from which the preconditioner is constructed for use in $ksp(A00,Ap00)$ to approximate the action of $A00^{-1}$
146: . A01 - the upper-right block of the original matrix $A = [A00 A01; A10 A11]$
147: . A10 - the lower-left block of the original matrix $A = [A00 A01; A10 A11]$
148: - A11 - (optional) the lower-right block of the original matrix $A = [A00 A01; A10 A11]$
150: Output Parameter:
151: . S - the matrix that behaves as the Schur complement $S = A11 - A10 ksp(A00,Ap00) A01$
153: Level: intermediate
155: Notes:
156: The Schur complement is NOT explicitly formed! Rather, this function returns a virtual Schur complement
157: that can compute the matrix-vector product by using formula $S = A11 - A10 A^{-1} A01$
158: for Schur complement `S` and a `KSP` solver to approximate the action of $A^{-1}$.
160: All four matrices must have the same MPI communicator.
162: `A00` and `A11` must be square matrices.
164: `MatGetSchurComplement()` takes as arguments the index sets for the submatrices and returns both the virtual Schur complement (what this returns) plus
165: a sparse approximation to the Schur complement (useful for building a preconditioner for the Schur complement) which can be obtained from this
166: matrix with `MatSchurComplementGetPmat()`
168: Developer Notes:
169: The API that includes `MatGetSchurComplement()`, `MatCreateSchurComplement()`, `MatSchurComplementGetPmat()` should be refactored to
170: remove redundancy and be clearer and simpler.
172: .seealso: [](ch_ksp), `MatCreateNormal()`, `MatMult()`, `MatCreate()`, `MatSchurComplementGetKSP()`, `MatSchurComplementUpdateSubMatrices()`, `MatCreateTranspose()`, `MatGetSchurComplement()`,
173: `MatSchurComplementGetPmat()`, `MatSchurComplementSetSubMatrices()`
174: @*/
175: PetscErrorCode MatCreateSchurComplement(Mat A00, Mat Ap00, Mat A01, Mat A10, Mat A11, Mat *S)
176: {
177: PetscFunctionBegin;
178: PetscCall(KSPInitializePackage());
179: PetscCall(MatCreate(PetscObjectComm((PetscObject)A00), S));
180: PetscCall(MatSetType(*S, MATSCHURCOMPLEMENT));
181: PetscCall(MatSchurComplementSetSubMatrices(*S, A00, Ap00, A01, A10, A11));
182: PetscFunctionReturn(PETSC_SUCCESS);
183: }
185: /*@
186: MatSchurComplementSetSubMatrices - Sets the matrices that define the Schur complement
188: Collective
190: Input Parameters:
191: + S - matrix obtained with `MatSetType`(S,`MATSCHURCOMPLEMENT`)
192: . A00 - the upper-left block of the original matrix $A = [A00 A01; A10 A11]$
193: . Ap00 - matrix from which the preconditioner is constructed for use in $ksp(A00,Ap00)$ to approximate the action of $A00^{-1}$
194: . A01 - the upper-right block of the original matrix $A = [A00 A01; A10 A11]$
195: . A10 - the lower-left block of the original matrix $A = [A00 A01; A10 A11]$
196: - A11 - (optional) the lower-right block of the original matrix $A = [A00 A01; A10 A11]$
198: Level: intermediate
200: Notes:
201: The Schur complement is NOT explicitly formed! Rather, this
202: object performs the matrix-vector product of the Schur complement by using formula $S = A11 - A10 ksp(A00,Ap00) A01$
204: All four matrices must have the same MPI communicator.
206: `A00` and `A11` must be square matrices.
208: This is to be used in the context of code such as
209: .vb
210: MatSetType(S,MATSCHURCOMPLEMENT);
211: MatSchurComplementSetSubMatrices(S,...);
212: .ve
213: while `MatSchurComplementUpdateSubMatrices()` should only be called after `MatCreateSchurComplement()` or `MatSchurComplementSetSubMatrices()`
215: .seealso: [](ch_ksp), `Mat`, `MatCreateNormal()`, `MatMult()`, `MatCreate()`, `MatSchurComplementGetKSP()`, `MatSchurComplementUpdateSubMatrices()`, `MatCreateTranspose()`, `MatCreateSchurComplement()`, `MatGetSchurComplement()`
216: @*/
217: PetscErrorCode MatSchurComplementSetSubMatrices(Mat S, Mat A00, Mat Ap00, Mat A01, Mat A10, Mat A11)
218: {
219: Mat_SchurComplement *Na = (Mat_SchurComplement *)S->data;
220: PetscBool isschur;
222: PetscFunctionBegin;
223: PetscCall(PetscObjectTypeCompare((PetscObject)S, MATSCHURCOMPLEMENT, &isschur));
224: if (!isschur) PetscFunctionReturn(PETSC_SUCCESS);
225: PetscCheck(!S->assembled, PetscObjectComm((PetscObject)S), PETSC_ERR_ARG_WRONGSTATE, "Use MatSchurComplementUpdateSubMatrices() for already used matrix");
230: PetscCheckSameComm(A00, 2, Ap00, 3);
231: PetscCheckSameComm(A00, 2, A01, 4);
232: PetscCheckSameComm(A00, 2, A10, 5);
233: 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);
234: 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);
235: 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);
236: 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);
237: 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);
238: if (A11) {
240: PetscCheckSameComm(A00, 2, A11, 6);
241: 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);
242: }
244: PetscCall(MatSetSizes(S, A10->rmap->n, A01->cmap->n, A10->rmap->N, A01->cmap->N));
245: PetscCall(PetscObjectReference((PetscObject)A00));
246: PetscCall(PetscObjectReference((PetscObject)Ap00));
247: PetscCall(PetscObjectReference((PetscObject)A01));
248: PetscCall(PetscObjectReference((PetscObject)A10));
249: PetscCall(PetscObjectReference((PetscObject)A11));
250: Na->A = A00;
251: Na->Ap = Ap00;
252: Na->B = A01;
253: Na->C = A10;
254: Na->D = A11;
255: PetscCall(MatSetUp(S));
256: PetscCall(KSPSetOperators(Na->ksp, A00, Ap00));
257: S->assembled = PETSC_TRUE;
258: PetscFunctionReturn(PETSC_SUCCESS);
259: }
261: /*@
262: MatSchurComplementGetKSP - Gets the `KSP` object that is used to solve with `A00` in the Schur complement matrix $S = A11 - A10 ksp(A00,Ap00) A01$
264: Not Collective
266: Input Parameter:
267: . S - matrix obtained with `MatCreateSchurComplement()` (or equivalent) and implementing the action of $ A11 - A10 ksp(A00,Ap00) A01 $
269: Output Parameter:
270: . ksp - the linear solver object
272: Level: intermediate
274: .seealso: [](ch_ksp), `Mat`, `MatSchurComplementSetKSP()`, `MatCreateSchurComplement()`, `MatCreateNormal()`, `MatMult()`, `MatCreate()`
275: @*/
276: PetscErrorCode MatSchurComplementGetKSP(Mat S, KSP *ksp)
277: {
278: Mat_SchurComplement *Na;
279: PetscBool isschur;
281: PetscFunctionBegin;
283: PetscCall(PetscObjectTypeCompare((PetscObject)S, MATSCHURCOMPLEMENT, &isschur));
284: PetscCheck(isschur, PetscObjectComm((PetscObject)S), PETSC_ERR_ARG_WRONG, "Not for type %s", ((PetscObject)S)->type_name);
285: PetscAssertPointer(ksp, 2);
286: Na = (Mat_SchurComplement *)S->data;
287: *ksp = Na->ksp;
288: PetscFunctionReturn(PETSC_SUCCESS);
289: }
291: /*@
292: MatSchurComplementSetKSP - Sets the `KSP` object that is used to solve with `A00` in the Schur complement matrix $ S = A11 - A10 ksp(A00,Ap00) A01$
294: Not Collective
296: Input Parameters:
297: + S - matrix created with `MatCreateSchurComplement()`
298: - ksp - the linear solver object
300: Level: developer
302: Developer Notes:
303: This is used in `PCFIELDSPLIT` to reuse the 0-split `KSP` to implement $ksp(A00,Ap00)$ in `S`.
304: The `KSP` operators are overwritten with `A00` and `Ap00` currently set in `S`.
306: .seealso: [](ch_ksp), `Mat`, `MatSchurComplementGetKSP()`, `MatCreateSchurComplement()`, `MatCreateNormal()`, `MatMult()`, `MatCreate()`, `MATSCHURCOMPLEMENT`
307: @*/
308: PetscErrorCode MatSchurComplementSetKSP(Mat S, KSP ksp)
309: {
310: Mat_SchurComplement *Na;
311: PetscBool isschur;
313: PetscFunctionBegin;
315: PetscCall(PetscObjectTypeCompare((PetscObject)S, MATSCHURCOMPLEMENT, &isschur));
316: if (!isschur) PetscFunctionReturn(PETSC_SUCCESS);
318: Na = (Mat_SchurComplement *)S->data;
319: PetscCall(PetscObjectReference((PetscObject)ksp));
320: PetscCall(KSPDestroy(&Na->ksp));
321: Na->ksp = ksp;
322: PetscCall(KSPSetOperators(Na->ksp, Na->A, Na->Ap));
323: PetscFunctionReturn(PETSC_SUCCESS);
324: }
326: /*@
327: MatSchurComplementUpdateSubMatrices - Updates the Schur complement matrix object with new submatrices
329: Collective
331: Input Parameters:
332: + S - matrix obtained with `MatCreateSchurComplement()` (or `MatSchurSetSubMatrices()`) and implementing the action of $A11 - A10 ksp(A00,Ap00) A01$
333: . A00 - the upper-left block of the original matrix $A = [A00 A01; A10 A11]$
334: . Ap00 - matrix from which the preconditioner is constructed for use in $ksp(A00,Ap00)$ to approximate the action of $A00^{-1}$
335: . A01 - the upper-right block of the original matrix $A = [A00 A01; A10 A11]$
336: . A10 - the lower-left block of the original matrix $A = [A00 A01; A10 A11]$
337: - A11 - (optional) the lower-right block of the original matrix $A = [A00 A01; A10 A11]$
339: Level: intermediate
341: Notes:
342: All four matrices must have the same MPI communicator
344: `A00` and `A11` must be square matrices
346: All of the matrices provided must have the same sizes as was used with `MatCreateSchurComplement()` or `MatSchurComplementSetSubMatrices()`
347: though they need not be the same matrices.
349: This can only be called after `MatCreateSchurComplement()` or `MatSchurComplementSetSubMatrices()`, it cannot be called immediately after `MatSetType`(S,`MATSCHURCOMPLEMENT`);
351: Developer Notes:
352: This code is almost identical to `MatSchurComplementSetSubMatrices()`. The API should be refactored.
354: .seealso: [](ch_ksp), `Mat`, `MatCreateNormal()`, `MatMult()`, `MatCreate()`, `MatSchurComplementGetKSP()`, `MatCreateSchurComplement()`
355: @*/
356: PetscErrorCode MatSchurComplementUpdateSubMatrices(Mat S, Mat A00, Mat Ap00, Mat A01, Mat A10, Mat A11)
357: {
358: Mat_SchurComplement *Na = (Mat_SchurComplement *)S->data;
359: PetscBool isschur;
361: PetscFunctionBegin;
363: PetscCall(PetscObjectTypeCompare((PetscObject)S, MATSCHURCOMPLEMENT, &isschur));
364: if (!isschur) PetscFunctionReturn(PETSC_SUCCESS);
365: PetscCheck(S->assembled, PetscObjectComm((PetscObject)S), PETSC_ERR_ARG_WRONGSTATE, "Use MatSchurComplementSetSubMatrices() for a new matrix");
370: PetscCheckSameComm(A00, 2, Ap00, 3);
371: PetscCheckSameComm(A00, 2, A01, 4);
372: PetscCheckSameComm(A00, 2, A10, 5);
373: 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);
374: 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);
375: 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);
376: 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);
377: 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);
378: if (A11) {
380: PetscCheckSameComm(A00, 2, A11, 6);
381: 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);
382: }
384: PetscCall(PetscObjectReference((PetscObject)A00));
385: PetscCall(PetscObjectReference((PetscObject)Ap00));
386: PetscCall(PetscObjectReference((PetscObject)A01));
387: PetscCall(PetscObjectReference((PetscObject)A10));
388: PetscCall(PetscObjectReference((PetscObject)A11));
390: PetscCall(MatDestroy(&Na->A));
391: PetscCall(MatDestroy(&Na->Ap));
392: PetscCall(MatDestroy(&Na->B));
393: PetscCall(MatDestroy(&Na->C));
394: PetscCall(MatDestroy(&Na->D));
396: Na->A = A00;
397: Na->Ap = Ap00;
398: Na->B = A01;
399: Na->C = A10;
400: Na->D = A11;
402: PetscCall(KSPSetOperators(Na->ksp, A00, Ap00));
403: PetscFunctionReturn(PETSC_SUCCESS);
404: }
406: /*@
407: MatSchurComplementGetSubMatrices - Get the individual submatrices in the Schur complement
409: Collective
411: Input Parameter:
412: . S - matrix obtained with `MatCreateSchurComplement()` (or equivalent) and implementing the action of $A11 - A10 ksp(A00,Ap00) A01$
414: Output Parameters:
415: + A00 - the upper-left block of the original matrix $A = [A00 A01; A10 A11]$
416: . Ap00 - matrix from which the preconditioner is constructed for use in $ksp(A00,Ap00)$ to approximate the action of $A^{-1}$
417: . A01 - the upper-right block of the original matrix $A = [A00 A01; A10 A11]$
418: . A10 - the lower-left block of the original matrix $A = [A00 A01; A10 A11]$
419: - A11 - (optional) the lower-right block of the original matrix $A = [A00 A01; A10 A11]$
421: Level: intermediate
423: Note:
424: Use `NULL` for any unneeded output argument.
426: The reference counts of the submatrices are not increased before they are returned and the matrices should not be modified or destroyed.
428: .seealso: [](ch_ksp), `MatCreateNormal()`, `MatMult()`, `MatCreate()`, `MatSchurComplementGetKSP()`, `MatCreateSchurComplement()`, `MatSchurComplementUpdateSubMatrices()`
429: @*/
430: PetscErrorCode MatSchurComplementGetSubMatrices(Mat S, Mat *A00, Mat *Ap00, Mat *A01, Mat *A10, Mat *A11)
431: {
432: Mat_SchurComplement *Na = (Mat_SchurComplement *)S->data;
433: PetscBool flg;
435: PetscFunctionBegin;
437: PetscCall(PetscObjectTypeCompare((PetscObject)S, MATSCHURCOMPLEMENT, &flg));
438: PetscCheck(flg, PetscObjectComm((PetscObject)S), PETSC_ERR_ARG_WRONG, "Not for type %s", ((PetscObject)S)->type_name);
439: if (A00) *A00 = Na->A;
440: if (Ap00) *Ap00 = Na->Ap;
441: if (A01) *A01 = Na->B;
442: if (A10) *A10 = Na->C;
443: if (A11) *A11 = Na->D;
444: PetscFunctionReturn(PETSC_SUCCESS);
445: }
447: #include <petsc/private/kspimpl.h>
449: /*@
450: MatSchurComplementComputeExplicitOperator - Compute the Schur complement matrix explicitly
452: Collective
454: Input Parameter:
455: . A - the matrix obtained with `MatCreateSchurComplement()`
457: Output Parameter:
458: . S - the Schur complement matrix
460: Level: advanced
462: Notes:
463: This can be expensive when `S` is large, 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: `S` will automatically have the same prefix as `A` appended by `explicit_operator_`,
468: there are three options available: `-fieldsplit_1_explicit_operator_mat_type`,
469: `-fieldsplit_1_explicit_operator_mat_symmetric`, and `-fieldsplit_1_explicit_operator_mat_hermitian`
471: Developer Note:
472: The three aforementioned should not be parsed and used in this routine, but rather in `MatSetFromOptions()`
474: .seealso: [](ch_ksp), `MatCreateSchurComplement()`, `MatSchurComplementUpdateSubMatrices()`, `MatSchurComplementGetPmat()`
475: @*/
476: PetscErrorCode MatSchurComplementComputeExplicitOperator(Mat A, Mat *S)
477: {
478: Mat P, B, C, D, E = NULL, Bd, AinvBd, sub = NULL;
479: MatType mtype;
480: VecType vtype;
481: KSP ksp;
482: PetscInt n, N, m, M;
483: PetscBool flg = PETSC_FALSE, set, symm;
484: char prefix[256], type[256];
486: PetscFunctionBegin;
487: PetscAssertPointer(S, 2);
489: PetscCall(PetscObjectQuery((PetscObject)A, "AinvB", (PetscObject *)&AinvBd));
490: set = (PetscBool)(AinvBd != NULL);
491: if (set && AinvBd->cmap->N == -1) PetscFunctionReturn(PETSC_SUCCESS); // early bail out if composed Mat is uninitialized
492: PetscCall(MatSchurComplementGetSubMatrices(A, &P, NULL, &B, &C, &D));
493: PetscCall(MatGetVecType(B, &vtype));
494: PetscCall(MatGetLocalSize(B, &m, &n));
495: PetscCall(MatSchurComplementGetKSP(A, &ksp));
496: PetscCall(KSPSetUp(ksp));
497: if (set) {
498: PetscCheck(AinvBd->cmap->N >= A->cmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_SIZ, "Composed Mat should have at least as many columns as the Schur complement (%" PetscInt_FMT " >= %" PetscInt_FMT ")", AinvBd->cmap->N, A->cmap->N);
499: PetscCall(MatGetType(AinvBd, &mtype));
500: if (AinvBd->cmap->N > A->cmap->N) {
501: Mat s[2];
503: PetscCall(MatDuplicate(AinvBd, MAT_DO_NOT_COPY_VALUES, &Bd));
504: PetscCall(MatDenseGetSubMatrix(Bd, PETSC_DECIDE, PETSC_DECIDE, A->cmap->N, AinvBd->cmap->N, s));
505: PetscCall(MatDenseGetSubMatrix(AinvBd, PETSC_DECIDE, PETSC_DECIDE, A->cmap->N, AinvBd->cmap->N, s + 1));
506: PetscCall(MatCopy(s[1], s[0], SAME_NONZERO_PATTERN)); // copy the last columns of the composed Mat, which are likely the input columns of PCApply_FieldSplit_Schur()
507: PetscCall(MatDenseRestoreSubMatrix(AinvBd, s + 1));
508: PetscCall(MatDenseRestoreSubMatrix(Bd, s));
509: PetscCall(MatDenseGetSubMatrix(Bd, PETSC_DECIDE, PETSC_DECIDE, 0, A->cmap->N, &sub));
510: PetscCall(MatConvert(B, mtype, MAT_REUSE_MATRIX, &sub)); // copy A01 into the first columns of the block of RHS of KSPMatSolve()
511: PetscCall(MatDenseRestoreSubMatrix(Bd, &sub));
512: } else PetscCall(MatConvert(B, mtype, MAT_INITIAL_MATRIX, &Bd));
513: } else {
514: PetscCall(MatGetSize(B, &M, &N));
515: PetscCall(MatCreateDenseFromVecType(PetscObjectComm((PetscObject)A), vtype, m, n, M, N, PETSC_DECIDE, NULL, &AinvBd));
516: PetscCall(MatGetType(AinvBd, &mtype));
517: PetscCall(MatConvert(B, mtype, MAT_INITIAL_MATRIX, &Bd));
518: }
519: PetscCall(KSPMatSolve(ksp, Bd, AinvBd));
520: if (set && AinvBd->cmap->N > A->cmap->N) {
521: Mat AinvB;
522: PetscScalar *v;
523: PetscMemType type;
525: PetscCall(MatDenseGetArrayWriteAndMemType(AinvBd, &v, &type)); // no easy way to resize a Mat, so create a new one with the same data pointer
526: PetscCall(MatCreateDenseWithMemType(PetscObjectComm((PetscObject)A), type, AinvBd->rmap->n, A->cmap->n, AinvBd->rmap->N, A->cmap->N, PETSC_DECIDE, v, &AinvB));
527: PetscCall(MatDenseReplaceArrayWithMemType(AinvB, type, v)); // let MatDestroy() free the data pointer
528: PetscCall(MatDenseRestoreArrayWriteAndMemType(AinvBd, &v));
529: PetscCall(MatHeaderReplace(AinvBd, &AinvB)); // replace the input composed Mat with just A00^-1 A01 (trailing columns are removed)
530: }
531: PetscCall(MatDestroy(&Bd));
532: if (!set) PetscCall(MatFilter(AinvBd, PETSC_SMALL, PETSC_FALSE, PETSC_FALSE));
533: if (D && !*S) {
534: PetscCall(MatGetLocalSize(D, &m, &n));
535: PetscCall(MatGetSize(D, &M, &N));
536: PetscCall(MatCreateDenseFromVecType(PetscObjectComm((PetscObject)A), vtype, m, n, M, N, PETSC_DECIDE, NULL, S));
537: } else if (*S) {
538: PetscCall(MatGetType(AinvBd, &mtype));
539: PetscCall(MatSetType(*S, mtype));
540: }
541: PetscCall(MatMatMult(C, AinvBd, *S ? MAT_REUSE_MATRIX : MAT_INITIAL_MATRIX, PETSC_DETERMINE, S));
542: if (!set) PetscCall(MatDestroy(&AinvBd));
543: else {
544: PetscCall(MatScale(AinvBd, -1.0));
545: PetscCall(MatFilter(AinvBd, PETSC_MACHINE_EPSILON, PETSC_FALSE, PETSC_FALSE));
546: PetscCall(MatFilter(*S, PETSC_MACHINE_EPSILON, PETSC_FALSE, PETSC_FALSE));
547: }
548: if (D) {
549: PetscCall(PetscObjectTypeCompareAny((PetscObject)D, &flg, MATSEQSBAIJ, MATMPISBAIJ, ""));
550: if (flg) {
551: PetscCall(MatIsSymmetricKnown(A, &set, &symm));
552: if (!set || !symm) PetscCall(MatConvert(D, MATBAIJ, MAT_INITIAL_MATRIX, &E)); /* convert the (1,1) block to nonsymmetric storage for MatAXPY() */
553: }
554: 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 */
555: if (!E && flg) PetscCall(MatConvert(*S, MATSBAIJ, MAT_INPLACE_MATRIX, S)); /* if A is symmetric and the (1,1) block is a MatSBAIJ, return S as a MatSBAIJ since the lower triangular part is invalid */
556: }
557: PetscCall(MatDestroy(&E));
558: PetscCall(MatScale(*S, -1.0));
559: PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sexplicit_operator_", ((PetscObject)A)->prefix ? ((PetscObject)A)->prefix : ""));
560: PetscCall(MatSetOptionsPrefix(*S, prefix));
561: PetscObjectOptionsBegin((PetscObject)*S);
562: PetscCall(PetscOptionsFList("-mat_type", "Matrix type", "MatSetType", MatList, !E && flg ? MATSBAIJ : mtype, type, 256, &set));
563: if (set) PetscCall(MatConvert(*S, type, MAT_INPLACE_MATRIX, S));
564: flg = PETSC_FALSE;
565: PetscCall(PetscOptionsBool("-mat_symmetric", "Sets the MAT_SYMMETRIC option", "MatSetOption", flg, &flg, &set));
566: if (set) PetscCall(MatSetOption(*S, MAT_SYMMETRIC, flg));
567: if (PetscDefined(USE_COMPLEX)) {
568: flg = PETSC_FALSE;
569: PetscCall(PetscOptionsBool("-mat_hermitian", "Sets the MAT_HERMITIAN option", "MatSetOption", flg, &flg, &set));
570: if (set) PetscCall(MatSetOption(*S, MAT_HERMITIAN, flg));
571: }
572: PetscOptionsEnd();
573: PetscFunctionReturn(PETSC_SUCCESS);
574: }
576: /* Developer Notes:
577: This should be implemented with a MatCreate_SchurComplement() as that is the standard design for new Mat classes. */
578: PetscErrorCode MatGetSchurComplement_Basic(Mat mat, IS isrow0, IS iscol0, IS isrow1, IS iscol1, MatReuse mreuse, Mat *S, MatSchurComplementAinvType ainvtype, MatReuse preuse, Mat *Sp)
579: {
580: Mat A = NULL, Ap = NULL, B = NULL, C = NULL, D = NULL;
581: MatReuse reuse;
583: PetscFunctionBegin;
593: if (mreuse == MAT_IGNORE_MATRIX && preuse == MAT_IGNORE_MATRIX) PetscFunctionReturn(PETSC_SUCCESS);
597: PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
599: reuse = MAT_INITIAL_MATRIX;
600: if (mreuse == MAT_REUSE_MATRIX) {
601: PetscCall(MatSchurComplementGetSubMatrices(*S, &A, &Ap, &B, &C, &D));
602: PetscCheck(A && Ap && B && C, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Attempting to reuse matrix but Schur complement matrices unset");
603: PetscCheck(A == Ap, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Matrix for constructing the preconditioner does not match operator");
604: PetscCall(MatDestroy(&Ap)); /* get rid of extra reference */
605: reuse = MAT_REUSE_MATRIX;
606: }
607: PetscCall(MatCreateSubMatrix(mat, isrow0, iscol0, reuse, &A));
608: PetscCall(MatCreateSubMatrix(mat, isrow0, iscol1, reuse, &B));
609: PetscCall(MatCreateSubMatrix(mat, isrow1, iscol0, reuse, &C));
610: PetscCall(MatCreateSubMatrix(mat, isrow1, iscol1, reuse, &D));
611: switch (mreuse) {
612: case MAT_INITIAL_MATRIX:
613: PetscCall(MatCreateSchurComplement(A, A, B, C, D, S));
614: break;
615: case MAT_REUSE_MATRIX:
616: PetscCall(MatSchurComplementUpdateSubMatrices(*S, A, A, B, C, D));
617: break;
618: default:
619: PetscCheck(mreuse == MAT_IGNORE_MATRIX, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Unrecognized value of mreuse %d", (int)mreuse);
620: }
621: if (preuse != MAT_IGNORE_MATRIX) PetscCall(MatCreateSchurComplementPmat(A, B, C, D, ainvtype, preuse, Sp));
622: PetscCall(MatDestroy(&A));
623: PetscCall(MatDestroy(&B));
624: PetscCall(MatDestroy(&C));
625: PetscCall(MatDestroy(&D));
626: PetscFunctionReturn(PETSC_SUCCESS);
627: }
629: /*@
630: MatGetSchurComplement - Obtain the Schur complement from eliminating part of the matrix in another part.
632: Collective
634: Input Parameters:
635: + A - matrix in which the complement is to be taken
636: . isrow0 - rows to eliminate
637: . iscol0 - columns to eliminate, (isrow0,iscol0) should be square and nonsingular
638: . isrow1 - rows in which the Schur complement is formed
639: . iscol1 - columns in which the Schur complement is formed
640: . mreuse - `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`, use `MAT_IGNORE_MATRIX` to put nothing in `S`
641: . ainvtype - the type of approximation used for the inverse of the (0,0) block used in forming `Sp`:
642: `MAT_SCHUR_COMPLEMENT_AINV_DIAG`, `MAT_SCHUR_COMPLEMENT_AINV_LUMP`, `MAT_SCHUR_COMPLEMENT_AINV_BLOCK_DIAG`, or `MAT_SCHUR_COMPLEMENT_AINV_FULL`
643: - preuse - `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`, use `MAT_IGNORE_MATRIX` to put nothing in `Sp`
645: Output Parameters:
646: + S - exact Schur complement, often of type `MATSCHURCOMPLEMENT` which is difficult to use for preconditioning
647: - Sp - approximate Schur complement from which a preconditioner can be built $A11 - A10 inv(DIAGFORM(A00)) A01$
649: Level: advanced
651: Notes:
652: Since the real Schur complement is usually dense, providing a good approximation to `Sp` usually requires
653: application-specific information.
655: Sometimes users would like to provide problem-specific data in the Schur complement, usually only for special row
656: 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
657: "MatGetSchurComplement_C" to their function. If their function needs to fall back to the default implementation, it
658: should call `MatGetSchurComplement_Basic()`.
660: `MatCreateSchurComplement()` takes as arguments the four submatrices and returns the virtual Schur complement (what this function returns in S).
662: `MatSchurComplementGetPmat()` takes the virtual Schur complement and returns an explicit approximate Schur complement (what this returns in Sp).
664: In other words calling `MatCreateSchurComplement()` followed by `MatSchurComplementGetPmat()` produces the same output as this function but with slightly different
665: inputs. The actually submatrices of the original block matrix instead of index sets to the submatrices.
667: Developer Notes:
668: The API that includes `MatGetSchurComplement()`, `MatCreateSchurComplement()`, `MatSchurComplementGetPmat()` should be refactored to
669: remove redundancy and be clearer and simpler.
671: .seealso: [](ch_ksp), `MatCreateSubMatrix()`, `PCFIELDSPLIT`, `MatCreateSchurComplement()`, `MatSchurComplementAinvType`
672: @*/
673: PetscErrorCode MatGetSchurComplement(Mat A, IS isrow0, IS iscol0, IS isrow1, IS iscol1, MatReuse mreuse, Mat *S, MatSchurComplementAinvType ainvtype, MatReuse preuse, Mat *Sp)
674: {
675: PetscErrorCode (*f)(Mat, IS, IS, IS, IS, MatReuse, Mat *, MatReuse, Mat *) = NULL;
677: PetscFunctionBegin;
689: PetscCheck(!A->factortype, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
690: 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. */
691: PetscCall(PetscObjectQueryFunction((PetscObject)*S, "MatGetSchurComplement_C", &f));
692: }
693: if (f) PetscCall((*f)(A, isrow0, iscol0, isrow1, iscol1, mreuse, S, preuse, Sp));
694: else PetscCall(MatGetSchurComplement_Basic(A, isrow0, iscol0, isrow1, iscol1, mreuse, S, ainvtype, preuse, Sp));
695: PetscFunctionReturn(PETSC_SUCCESS);
696: }
698: /*@
699: MatSchurComplementSetAinvType - set the type of approximation used for the inverse of the (0,0) block used in forming `Sp` in `MatSchurComplementGetPmat()`
701: Not Collective
703: Input Parameters:
704: + S - matrix obtained with `MatCreateSchurComplement()` (or equivalent) and implementing the action of $A11 - A10 ksp(A00,Ap00) A01$
705: - ainvtype - type of approximation to be used to form approximate Schur complement $Sp = A11 - A10 inv(DIAGFORM(A00)) A01$:
706: `MAT_SCHUR_COMPLEMENT_AINV_DIAG`, `MAT_SCHUR_COMPLEMENT_AINV_LUMP`, `MAT_SCHUR_COMPLEMENT_AINV_BLOCK_DIAG`, or `MAT_SCHUR_COMPLEMENT_AINV_FULL`
708: Options Database Key:
709: . -mat_schur_complement_ainv_type (diag|lump|blockdiag|full) - set Schur complement type
711: Level: advanced
713: .seealso: [](ch_ksp), `MatSchurComplementAinvType`, `MatCreateSchurComplement()`, `MatGetSchurComplement()`, `MatSchurComplementGetPmat()`, `MatSchurComplementGetAinvType()`
714: @*/
715: PetscErrorCode MatSchurComplementSetAinvType(Mat S, MatSchurComplementAinvType ainvtype)
716: {
717: PetscBool isschur;
718: Mat_SchurComplement *schur;
720: PetscFunctionBegin;
722: PetscCall(PetscObjectTypeCompare((PetscObject)S, MATSCHURCOMPLEMENT, &isschur));
723: if (!isschur) PetscFunctionReturn(PETSC_SUCCESS);
725: schur = (Mat_SchurComplement *)S->data;
726: 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);
727: schur->ainvtype = ainvtype;
728: PetscFunctionReturn(PETSC_SUCCESS);
729: }
731: /*@
732: MatSchurComplementGetAinvType - get the type of approximation for the inverse of the (0,0) block used in forming `Sp` in `MatSchurComplementGetPmat()`
734: Not Collective
736: Input Parameter:
737: . S - matrix obtained with `MatCreateSchurComplement()` (or equivalent) and implementing the action of $A11 - A10 ksp(A00,Ap00) A01$
739: Output Parameter:
740: . ainvtype - type of approximation used to form approximate Schur complement Sp = A11 - A10 inv(DIAGFORM(A00)) A01:
741: `MAT_SCHUR_COMPLEMENT_AINV_DIAG`, `MAT_SCHUR_COMPLEMENT_AINV_LUMP`, `MAT_SCHUR_COMPLEMENT_AINV_BLOCK_DIAG`, or `MAT_SCHUR_COMPLEMENT_AINV_FULL`
743: Level: advanced
745: .seealso: [](ch_ksp), `MatSchurComplementAinvType`, `MatCreateSchurComplement()`, `MatGetSchurComplement()`, `MatSchurComplementGetPmat()`, `MatSchurComplementSetAinvType()`
746: @*/
747: PetscErrorCode MatSchurComplementGetAinvType(Mat S, MatSchurComplementAinvType *ainvtype)
748: {
749: PetscBool isschur;
750: Mat_SchurComplement *schur;
752: PetscFunctionBegin;
754: PetscCall(PetscObjectTypeCompare((PetscObject)S, MATSCHURCOMPLEMENT, &isschur));
755: PetscCheck(isschur, PetscObjectComm((PetscObject)S), PETSC_ERR_ARG_WRONG, "Not for type %s", ((PetscObject)S)->type_name);
756: schur = (Mat_SchurComplement *)S->data;
757: if (ainvtype) *ainvtype = schur->ainvtype;
758: PetscFunctionReturn(PETSC_SUCCESS);
759: }
761: /*@
762: MatCreateSchurComplementPmat - create a matrix for preconditioning the Schur complement by explicitly assembling the sparse matrix
763: $Sp = A11 - A10 inv(DIAGFORM(A00)) A01$
765: Collective
767: Input Parameters:
768: + A00 - the upper-left part of the original matrix $A = [A00 A01; A10 A11]$
769: . A01 - (optional) the upper-right part of the original matrix $A = [A00 A01; A10 A11]$
770: . A10 - (optional) the lower-left part of the original matrix $A = [A00 A01; A10 A11]$
771: . A11 - (optional) the lower-right part of the original matrix $A = [A00 A01; A10 A11]$
772: . ainvtype - type of approximation for DIAGFORM(A00) used when forming $Sp = A11 - A10 inv(DIAGFORM(A00)) A01$. See `MatSchurComplementAinvType`.
773: - 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`
775: Output Parameter:
776: . Sp - approximate Schur complement suitable for constructing a preconditioner for the true Schur complement $S = A11 - A10 inv(A00) A01$
778: Level: advanced
780: .seealso: [](ch_ksp), `MatCreateSchurComplement()`, `MatGetSchurComplement()`, `MatSchurComplementGetPmat()`, `MatSchurComplementAinvType`
781: @*/
782: PetscErrorCode MatCreateSchurComplementPmat(Mat A00, Mat A01, Mat A10, Mat A11, MatSchurComplementAinvType ainvtype, MatReuse preuse, Mat *Sp)
783: {
784: PetscInt N00;
786: PetscFunctionBegin;
787: /* 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. */
788: /* TODO: Perhaps should create an appropriately-sized zero matrix of the same type as A00? */
790: if (preuse == MAT_IGNORE_MATRIX) PetscFunctionReturn(PETSC_SUCCESS);
792: /* A zero size A00 or empty A01 or A10 imply S = A11. */
793: PetscCall(MatGetSize(A00, &N00, NULL));
794: if (!A01 || !A10 || !N00) {
795: if (preuse == MAT_INITIAL_MATRIX) {
796: PetscCall(MatDuplicate(A11, MAT_COPY_VALUES, Sp));
797: } else { /* MAT_REUSE_MATRIX */
798: /* TODO: when can we pass SAME_NONZERO_PATTERN? */
799: PetscCall(MatCopy(A11, *Sp, DIFFERENT_NONZERO_PATTERN));
800: }
801: } else {
802: Mat AdB, T;
803: Vec diag;
804: PetscBool flg;
806: if (ainvtype == MAT_SCHUR_COMPLEMENT_AINV_LUMP || ainvtype == MAT_SCHUR_COMPLEMENT_AINV_DIAG) {
807: PetscCall(PetscObjectTypeCompare((PetscObject)A01, MATTRANSPOSEVIRTUAL, &flg));
808: if (flg) {
809: PetscCall(MatTransposeGetMat(A01, &T));
810: PetscCall(MatTranspose(T, MAT_INITIAL_MATRIX, &AdB));
811: } else {
812: PetscCall(PetscObjectTypeCompare((PetscObject)A01, MATHERMITIANTRANSPOSEVIRTUAL, &flg));
813: if (flg) {
814: PetscCall(MatHermitianTransposeGetMat(A01, &T));
815: PetscCall(MatHermitianTranspose(T, MAT_INITIAL_MATRIX, &AdB));
816: }
817: }
818: if (!flg) PetscCall(MatDuplicate(A01, MAT_COPY_VALUES, &AdB));
819: else {
820: PetscScalar shift, scale;
822: PetscCall(MatShellGetScalingShifts(A01, &shift, &scale, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Mat *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED));
823: PetscCall(MatShift(AdB, shift));
824: PetscCall(MatScale(AdB, scale));
825: }
826: PetscCall(MatCreateVecs(A00, &diag, NULL));
827: if (ainvtype == MAT_SCHUR_COMPLEMENT_AINV_LUMP) PetscCall(MatGetRowSum(A00, diag));
828: else PetscCall(MatGetDiagonal(A00, diag));
829: PetscCall(VecReciprocal(diag));
830: PetscCall(MatDiagonalScale(AdB, diag, NULL));
831: PetscCall(VecDestroy(&diag));
832: } else if (ainvtype == MAT_SCHUR_COMPLEMENT_AINV_BLOCK_DIAG) {
833: Mat A00_inv;
834: MatType type;
835: MPI_Comm comm;
837: PetscCall(PetscObjectGetComm((PetscObject)A00, &comm));
838: PetscCall(MatGetType(A00, &type));
839: PetscCall(MatCreate(comm, &A00_inv));
840: PetscCall(MatSetType(A00_inv, type));
841: PetscCall(MatInvertBlockDiagonalMat(A00, A00_inv));
842: PetscCall(MatMatMult(A00_inv, A01, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &AdB));
843: PetscCall(MatDestroy(&A00_inv));
844: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unknown MatSchurComplementAinvType: %d", ainvtype);
845: /* Cannot really reuse Sp in MatMatMult() because of MatAYPX() -->
846: MatAXPY() --> MatHeaderReplace() --> MatDestroy_XXX_MatMatMult() */
847: if (preuse == MAT_REUSE_MATRIX) PetscCall(MatDestroy(Sp));
848: PetscCall(MatMatMult(A10, AdB, MAT_INITIAL_MATRIX, PETSC_DETERMINE, Sp));
849: PetscCall(MatScale(*Sp, -1.0));
850: if (A11) { /* TODO: when can we pass SAME_NONZERO_PATTERN? */
851: PetscCall(MatAXPY(*Sp, 1.0, A11, DIFFERENT_NONZERO_PATTERN));
852: }
853: PetscCall(MatDestroy(&AdB));
854: }
855: PetscFunctionReturn(PETSC_SUCCESS);
856: }
858: static PetscErrorCode MatSchurComplementGetPmat_Basic(Mat S, MatReuse preuse, Mat *Sp)
859: {
860: Mat A, B, C, D;
861: Mat_SchurComplement *schur = (Mat_SchurComplement *)S->data;
862: MatNullSpace sp;
864: PetscFunctionBegin;
865: if (preuse == MAT_IGNORE_MATRIX) PetscFunctionReturn(PETSC_SUCCESS);
866: PetscCall(MatSchurComplementGetSubMatrices(S, &A, NULL, &B, &C, &D));
867: PetscCheck(A, PetscObjectComm((PetscObject)S), PETSC_ERR_ARG_WRONGSTATE, "Schur complement component matrices unset");
868: if (schur->ainvtype != MAT_SCHUR_COMPLEMENT_AINV_FULL) PetscCall(MatCreateSchurComplementPmat(A, B, C, D, schur->ainvtype, preuse, Sp));
869: else {
870: if (preuse == MAT_REUSE_MATRIX) PetscCall(MatDestroy(Sp));
871: PetscCall(MatSchurComplementComputeExplicitOperator(S, Sp));
872: }
873: /* If the Schur complement has a nullspace, then Sp nullspace contains it, independently of the ainv type */
874: PetscCall(MatGetNullSpace(S, &sp));
875: if (sp) PetscCall(MatSetNullSpace(*Sp, sp));
876: PetscCall(MatGetTransposeNullSpace(S, &sp));
877: if (sp) PetscCall(MatSetTransposeNullSpace(*Sp, sp));
878: PetscFunctionReturn(PETSC_SUCCESS);
879: }
881: /*@
882: MatSchurComplementGetPmat - Obtain a matrix for preconditioning the Schur complement by assembling $Sp = A11 - A10 inv(DIAGFORM(A00)) A01$
884: Collective
886: Input Parameters:
887: + S - matrix obtained with MatCreateSchurComplement() (or equivalent) that implements the action of $A11 - A10 ksp(A00,Ap00) A01$
888: - 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`
890: Output Parameter:
891: . Sp - approximate Schur complement suitable for preconditioning the exact Schur complement $S = A11 - A10 inv(A00) A01$
893: Level: advanced
895: Notes:
896: The approximation of `Sp` depends on the argument passed to `MatSchurComplementSetAinvType()`
897: `MAT_SCHUR_COMPLEMENT_AINV_DIAG`, `MAT_SCHUR_COMPLEMENT_AINV_LUMP`, `MAT_SCHUR_COMPLEMENT_AINV_BLOCK_DIAG`, or `MAT_SCHUR_COMPLEMENT_AINV_FULL`
898: -mat_schur_complement_ainv_type <diag,lump,blockdiag,full>
900: Sometimes users would like to provide problem-specific data in the Schur complement, usually only
901: for special row and column index sets. In that case, the user should call `PetscObjectComposeFunction()` to set
902: "MatSchurComplementGetPmat_C" to their function. If their function needs to fall back to the default implementation,
903: it should call `MatSchurComplementGetPmat_Basic()`.
905: Developer Notes:
906: The API that includes `MatGetSchurComplement()`, `MatCreateSchurComplement()`, `MatSchurComplementGetPmat()` should be refactored to
907: remove redundancy and be clearer and simpler.
909: This routine should be called `MatSchurComplementCreatePmat()`
911: .seealso: [](ch_ksp), `MatCreateSubMatrix()`, `PCFIELDSPLIT`, `MatGetSchurComplement()`, `MatCreateSchurComplement()`, `MatSchurComplementSetAinvType()`
912: @*/
913: PetscErrorCode MatSchurComplementGetPmat(Mat S, MatReuse preuse, Mat *Sp)
914: {
915: PetscErrorCode (*f)(Mat, MatReuse, Mat *);
917: PetscFunctionBegin;
921: if (preuse != MAT_IGNORE_MATRIX) {
922: PetscAssertPointer(Sp, 3);
923: if (preuse == MAT_INITIAL_MATRIX) *Sp = NULL;
925: }
926: PetscCheck(!S->factortype, PetscObjectComm((PetscObject)S), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
928: PetscCall(PetscObjectQueryFunction((PetscObject)S, "MatSchurComplementGetPmat_C", &f));
929: if (f) PetscCall((*f)(S, preuse, Sp));
930: else PetscCall(MatSchurComplementGetPmat_Basic(S, preuse, Sp));
931: PetscFunctionReturn(PETSC_SUCCESS);
932: }
934: static PetscErrorCode MatProductNumeric_SchurComplement_Dense(Mat C)
935: {
936: Mat_Product *product = C->product;
937: Mat_SchurComplement *Na = (Mat_SchurComplement *)product->A->data;
938: Mat work1, work2;
939: PetscScalar *v;
940: PetscInt lda;
942: PetscFunctionBegin;
943: PetscCall(MatMatMult(Na->B, product->B, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &work1));
944: PetscCall(MatDuplicate(work1, MAT_DO_NOT_COPY_VALUES, &work2));
945: PetscCall(KSPMatSolve(Na->ksp, work1, work2));
946: PetscCall(MatDestroy(&work1));
947: PetscCall(MatDenseGetArrayWrite(C, &v));
948: PetscCall(MatDenseGetLDA(C, &lda));
949: PetscCall(MatCreateDense(PetscObjectComm((PetscObject)C), C->rmap->n, C->cmap->n, C->rmap->N, C->cmap->N, v, &work1));
950: PetscCall(MatDenseSetLDA(work1, lda));
951: PetscCall(MatMatMult(Na->C, work2, MAT_REUSE_MATRIX, PETSC_DETERMINE, &work1));
952: PetscCall(MatDenseRestoreArrayWrite(C, &v));
953: PetscCall(MatDestroy(&work2));
954: PetscCall(MatDestroy(&work1));
955: if (Na->D) {
956: PetscCall(MatMatMult(Na->D, product->B, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &work1));
957: PetscCall(MatAYPX(C, -1.0, work1, SAME_NONZERO_PATTERN));
958: PetscCall(MatDestroy(&work1));
959: } else PetscCall(MatScale(C, -1.0));
960: PetscFunctionReturn(PETSC_SUCCESS);
961: }
963: static PetscErrorCode MatProductSymbolic_SchurComplement_Dense(Mat C)
964: {
965: Mat_Product *product = C->product;
966: Mat A = product->A, B = product->B;
967: PetscInt m = A->rmap->n, n = B->cmap->n, M = A->rmap->N, N = B->cmap->N;
968: PetscBool flg;
970: PetscFunctionBegin;
971: PetscCall(MatSetSizes(C, m, n, M, N));
972: PetscCall(PetscObjectBaseTypeCompareAny((PetscObject)C, &flg, MATSEQDENSE, MATMPIDENSE, ""));
973: if (!flg) {
974: PetscCall(MatSetType(C, ((PetscObject)B)->type_name));
975: C->ops->productsymbolic = MatProductSymbolic_SchurComplement_Dense;
976: }
977: PetscCall(MatSetUp(C));
978: C->ops->productnumeric = MatProductNumeric_SchurComplement_Dense;
979: PetscFunctionReturn(PETSC_SUCCESS);
980: }
982: static PetscErrorCode MatProductSetFromOptions_SchurComplement_Dense(Mat C)
983: {
984: Mat_Product *product = C->product;
986: PetscFunctionBegin;
987: if (product->type != MATPRODUCT_AB) PetscFunctionReturn(PETSC_SUCCESS);
988: C->ops->productsymbolic = MatProductSymbolic_SchurComplement_Dense;
989: PetscFunctionReturn(PETSC_SUCCESS);
990: }
992: static PetscErrorCode MatProductNumeric_SchurComplement_Any(Mat C)
993: {
994: Mat_SchurComplement *Na = (Mat_SchurComplement *)C->data;
996: PetscFunctionBegin;
997: if (Na->D && Na->D->product) PetscCall(MatProductNumeric(Na->D));
998: if (Na->B->product) PetscCall(MatProductNumeric(Na->B));
999: if (Na->C->product) PetscCall(MatProductNumeric(Na->C));
1000: C->assembled = PETSC_TRUE;
1001: PetscFunctionReturn(PETSC_SUCCESS);
1002: }
1004: static PetscErrorCode MatProductSymbolic_SchurComplement_Any(Mat C)
1005: {
1006: Mat_SchurComplement *Na = (Mat_SchurComplement *)C->data;
1008: PetscFunctionBegin;
1009: if (Na->D && Na->D->product) PetscCall(MatProductSymbolic(Na->D));
1010: if (Na->B->product) PetscCall(MatProductSymbolic(Na->B));
1011: if (Na->C->product) PetscCall(MatProductSymbolic(Na->C));
1012: C->ops->productnumeric = MatProductNumeric_SchurComplement_Any;
1013: C->preallocated = PETSC_TRUE;
1014: C->assembled = PETSC_FALSE;
1015: PetscFunctionReturn(PETSC_SUCCESS);
1016: }
1018: static PetscErrorCode MatProductSetFromOptions_SchurComplement_Any(Mat C)
1019: {
1020: Mat_Product *product = C->product;
1021: Mat_SchurComplement *Na, *Ca;
1022: Mat B = product->B, S = product->A, pB = NULL, pC = NULL, pD = NULL;
1023: KSP ksp;
1024: PetscInt m = PETSC_DECIDE, n = PETSC_DECIDE, M = PETSC_DECIDE, N = PETSC_DECIDE;
1025: MatProductType pbtype = MATPRODUCT_UNSPECIFIED, pctype = MATPRODUCT_UNSPECIFIED;
1026: PetscBool isschur;
1028: PetscFunctionBegin;
1029: if (product->type == MATPRODUCT_ABC || product->type == MATPRODUCT_AtB) PetscFunctionReturn(PETSC_SUCCESS);
1030: /* A * S not yet supported (should be easy though) */
1031: PetscCall(PetscObjectTypeCompare((PetscObject)S, MATSCHURCOMPLEMENT, &isschur));
1032: if (!isschur) PetscFunctionReturn(PETSC_SUCCESS);
1034: Na = (Mat_SchurComplement *)S->data;
1035: if (Na->D) {
1036: PetscCall(MatProductCreate(Na->D, B, NULL, &pD));
1037: PetscCall(MatProductSetType(pD, product->type));
1038: PetscCall(MatProductSetFromOptions(pD));
1039: }
1040: if (pD && !pD->ops->productsymbolic) {
1041: PetscCall(MatDestroy(&pD));
1042: PetscFunctionReturn(PETSC_SUCCESS);
1043: }
1045: /* S = A11 - A10 M A01 */
1046: switch (product->type) {
1047: case MATPRODUCT_AB: /* A11 B - A10 * M * A01 * B */
1048: pbtype = product->type;
1049: PetscCall(PetscObjectReference((PetscObject)Na->C));
1050: pC = Na->C;
1051: m = S->rmap->n;
1052: M = S->rmap->N;
1053: n = B->cmap->n;
1054: N = B->cmap->N;
1055: break;
1056: case MATPRODUCT_ABt: /* A11 B^t - A10 * M * A01 * B^t */
1057: pbtype = product->type;
1058: PetscCall(PetscObjectReference((PetscObject)Na->C));
1059: pC = Na->C;
1060: m = S->rmap->n;
1061: M = S->rmap->N;
1062: n = B->rmap->n;
1063: N = B->rmap->N;
1064: break;
1065: case MATPRODUCT_PtAP: /* Pt A11 P - Pt * A10 * M * A01 * P */
1066: pbtype = MATPRODUCT_AB;
1067: pctype = MATPRODUCT_AtB;
1068: m = B->cmap->n;
1069: M = B->cmap->N;
1070: n = B->cmap->n;
1071: N = B->cmap->N;
1072: break;
1073: case MATPRODUCT_RARt: /* R A11 Rt - R * A10 * M * A01 * Rt */
1074: pbtype = MATPRODUCT_ABt;
1075: pctype = MATPRODUCT_AB;
1076: m = B->rmap->n;
1077: M = B->rmap->N;
1078: n = B->rmap->n;
1079: N = B->rmap->N;
1080: break;
1081: default:
1082: break;
1083: }
1084: PetscCall(MatProductCreate(Na->B, B, NULL, &pB));
1085: PetscCall(MatProductSetType(pB, pbtype));
1086: PetscCall(MatProductSetFromOptions(pB));
1087: if (!pB->ops->productsymbolic) {
1088: PetscCall(MatDestroy(&pB));
1089: PetscFunctionReturn(PETSC_SUCCESS);
1090: }
1091: if (pC == NULL) { /* Some work can in principle be saved here if we recognize symmetry */
1092: PetscCall(MatProductCreate(B, Na->C, NULL, &pC));
1093: PetscCall(MatProductSetType(pC, pctype));
1094: PetscCall(MatProductSetFromOptions(pC));
1095: if (!pC->ops->productsymbolic) {
1096: PetscCall(MatDestroy(&pC));
1097: PetscFunctionReturn(PETSC_SUCCESS);
1098: }
1099: }
1100: PetscCall(MatSetType(C, MATSCHURCOMPLEMENT));
1101: PetscCall(MatSetSizes(C, m, n, M, N));
1102: PetscCall(PetscLayoutSetUp(C->rmap));
1103: PetscCall(PetscLayoutSetUp(C->cmap));
1104: PetscCall(PetscObjectReference((PetscObject)Na->A));
1105: PetscCall(PetscObjectReference((PetscObject)Na->Ap));
1106: Ca = (Mat_SchurComplement *)C->data;
1107: Ca->A = Na->A;
1108: Ca->Ap = Na->Ap;
1109: Ca->B = pB;
1110: Ca->C = pC;
1111: Ca->D = pD;
1112: C->ops->productsymbolic = MatProductSymbolic_SchurComplement_Any;
1113: PetscCall(MatSchurComplementGetKSP(S, &ksp));
1114: PetscCall(MatSchurComplementSetKSP(C, ksp));
1115: PetscFunctionReturn(PETSC_SUCCESS);
1116: }
1118: /*MC
1119: MATSCHURCOMPLEMENT - "schurcomplement" - Matrix type that behaves like the Schur complement of a matrix.
1121: Level: intermediate
1123: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatType`, `MatCreateSchurComplement()`, `MatSchurComplementComputeExplicitOperator()`,
1124: `MatSchurComplementGetSubMatrices()`, `MatSchurComplementGetKSP()`
1125: M*/
1126: PETSC_EXTERN PetscErrorCode MatCreate_SchurComplement(Mat N)
1127: {
1128: Mat_SchurComplement *Na;
1130: PetscFunctionBegin;
1131: PetscCall(PetscNew(&Na));
1132: N->data = (void *)Na;
1134: N->ops->destroy = MatDestroy_SchurComplement;
1135: N->ops->getvecs = MatCreateVecs_SchurComplement;
1136: N->ops->view = MatView_SchurComplement;
1137: N->ops->mult = MatMult_SchurComplement;
1138: N->ops->multtranspose = MatMultTranspose_SchurComplement;
1139: N->ops->multadd = MatMultAdd_SchurComplement;
1140: N->ops->setfromoptions = MatSetFromOptions_SchurComplement;
1141: N->assembled = PETSC_FALSE;
1142: N->preallocated = PETSC_FALSE;
1144: PetscCall(KSPCreate(PetscObjectComm((PetscObject)N), &Na->ksp));
1145: PetscCall(PetscObjectChangeTypeName((PetscObject)N, MATSCHURCOMPLEMENT));
1146: PetscCall(PetscObjectComposeFunction((PetscObject)N, "MatProductSetFromOptions_schurcomplement_seqdense_C", MatProductSetFromOptions_SchurComplement_Dense));
1147: PetscCall(PetscObjectComposeFunction((PetscObject)N, "MatProductSetFromOptions_schurcomplement_mpidense_C", MatProductSetFromOptions_SchurComplement_Dense));
1148: PetscCall(PetscObjectComposeFunction((PetscObject)N, "MatProductSetFromOptions_anytype_C", MatProductSetFromOptions_SchurComplement_Any));
1149: PetscFunctionReturn(PETSC_SUCCESS);
1150: }