Actual source code: ex2.c

petsc-3.12.0 2019-09-29
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  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;
 26:   PetscInt       N = 2,rowidx,colidx;
 27:   Vec            u,b,r;
 28:   KSP            ksp;
 29:   PetscReal      norm;
 30:   PetscMPIInt    rank,size;
 31:   PetscScalar    v;

 33:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
 34:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 35:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

 37:   /* create stiffness matrix C = [1 2; 2 3] */
 38:   MatCreate(PETSC_COMM_WORLD,&C);
 39:   MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);
 40:   MatSetFromOptions(C);
 41:   MatSetUp(C);
 42:   if (!rank) {
 43:     rowidx = 0; colidx = 0; v = 1.0;
 44:     MatSetValues(C,1,&rowidx,1,&colidx,&v,INSERT_VALUES);
 45:     rowidx = 0; colidx = 1; v = 2.0;
 46:     MatSetValues(C,1,&rowidx,1,&colidx,&v,INSERT_VALUES);

 48:     rowidx = 1; colidx = 0; v = 2.0;
 49:     MatSetValues(C,1,&rowidx,1,&colidx,&v,INSERT_VALUES);
 50:     rowidx = 1; colidx = 1; v = 3.0;
 51:     MatSetValues(C,1,&rowidx,1,&colidx,&v,INSERT_VALUES);
 52:   }
 53:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
 54:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

 56:   /* create right hand side and solution */
 57:   VecCreate(PETSC_COMM_WORLD,&u);
 58:   VecSetSizes(u,PETSC_DECIDE,N);
 59:   VecSetFromOptions(u);
 60:   VecDuplicate(u,&b);
 61:   VecDuplicate(u,&r);
 62:   VecSet(u,0.0);
 63:   VecSet(b,1.0);

 65:   /* solve linear system C*u = b */
 66:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 67:   KSPSetOperators(ksp,C,C);
 68:   KSPSetFromOptions(ksp);
 69:   KSPSolve(ksp,b,u);

 71:   /* check residual r = C*u - b */
 72:   MatMult(C,u,r);
 73:   VecAXPY(r,-1.0,b);
 74:   VecNorm(r,NORM_2,&norm);
 75:   PetscPrintf(PETSC_COMM_WORLD,"|| C*u - b|| = %g\n",(double)norm);

 77:   /* solve C^T*u = b twice */
 78:   KSPSolveTranspose(ksp,b,u);
 79:   /* check residual r = C^T*u - b */
 80:   MatMultTranspose(C,u,r);
 81:   VecAXPY(r,-1.0,b);
 82:   VecNorm(r,NORM_2,&norm);
 83:   PetscPrintf(PETSC_COMM_WORLD,"|| C^T*u - b|| =  %g\n",(double)norm);

 85:   KSPSolveTranspose(ksp,b,u);
 86:   MatMultTranspose(C,u,r);
 87:   VecAXPY(r,-1.0,b);
 88:   VecNorm(r,NORM_2,&norm);
 89:   PetscPrintf(PETSC_COMM_WORLD,"|| C^T*u - b|| =  %g\n",(double)norm);

 91:   /* solve C*u = b again */
 92:   KSPSolve(ksp,b,u);
 93:   MatMult(C,u,r);
 94:   VecAXPY(r,-1.0,b);
 95:   VecNorm(r,NORM_2,&norm);
 96:   PetscPrintf(PETSC_COMM_WORLD,"|| C*u - b|| = %g\n",(double)norm);

 98:   KSPDestroy(&ksp);
 99:   VecDestroy(&u);
100:   VecDestroy(&r);
101:   VecDestroy(&b);
102:   MatDestroy(&C);
103:   PetscFinalize();
104:   return ierr;
105: }