2: static char help[] = "Tests MatNorm(), MatLUFactor(), MatSolve() and MatSolveAdd().\n\n";

  4: #include <petscmat.h>

  8: int main(int argc,char **args)
  9: {
 10:   Mat            C;
 11:   PetscInt       i,j,m = 3,n = 3,Ii,J;
 13:   PetscBool      flg;
 14:   PetscScalar    v;
 15:   IS             perm,iperm;
 16:   Vec            x,u,b,y;
 17:   PetscReal      norm,tol=PETSC_SMALL;
 18:   MatFactorInfo  info;
 19:   PetscMPIInt    size;

 21:   PetscInitialize(&argc,&args,(char*)0,help);
 22:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 23:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"This is a uniprocessor example only!");
 24:   MatCreate(PETSC_COMM_WORLD,&C);
 25:   MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
 26:   MatSetFromOptions(C);
 27:   MatSetUp(C);
 28:   PetscOptionsHasName(NULL,"-symmetric",&flg);
 29:   if (flg) {  /* Treat matrix as symmetric only if we set this flag */
 30:     MatSetOption(C,MAT_SYMMETRIC,PETSC_TRUE);
 31:     MatSetOption(C,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
 32:   }

 34:   /* Create the matrix for the five point stencil, YET AGAIN */
 35:   for (i=0; i<m; i++) {
 36:     for (j=0; j<n; j++) {
 37:       v = -1.0;  Ii = j + n*i;
 38:       if (i>0)   {J = Ii - n; MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);}
 39:       if (i<m-1) {J = Ii + n; MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);}
 40:       if (j>0)   {J = Ii - 1; MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);}
 41:       if (j<n-1) {J = Ii + 1; MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);}
 42:       v = 4.0; MatSetValues(C,1,&Ii,1,&Ii,&v,INSERT_VALUES);
 43:     }
 44:   }
 45:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
 46:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
 47:   MatGetOrdering(C,MATORDERINGRCM,&perm,&iperm);
 48:   MatView(C,PETSC_VIEWER_STDOUT_WORLD);
 49:   ISView(perm,PETSC_VIEWER_STDOUT_SELF);
 50:   VecCreateSeq(PETSC_COMM_SELF,m*n,&u);
 51:   VecSet(u,1.0);
 52:   VecDuplicate(u,&x);
 53:   VecDuplicate(u,&b);
 54:   VecDuplicate(u,&y);
 55:   MatMult(C,u,b);
 56:   VecCopy(b,y);
 57:   VecScale(y,2.0);

 59:   MatNorm(C,NORM_FROBENIUS,&norm);
 60:   PetscPrintf(PETSC_COMM_SELF,"Frobenius norm of matrix %g\n",(double)norm);
 61:   MatNorm(C,NORM_1,&norm);
 62:   PetscPrintf(PETSC_COMM_SELF,"One  norm of matrix %g\n",(double)norm);
 63:   MatNorm(C,NORM_INFINITY,&norm);
 64:   PetscPrintf(PETSC_COMM_SELF,"Infinity norm of matrix %g\n",(double)norm);

 66:   MatFactorInfoInitialize(&info);
 67:   info.fill          = 2.0;
 68:   info.dtcol         = 0.0;
 69:   info.zeropivot     = 1.e-14;
 70:   info.pivotinblocks = 1.0;

 72:   MatLUFactor(C,perm,iperm,&info);

 74:   /* Test MatSolve */
 75:   MatSolve(C,b,x);
 76:   VecView(b,PETSC_VIEWER_STDOUT_SELF);
 77:   VecView(x,PETSC_VIEWER_STDOUT_SELF);
 78:   VecAXPY(x,-1.0,u);
 79:   VecNorm(x,NORM_2,&norm);
 80:   if (norm > tol) {
 81:     PetscPrintf(PETSC_COMM_SELF,"MatSolve: Norm of error %g\n",(double)norm);
 82:   }

 84:   /* Test MatSolveAdd */
 85:   MatSolveAdd(C,b,y,x);
 86:   VecAXPY(x,-1.0,y);
 87:   VecAXPY(x,-1.0,u);
 88:   VecNorm(x,NORM_2,&norm);
 89:   if (norm > tol) {
 90:     PetscPrintf(PETSC_COMM_SELF,"MatSolveAdd(): Norm of error %g\n",(double)norm);
 91:   }

 93:   ISDestroy(&perm);
 94:   ISDestroy(&iperm);
 95:   VecDestroy(&u);
 96:   VecDestroy(&y);
 97:   VecDestroy(&b);
 98:   VecDestroy(&x);
 99:   MatDestroy(&C);
100:   PetscFinalize();
101:   return 0;
102: }