2: static char help[] = "Solves a tridiagonal linear system with KSP. \n\
  3: It illustrates how to do one symbolic factorization and multiple numeric factorizations using same matrix structure. \n\n";

  5:  #include <petscksp.h>
  6: int main(int argc,char **args)
  7: {
  8:   Vec            x, b, u;      /* approx solution, RHS, exact solution */
  9:   Mat            A;            /* linear system matrix */
 10:   KSP            ksp;          /* linear solver context */
 11:   PC             pc;           /* preconditioner context */
 12:   PetscReal      norm;         /* norm of solution error */
 14:   PetscInt       i,col[3],its,rstart,rend,N=10,num_numfac;
 15:   PetscScalar    value[3];

 17:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
 18:   PetscOptionsGetInt(NULL,NULL,"-N",&N,NULL);

 20:   /* Create and assemble matrix. */
 21:   MatCreate(PETSC_COMM_WORLD,&A);
 22:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
 23:   MatSetFromOptions(A);
 24:   MatSetUp(A);
 25:   MatGetOwnershipRange(A,&rstart,&rend);

 27:   value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
 28:   for (i=rstart; i<rend; i++) {
 29:     col[0] = i-1; col[1] = i; col[2] = i+1;
 30:     if (i == 0) {
 31:       MatSetValues(A,1,&i,2,col+1,value+1,INSERT_VALUES);
 32:     } else if (i == N-1) {
 33:       MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
 34:     } else {
 35:       MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
 36:     }
 37:   }
 38:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 39:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 40:   MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

 42:   /* Create vectors */
 43:   MatCreateVecs(A,&x,&b);
 44:   VecDuplicate(x,&u);

 46:   /* Set exact solution; then compute right-hand-side vector. */
 47:   VecSet(u,1.0);
 48:   MatMult(A,u,b);

 50:   /* Create the linear solver and set various options. */
 51:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 52:   KSPGetPC(ksp,&pc);
 53:   PCSetType(pc,PCJACOBI);
 54:   KSPSetTolerances(ksp,1.e-5,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
 55:   KSPSetOperators(ksp,A,A);
 56:   KSPSetFromOptions(ksp);

 58:   num_numfac = 1;
 59:   PetscOptionsGetInt(NULL,NULL,"-num_numfac",&num_numfac,NULL);
 60:   while (num_numfac--) {
 61:     /* An example on how to update matrix A for repeated numerical factorization and solve. */
 62:     PetscScalar one=1.0;
 63:     PetscInt    i = 0;
 64:     MatSetValues(A,1,&i,1,&i,&one,ADD_VALUES);
 65:     MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 66:     MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 67:     /* Update b */
 68:     MatMult(A,u,b);

 70:     /* Solve the linear system */
 71:     KSPSolve(ksp,b,x);

 73:     /* Check the solution and clean up */
 74:     VecAXPY(x,-1.0,u);
 75:     VecNorm(x,NORM_2,&norm);
 76:     KSPGetIterationNumber(ksp,&its);
 77:     if (norm > 100*PETSC_MACHINE_EPSILON) {
 78:       PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);
 79:     }
 80:   }

 82:   /* Free work space. */
 83:   VecDestroy(&x); VecDestroy(&u);
 84:   VecDestroy(&b); MatDestroy(&A);
 85:   KSPDestroy(&ksp);

 87:   PetscFinalize();
 88:   return ierr;
 89: }

 91: /*TEST

 93:     test:
 94:       args: -num_numfac 2 -pc_type lu

 96:     test:
 97:       suffix: 2
 98:       args: -num_numfac 2 -pc_type lu -pc_factor_mat_solver_type mumps
 99:       requires: mumps

101:     test:
102:       suffix: 3
103:       nsize: 3
104:       args: -num_numfac 2 -pc_type lu -pc_factor_mat_solver_type mumps
105:       requires: mumps

107: TEST*/