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

  4:  #include <petscmat.h>

  6: int main(int argc,char **args)
  7: {
  8:   Mat            C;
  9:   PetscInt       i,j,m = 3,n = 3,Ii,J;
 11:   PetscBool      flg;
 12:   PetscScalar    v;
 13:   IS             perm,iperm;
 14:   Vec            x,u,b,y;
 15:   PetscReal      norm,tol=PETSC_SMALL;
 16:   MatFactorInfo  info;
 17:   PetscMPIInt    size;

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

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

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

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

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

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

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

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