Actual source code: ex245.c
2: static char help[] = "Tests LU, Cholesky factorization and MatMatSolve() for a ScaLAPACK dense matrix.\n\n";
4: #include <petscmat.h>
6: int main(int argc, char **argv)
7: {
8: Mat A, F, B, X, C, Aher, G;
9: Vec b, x, c, d, e;
10: PetscInt m = 5, n, p, i, j, nrows, ncols;
11: PetscScalar *v, *barray, rval;
12: PetscReal norm, tol = 1.e5 * PETSC_MACHINE_EPSILON;
13: PetscMPIInt size, rank;
14: PetscRandom rand;
15: const PetscInt *rows, *cols;
16: IS isrows, iscols;
17: PetscBool mats_view = PETSC_FALSE;
19: PetscFunctionBeginUser;
20: PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
21: PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
22: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
24: PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &rand));
25: PetscCall(PetscRandomSetFromOptions(rand));
27: /* Get local dimensions of matrices */
28: PetscCall(PetscOptionsGetInt(NULL, NULL, "-m", &m, NULL));
29: n = m;
30: PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL));
31: p = m / 2;
32: PetscCall(PetscOptionsGetInt(NULL, NULL, "-p", &p, NULL));
33: PetscCall(PetscOptionsHasName(NULL, NULL, "-mats_view", &mats_view));
35: /* Create matrix A */
36: PetscCall(PetscPrintf(PETSC_COMM_WORLD, " Create ScaLAPACK matrix A\n"));
37: PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
38: PetscCall(MatSetSizes(A, m, n, PETSC_DECIDE, PETSC_DECIDE));
39: PetscCall(MatSetType(A, MATSCALAPACK));
40: PetscCall(MatSetFromOptions(A));
41: PetscCall(MatSetUp(A));
42: /* Set local matrix entries */
43: PetscCall(MatGetOwnershipIS(A, &isrows, &iscols));
44: PetscCall(ISGetLocalSize(isrows, &nrows));
45: PetscCall(ISGetIndices(isrows, &rows));
46: PetscCall(ISGetLocalSize(iscols, &ncols));
47: PetscCall(ISGetIndices(iscols, &cols));
48: PetscCall(PetscMalloc1(nrows * ncols, &v));
49: for (i = 0; i < nrows; i++) {
50: for (j = 0; j < ncols; j++) {
51: PetscCall(PetscRandomGetValue(rand, &rval));
52: v[i * ncols + j] = rval;
53: }
54: }
55: PetscCall(MatSetValues(A, nrows, rows, ncols, cols, v, INSERT_VALUES));
56: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
57: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
58: PetscCall(ISRestoreIndices(isrows, &rows));
59: PetscCall(ISRestoreIndices(iscols, &cols));
60: PetscCall(ISDestroy(&isrows));
61: PetscCall(ISDestroy(&iscols));
62: PetscCall(PetscFree(v));
63: if (mats_view) {
64: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "A: nrows %" PetscInt_FMT ", m %" PetscInt_FMT "; ncols %" PetscInt_FMT ", n %" PetscInt_FMT "\n", nrows, m, ncols, n));
65: PetscCall(MatView(A, PETSC_VIEWER_STDOUT_WORLD));
66: }
68: /* Create rhs matrix B */
69: PetscCall(PetscPrintf(PETSC_COMM_WORLD, " Create rhs matrix B\n"));
70: PetscCall(MatCreate(PETSC_COMM_WORLD, &B));
71: PetscCall(MatSetSizes(B, m, p, PETSC_DECIDE, PETSC_DECIDE));
72: PetscCall(MatSetType(B, MATSCALAPACK));
73: PetscCall(MatSetFromOptions(B));
74: PetscCall(MatSetUp(B));
75: PetscCall(MatGetOwnershipIS(B, &isrows, &iscols));
76: PetscCall(ISGetLocalSize(isrows, &nrows));
77: PetscCall(ISGetIndices(isrows, &rows));
78: PetscCall(ISGetLocalSize(iscols, &ncols));
79: PetscCall(ISGetIndices(iscols, &cols));
80: PetscCall(PetscMalloc1(nrows * ncols, &v));
81: for (i = 0; i < nrows; i++) {
82: for (j = 0; j < ncols; j++) {
83: PetscCall(PetscRandomGetValue(rand, &rval));
84: v[i * ncols + j] = rval;
85: }
86: }
87: PetscCall(MatSetValues(B, nrows, rows, ncols, cols, v, INSERT_VALUES));
88: PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
89: PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
90: PetscCall(ISRestoreIndices(isrows, &rows));
91: PetscCall(ISRestoreIndices(iscols, &cols));
92: PetscCall(ISDestroy(&isrows));
93: PetscCall(ISDestroy(&iscols));
94: PetscCall(PetscFree(v));
95: if (mats_view) {
96: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "B: nrows %" PetscInt_FMT ", m %" PetscInt_FMT "; ncols %" PetscInt_FMT ", p %" PetscInt_FMT "\n", nrows, m, ncols, p));
97: PetscCall(MatView(B, PETSC_VIEWER_STDOUT_WORLD));
98: }
100: /* Create rhs vector b and solution x (same size as b) */
101: PetscCall(VecCreate(PETSC_COMM_WORLD, &b));
102: PetscCall(VecSetSizes(b, m, PETSC_DECIDE));
103: PetscCall(VecSetFromOptions(b));
104: PetscCall(VecGetArray(b, &barray));
105: for (j = 0; j < m; j++) {
106: PetscCall(PetscRandomGetValue(rand, &rval));
107: barray[j] = rval;
108: }
109: PetscCall(VecRestoreArray(b, &barray));
110: PetscCall(VecAssemblyBegin(b));
111: PetscCall(VecAssemblyEnd(b));
112: if (mats_view) {
113: PetscCall(PetscSynchronizedPrintf(PETSC_COMM_WORLD, "[%d] b: m %" PetscInt_FMT "\n", rank, m));
114: PetscCall(PetscSynchronizedFlush(PETSC_COMM_WORLD, PETSC_STDOUT));
115: PetscCall(VecView(b, PETSC_VIEWER_STDOUT_WORLD));
116: }
117: PetscCall(VecDuplicate(b, &x));
119: /* Create matrix X - same size as B */
120: PetscCall(PetscPrintf(PETSC_COMM_WORLD, " Create solution matrix X\n"));
121: PetscCall(MatDuplicate(B, MAT_DO_NOT_COPY_VALUES, &X));
123: /* Cholesky factorization */
124: /*------------------------*/
125: PetscCall(PetscPrintf(PETSC_COMM_WORLD, " Create ScaLAPACK matrix Aher\n"));
126: PetscCall(MatHermitianTranspose(A, MAT_INITIAL_MATRIX, &Aher));
127: PetscCall(MatAXPY(Aher, 1.0, A, SAME_NONZERO_PATTERN)); /* Aher = A + A^T */
128: PetscCall(MatShift(Aher, 100.0)); /* add 100.0 to diagonals of Aher to make it spd */
129: if (mats_view) {
130: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Aher:\n"));
131: PetscCall(MatView(Aher, PETSC_VIEWER_STDOUT_WORLD));
132: }
134: /* Cholesky factorization */
135: /*------------------------*/
136: PetscCall(PetscPrintf(PETSC_COMM_WORLD, " Test Cholesky Solver \n"));
137: /* In-place Cholesky */
138: /* Create matrix factor G, with a copy of Aher */
139: PetscCall(MatDuplicate(Aher, MAT_COPY_VALUES, &G));
141: /* G = L * L^T */
142: PetscCall(MatCholeskyFactor(G, 0, 0));
143: if (mats_view) {
144: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Cholesky Factor G:\n"));
145: PetscCall(MatView(G, PETSC_VIEWER_STDOUT_WORLD));
146: }
148: /* Solve L * L^T x = b and L * L^T * X = B */
149: PetscCall(MatSolve(G, b, x));
150: PetscCall(MatMatSolve(G, B, X));
151: PetscCall(MatDestroy(&G));
153: /* Out-place Cholesky */
154: PetscCall(MatGetFactor(Aher, MATSOLVERSCALAPACK, MAT_FACTOR_CHOLESKY, &G));
155: PetscCall(MatCholeskyFactorSymbolic(G, Aher, 0, NULL));
156: PetscCall(MatCholeskyFactorNumeric(G, Aher, NULL));
157: if (mats_view) PetscCall(MatView(G, PETSC_VIEWER_STDOUT_WORLD));
158: PetscCall(MatSolve(G, b, x));
159: PetscCall(MatMatSolve(G, B, X));
160: PetscCall(MatDestroy(&G));
162: /* Check norm(Aher*x - b) */
163: PetscCall(VecCreate(PETSC_COMM_WORLD, &c));
164: PetscCall(VecSetSizes(c, m, PETSC_DECIDE));
165: PetscCall(VecSetFromOptions(c));
166: PetscCall(MatMult(Aher, x, c));
167: PetscCall(VecAXPY(c, -1.0, b));
168: PetscCall(VecNorm(c, NORM_1, &norm));
169: if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Warning: ||Aher*x - b||=%g for Cholesky\n", (double)norm));
171: /* Check norm(Aher*X - B) */
172: PetscCall(MatMatMult(Aher, X, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &C));
173: PetscCall(MatAXPY(C, -1.0, B, SAME_NONZERO_PATTERN));
174: PetscCall(MatNorm(C, NORM_1, &norm));
175: if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Warning: ||Aher*X - B||=%g for Cholesky\n", (double)norm));
177: /* LU factorization */
178: /*------------------*/
179: PetscCall(PetscPrintf(PETSC_COMM_WORLD, " Test LU Solver \n"));
180: /* In-place LU */
181: /* Create matrix factor F, with a copy of A */
182: PetscCall(MatDuplicate(A, MAT_COPY_VALUES, &F));
183: /* Create vector d to test MatSolveAdd() */
184: PetscCall(VecDuplicate(x, &d));
185: PetscCall(VecCopy(x, d));
187: /* PF=LU factorization */
188: PetscCall(MatLUFactor(F, 0, 0, NULL));
190: /* Solve LUX = PB */
191: PetscCall(MatSolveAdd(F, b, d, x));
192: PetscCall(MatMatSolve(F, B, X));
193: PetscCall(MatDestroy(&F));
195: /* Check norm(A*X - B) */
196: PetscCall(VecCreate(PETSC_COMM_WORLD, &e));
197: PetscCall(VecSetSizes(e, m, PETSC_DECIDE));
198: PetscCall(VecSetFromOptions(e));
199: PetscCall(MatMult(A, x, c));
200: PetscCall(MatMult(A, d, e));
201: PetscCall(VecAXPY(c, -1.0, e));
202: PetscCall(VecAXPY(c, -1.0, b));
203: PetscCall(VecNorm(c, NORM_1, &norm));
204: if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Warning: ||A*x - b||=%g for LU\n", (double)norm));
205: /* Reuse product C; replace Aher with A */
206: PetscCall(MatProductReplaceMats(A, NULL, NULL, C));
207: PetscCall(MatMatMult(A, X, MAT_REUSE_MATRIX, PETSC_DEFAULT, &C));
208: PetscCall(MatAXPY(C, -1.0, B, SAME_NONZERO_PATTERN));
209: PetscCall(MatNorm(C, NORM_1, &norm));
210: if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Warning: ||A*X - B||=%g for LU\n", (double)norm));
212: /* Out-place LU */
213: PetscCall(MatGetFactor(A, MATSOLVERSCALAPACK, MAT_FACTOR_LU, &F));
214: PetscCall(MatLUFactorSymbolic(F, A, 0, 0, NULL));
215: PetscCall(MatLUFactorNumeric(F, A, NULL));
216: if (mats_view) PetscCall(MatView(F, PETSC_VIEWER_STDOUT_WORLD));
217: PetscCall(MatSolve(F, b, x));
218: PetscCall(MatMatSolve(F, B, X));
219: PetscCall(MatDestroy(&F));
221: /* Free space */
222: PetscCall(MatDestroy(&A));
223: PetscCall(MatDestroy(&Aher));
224: PetscCall(MatDestroy(&B));
225: PetscCall(MatDestroy(&C));
226: PetscCall(MatDestroy(&X));
227: PetscCall(VecDestroy(&b));
228: PetscCall(VecDestroy(&c));
229: PetscCall(VecDestroy(&d));
230: PetscCall(VecDestroy(&e));
231: PetscCall(VecDestroy(&x));
232: PetscCall(PetscRandomDestroy(&rand));
233: PetscCall(PetscFinalize());
234: return 0;
235: }
237: /*TEST
239: build:
240: requires: scalapack
242: test:
243: nsize: 2
244: output_file: output/ex245.out
246: test:
247: suffix: 2
248: nsize: 6
249: output_file: output/ex245.out
251: TEST*/