2: static char help[] = "Tests reusing MPI parallel matrices and MatGetValues().\n\
  3: To test the parallel matrix assembly, this example intentionally lays out\n\
  4: the matrix across processors differently from the way it is assembled.\n\
  5: This example uses bilinear elements on the unit square.  Input arguments are:\n\
  6:   -m <size> : problem size\n\n";

  8: #include <petscmat.h>

 12: int FormElementStiffness(PetscReal H,PetscScalar *Ke)
 13: {
 15:   Ke[0]  = H/6.0;    Ke[1]  = -.125*H; Ke[2]  = H/12.0;   Ke[3]  = -.125*H;
 16:   Ke[4]  = -.125*H;  Ke[5]  = H/6.0;   Ke[6]  = -.125*H;  Ke[7]  = H/12.0;
 17:   Ke[8]  = H/12.0;   Ke[9]  = -.125*H; Ke[10] = H/6.0;    Ke[11] = -.125*H;
 18:   Ke[12] = -.125*H;  Ke[13] = H/12.0;  Ke[14] = -.125*H;  Ke[15] = H/6.0;
 19:   return(0);
 20: }

 24: int main(int argc,char **args)
 25: {
 26:   Mat            C;
 27:   Vec            u,b;
 29:   PetscMPIInt    size,rank;
 30:   PetscInt       i,m = 5,N,start,end,M,idx[4];
 31:   PetscInt       j,nrsub,ncsub,*rsub,*csub,mystart,myend;
 32:   PetscBool      flg;
 33:   PetscScalar    one = 1.0,Ke[16],*vals;
 34:   PetscReal      h,norm;

 36:   PetscInitialize(&argc,&args,(char*)0,help);
 37:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);

 39:   N    = (m+1)*(m+1); /* dimension of matrix */
 40:   M    = m*m;      /* number of elements */
 41:   h    = 1.0/m;    /* mesh width */
 42:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 43:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

 45:   /* Create stiffness matrix */
 46:   MatCreate(PETSC_COMM_WORLD,&C);
 47:   MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);
 48:   MatSetFromOptions(C);
 49:   MatSetUp(C);

 51:   start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
 52:   end   = start + M/size + ((M%size) > rank);

 54:   /* Form the element stiffness for the Laplacian */
 55:   FormElementStiffness(h*h,Ke);
 56:   for (i=start; i<end; i++) {
 57:     /* location of lower left corner of element */
 58:     /* node numbers for the four corners of element */
 59:     idx[0] = (m+1)*(i/m) + (i % m);
 60:     idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
 61:     MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);
 62:   }
 63:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
 64:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

 66:   /* Assemble the matrix again */
 67:   MatZeroEntries(C);

 69:   for (i=start; i<end; i++) {
 70:     /* location of lower left corner of element */
 71:     /* node numbers for the four corners of element */
 72:     idx[0] = (m+1)*(i/m) + (i % m);
 73:     idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
 74:     MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);
 75:   }
 76:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
 77:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

 79:   /* Create test vectors */
 80:   VecCreate(PETSC_COMM_WORLD,&u);
 81:   VecSetSizes(u,PETSC_DECIDE,N);
 82:   VecSetFromOptions(u);
 83:   VecDuplicate(u,&b);
 84:   VecSet(u,one);

 86:   /* Check error */
 87:   MatMult(C,u,b);
 88:   VecNorm(b,NORM_2,&norm);
 89:   if (norm > PETSC_SQRT_MACHINE_EPSILON) {
 90:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error b %g should be near 0\n",(double)norm);
 91:   }

 93:   /* Now test MatGetValues() */
 94:   PetscOptionsHasName(NULL,NULL,"-get_values",&flg);
 95:   if (flg) {
 96:     MatGetOwnershipRange(C,&mystart,&myend);
 97:     nrsub = myend - mystart; ncsub = 4;
 98:     PetscMalloc1(nrsub*ncsub,&vals);
 99:     PetscMalloc1(nrsub,&rsub);
100:     PetscMalloc1(ncsub,&csub);
101:     for (i=myend-1; i>=mystart; i--) rsub[myend-i-1] = i;
102:     for (i=0; i<ncsub; i++) csub[i] = 2*(ncsub-i) + mystart;
103:     MatGetValues(C,nrsub,rsub,ncsub,csub,vals);
104:     MatView(C,PETSC_VIEWER_STDOUT_WORLD);
105:     PetscSynchronizedPrintf(PETSC_COMM_WORLD,"processor number %d: start=%D, end=%D, mystart=%D, myend=%D\n",rank,start,end,mystart,myend);
106:     for (i=0; i<nrsub; i++) {
107:       for (j=0; j<ncsub; j++) {
108:         if (PetscImaginaryPart(vals[i*ncsub+j]) != 0.0) {
109:           PetscSynchronizedPrintf(PETSC_COMM_WORLD,"  C[%D, %D] = %g + %g i\n",rsub[i],csub[j],(double)PetscRealPart(vals[i*ncsub+j]),(double)PetscImaginaryPart(vals[i*ncsub+j]));
110:         } else {
111:           PetscSynchronizedPrintf(PETSC_COMM_WORLD,"  C[%D, %D] = %g\n",rsub[i],csub[j],(double)PetscRealPart(vals[i*ncsub+j]));
112:         }
113:       }
114:     }
115:     PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
116:     PetscFree(rsub);
117:     PetscFree(csub);
118:     PetscFree(vals);
119:   }

121:   /* Free data structures */
122:   VecDestroy(&u);
123:   VecDestroy(&b);
124:   MatDestroy(&C);
125:   PetscFinalize();
126:   return 0;
127: }