2: static char help[] = "Solves a tridiagonal linear system with KSP. \n\
  3:                       Modified from ex1.c to illustrate reuse of preconditioner \n\
  4:                       Written as requested by [petsc-maint #63875] \n\n";

  6: #include <petscksp.h>

  8: int main(int argc,char **args)
  9: {
 10:   Vec            x,x2,b,u;     /* approx solution, RHS, exact solution */
 11:   Mat            A;            /* linear system matrix */
 12:   KSP            ksp;          /* linear solver context */
 13:   PC             pc;           /* preconditioner context */
 14:   PetscReal      norm,tol=100.*PETSC_MACHINE_EPSILON; /* norm of solution error */
 15:   PetscInt       i,n = 10,col[3],its;
 16:   PetscMPIInt    rank,size;
 17:   PetscScalar    one = 1.0,value[3];

 19:   PetscInitialize(&argc,&args,(char*)0,help);
 20:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 21:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 22:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);

 24:   /* Create vectors.*/
 25:   VecCreate(PETSC_COMM_WORLD,&x);
 26:   PetscObjectSetName((PetscObject) x, "Solution");
 27:   VecSetSizes(x,PETSC_DECIDE,n);
 28:   VecSetFromOptions(x);
 29:   VecDuplicate(x,&b);
 30:   VecDuplicate(x,&u);
 31:   VecDuplicate(x,&x2);

 33:   /* Create matrix. Only proc[0] sets values - not efficient for parallel processing!
 34:      See ex23.c for efficient parallel assembly matrix */
 35:   MatCreate(PETSC_COMM_WORLD,&A);
 36:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
 37:   MatSetFromOptions(A);
 38:   MatSetUp(A);

 40:   if (rank == 0) {
 41:     value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
 42:     for (i=1; i<n-1; i++) {
 43:       col[0] = i-1; col[1] = i; col[2] = i+1;
 44:       MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
 45:     }
 46:     i    = n - 1; col[0] = n - 2; col[1] = n - 1;
 47:     MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
 48:     i    = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
 49:     MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);

 51:     i    = 0; col[0] = n-1; value[0] = 0.5; /* make A non-symmetric */
 52:     MatSetValues(A,1,&i,1,col,value,INSERT_VALUES);
 53:   }
 54:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 55:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 57:   /* Set exact solution */
 58:   VecSet(u,one);

 60:   /* Create linear solver context */
 61:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 62:   KSPSetOperators(ksp,A,A);
 63:   KSPGetPC(ksp,&pc);
 64:   PCSetType(pc,PCLU);
 65: #if defined(PETSC_HAVE_MUMPS)
 66:   if (size > 1) {
 67:     PCFactorSetMatSolverType(pc,MATSOLVERMUMPS);
 68:   }
 69: #endif
 70:   KSPSetFromOptions(ksp);

 72:   /* 1. Solve linear system A x = b */
 73:   MatMult(A,u,b);
 74:   KSPSolve(ksp,b,x);

 76:   /* Check the error */
 77:   VecAXPY(x,-1.0,u);
 78:   VecNorm(x,NORM_2,&norm);
 79:   KSPGetIterationNumber(ksp,&its);
 80:   if (norm > tol) {
 81:     PetscPrintf(PETSC_COMM_WORLD,"1. Norm of error for Ax=b: %g, Iterations %D\n",(double)norm,its);
 82:   }

 84:   /* 2. Solve linear system A^T x = b*/
 85:   MatMultTranspose(A,u,b);
 86:   KSPSolveTranspose(ksp,b,x2);

 88:   /* Check the error */
 89:   VecAXPY(x2,-1.0,u);
 90:   VecNorm(x2,NORM_2,&norm);
 91:   KSPGetIterationNumber(ksp,&its);
 92:   if (norm > tol) {
 93:     PetscPrintf(PETSC_COMM_WORLD,"2. Norm of error for A^T x=b: %g, Iterations %D\n",(double)norm,its);
 94:   }

 96:   /* 3. Change A and solve A x = b with an iterative solver using A=LU as a preconditioner*/
 97:   if (rank == 0) {
 98:     i    = 0; col[0] = n-1; value[0] = 1.e-2;
 99:     MatSetValues(A,1,&i,1,col,value,ADD_VALUES);
100:   }
101:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
102:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

104:   MatMult(A,u,b);
105:   KSPSolve(ksp,b,x);

107:   /* Check the error */
108:   VecAXPY(x,-1.0,u);
109:   VecNorm(x,NORM_2,&norm);
110:   KSPGetIterationNumber(ksp,&its);
111:   if (norm > tol) {
112:     PetscPrintf(PETSC_COMM_WORLD,"3. Norm of error for (A+Delta) x=b: %g, Iterations %D\n",(double)norm,its);
113:   }

115:   /* Free work space. */
116:   VecDestroy(&x);
117:   VecDestroy(&u);
118:   VecDestroy(&x2);
119:   VecDestroy(&b);
120:   MatDestroy(&A);
121:   KSPDestroy(&ksp);

123:   PetscFinalize();
124:   return 0;
125: }

127: /*TEST

129:    test:
130:       requires: mumps

132:    test:
133:       suffix: 2
134:       nsize: 2
135:       requires: mumps
136:       output_file: output/ex53.out

138: TEST*/