Actual source code: ex30.c
2: 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\
3: Input parameters are:\n\
4: -lf <level> : level of fill for ILU (default is 0)\n\
5: -lu : use full LU or Cholesky factorization\n\
6: -m <value>,-n <value> : grid dimensions\n\
7: Note that most users should employ the KSP interface to the\n\
8: linear solvers instead of using the factorization routines\n\
9: directly.\n\n";
11: #include <petscmat.h>
13: int main(int argc, char **args)
14: {
15: Mat C, A;
16: PetscInt i, j, m = 5, n = 5, Ii, J, lf = 0;
17: PetscBool LU = PETSC_FALSE, CHOLESKY, TRIANGULAR = PETSC_FALSE, MATDSPL = PETSC_FALSE, flg, matordering;
18: PetscScalar v;
19: IS row, col;
20: PetscViewer viewer1, viewer2;
21: MatFactorInfo info;
22: Vec x, y, b, ytmp;
23: PetscReal norm2, norm2_inplace, tol = 100. * PETSC_MACHINE_EPSILON;
24: PetscRandom rdm;
25: PetscMPIInt size;
27: PetscFunctionBeginUser;
28: PetscCall(PetscInitialize(&argc, &args, (char *)0, help));
29: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
30: PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");
31: PetscCall(PetscOptionsGetInt(NULL, NULL, "-m", &m, NULL));
32: PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL));
33: PetscCall(PetscOptionsGetInt(NULL, NULL, "-lf", &lf, NULL));
35: PetscCall(PetscViewerDrawOpen(PETSC_COMM_SELF, 0, 0, 0, 0, 400, 400, &viewer1));
36: PetscCall(PetscViewerDrawOpen(PETSC_COMM_SELF, 0, 0, 400, 0, 400, 400, &viewer2));
38: PetscCall(MatCreate(PETSC_COMM_SELF, &C));
39: PetscCall(MatSetSizes(C, m * n, m * n, m * n, m * n));
40: PetscCall(MatSetFromOptions(C));
41: PetscCall(MatSetUp(C));
43: /* Create matrix C in seqaij format and sC in seqsbaij. (This is five-point stencil with some extra elements) */
44: for (i = 0; i < m; i++) {
45: for (j = 0; j < n; j++) {
46: v = -1.0;
47: Ii = j + n * i;
48: J = Ii - n;
49: if (J >= 0) PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
50: J = Ii + n;
51: if (J < m * n) PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
52: J = Ii - 1;
53: if (J >= 0) PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
54: J = Ii + 1;
55: if (J < m * n) PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
56: v = 4.0;
57: PetscCall(MatSetValues(C, 1, &Ii, 1, &Ii, &v, INSERT_VALUES));
58: }
59: }
60: PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
61: PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
63: PetscCall(MatIsSymmetric(C, 0.0, &flg));
64: PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_SUP, "C is non-symmetric");
66: /* Create vectors for error checking */
67: PetscCall(MatCreateVecs(C, &x, &b));
68: PetscCall(VecDuplicate(x, &y));
69: PetscCall(VecDuplicate(x, &ytmp));
70: PetscCall(PetscRandomCreate(PETSC_COMM_SELF, &rdm));
71: PetscCall(PetscRandomSetFromOptions(rdm));
72: PetscCall(VecSetRandom(x, rdm));
73: PetscCall(MatMult(C, x, b));
75: PetscCall(PetscOptionsHasName(NULL, NULL, "-mat_ordering", &matordering));
76: if (matordering) {
77: PetscCall(MatGetOrdering(C, MATORDERINGRCM, &row, &col));
78: } else {
79: PetscCall(MatGetOrdering(C, MATORDERINGNATURAL, &row, &col));
80: }
82: PetscCall(PetscOptionsHasName(NULL, NULL, "-display_matrices", &MATDSPL));
83: if (MATDSPL) {
84: printf("original matrix:\n");
85: PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_SELF, PETSC_VIEWER_ASCII_INFO));
86: PetscCall(MatView(C, PETSC_VIEWER_STDOUT_SELF));
87: PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_SELF));
88: PetscCall(MatView(C, PETSC_VIEWER_STDOUT_SELF));
89: PetscCall(MatView(C, viewer1));
90: }
92: /* Compute LU or ILU factor A */
93: PetscCall(MatFactorInfoInitialize(&info));
95: info.fill = 1.0;
96: info.diagonal_fill = 0;
97: info.zeropivot = 0.0;
99: PetscCall(PetscOptionsHasName(NULL, NULL, "-lu", &LU));
100: if (LU) {
101: printf("Test LU...\n");
102: PetscCall(MatGetFactor(C, MATSOLVERPETSC, MAT_FACTOR_LU, &A));
103: PetscCall(MatLUFactorSymbolic(A, C, row, col, &info));
104: } else {
105: printf("Test ILU...\n");
106: info.levels = lf;
108: PetscCall(MatGetFactor(C, MATSOLVERPETSC, MAT_FACTOR_ILU, &A));
109: PetscCall(MatILUFactorSymbolic(A, C, row, col, &info));
110: }
111: PetscCall(MatLUFactorNumeric(A, C, &info));
113: /* Solve A*y = b, then check the error */
114: PetscCall(MatSolve(A, b, y));
115: PetscCall(VecAXPY(y, -1.0, x));
116: PetscCall(VecNorm(y, NORM_2, &norm2));
117: PetscCall(MatDestroy(&A));
119: /* Test in-place ILU(0) and compare it with the out-place ILU(0) */
120: if (!LU && lf == 0) {
121: PetscCall(MatDuplicate(C, MAT_COPY_VALUES, &A));
122: PetscCall(MatILUFactor(A, row, col, &info));
123: /*
124: printf("In-place factored matrix:\n");
125: PetscCall(MatView(C,PETSC_VIEWER_STDOUT_SELF));
126: */
127: PetscCall(MatSolve(A, b, y));
128: PetscCall(VecAXPY(y, -1.0, x));
129: PetscCall(VecNorm(y, NORM_2, &norm2_inplace));
130: 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);
131: PetscCall(MatDestroy(&A));
132: }
134: /* Test Cholesky and ICC on seqaij matrix with matrix reordering on aij matrix C */
135: CHOLESKY = LU;
136: if (CHOLESKY) {
137: printf("Test Cholesky...\n");
138: lf = -1;
139: PetscCall(MatGetFactor(C, MATSOLVERPETSC, MAT_FACTOR_CHOLESKY, &A));
140: PetscCall(MatCholeskyFactorSymbolic(A, C, row, &info));
141: } else {
142: printf("Test ICC...\n");
143: info.levels = lf;
144: info.fill = 1.0;
145: info.diagonal_fill = 0;
146: info.zeropivot = 0.0;
148: PetscCall(MatGetFactor(C, MATSOLVERPETSC, MAT_FACTOR_ICC, &A));
149: PetscCall(MatICCFactorSymbolic(A, C, row, &info));
150: }
151: PetscCall(MatCholeskyFactorNumeric(A, C, &info));
153: /* test MatForwardSolve() and MatBackwardSolve() with matrix reordering on aij matrix C */
154: if (lf == -1) {
155: PetscCall(PetscOptionsHasName(NULL, NULL, "-triangular_solve", &TRIANGULAR));
156: if (TRIANGULAR) {
157: printf("Test MatForwardSolve...\n");
158: PetscCall(MatForwardSolve(A, b, ytmp));
159: printf("Test MatBackwardSolve...\n");
160: PetscCall(MatBackwardSolve(A, ytmp, y));
161: PetscCall(VecAXPY(y, -1.0, x));
162: PetscCall(VecNorm(y, NORM_2, &norm2));
163: if (norm2 > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, "MatForwardSolve and BackwardSolve: Norm of error=%g\n", (double)norm2));
164: }
165: }
167: PetscCall(MatSolve(A, b, y));
168: PetscCall(MatDestroy(&A));
169: PetscCall(VecAXPY(y, -1.0, x));
170: PetscCall(VecNorm(y, NORM_2, &norm2));
171: if (lf == -1 && norm2 > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, " reordered SEQAIJ: Cholesky/ICC levels %" PetscInt_FMT ", residual %g\n", lf, (double)norm2));
173: /* Test in-place ICC(0) and compare it with the out-place ICC(0) */
174: if (!CHOLESKY && lf == 0 && !matordering) {
175: PetscCall(MatConvert(C, MATSBAIJ, MAT_INITIAL_MATRIX, &A));
176: PetscCall(MatICCFactor(A, row, &info));
177: /*
178: printf("In-place factored matrix:\n");
179: PetscCall(MatView(A,PETSC_VIEWER_STDOUT_SELF));
180: */
181: PetscCall(MatSolve(A, b, y));
182: PetscCall(VecAXPY(y, -1.0, x));
183: PetscCall(VecNorm(y, NORM_2, &norm2_inplace));
184: 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);
185: PetscCall(MatDestroy(&A));
186: }
188: /* Free data structures */
189: PetscCall(ISDestroy(&row));
190: PetscCall(ISDestroy(&col));
191: PetscCall(MatDestroy(&C));
192: PetscCall(PetscViewerDestroy(&viewer1));
193: PetscCall(PetscViewerDestroy(&viewer2));
194: PetscCall(PetscRandomDestroy(&rdm));
195: PetscCall(VecDestroy(&x));
196: PetscCall(VecDestroy(&y));
197: PetscCall(VecDestroy(&ytmp));
198: PetscCall(VecDestroy(&b));
199: PetscCall(PetscFinalize());
200: return 0;
201: }
203: /*TEST
205: test:
206: args: -mat_ordering -display_matrices -nox
207: filter: grep -v " MPI process"
209: test:
210: suffix: 2
211: args: -mat_ordering -display_matrices -nox -lu
213: test:
214: suffix: 3
215: args: -mat_ordering -lu -triangular_solve
217: test:
218: suffix: 4
220: test:
221: suffix: 5
222: args: -lu
224: test:
225: suffix: 6
226: args: -lu -triangular_solve
227: output_file: output/ex30_3.out
229: TEST*/