2: static char help[] = "Tests ILU and ICC factorization with and without matrix ordering on seqsbaij format. Modified from ex30.c\n\
  3:   Input parameters are:\n\
  4:   -lf <level> : level of fill for ILU (default is 0)\n\
  5:   -lu : use full LU or Cholesky factorization\n\
  6:   -m <value>,-n <value> : grid dimensions\n\
  7: Note that most users should employ the KSP interface to the\n\
  8: linear solvers instead of using the factorization routines\n\
  9: directly.\n\n";

 11:  #include <petscmat.h>

 13: int main(int argc,char **args)
 14: {
 15:   Mat            C,sC,sA;
 16:   PetscInt       i,j,m = 5,n = 5,Ii,J,lf = 0;
 18:   PetscBool      CHOLESKY=PETSC_FALSE,TRIANGULAR=PETSC_FALSE,flg;
 19:   PetscScalar    v;
 20:   IS             row,col;
 21:   MatFactorInfo  info;
 22:   Vec            x,y,b,ytmp;
 23:   PetscReal      norm2,tol = 100*PETSC_MACHINE_EPSILON;
 24:   PetscRandom    rdm;
 25:   PetscMPIInt    size;

 27:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
 28:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 29:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!");
 30:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 31:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 32:   PetscOptionsGetInt(NULL,NULL,"-lf",&lf,NULL);

 34:   MatCreate(PETSC_COMM_SELF,&C);
 35:   MatSetSizes(C,m*n,m*n,m*n,m*n);
 36:   MatSetFromOptions(C);
 37:   MatSetUp(C);

 39:   /* Create matrix C in seqaij format and sC in seqsbaij. (This is five-point stencil with some extra elements) */
 40:   for (i=0; i<m; i++) {
 41:     for (j=0; j<n; j++) {
 42:       v = -1.0;  Ii = j + n*i;
 43:       J = Ii - n; if (J>=0)  {MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);}
 44:       J = Ii + n; if (J<m*n) {MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);}
 45:       J = Ii - 1; if (J>=0)  {MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);}
 46:       J = Ii + 1; if (J<m*n) {MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);}
 47:       v = 4.0; MatSetValues(C,1,&Ii,1,&Ii,&v,INSERT_VALUES);
 48:     }
 49:   }
 50:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
 51:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

 53:   MatIsSymmetric(C,0.0,&flg);
 54:   if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"C is non-symmetric");
 55:   MatConvert(C,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&sC);

 57:   /* Create vectors for error checking */
 58:   MatCreateVecs(C,&x,&b);
 59:   VecDuplicate(x,&y);
 60:   VecDuplicate(x,&ytmp);
 61:   PetscRandomCreate(PETSC_COMM_SELF,&rdm);
 62:   PetscRandomSetFromOptions(rdm);
 63:   VecSetRandom(x,rdm);
 64:   MatMult(C,x,b);

 66:   MatGetOrdering(C,MATORDERINGNATURAL,&row,&col);

 68:   /* Compute CHOLESKY or ICC factor sA */
 69:   MatFactorInfoInitialize(&info);

 71:   info.fill          = 1.0;
 72:   info.diagonal_fill = 0;
 73:   info.zeropivot     = 0.0;

 75:   PetscOptionsHasName(NULL,NULL,"-cholesky",&CHOLESKY);
 76:   if (CHOLESKY) {
 77:     PetscPrintf(PETSC_COMM_SELF,"Test CHOLESKY...\n");
 78:     MatGetFactor(sC,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&sA);
 79:     MatCholeskyFactorSymbolic(sA,sC,row,&info);
 80:   } else {
 81:     PetscPrintf(PETSC_COMM_SELF,"Test ICC...\n");
 82:     info.levels = lf;

 84:     MatGetFactor(sC,MATSOLVERPETSC,MAT_FACTOR_ICC,&sA);
 85:     MatICCFactorSymbolic(sA,sC,row,&info);
 86:   }
 87:   MatCholeskyFactorNumeric(sA,sC,&info);

 89:   /* test MatForwardSolve() and MatBackwardSolve() with matrix reordering on aij matrix C */
 90:   if (CHOLESKY) {
 91:     PetscOptionsHasName(NULL,NULL,"-triangular_solve",&TRIANGULAR);
 92:     if (TRIANGULAR) {
 93:       PetscPrintf(PETSC_COMM_SELF,"Test MatForwardSolve...\n");
 94:       MatForwardSolve(sA,b,ytmp);
 95:       PetscPrintf(PETSC_COMM_SELF,"Test MatBackwardSolve...\n");
 96:       MatBackwardSolve(sA,ytmp,y);
 97:       VecAXPY(y,-1.0,x);
 98:       VecNorm(y,NORM_2,&norm2);
 99:       if (norm2 > tol) {
100:         PetscPrintf(PETSC_COMM_SELF,"MatForwardSolve and BackwardSolve: Norm of error=%g\n",(double)norm2);
101:       }
102:     }
103:   }

105:   MatSolve(sA,b,y);
106:   MatDestroy(&sC);
107:   MatDestroy(&sA);
108:   VecAXPY(y,-1.0,x);
109:   VecNorm(y,NORM_2,&norm2);
110:   if (lf == -1 && norm2 > tol) {
111:     PetscPrintf(PETSC_COMM_SELF, " reordered SEQAIJ:   Cholesky/ICC levels %D, residual %g\n",lf,(double)norm2);
112:   }

114:   /* Free data structures */
115:   MatDestroy(&C);
116:   ISDestroy(&row);
117:   ISDestroy(&col);
118:   PetscRandomDestroy(&rdm);
119:   VecDestroy(&x);
120:   VecDestroy(&y);
121:   VecDestroy(&ytmp);
122:   VecDestroy(&b);
123:   PetscFinalize();
124:   return ierr;
125: }


128: /*TEST

130:    test:
131:       output_file: output/ex128.out

133:    test:
134:       suffix: 2
135:       args: -cholesky -triangular_solve

137: TEST*/