Actual source code: ex30.c
1: static char help[] = "Tests ILU and ICC factorization with and without matrix ordering on seqaij format, and illustrates drawing of matrix sparsity structure with MatView().\n\
2: Input parameters are:\n\
3: -lf <level> : level of fill for ILU (default is 0)\n\
4: -lu : use full LU or Cholesky factorization\n\
5: -m <value>,-n <value> : grid dimensions\n\
6: Note that most users should employ the KSP interface to the\n\
7: linear solvers instead of using the factorization routines\n\
8: directly.\n\n";
10: #include <petscmat.h>
12: int main(int argc, char **args)
13: {
14: Mat C, A;
15: PetscInt i, j, m = 5, n = 5, Ii, J, lf = 0;
16: PetscBool LU = PETSC_FALSE, CHOLESKY, TRIANGULAR = PETSC_FALSE, MATDSPL = PETSC_FALSE, flg, matordering;
17: PetscScalar v;
18: IS row, col;
19: PetscViewer viewer1, viewer2;
20: MatFactorInfo info;
21: Vec x, y, b, ytmp;
22: PetscReal norm2, norm2_inplace, tol = 100. * PETSC_MACHINE_EPSILON;
23: PetscRandom rdm;
24: PetscMPIInt size;
26: PetscFunctionBeginUser;
27: PetscCall(PetscInitialize(&argc, &args, (char *)0, help));
28: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
29: PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");
30: PetscCall(PetscOptionsGetInt(NULL, NULL, "-m", &m, NULL));
31: PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL));
32: PetscCall(PetscOptionsGetInt(NULL, NULL, "-lf", &lf, NULL));
34: PetscCall(PetscViewerDrawOpen(PETSC_COMM_SELF, 0, 0, 0, 0, 400, 400, &viewer1));
35: PetscCall(PetscViewerDrawOpen(PETSC_COMM_SELF, 0, 0, 400, 0, 400, 400, &viewer2));
37: PetscCall(MatCreate(PETSC_COMM_SELF, &C));
38: PetscCall(MatSetSizes(C, m * n, m * n, m * n, m * n));
39: PetscCall(MatSetFromOptions(C));
40: PetscCall(MatSetUp(C));
42: /* Create matrix C in seqaij format and sC in seqsbaij. (This is five-point stencil with some extra elements) */
43: for (i = 0; i < m; i++) {
44: for (j = 0; j < n; j++) {
45: v = -1.0;
46: Ii = j + n * i;
47: J = Ii - n;
48: if (J >= 0) PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
49: J = Ii + n;
50: if (J < m * n) PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
51: J = Ii - 1;
52: if (J >= 0) PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
53: J = Ii + 1;
54: if (J < m * n) PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
55: v = 4.0;
56: PetscCall(MatSetValues(C, 1, &Ii, 1, &Ii, &v, INSERT_VALUES));
57: }
58: }
59: PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
60: PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
62: PetscCall(MatIsSymmetric(C, 0.0, &flg));
63: PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_SUP, "C is non-symmetric");
65: /* Create vectors for error checking */
66: PetscCall(MatCreateVecs(C, &x, &b));
67: PetscCall(VecDuplicate(x, &y));
68: PetscCall(VecDuplicate(x, &ytmp));
69: PetscCall(PetscRandomCreate(PETSC_COMM_SELF, &rdm));
70: PetscCall(PetscRandomSetFromOptions(rdm));
71: PetscCall(VecSetRandom(x, rdm));
72: PetscCall(MatMult(C, x, b));
74: PetscCall(PetscOptionsHasName(NULL, NULL, "-mat_ordering", &matordering));
75: if (matordering) {
76: PetscCall(MatGetOrdering(C, MATORDERINGRCM, &row, &col));
77: } else {
78: PetscCall(MatGetOrdering(C, MATORDERINGNATURAL, &row, &col));
79: }
81: PetscCall(PetscOptionsHasName(NULL, NULL, "-display_matrices", &MATDSPL));
82: if (MATDSPL) {
83: printf("original matrix:\n");
84: PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_SELF, PETSC_VIEWER_ASCII_INFO));
85: PetscCall(MatView(C, PETSC_VIEWER_STDOUT_SELF));
86: PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_SELF));
87: PetscCall(MatView(C, PETSC_VIEWER_STDOUT_SELF));
88: PetscCall(MatView(C, viewer1));
89: }
91: /* Compute LU or ILU factor A */
92: PetscCall(MatFactorInfoInitialize(&info));
94: info.fill = 1.0;
95: info.diagonal_fill = 0;
96: info.zeropivot = 0.0;
98: PetscCall(PetscOptionsHasName(NULL, NULL, "-lu", &LU));
99: if (LU) {
100: printf("Test LU...\n");
101: PetscCall(MatGetFactor(C, MATSOLVERPETSC, MAT_FACTOR_LU, &A));
102: PetscCall(MatLUFactorSymbolic(A, C, row, col, &info));
103: } else {
104: printf("Test ILU...\n");
105: info.levels = lf;
107: PetscCall(MatGetFactor(C, MATSOLVERPETSC, MAT_FACTOR_ILU, &A));
108: PetscCall(MatILUFactorSymbolic(A, C, row, col, &info));
109: }
110: PetscCall(MatLUFactorNumeric(A, C, &info));
112: /* Solve A*y = b, then check the error */
113: PetscCall(MatSolve(A, b, y));
114: PetscCall(VecAXPY(y, -1.0, x));
115: PetscCall(VecNorm(y, NORM_2, &norm2));
116: PetscCall(MatDestroy(&A));
118: /* Test in-place ILU(0) and compare it with the out-place ILU(0) */
119: if (!LU && lf == 0) {
120: PetscCall(MatDuplicate(C, MAT_COPY_VALUES, &A));
121: PetscCall(MatILUFactor(A, row, col, &info));
122: /*
123: printf("In-place factored matrix:\n");
124: PetscCall(MatView(C,PETSC_VIEWER_STDOUT_SELF));
125: */
126: PetscCall(MatSolve(A, b, y));
127: PetscCall(VecAXPY(y, -1.0, x));
128: PetscCall(VecNorm(y, NORM_2, &norm2_inplace));
129: PetscCheck(PetscAbs(norm2 - norm2_inplace) <= tol, PETSC_COMM_SELF, PETSC_ERR_PLIB, "ILU(0) %g and in-place ILU(0) %g give different residuals", (double)norm2, (double)norm2_inplace);
130: PetscCall(MatDestroy(&A));
131: }
133: /* Test Cholesky and ICC on seqaij matrix with matrix reordering on aij matrix C */
134: CHOLESKY = LU;
135: if (CHOLESKY) {
136: printf("Test Cholesky...\n");
137: lf = -1;
138: PetscCall(MatGetFactor(C, MATSOLVERPETSC, MAT_FACTOR_CHOLESKY, &A));
139: PetscCall(MatCholeskyFactorSymbolic(A, C, row, &info));
140: } else {
141: printf("Test ICC...\n");
142: info.levels = lf;
143: info.fill = 1.0;
144: info.diagonal_fill = 0;
145: info.zeropivot = 0.0;
147: PetscCall(MatGetFactor(C, MATSOLVERPETSC, MAT_FACTOR_ICC, &A));
148: PetscCall(MatICCFactorSymbolic(A, C, row, &info));
149: }
150: PetscCall(MatCholeskyFactorNumeric(A, C, &info));
152: /* test MatForwardSolve() and MatBackwardSolve() with matrix reordering on aij matrix C */
153: if (lf == -1) {
154: PetscCall(PetscOptionsHasName(NULL, NULL, "-triangular_solve", &TRIANGULAR));
155: if (TRIANGULAR) {
156: printf("Test MatForwardSolve...\n");
157: PetscCall(MatForwardSolve(A, b, ytmp));
158: printf("Test MatBackwardSolve...\n");
159: PetscCall(MatBackwardSolve(A, ytmp, y));
160: PetscCall(VecAXPY(y, -1.0, x));
161: PetscCall(VecNorm(y, NORM_2, &norm2));
162: if (norm2 > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, "MatForwardSolve and BackwardSolve: Norm of error=%g\n", (double)norm2));
163: }
164: }
166: PetscCall(MatSolve(A, b, y));
167: PetscCall(MatDestroy(&A));
168: PetscCall(VecAXPY(y, -1.0, x));
169: PetscCall(VecNorm(y, NORM_2, &norm2));
170: if (lf == -1 && norm2 > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, " reordered SEQAIJ: Cholesky/ICC levels %" PetscInt_FMT ", residual %g\n", lf, (double)norm2));
172: /* Test in-place ICC(0) and compare it with the out-place ICC(0) */
173: if (!CHOLESKY && lf == 0 && !matordering) {
174: PetscCall(MatConvert(C, MATSBAIJ, MAT_INITIAL_MATRIX, &A));
175: PetscCall(MatICCFactor(A, row, &info));
176: /*
177: printf("In-place factored matrix:\n");
178: PetscCall(MatView(A,PETSC_VIEWER_STDOUT_SELF));
179: */
180: PetscCall(MatSolve(A, b, y));
181: PetscCall(VecAXPY(y, -1.0, x));
182: PetscCall(VecNorm(y, NORM_2, &norm2_inplace));
183: PetscCheck(PetscAbs(norm2 - norm2_inplace) <= tol, PETSC_COMM_SELF, PETSC_ERR_PLIB, "ICC(0) %g and in-place ICC(0) %g give different residuals", (double)norm2, (double)norm2_inplace);
184: PetscCall(MatDestroy(&A));
185: }
187: /* Free data structures */
188: PetscCall(ISDestroy(&row));
189: PetscCall(ISDestroy(&col));
190: PetscCall(MatDestroy(&C));
191: PetscCall(PetscViewerDestroy(&viewer1));
192: PetscCall(PetscViewerDestroy(&viewer2));
193: PetscCall(PetscRandomDestroy(&rdm));
194: PetscCall(VecDestroy(&x));
195: PetscCall(VecDestroy(&y));
196: PetscCall(VecDestroy(&ytmp));
197: PetscCall(VecDestroy(&b));
198: PetscCall(PetscFinalize());
199: return 0;
200: }
202: /*TEST
204: test:
205: args: -mat_ordering -display_matrices -nox
206: filter: grep -v " MPI process"
208: test:
209: suffix: 2
210: args: -mat_ordering -display_matrices -nox -lu
212: test:
213: suffix: 3
214: args: -mat_ordering -lu -triangular_solve
216: test:
217: suffix: 4
219: test:
220: suffix: 5
221: args: -lu
223: test:
224: suffix: 6
225: args: -lu -triangular_solve
226: output_file: output/ex30_3.out
228: TEST*/