Actual source code: ex145.c
1: static char help[] = "Tests LU, Cholesky factorization and MatMatSolve() for an Elemental dense matrix.\n\n";
3: #include <petscmat.h>
5: int main(int argc, char **argv)
6: {
7: Mat A, F, B, X, C, Aher, G;
8: Vec b, x, c, d, e;
9: PetscInt m = 5, n, p, i, j, nrows, ncols;
10: PetscScalar *v, *barray, rval;
11: PetscReal norm, tol = 1.e-11;
12: PetscMPIInt size, rank;
13: PetscRandom rand;
14: const PetscInt *rows, *cols;
15: IS isrows, iscols;
16: PetscBool mats_view = PETSC_FALSE;
17: MatFactorInfo finfo;
19: PetscFunctionBeginUser;
20: PetscCall(PetscInitialize(&argc, &argv, NULL, 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 Elemental matrix A\n"));
37: PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
38: PetscCall(MatSetSizes(A, m, n, PETSC_DECIDE, PETSC_DECIDE));
39: PetscCall(MatSetType(A, MATELEMENTAL));
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, MATELEMENTAL));
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(MatCreate(PETSC_COMM_WORLD, &X));
122: PetscCall(MatSetSizes(X, m, p, PETSC_DECIDE, PETSC_DECIDE));
123: PetscCall(MatSetType(X, MATELEMENTAL));
124: PetscCall(MatSetFromOptions(X));
125: PetscCall(MatSetUp(X));
126: PetscCall(MatAssemblyBegin(X, MAT_FINAL_ASSEMBLY));
127: PetscCall(MatAssemblyEnd(X, MAT_FINAL_ASSEMBLY));
129: /* Cholesky factorization */
130: /*------------------------*/
131: PetscCall(PetscPrintf(PETSC_COMM_WORLD, " Create Elemental matrix Aher\n"));
132: PetscCall(MatHermitianTranspose(A, MAT_INITIAL_MATRIX, &Aher));
133: PetscCall(MatAXPY(Aher, 1.0, A, SAME_NONZERO_PATTERN)); /* Aher = A + A^T */
134: if (rank == 0) { /* add 100.0 to diagonals of Aher to make it spd */
136: /* TODO: Replace this with a call to El::ShiftDiagonal( A, 100.),
137: or at least pre-allocate the right amount of space */
138: PetscInt M, N;
139: PetscCall(MatGetSize(Aher, &M, &N));
140: for (i = 0; i < M; i++) {
141: rval = 100.0;
142: PetscCall(MatSetValues(Aher, 1, &i, 1, &i, &rval, ADD_VALUES));
143: }
144: }
145: PetscCall(MatAssemblyBegin(Aher, MAT_FINAL_ASSEMBLY));
146: PetscCall(MatAssemblyEnd(Aher, MAT_FINAL_ASSEMBLY));
147: if (mats_view) {
148: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Aher:\n"));
149: PetscCall(MatView(Aher, PETSC_VIEWER_STDOUT_WORLD));
150: }
152: /* Cholesky factorization */
153: /*------------------------*/
154: PetscCall(PetscPrintf(PETSC_COMM_WORLD, " Test Cholesky Solver \n"));
155: /* In-place Cholesky */
156: /* Create matrix factor G, then copy Aher to G */
157: PetscCall(MatCreate(PETSC_COMM_WORLD, &G));
158: PetscCall(MatSetSizes(G, m, n, PETSC_DECIDE, PETSC_DECIDE));
159: PetscCall(MatSetType(G, MATELEMENTAL));
160: PetscCall(MatSetFromOptions(G));
161: PetscCall(MatSetUp(G));
162: PetscCall(MatAssemblyBegin(G, MAT_FINAL_ASSEMBLY));
163: PetscCall(MatAssemblyEnd(G, MAT_FINAL_ASSEMBLY));
164: PetscCall(MatCopy(Aher, G, SAME_NONZERO_PATTERN));
166: /* Only G = U^T * U is implemented for now */
167: PetscCall(MatCholeskyFactor(G, 0, 0));
168: if (mats_view) {
169: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Cholesky Factor G:\n"));
170: PetscCall(MatView(G, PETSC_VIEWER_STDOUT_WORLD));
171: }
173: /* Solve U^T * U x = b and U^T * U X = B */
174: PetscCall(MatSolve(G, b, x));
175: PetscCall(MatMatSolve(G, B, X));
176: PetscCall(MatDestroy(&G));
178: /* Out-place Cholesky */
179: PetscCall(MatGetFactor(Aher, MATSOLVERELEMENTAL, MAT_FACTOR_CHOLESKY, &G));
180: PetscCall(MatCholeskyFactorSymbolic(G, Aher, 0, &finfo));
181: PetscCall(MatCholeskyFactorNumeric(G, Aher, &finfo));
182: if (mats_view) PetscCall(MatView(G, PETSC_VIEWER_STDOUT_WORLD));
183: PetscCall(MatSolve(G, b, x));
184: PetscCall(MatMatSolve(G, B, X));
185: PetscCall(MatDestroy(&G));
187: /* Check norm(Aher*x - b) */
188: PetscCall(VecCreate(PETSC_COMM_WORLD, &c));
189: PetscCall(VecSetSizes(c, m, PETSC_DECIDE));
190: PetscCall(VecSetFromOptions(c));
191: PetscCall(MatMult(Aher, x, c));
192: PetscCall(VecAXPY(c, -1.0, b));
193: PetscCall(VecNorm(c, NORM_1, &norm));
194: if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Warning: |Aher*x - b| for Cholesky %g\n", (double)norm));
196: /* Check norm(Aher*X - B) */
197: PetscCall(MatMatMult(Aher, X, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &C));
198: PetscCall(MatAXPY(C, -1.0, B, SAME_NONZERO_PATTERN));
199: PetscCall(MatNorm(C, NORM_1, &norm));
200: if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Warning: |Aher*X - B| for Cholesky %g\n", (double)norm));
202: /* LU factorization */
203: /*------------------*/
204: PetscCall(PetscPrintf(PETSC_COMM_WORLD, " Test LU Solver \n"));
205: /* In-place LU */
206: /* Create matrix factor F, then copy A to F */
207: PetscCall(MatCreate(PETSC_COMM_WORLD, &F));
208: PetscCall(MatSetSizes(F, m, n, PETSC_DECIDE, PETSC_DECIDE));
209: PetscCall(MatSetType(F, MATELEMENTAL));
210: PetscCall(MatSetFromOptions(F));
211: PetscCall(MatSetUp(F));
212: PetscCall(MatAssemblyBegin(F, MAT_FINAL_ASSEMBLY));
213: PetscCall(MatAssemblyEnd(F, MAT_FINAL_ASSEMBLY));
214: PetscCall(MatCopy(A, F, SAME_NONZERO_PATTERN));
215: /* Create vector d to test MatSolveAdd() */
216: PetscCall(VecDuplicate(x, &d));
217: PetscCall(VecCopy(x, d));
219: /* PF=LU or F=LU factorization - perms is ignored by Elemental;
220: set finfo.dtcol !0 or 0 to enable/disable partial pivoting */
221: finfo.dtcol = 0.1;
222: PetscCall(MatLUFactor(F, 0, 0, &finfo));
224: /* Solve LUX = PB or LUX = B */
225: PetscCall(MatSolveAdd(F, b, d, x));
226: PetscCall(MatMatSolve(F, B, X));
227: PetscCall(MatDestroy(&F));
229: /* Check norm(A*X - B) */
230: PetscCall(VecCreate(PETSC_COMM_WORLD, &e));
231: PetscCall(VecSetSizes(e, m, PETSC_DECIDE));
232: PetscCall(VecSetFromOptions(e));
233: PetscCall(MatMult(A, x, c));
234: PetscCall(MatMult(A, d, e));
235: PetscCall(VecAXPY(c, -1.0, e));
236: PetscCall(VecAXPY(c, -1.0, b));
237: PetscCall(VecNorm(c, NORM_1, &norm));
238: if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Warning: |A*x - b| for LU %g\n", (double)norm));
239: /* Reuse product C; replace Aher with A */
240: PetscCall(MatProductReplaceMats(A, NULL, NULL, C));
241: PetscCall(MatMatMult(A, X, MAT_REUSE_MATRIX, PETSC_DETERMINE, &C));
242: PetscCall(MatAXPY(C, -1.0, B, SAME_NONZERO_PATTERN));
243: PetscCall(MatNorm(C, NORM_1, &norm));
244: if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Warning: |A*X - B| for LU %g\n", (double)norm));
246: /* Out-place LU */
247: PetscCall(MatGetFactor(A, MATSOLVERELEMENTAL, MAT_FACTOR_LU, &F));
248: PetscCall(MatLUFactorSymbolic(F, A, 0, 0, &finfo));
249: PetscCall(MatLUFactorNumeric(F, A, &finfo));
250: if (mats_view) PetscCall(MatView(F, PETSC_VIEWER_STDOUT_WORLD));
251: PetscCall(MatSolve(F, b, x));
252: PetscCall(MatMatSolve(F, B, X));
253: PetscCall(MatDestroy(&F));
255: /* Free space */
256: PetscCall(MatDestroy(&A));
257: PetscCall(MatDestroy(&Aher));
258: PetscCall(MatDestroy(&B));
259: PetscCall(MatDestroy(&C));
260: PetscCall(MatDestroy(&X));
261: PetscCall(VecDestroy(&b));
262: PetscCall(VecDestroy(&c));
263: PetscCall(VecDestroy(&d));
264: PetscCall(VecDestroy(&e));
265: PetscCall(VecDestroy(&x));
266: PetscCall(PetscRandomDestroy(&rand));
267: PetscCall(PetscFinalize());
268: return 0;
269: }
271: /*TEST
273: build:
274: requires: elemental
276: test:
277: nsize: 2
278: output_file: output/ex145.out
280: test:
281: suffix: 2
282: nsize: 6
283: output_file: output/ex145.out
285: TEST*/