Actual source code: ex2.c
2: static char help[] = "Tests repeated solving linear system on 2 by 2 matrix provided by MUMPS developer, Dec 17, 2012.\n\n";
3: /*
4: We have investigated the problem further, and we have
5: been able to reproduce it and obtain an erroneous
6: solution with an even smaller, 2x2, matrix:
7: [1 2]
8: [2 3]
9: and a right-hand side vector with all ones (1,1)
10: The correct solution is the vector (-1,1), in both solves.
12: mpiexec -n 2 ./ex2 -ksp_type preonly -pc_type lu -pc_factor_mat_solver_type mumps -mat_mumps_icntl_7 6 -mat_mumps_cntl_1 0.99
14: With this combination of options, I get off-diagonal pivots during the
15: factorization, which is the cause of the problem (different isol_loc
16: returned in the second solve, whereas, as I understand it, Petsc expects
17: isol_loc not to change between successive solves).
18: */
20: #include <petscksp.h>
22: int main(int argc, char **args)
23: {
24: Mat C;
25: PetscInt N = 2, rowidx, colidx;
26: Vec u, b, r;
27: KSP ksp;
28: PetscReal norm;
29: PetscMPIInt rank, size;
30: PetscScalar v;
32: PetscFunctionBeginUser;
33: PetscCall(PetscInitialize(&argc, &args, (char *)0, help));
34: PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
35: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
37: /* create stiffness matrix C = [1 2; 2 3] */
38: PetscCall(MatCreate(PETSC_COMM_WORLD, &C));
39: PetscCall(MatSetSizes(C, PETSC_DECIDE, PETSC_DECIDE, N, N));
40: PetscCall(MatSetFromOptions(C));
41: PetscCall(MatSetUp(C));
42: if (rank == 0) {
43: rowidx = 0;
44: colidx = 0;
45: v = 1.0;
46: PetscCall(MatSetValues(C, 1, &rowidx, 1, &colidx, &v, INSERT_VALUES));
47: rowidx = 0;
48: colidx = 1;
49: v = 2.0;
50: PetscCall(MatSetValues(C, 1, &rowidx, 1, &colidx, &v, INSERT_VALUES));
52: rowidx = 1;
53: colidx = 0;
54: v = 2.0;
55: PetscCall(MatSetValues(C, 1, &rowidx, 1, &colidx, &v, INSERT_VALUES));
56: rowidx = 1;
57: colidx = 1;
58: v = 3.0;
59: PetscCall(MatSetValues(C, 1, &rowidx, 1, &colidx, &v, INSERT_VALUES));
60: }
61: PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
62: PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
64: /* create right hand side and solution */
65: PetscCall(VecCreate(PETSC_COMM_WORLD, &u));
66: PetscCall(VecSetSizes(u, PETSC_DECIDE, N));
67: PetscCall(VecSetFromOptions(u));
68: PetscCall(VecDuplicate(u, &b));
69: PetscCall(VecDuplicate(u, &r));
70: PetscCall(VecSet(u, 0.0));
71: PetscCall(VecSet(b, 1.0));
73: /* solve linear system C*u = b */
74: PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
75: PetscCall(KSPSetOperators(ksp, C, C));
76: PetscCall(KSPSetFromOptions(ksp));
77: PetscCall(KSPSolve(ksp, b, u));
79: /* check residual r = C*u - b */
80: PetscCall(MatMult(C, u, r));
81: PetscCall(VecAXPY(r, -1.0, b));
82: PetscCall(VecNorm(r, NORM_2, &norm));
83: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "|| C*u - b|| = %g\n", (double)norm));
85: /* solve C^T*u = b twice */
86: PetscCall(KSPSolveTranspose(ksp, b, u));
87: /* check residual r = C^T*u - b */
88: PetscCall(MatMultTranspose(C, u, r));
89: PetscCall(VecAXPY(r, -1.0, b));
90: PetscCall(VecNorm(r, NORM_2, &norm));
91: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "|| C^T*u - b|| = %g\n", (double)norm));
93: PetscCall(KSPSolveTranspose(ksp, b, u));
94: PetscCall(MatMultTranspose(C, u, r));
95: PetscCall(VecAXPY(r, -1.0, b));
96: PetscCall(VecNorm(r, NORM_2, &norm));
97: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "|| C^T*u - b|| = %g\n", (double)norm));
99: /* solve C*u = b again */
100: PetscCall(KSPSolve(ksp, b, u));
101: PetscCall(MatMult(C, u, r));
102: PetscCall(VecAXPY(r, -1.0, b));
103: PetscCall(VecNorm(r, NORM_2, &norm));
104: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "|| C*u - b|| = %g\n", (double)norm));
106: PetscCall(KSPDestroy(&ksp));
107: PetscCall(VecDestroy(&u));
108: PetscCall(VecDestroy(&r));
109: PetscCall(VecDestroy(&b));
110: PetscCall(MatDestroy(&C));
111: PetscCall(PetscFinalize());
112: return 0;
113: }