Actual source code: ex21.c
1: static const char help[] = "Tests MatGetSchurComplement\n";
3: #include <petscksp.h>
5: PetscErrorCode Create(MPI_Comm comm, Mat *inA, IS *is0, IS *is1)
6: {
7: Mat A;
8: PetscInt r, rend, M;
9: PetscMPIInt rank;
12: *inA = 0;
13: MatCreate(comm, &A);
14: MatSetSizes(A, 4, 4, PETSC_DETERMINE, PETSC_DETERMINE);
15: MatSetFromOptions(A);
16: MatSetUp(A);
17: MatGetOwnershipRange(A, &r, &rend);
18: MatGetSize(A, &M, NULL);
20: ISCreateStride(comm, 2, r, 1, is0);
21: ISCreateStride(comm, 2, r + 2, 1, is1);
23: MPI_Comm_rank(comm, &rank);
25: {
26: PetscInt rows[4], cols0[5], cols1[5], cols2[3], cols3[3];
27: PetscScalar RR = 1000. * rank, vals0[5], vals1[4], vals2[3], vals3[3];
29: rows[0] = r;
30: rows[1] = r + 1;
31: rows[2] = r + 2;
32: rows[3] = r + 3;
34: cols0[0] = r + 0;
35: cols0[1] = r + 1;
36: cols0[2] = r + 3;
37: cols0[3] = (r + 4) % M;
38: cols0[4] = (r + M - 4) % M;
40: cols1[0] = r + 1;
41: cols1[1] = r + 2;
42: cols1[2] = (r + 4 + 1) % M;
43: cols1[3] = (r + M - 4 + 1) % M;
45: cols2[0] = r;
46: cols2[1] = r + 2;
47: cols2[2] = (r + 4 + 2) % M;
49: cols3[0] = r + 1;
50: cols3[1] = r + 3;
51: cols3[2] = (r + 4 + 3) % M;
53: vals0[0] = RR + 1.;
54: vals0[1] = RR + 2.;
55: vals0[2] = RR + 3.;
56: vals0[3] = RR + 4.;
57: vals0[4] = RR + 5.;
59: vals1[0] = RR + 6.;
60: vals1[1] = RR + 7.;
61: vals1[2] = RR + 8.;
62: vals1[3] = RR + 9.;
64: vals2[0] = RR + 10.;
65: vals2[1] = RR + 11.;
66: vals2[2] = RR + 12.;
68: vals3[0] = RR + 13.;
69: vals3[1] = RR + 14.;
70: vals3[2] = RR + 15.;
71: MatSetValues(A, 1, &rows[0], 5, cols0, vals0, INSERT_VALUES);
72: MatSetValues(A, 1, &rows[1], 4, cols1, vals1, INSERT_VALUES);
73: MatSetValues(A, 1, &rows[2], 3, cols2, vals2, INSERT_VALUES);
74: MatSetValues(A, 1, &rows[3], 3, cols3, vals3, INSERT_VALUES);
75: }
76: MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
77: MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
78: *inA = A;
79: return 0;
80: }
82: PetscErrorCode Destroy(Mat *A, IS *is0, IS *is1)
83: {
85: MatDestroy(A);
86: ISDestroy(is0);
87: ISDestroy(is1);
88: return 0;
89: }
91: int main(int argc, char *argv[])
92: {
93: Mat A, S = NULL, Sexplicit = NULL, Sp, B, C;
94: MatSchurComplementAinvType ainv_type = MAT_SCHUR_COMPLEMENT_AINV_DIAG;
95: IS is0, is1;
96: PetscBool flg;
97: PetscInt m, N = 10;
100: PetscInitialize(&argc, &argv, 0, help);
101: PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "ex21", "KSP");
102: PetscOptionsEnum("-mat_schur_complement_ainv_type", "Type of approximation for inv(A00) used when assembling Sp = A11 - A10 inv(A00) A01", "MatSchurComplementAinvType", MatSchurComplementAinvTypes, (PetscEnum)ainv_type, (PetscEnum *)&ainv_type, NULL);
103: PetscOptionsEnd();
105: /* Test the Schur complement one way */
106: Create(PETSC_COMM_WORLD, &A, &is0, &is1);
107: MatView(A, PETSC_VIEWER_STDOUT_WORLD);
108: ISView(is0, PETSC_VIEWER_STDOUT_WORLD);
109: ISView(is1, PETSC_VIEWER_STDOUT_WORLD);
110: MatGetSchurComplement(A, is0, is0, is1, is1, MAT_INITIAL_MATRIX, &S, ainv_type, MAT_IGNORE_MATRIX, NULL);
111: MatSetFromOptions(S);
112: MatComputeOperator(S, MATAIJ, &Sexplicit);
113: PetscPrintf(PETSC_COMM_WORLD, "\nExplicit Schur complement of (0,0) in (1,1)\n");
114: MatView(Sexplicit, PETSC_VIEWER_STDOUT_WORLD);
115: if (ainv_type == MAT_SCHUR_COMPLEMENT_AINV_DIAG) {
116: MatSchurComplementSetAinvType(S, MAT_SCHUR_COMPLEMENT_AINV_FULL);
117: MatSchurComplementGetPmat(S, MAT_INITIAL_MATRIX, &Sp);
118: MatMultEqual(Sp, Sexplicit, 10, &flg);
120: MatSchurComplementSetAinvType(S, MAT_SCHUR_COMPLEMENT_AINV_DIAG);
121: MatDestroy(&Sp);
122: }
123: Destroy(&A, &is0, &is1);
124: if (ainv_type == MAT_SCHUR_COMPLEMENT_AINV_DIAG) {
125: MatGetLocalSize(Sexplicit, &m, NULL);
126: MatCreateDense(PetscObjectComm((PetscObject)Sexplicit), m, PETSC_DECIDE, PETSC_DECIDE, N, NULL, &B);
127: MatSetRandom(B, NULL);
128: MatMatMult(S, B, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &C);
129: MatMatMultEqual(Sexplicit, B, C, 10, &flg);
131: MatDestroy(&C);
132: MatDestroy(&B);
133: }
134: MatDestroy(&S);
135: MatDestroy(&Sexplicit);
137: /* And the other */
138: Create(PETSC_COMM_WORLD, &A, &is0, &is1);
139: MatGetSchurComplement(A, is1, is1, is0, is0, MAT_INITIAL_MATRIX, &S, ainv_type, MAT_IGNORE_MATRIX, NULL);
140: MatSetFromOptions(S);
141: MatComputeOperator(S, MATAIJ, &Sexplicit);
142: PetscPrintf(PETSC_COMM_WORLD, "\nExplicit Schur complement of (1,1) in (0,0)\n");
143: MatView(Sexplicit, PETSC_VIEWER_STDOUT_WORLD);
144: if (ainv_type == MAT_SCHUR_COMPLEMENT_AINV_DIAG) {
145: MatSchurComplementSetAinvType(S, MAT_SCHUR_COMPLEMENT_AINV_FULL);
146: MatSchurComplementGetPmat(S, MAT_INITIAL_MATRIX, &Sp);
147: MatMultEqual(Sp, Sexplicit, 10, &flg);
149: MatSchurComplementSetAinvType(S, MAT_SCHUR_COMPLEMENT_AINV_DIAG);
150: MatDestroy(&Sp);
151: }
152: Destroy(&A, &is0, &is1);
153: if (ainv_type == MAT_SCHUR_COMPLEMENT_AINV_DIAG) {
154: MatGetLocalSize(Sexplicit, &m, NULL);
155: MatCreateDense(PetscObjectComm((PetscObject)Sexplicit), m, PETSC_DECIDE, PETSC_DECIDE, N, NULL, &B);
156: MatSetRandom(B, NULL);
157: MatMatMult(S, B, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &C);
158: MatMatMultEqual(Sexplicit, B, C, 10, &flg);
160: MatDestroy(&C);
161: MatDestroy(&B);
162: }
163: MatDestroy(&S);
164: MatDestroy(&Sexplicit);
166: /* This time just the preconditioning matrix. */
167: Create(PETSC_COMM_WORLD, &A, &is0, &is1);
168: MatGetSchurComplement(A, is0, is0, is1, is1, MAT_IGNORE_MATRIX, NULL, ainv_type, MAT_INITIAL_MATRIX, &S);
169: MatSetFromOptions(S);
170: PetscPrintf(PETSC_COMM_WORLD, "\nPreconditioning Schur complement of (0,0) in (1,1)\n");
171: MatView(S, PETSC_VIEWER_STDOUT_WORLD);
172: /* Modify and refresh */
173: MatShift(A, 1.);
174: MatGetSchurComplement(A, is0, is0, is1, is1, MAT_IGNORE_MATRIX, NULL, ainv_type, MAT_REUSE_MATRIX, &S);
175: PetscPrintf(PETSC_COMM_WORLD, "\nAfter update\n");
176: MatView(S, PETSC_VIEWER_STDOUT_WORLD);
177: Destroy(&A, &is0, &is1);
178: MatDestroy(&S);
180: PetscFinalize();
181: return 0;
182: }
184: /*TEST
185: test:
186: suffix: diag_1
187: args: -mat_schur_complement_ainv_type diag
188: nsize: 1
189: test:
190: suffix: blockdiag_1
191: args: -mat_schur_complement_ainv_type blockdiag
192: nsize: 1
193: test:
194: suffix: diag_2
195: args: -mat_schur_complement_ainv_type diag
196: nsize: 2
197: test:
198: suffix: blockdiag_2
199: args: -mat_schur_complement_ainv_type blockdiag
200: nsize: 2
201: test:
202: # does not work with single because residual norm computed by GMRES recurrence formula becomes invalid
203: requires: !single
204: suffix: diag_3
205: args: -mat_schur_complement_ainv_type diag -ksp_rtol 1e-12
206: nsize: 3
207: test:
208: # does not work with single because residual norm computed by GMRES recurrence formula becomes invalid
209: requires: !single
210: suffix: blockdiag_3
211: args: -mat_schur_complement_ainv_type blockdiag
212: nsize: 3
213: TEST*/