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>

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

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

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

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

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

 54:     i    = 0; col[0] = n-1; value[0] = 0.5; /* make A non-symmetric */
 55:     MatSetValues(A,1,&i,1,col,value,INSERT_VALUES);
 56:   }
 57:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 58:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 60:   /* Set exact solution */
 61:   VecSet(u,one);

 63:   /* Create linear solver context */
 64:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 65:   KSPSetOperators(ksp,A,A);
 66:   KSPGetPC(ksp,&pc);
 67:   PCSetType(pc,PCLU);
 68: #if defined(PETSC_HAVE_MUMPS)
 69:   if (size > 1) {
 70:     PCFactorSetMatSolverPackage(pc,MATSOLVERMUMPS);
 71:   }
 72: #endif
 73:   KSPSetFromOptions(ksp);

 75:   /* 1. Solve linear system A x = b */
 76:   MatMult(A,u,b);
 77:   KSPSolve(ksp,b,x);

 79:   /* Check the error */
 80:   VecAXPY(x,neg_one,u);
 81:   VecNorm(x,NORM_2,&norm);
 82:   KSPGetIterationNumber(ksp,&its);
 83:   if (norm > tol) {
 84:     PetscPrintf(PETSC_COMM_WORLD,"1. Norm of error for Ax=b: %g, Iterations %D\n",(double)norm,its);
 85:   }

 87:   /* 2. Solve linear system A^T x = b*/
 88:   MatMultTranspose(A,u,b);
 89:   KSPSolveTranspose(ksp,b,x2);

 91:   /* Check the error */
 92:   VecAXPY(x2,neg_one,u);
 93:   VecNorm(x2,NORM_2,&norm);
 94:   KSPGetIterationNumber(ksp,&its);
 95:   if (norm > tol) {
 96:     PetscPrintf(PETSC_COMM_WORLD,"2. Norm of error for A^T x=b: %g, Iterations %D\n",(double)norm,its);
 97:   }

 99:   /* 3. Change A and solve A x = b with an iterative solver using A=LU as a preconditioner*/
100:   if (!rank) {
101:     i    = 0; col[0] = n-1; value[0] = 1.e-2;
102:     MatSetValues(A,1,&i,1,col,value,ADD_VALUES);
103:   }
104:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
105:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

107:   MatMult(A,u,b);
108:   KSPSolve(ksp,b,x);

110:   /* Check the error */
111:   VecAXPY(x,neg_one,u);
112:   VecNorm(x,NORM_2,&norm);
113:   KSPGetIterationNumber(ksp,&its);
114:   if (norm > tol) {
115:     PetscPrintf(PETSC_COMM_WORLD,"3. Norm of error for (A+Delta) x=b: %g, Iterations %D\n",(double)norm,its);
116:   }

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

126:   PetscFinalize();
127:   return 0;
128: }