Actual source code: ex214.c


  2: static char help[] = "Tests MatMatSolve() and MatMatTransposeSolve() for computing inv(A) with MUMPS.\n\
  3: Example: mpiexec -n <np> ./ex214 -displ \n\n";

  5: #include <petscmat.h>

  7: int main(int argc, char **args)
  8: {
  9:   PetscMPIInt size, rank;
 10: #if defined(PETSC_HAVE_MUMPS)
 11:   Mat         A, RHS, C, F, X, AX, spRHST;
 12:   PetscInt    m, n, nrhs, M, N, i, Istart, Iend, Ii, j, J, test;
 13:   PetscScalar v;
 14:   PetscReal   norm, tol = PETSC_SQRT_MACHINE_EPSILON;
 15:   PetscRandom rand;
 16:   PetscBool   displ = PETSC_FALSE;
 17:   char        solver[256];
 18: #endif

 20:   PetscFunctionBeginUser;
 21:   PetscCall(PetscInitialize(&argc, &args, (char *)0, help));
 22:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
 23:   PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));

 25: #if !defined(PETSC_HAVE_MUMPS)
 26:   if (rank == 0) PetscCall(PetscPrintf(PETSC_COMM_SELF, "This example requires MUMPS, exit...\n"));
 27:   PetscCall(PetscFinalize());
 28:   return 0;
 29: #else

 31:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-displ", &displ, NULL));

 33:   /* Create matrix A */
 34:   m = 4;
 35:   n = 4;
 36:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-m", &m, NULL));
 37:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL));

 39:   PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
 40:   PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, m * n, m * n));
 41:   PetscCall(MatSetFromOptions(A));
 42:   PetscCall(MatMPIAIJSetPreallocation(A, 5, NULL, 5, NULL));
 43:   PetscCall(MatSeqAIJSetPreallocation(A, 5, NULL));

 45:   PetscCall(MatGetOwnershipRange(A, &Istart, &Iend));
 46:   for (Ii = Istart; Ii < Iend; Ii++) {
 47:     v = -1.0;
 48:     i = Ii / n;
 49:     j = Ii - i * n;
 50:     if (i > 0) {
 51:       J = Ii - n;
 52:       PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, ADD_VALUES));
 53:     }
 54:     if (i < m - 1) {
 55:       J = Ii + n;
 56:       PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, ADD_VALUES));
 57:     }
 58:     if (j > 0) {
 59:       J = Ii - 1;
 60:       PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, ADD_VALUES));
 61:     }
 62:     if (j < n - 1) {
 63:       J = Ii + 1;
 64:       PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, ADD_VALUES));
 65:     }
 66:     v = 4.0;
 67:     PetscCall(MatSetValues(A, 1, &Ii, 1, &Ii, &v, ADD_VALUES));
 68:   }
 69:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
 70:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));

 72:   PetscCall(MatGetLocalSize(A, &m, &n));
 73:   PetscCall(MatGetSize(A, &M, &N));
 74:   PetscCheck(m == n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "This example is not intended for rectangular matrices (%" PetscInt_FMT ", %" PetscInt_FMT ")", m, n);

 76:   /* Create dense matrix C and X; C holds true solution with identical columns */
 77:   nrhs = N;
 78:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-nrhs", &nrhs, NULL));
 79:   PetscCall(MatCreate(PETSC_COMM_WORLD, &C));
 80:   PetscCall(MatSetSizes(C, m, PETSC_DECIDE, PETSC_DECIDE, nrhs));
 81:   PetscCall(MatSetType(C, MATDENSE));
 82:   PetscCall(MatSetFromOptions(C));
 83:   PetscCall(MatSetUp(C));

 85:   PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &rand));
 86:   PetscCall(PetscRandomSetFromOptions(rand));
 87:   PetscCall(MatSetRandom(C, rand));
 88:   PetscCall(MatDuplicate(C, MAT_DO_NOT_COPY_VALUES, &X));

 90:   PetscCall(PetscStrncpy(solver, MATSOLVERMUMPS, sizeof(solver)));
 91:   if (rank == 0 && displ) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Solving with %s: nrhs %" PetscInt_FMT ", size mat %" PetscInt_FMT " x %" PetscInt_FMT "\n", solver, nrhs, M, N));

 93:   for (test = 0; test < 2; test++) {
 94:     if (test == 0) {
 95:       /* Test LU Factorization */
 96:       PetscCall(PetscPrintf(PETSC_COMM_WORLD, "test LU factorization\n"));
 97:       PetscCall(MatGetFactor(A, solver, MAT_FACTOR_LU, &F));
 98:       PetscCall(MatLUFactorSymbolic(F, A, NULL, NULL, NULL));
 99:       PetscCall(MatLUFactorNumeric(F, A, NULL));
100:     } else {
101:       /* Test Cholesky Factorization */
102:       PetscBool flg;
103:       PetscCall(MatIsSymmetric(A, 0.0, &flg));
104:       PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "A must be symmetric for Cholesky factorization");

106:       PetscCall(PetscPrintf(PETSC_COMM_WORLD, "test Cholesky factorization\n"));
107:       PetscCall(MatGetFactor(A, solver, MAT_FACTOR_CHOLESKY, &F));
108:       PetscCall(MatCholeskyFactorSymbolic(F, A, NULL, NULL));
109:       PetscCall(MatCholeskyFactorNumeric(F, A, NULL));
110:     }

112:     /* (1) Test MatMatSolve(): dense RHS = A*C, C: true solutions */
113:     /* ---------------------------------------------------------- */
114:     PetscCall(MatMatMult(A, C, MAT_INITIAL_MATRIX, 2.0, &RHS));
115:     PetscCall(MatMatSolve(F, RHS, X));
116:     /* Check the error */
117:     PetscCall(MatAXPY(X, -1.0, C, SAME_NONZERO_PATTERN));
118:     PetscCall(MatNorm(X, NORM_FROBENIUS, &norm));
119:     if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, "(1) MatMatSolve: Norm of error %g\n", norm));

121:     /* Test X=RHS */
122:     PetscCall(MatMatSolve(F, RHS, RHS));
123:     /* Check the error */
124:     PetscCall(MatAXPY(RHS, -1.0, C, SAME_NONZERO_PATTERN));
125:     PetscCall(MatNorm(RHS, NORM_FROBENIUS, &norm));
126:     if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, "(1.1) MatMatSolve: Norm of error %g\n", norm));

128:     /* (2) Test MatMatSolve() for inv(A) with dense RHS:
129:      RHS = [e[0],...,e[nrhs-1]], dense X holds first nrhs columns of inv(A) */
130:     /* -------------------------------------------------------------------- */
131:     PetscCall(MatZeroEntries(RHS));
132:     for (i = 0; i < nrhs; i++) {
133:       v = 1.0;
134:       PetscCall(MatSetValues(RHS, 1, &i, 1, &i, &v, INSERT_VALUES));
135:     }
136:     PetscCall(MatAssemblyBegin(RHS, MAT_FINAL_ASSEMBLY));
137:     PetscCall(MatAssemblyEnd(RHS, MAT_FINAL_ASSEMBLY));

139:     PetscCall(MatMatSolve(F, RHS, X));
140:     if (displ) {
141:       if (rank == 0) PetscCall(PetscPrintf(PETSC_COMM_SELF, " \n(2) first %" PetscInt_FMT " columns of inv(A) with dense RHS:\n", nrhs));
142:       PetscCall(MatView(X, PETSC_VIEWER_STDOUT_WORLD));
143:     }

145:     /* Check the residual */
146:     PetscCall(MatMatMult(A, X, MAT_INITIAL_MATRIX, 2.0, &AX));
147:     PetscCall(MatAXPY(AX, -1.0, RHS, SAME_NONZERO_PATTERN));
148:     PetscCall(MatNorm(AX, NORM_INFINITY, &norm));
149:     if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, "(2) MatMatSolve: Norm of residual %g\n", norm));
150:     PetscCall(MatZeroEntries(X));

152:     /* (3) Test MatMatTransposeSolve() for inv(A) with sparse RHS stored in the host:
153:      spRHST = [e[0],...,e[nrhs-1]]^T, dense X holds first nrhs columns of inv(A) */
154:     /* --------------------------------------------------------------------------- */
155:     /* Create spRHST: PETSc does not support compressed column format which is required by MUMPS for sparse RHS matrix,
156:      thus user must create spRHST=spRHS^T and call MatMatTransposeSolve() */
157:     PetscCall(MatCreate(PETSC_COMM_WORLD, &spRHST));
158:     if (rank == 0) {
159:       /* MUMPS requirs RHS be centralized on the host! */
160:       PetscCall(MatSetSizes(spRHST, nrhs, M, PETSC_DECIDE, PETSC_DECIDE));
161:     } else {
162:       PetscCall(MatSetSizes(spRHST, 0, 0, PETSC_DECIDE, PETSC_DECIDE));
163:     }
164:     PetscCall(MatSetType(spRHST, MATAIJ));
165:     PetscCall(MatSetFromOptions(spRHST));
166:     PetscCall(MatSetUp(spRHST));
167:     if (rank == 0) {
168:       v = 1.0;
169:       for (i = 0; i < nrhs; i++) PetscCall(MatSetValues(spRHST, 1, &i, 1, &i, &v, INSERT_VALUES));
170:     }
171:     PetscCall(MatAssemblyBegin(spRHST, MAT_FINAL_ASSEMBLY));
172:     PetscCall(MatAssemblyEnd(spRHST, MAT_FINAL_ASSEMBLY));

174:     PetscCall(MatMatTransposeSolve(F, spRHST, X));

176:     if (displ) {
177:       if (rank == 0) PetscCall(PetscPrintf(PETSC_COMM_SELF, " \n(3) first %" PetscInt_FMT " columns of inv(A) with sparse RHS:\n", nrhs));
178:       PetscCall(MatView(X, PETSC_VIEWER_STDOUT_WORLD));
179:     }

181:     /* Check the residual: R = A*X - RHS */
182:     PetscCall(MatMatMult(A, X, MAT_REUSE_MATRIX, 2.0, &AX));

184:     PetscCall(MatAXPY(AX, -1.0, RHS, SAME_NONZERO_PATTERN));
185:     PetscCall(MatNorm(AX, NORM_INFINITY, &norm));
186:     if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, "(3) MatMatSolve: Norm of residual %g\n", norm));

188:     /* (4) Test MatMatSolve() for inv(A) with selected entries:
189:      input: spRHS gives selected indices; output: spRHS holds selected entries of inv(A) */
190:     /* --------------------------------------------------------------------------------- */
191:     if (nrhs == N) { /* mumps requires nrhs = n */
192:       /* Create spRHS on proc[0] */
193:       Mat spRHS = NULL;

195:       /* Create spRHS = spRHST^T. Two matrices share internal matrix data structure */
196:       PetscCall(MatCreateTranspose(spRHST, &spRHS));
197:       PetscCall(MatMumpsGetInverse(F, spRHS));
198:       PetscCall(MatDestroy(&spRHS));

200:       PetscCall(MatMumpsGetInverseTranspose(F, spRHST));
201:       if (displ) {
202:         PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\nSelected entries of inv(A^T):\n"));
203:         PetscCall(MatView(spRHST, PETSC_VIEWER_STDOUT_WORLD));
204:       }
205:       PetscCall(MatDestroy(&spRHS));
206:     }
207:     PetscCall(MatDestroy(&AX));
208:     PetscCall(MatDestroy(&F));
209:     PetscCall(MatDestroy(&RHS));
210:     PetscCall(MatDestroy(&spRHST));
211:   }

213:   /* Free data structures */
214:   PetscCall(MatDestroy(&A));
215:   PetscCall(MatDestroy(&C));
216:   PetscCall(MatDestroy(&X));
217:   PetscCall(PetscRandomDestroy(&rand));
218:   PetscCall(PetscFinalize());
219:   return 0;
220: #endif
221: }

223: /*TEST

225:    test:
226:      requires: mumps double !complex

228:    test:
229:      suffix: 2
230:      requires: mumps double !complex
231:      nsize: 2

233: TEST*/