/*
  Assume that we are given a fine and coarse topology and the
  coarse degrees of freedom (DOFs) have been chosen. Assume also,
  that the global interpolation matrix dof_DOF has a prescribed
  nonzero pattern. Then, the fine degrees of freedom can be split
  into 4 groups (here "i" stands for "interior"):

  NODEidof - dofs which are interpolated only from the DOF
             in one coarse vertex
  EDGEidof - dofs which are interpolated only from the DOFs
             in one coarse edge
  FACEidof - dofs which are interpolated only from the DOFs
             in one coarse face
  ELEMidof - dofs which are interpolated only from the DOFs
             in one coarse element

  The interpolation operator dof_DOF can be build in 4 steps, by
  consequently filling-in the rows corresponding to the above groups.
  The code below uses harmonic extension to extend the interpolation
  from one group to the next.
*/
HYPRE_Int hypre_ND1AMGeInterpolation (hypre_ParCSRMatrix       * Aee,
                                hypre_ParCSRMatrix       * ELEM_idof,
                                hypre_ParCSRMatrix       * FACE_idof,
                                hypre_ParCSRMatrix       * EDGE_idof,
                                hypre_ParCSRMatrix       * ELEM_FACE,
                                hypre_ParCSRMatrix       * ELEM_EDGE,
                                HYPRE_Int                  num_OffProcRows,
                                hypre_MaxwellOffProcRow ** OffProcRows,
                                hypre_IJMatrix           * IJ_dof_DOF)
{
   HYPRE_Int ierr = 0;

   HYPRE_Int  i, j, k;
   HYPRE_Int *offproc_rnums, *swap;

   hypre_ParCSRMatrix * dof_DOF = hypre_IJMatrixObject(IJ_dof_DOF);
   hypre_ParCSRMatrix * ELEM_DOF = ELEM_EDGE;
   hypre_ParCSRMatrix * ELEM_FACEidof;
   hypre_ParCSRMatrix * ELEM_EDGEidof;
   hypre_CSRMatrix *A, *P;
   HYPRE_Int numELEM = hypre_CSRMatrixNumRows(hypre_ParCSRMatrixDiag(ELEM_EDGE));

   HYPRE_Int getrow_ierr;
   HYPRE_Int three_dimensional_problem;

   MPI_Comm comm= hypre_ParCSRMatrixComm(Aee);
   HYPRE_Int      myproc;

   hypre_MPI_Comm_rank(comm, &myproc);

#if 0
   hypre_IJMatrix * ij_dof_DOF = hypre_CTAlloc(hypre_IJMatrix, 1);
   /* Convert dof_DOF to IJ matrix, so we can use AddToValues */
   hypre_IJMatrixComm(ij_dof_DOF) = hypre_ParCSRMatrixComm(dof_DOF);
   hypre_IJMatrixRowPartitioning(ij_dof_DOF) =
      hypre_ParCSRMatrixRowStarts(dof_DOF);
   hypre_IJMatrixColPartitioning(ij_dof_DOF) =
      hypre_ParCSRMatrixColStarts(dof_DOF);
   hypre_IJMatrixObject(ij_dof_DOF) = dof_DOF;
   hypre_IJMatrixAssembleFlag(ij_dof_DOF) = 1;
#endif

  /* sort the offproc rows to get quicker comparison for later */
   if (num_OffProcRows)
   {
      offproc_rnums= hypre_TAlloc(HYPRE_Int, num_OffProcRows);
      swap         = hypre_TAlloc(HYPRE_Int, num_OffProcRows);
      for (i= 0; i< num_OffProcRows; i++)
      {
         offproc_rnums[i]=(OffProcRows[i] -> row);
         swap[i]         = i;
      }
   }

   if (num_OffProcRows > 1)
   {
      hypre_qsort2i(offproc_rnums, swap, 0, num_OffProcRows-1);
   }

   if (FACE_idof == EDGE_idof)
      three_dimensional_problem = 0;
   else
      three_dimensional_problem = 1;

   /* ELEM_FACEidof = ELEM_FACE x FACE_idof */
   if (three_dimensional_problem)
      ELEM_FACEidof = hypre_ParMatmul(ELEM_FACE, FACE_idof);

   /* ELEM_EDGEidof = ELEM_EDGE x EDGE_idof */
   ELEM_EDGEidof = hypre_ParMatmul(ELEM_EDGE, EDGE_idof);

   /* Loop over local coarse elements */
   k = hypre_ParCSRMatrixFirstRowIndex(ELEM_EDGE);
   for (i = 0; i < numELEM; i++, k++)
   {
      HYPRE_Int size1, size2;
      HYPRE_Int *col_ind0, *col_ind1, *col_ind2;

      HYPRE_Int num_DOF, *DOF0, *DOF;
      HYPRE_Int num_idof, *idof0, *idof;
      HYPRE_Int num_bdof, *bdof;

      double *boolean_data;

      /* Determine the coarse DOFs */
      hypre_ParCSRMatrixGetRow (ELEM_DOF, k, &num_DOF, &DOF0, &boolean_data);
      DOF= hypre_TAlloc(HYPRE_Int, num_DOF);
      for (j= 0; j< num_DOF; j++)
      {
         DOF[j]= DOF0[j];
      }
      hypre_ParCSRMatrixRestoreRow (ELEM_DOF, k, &num_DOF, &DOF0, &boolean_data);

      qsort0(DOF,0,num_DOF-1);

      /* Find the fine dofs interior for the current coarse element */
      hypre_ParCSRMatrixGetRow (ELEM_idof, k, &num_idof, &idof0, &boolean_data);
      idof= hypre_TAlloc(HYPRE_Int, num_idof);
      for (j= 0; j< num_idof; j++)
      {
         idof[j]= idof0[j];
      }
      hypre_ParCSRMatrixRestoreRow (ELEM_idof, k, &num_idof, &idof0, &boolean_data);

      /* Sort the interior dofs according to their global number */
      qsort0(idof,0,num_idof-1);

      /* Find the fine dofs on the boundary of the current coarse element */
      if (three_dimensional_problem)
      {
         hypre_ParCSRMatrixGetRow (ELEM_FACEidof, k, &size1, &col_ind0, &boolean_data);
         col_ind1= hypre_TAlloc(HYPRE_Int, size1);
         for (j= 0; j< size1; j++)
         {
            col_ind1[j]= col_ind0[j];
         }
         hypre_ParCSRMatrixRestoreRow (ELEM_FACEidof, k, &size1, &col_ind0, &boolean_data);
      }
      else
         size1 = 0;

      hypre_ParCSRMatrixGetRow (ELEM_EDGEidof, k, &size2, &col_ind0, &boolean_data);
      col_ind2= hypre_TAlloc(HYPRE_Int, size2);
      for (j= 0; j< size2; j++)
      {
         col_ind2[j]= col_ind0[j];
      }
      hypre_ParCSRMatrixRestoreRow (ELEM_EDGEidof, k, &size2, &col_ind0, &boolean_data);

      /* Merge and sort the boundary dofs according to their global number */
      num_bdof = size1 + size2;
      bdof = hypre_CTAlloc(HYPRE_Int, num_bdof);
      if (three_dimensional_problem)
         memcpy(bdof, col_ind1, size1*sizeof(HYPRE_Int));
      memcpy(bdof+size1, col_ind2, size2*sizeof(HYPRE_Int));

      qsort0(bdof,0,num_bdof-1);

      /* A = extract_rows(Aee, idof) */
      A = hypre_CSRMatrixCreate (num_idof, num_idof + num_bdof,
                                 num_idof * (num_idof + num_bdof));
      hypre_CSRMatrixInitialize(A);
      {
         HYPRE_Int *I = hypre_CSRMatrixI(A);
         HYPRE_Int *J = hypre_CSRMatrixJ(A);
         double *data = hypre_CSRMatrixData(A);

         HYPRE_Int *tmp_J;
         double *tmp_data;

         I[0] = 0;
         for (j = 0; j < num_idof; j++)
         {
            getrow_ierr= hypre_ParCSRMatrixGetRow (Aee, idof[j], &I[j+1], &tmp_J, &tmp_data);
            if (getrow_ierr <0)
               hypre_printf("getrow Aee off proc[%d] = \n",myproc);
            memcpy(J, tmp_J, I[j+1]*sizeof(HYPRE_Int));
            memcpy(data, tmp_data, I[j+1]*sizeof(double));
            J+= I[j+1];
            data+= I[j+1];
            hypre_ParCSRMatrixRestoreRow (Aee, idof[j], &I[j+1], &tmp_J, &tmp_data);
            I[j+1] += I[j];
         }
      }

      /* P = extract_rows(dof_DOF, idof+bdof) */
      P = hypre_CSRMatrixCreate (num_idof + num_bdof, num_DOF,
                                 (num_idof + num_bdof) * num_DOF);
      hypre_CSRMatrixInitialize(P);
      {
         HYPRE_Int *I = hypre_CSRMatrixI(P);
         HYPRE_Int *J = hypre_CSRMatrixJ(P);
         double *data = hypre_CSRMatrixData(P);
         HYPRE_Int     m;

         HYPRE_Int *tmp_J;
         double *tmp_data;
     
         I[0] = 0;
         for (j = 0; j < num_idof; j++)
         {
            getrow_ierr= hypre_ParCSRMatrixGetRow (dof_DOF, idof[j], &I[j+1], &tmp_J, &tmp_data);
            if (getrow_ierr >= 0)
            {
               memcpy(J, tmp_J, I[j+1]*sizeof(HYPRE_Int));
               memcpy(data, tmp_data, I[j+1]*sizeof(double));
               J+= I[j+1];
               data+= I[j+1];
               hypre_ParCSRMatrixRestoreRow (dof_DOF, idof[j], &I[j+1], &tmp_J, &tmp_data);
               I[j+1] += I[j];
            }
            else    /* row offproc */
            {
               hypre_ParCSRMatrixRestoreRow (dof_DOF, idof[j], &I[j+1], &tmp_J, &tmp_data);
              /* search for OffProcRows */
               m= 0;
               while (m < num_OffProcRows)
               {
                  if (offproc_rnums[m] == idof[j])
                  { 
                     break;
                  }
                  else
                  {
                     m++;
                  }
               }
               I[j+1]= (OffProcRows[swap[m]] -> ncols);
               tmp_J = (OffProcRows[swap[m]] -> cols);
               tmp_data= (OffProcRows[swap[m]] -> data);
               memcpy(J, tmp_J, I[j+1]*sizeof(HYPRE_Int));
               memcpy(data, tmp_data, I[j+1]*sizeof(double));
               J+= I[j+1];
               data+= I[j+1];
               I[j+1] += I[j];
            }

         }
         for ( ; j < num_idof + num_bdof; j++)
         {
            getrow_ierr= hypre_ParCSRMatrixGetRow (dof_DOF, bdof[j-num_idof], &I[j+1], &tmp_J, &tmp_data);
            if (getrow_ierr >= 0)
            {
               memcpy(J, tmp_J, I[j+1]*sizeof(HYPRE_Int));
               memcpy(data, tmp_data, I[j+1]*sizeof(double));
               J+= I[j+1];
               data+= I[j+1];
               hypre_ParCSRMatrixRestoreRow (dof_DOF, bdof[j-num_idof], &I[j+1], &tmp_J, &tmp_data);
               I[j+1] += I[j];
            }
            else    /* row offproc */
            {
               hypre_ParCSRMatrixRestoreRow (dof_DOF, bdof[j-num_idof], &I[j+1], &tmp_J, &tmp_data);
              /* search for OffProcRows */
               m= 0;
               while (m < num_OffProcRows)
               {
                  if (offproc_rnums[m] == bdof[j-num_idof])
                  {
                     break;
                  }
                  else
                  {
                     m++;
                  }
               }
               if (m>= num_OffProcRows)hypre_printf("here the mistake\n");
               I[j+1]= (OffProcRows[swap[m]] -> ncols);
               tmp_J = (OffProcRows[swap[m]] -> cols);
               tmp_data= (OffProcRows[swap[m]] -> data);
               memcpy(J, tmp_J, I[j+1]*sizeof(HYPRE_Int));
               memcpy(data, tmp_data, I[j+1]*sizeof(double));
               J+= I[j+1];
               data+= I[j+1];
               I[j+1] += I[j];
            }
         }
      }

      /* Pi = Aii^{-1} Aib Pb */
      hypre_HarmonicExtension (A, P, num_DOF, DOF,
                               num_idof, idof, num_bdof, bdof);

      /* Insert Pi in dof_DOF */
      {
         HYPRE_Int * ncols = hypre_CTAlloc(HYPRE_Int, num_idof);

         for (j = 0; j < num_idof; j++)
            ncols[j] = num_DOF;

         hypre_IJMatrixAddToValuesParCSR (IJ_dof_DOF,
                                          num_idof, ncols, idof,
                                          hypre_CSRMatrixJ(P),
                                          hypre_CSRMatrixData(P));

         hypre_TFree(ncols);
      }

      hypre_TFree(DOF);
      hypre_TFree(idof);
      if (three_dimensional_problem)
      {
         hypre_TFree(col_ind1);
      }
      hypre_TFree(col_ind2);
      hypre_TFree(bdof);

      hypre_CSRMatrixDestroy(A);
      hypre_CSRMatrixDestroy(P);
   }

#if 0
   hypre_TFree(ij_dof_DOF);
#endif

   if (three_dimensional_problem)
      hypre_ParCSRMatrixDestroy(ELEM_FACEidof);
   hypre_ParCSRMatrixDestroy(ELEM_EDGEidof);

   if (num_OffProcRows)
   {
      hypre_TFree(offproc_rnums);
      hypre_TFree(swap);
   }

   return ierr;
}
Esempio n. 2
0
int
main(int argc, char *argv[])
{
    GRID *g;
    DOF *u_h;
    MAT *A, *A0, *B;
    MAP *map;
    INT i;
    size_t nnz, mem, mem_peak;
    VEC *x, *y0, *y1, *y2;
    double t0, t1, dnz, dnz1, mflops, mop;
    char *fn = "../test/cube.dat";
    FLOAT mem_max = 300;
    INT refine = 0;

    phgOptionsRegisterFilename("-mesh_file", "Mesh file", (char **)&fn);
    phgOptionsRegisterInt("-loop_count", "Loop count", &loop_count);
    phgOptionsRegisterInt("-refine", "Refinement level", &refine);
    phgOptionsRegisterFloat("-mem_max", "Maximum memory", &mem_max);

    phgInit(&argc, &argv);
    g = phgNewGrid(-1);
    if (!phgImport(g, fn, FALSE))
	phgError(1, "can't read file \"%s\".\n", fn);
    phgRefineAllElements(g, refine);
    u_h = phgDofNew(g, DOF_DEFAULT, 1, "u_h", DofNoAction);

    while (TRUE) {
	phgPrintf("\n");
	if (phgBalanceGrid(g, 1.2, 1, NULL, 0.))
	    phgPrintf("Repartition mesh, %d submeshes, load imbalance: %lg\n",
			g->nprocs, (double)g->lif);
	map = phgMapCreate(u_h, NULL);
	A = phgMapCreateMat(map, map);
	A->handle_bdry_eqns = TRUE;
	build_matrix(A, u_h);
	phgMatAssemble(A);

	/* Note: A is unsymmetric (A' != A) if boundary entries not removed */
	phgMatRemoveBoundaryEntries(A);

#if 0
	/* test block matrix operation */
	A0 = phgMatCreateBlockMatrix(g->comm, 1, 1, &A, NULL);
#else
	A0 = A;
#endif

	phgPrintf("%d DOF, %d elems, %d submeshes, matrix size: %d, LIF: %lg\n",
			DofGetDataCountGlobal(u_h), g->nleaf_global,
			g->nprocs, A->rmap->nglobal, (double)g->lif);

	/* test PHG mat-vec multiply */
	x = phgMapCreateVec(A->cmap, 1);
	y1 = phgMapCreateVec(A->rmap, 1);
	phgVecRandomize(x, 123);
	phgMatVec(MAT_OP_N, 1.0, A0, x, 0.0, &y1);

	phgPerfGetMflops(g, NULL, NULL);	/* reset flops counter */
	t0 = phgGetTime(NULL);
	for (i = 0; i < loop_count; i++) {
	    phgMatVec(MAT_OP_N, 1.0, A0, x, 0.0, &y1);
	}
	t1 = phgGetTime(NULL);
	mflops = phgPerfGetMflops(g, NULL, NULL);
	y0 = phgVecCopy(y1, NULL);
	nnz = A->nnz_d + A->nnz_o;
#if USE_MPI
	dnz1 = nnz;
	MPI_Reduce(&dnz1, &dnz, 1, MPI_DOUBLE, MPI_SUM, 0, g->comm);
#else
	dnz = nnz;
#endif
	mop = loop_count * (dnz + dnz - A->rmap->nlocal) * 1e-6;

	phgPrintf("\n");
	t1 -= t0;
	phgPrintf("   PHG:  time %0.4lf, nnz %0.16lg, %0.2lfMF (%0.2lfMF)\n",
			t1, dnz, mop / (t1 == 0 ? 1. : t1), mflops);

	/* test trans(A)*x */
	phgPerfGetMflops(g, NULL, NULL);	/* reset flops counter */
	t0 = phgGetTime(NULL);
	for (i = 0; i < loop_count; i++) {
	    phgMatVec(MAT_OP_T, 1.0, A0, x, 0.0, &y1);
	}
	t1 = phgGetTime(NULL);
	mflops = phgPerfGetMflops(g, NULL, NULL);
	t1 -= t0;
	phgPrintf("  A'*x:  time %0.4lf, nnz %0.16lg, %0.2lfMF (%0.2lfMF), "
		  "err: %le\n", t1, dnz, mop / (t1 == 0 ? 1. : t1), mflops,
		 (double)phgVecNorm2(phgVecAXPBY(-1.0, y0, 1.0, &y1), 0, NULL));

	/* time A * trans(A) */
	phgPerfGetMflops(g, NULL, NULL);	/* reset flops counter */
	t0 = phgGetTime(NULL);
	B = phgMatMat(MAT_OP_N, MAT_OP_N, 1.0, A, A, 0.0, NULL);
	t1 = phgGetTime(NULL);
	mflops = phgPerfGetMflops(g, NULL, NULL);
	nnz = B->nnz_d + B->nnz_o;
#if USE_MPI
	dnz1 = nnz;
	MPI_Reduce(&dnz1, &dnz, 1, MPI_DOUBLE, MPI_SUM, 0, g->comm);
#else
	dnz = nnz;
#endif
	/* compare B*x <--> A*A*x */
	y2 = phgMatVec(MAT_OP_N, 1.0, B, x, 0.0, NULL);
	phgMatVec(MAT_OP_N, 1.0, A0, y0, 0.0, &y1);
	phgMatDestroy(&B);
	t1 -= t0;
	phgPrintf("   A*A:  time %0.4lf, nnz %0.16lg, %0.2lfMF, err: %le\n",
		  t1, dnz, mflops,
		 (double)phgVecNorm2(phgVecAXPBY(-1.0, y1, 1.0, &y2), 0, NULL));

#if USE_PETSC
	{
	    Mat ma, mb;
	    MatInfo info;
	    Vec va, vb, vc;
	    PetscScalar *vec;

	    ma = phgPetscCreateMatAIJ(A);
	    MatGetVecs(ma, PETSC_NULL, &va);
	    VecDuplicate(va, &vb);
	    VecGetArray(va, &vec);
	    memcpy(vec, x->data, x->map->nlocal * sizeof(*vec));
	    VecRestoreArray(va, &vec);
	    MatMult(ma, va, vb);
	    phgPerfGetMflops(g, NULL, NULL);	/* reset flops counter */
	    t0 = phgGetTime(NULL);
	    for (i = 0; i < loop_count; i++) {
		MatMult(ma, va, vb);
	    }
	    t1 = phgGetTime(NULL);
	    mflops = phgPerfGetMflops(g, NULL, NULL);
	    VecGetArray(vb, &vec);
	    memcpy(y1->data, vec, x->map->nlocal * sizeof(*vec));
	    VecRestoreArray(vb, &vec);

	    MatGetInfo(ma, MAT_GLOBAL_SUM, &info);
	    /*phgPrintf("    --------------------------------------------"
		      "-------------------------\n");*/
	    phgPrintf("\n");
	    t1 -= t0;
	    dnz = info.nz_used;
	    phgPrintf(" PETSc:  time %0.4lf, nnz %0.16lg, %0.2lfMF (%0.2lfMF), "
		      "err: %le\n", t1, dnz, mop / (t1==0 ? 1.:t1), mflops,
		 (double)phgVecNorm2(phgVecAXPBY(-1.0, y0, 1.0, &y1), 0, NULL));

	    phgPerfGetMflops(g, NULL, NULL);	/* reset flops counter */
	    t0 = phgGetTime(NULL);
	    for (i = 0; i < loop_count; i++) {
		MatMultTranspose(ma, va, vb);
	    }
	    t1 = phgGetTime(NULL);
	    mflops = phgPerfGetMflops(g, NULL, NULL);
	    VecGetArray(vb, &vec);
	    memcpy(y1->data, vec, x->map->nlocal * sizeof(*vec));
	    VecRestoreArray(vb, &vec);
	    t1 -= t0;
	    phgPrintf("  A'*x:  time %0.4lf, nnz %0.16lg, %0.2lfMF (%0.2lfMF), "
		      "err: %le\n", t1, dnz, mop / (t1==0 ? 1.:t1), mflops,
		(double)phgVecNorm2(phgVecAXPBY(-1.0, y0, 1.0, &y1), 0, NULL));

	    phgPerfGetMflops(g, NULL, NULL);	/* reset flops counter */
	    t0 = phgGetTime(NULL);
	    MatMatMult(ma, ma, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &mb);
	    t1 = phgGetTime(NULL);
	    mflops = phgPerfGetMflops(g, NULL, NULL);
	    t1 -= t0;
	    MatGetInfo(mb, MAT_GLOBAL_SUM, &info);
	    dnz = info.nz_used;
	    VecDuplicate(va, &vc);
	    /* compare B*x <--> A*A*x */
	    MatMult(ma, vb, vc);
	    MatMult(mb, va, vb);
	    VecGetArray(vb, &vec);
	    memcpy(y1->data, vec, x->map->nlocal * sizeof(*vec));
	    VecRestoreArray(vb, &vec);
	    VecGetArray(vc, &vec);
	    memcpy(y2->data, vec, x->map->nlocal * sizeof(*vec));
	    VecRestoreArray(vc, &vec);
	    phgPrintf("   A*A:  time %0.4lf, nnz %0.16lg, %0.2lfMF, err: %le\n",
		  t1, dnz, mflops,
		 (double)phgVecNorm2(phgVecAXPBY(-1.0, y1, 1.0, &y2), 0, NULL));

	    phgPetscMatDestroy(&mb);
	    phgPetscMatDestroy(&ma);
	    phgPetscVecDestroy(&va);
	    phgPetscVecDestroy(&vb);
	    phgPetscVecDestroy(&vc);
	}
#endif	/* USE_PETSC */

#if USE_HYPRE
	{
	    HYPRE_IJMatrix ma;
	    HYPRE_IJVector va, vb, vc;
	    HYPRE_ParCSRMatrix  par_ma;
	    hypre_ParCSRMatrix  *par_mb;
	    HYPRE_ParVector	par_va, par_vb, par_vc;
	    HYPRE_Int offset, *ni, start, end;
	    assert(sizeof(INT)==sizeof(int) && sizeof(FLOAT)==sizeof(double));
	    setup_hypre_mat(A, &ma);
	    ni = phgAlloc(2 * A->rmap->nlocal * sizeof(*ni));
	    offset = A->cmap->partition[A->cmap->rank];
	    for (i = 0; i < A->rmap->nlocal; i++)
		ni[i] = i + offset;
	    HYPRE_IJVectorCreate(g->comm, offset, offset + A->rmap->nlocal - 1,
				 &va);
	    HYPRE_IJVectorCreate(g->comm, offset, offset + A->rmap->nlocal - 1,
				 &vb);
	    HYPRE_IJVectorCreate(g->comm, offset, offset + A->rmap->nlocal - 1,
				 &vc);
	    HYPRE_IJVectorSetObjectType(va, HYPRE_PARCSR);
	    HYPRE_IJVectorSetObjectType(vb, HYPRE_PARCSR);
	    HYPRE_IJVectorSetObjectType(vc, HYPRE_PARCSR);
	    HYPRE_IJVectorSetMaxOffProcElmts(va, 0);
	    HYPRE_IJVectorSetMaxOffProcElmts(vb, 0);
	    HYPRE_IJVectorSetMaxOffProcElmts(vc, 0);
	    HYPRE_IJVectorInitialize(va);
	    HYPRE_IJVectorInitialize(vb);
	    HYPRE_IJVectorInitialize(vc);
	    HYPRE_IJMatrixGetObject(ma, (void **)(void *)&par_ma);
	    HYPRE_IJVectorGetObject(va, (void **)(void *)&par_va);
	    HYPRE_IJVectorGetObject(vb, (void **)(void *)&par_vb);
	    HYPRE_IJVectorGetObject(vc, (void **)(void *)&par_vc);
	    HYPRE_IJVectorSetValues(va, A->cmap->nlocal, ni, (double *)x->data);
	    HYPRE_IJVectorAssemble(va);
	    HYPRE_IJVectorAssemble(vb);
	    HYPRE_IJVectorAssemble(vc);

	    HYPRE_IJMatrixGetRowCounts(ma, A->cmap->nlocal,
					ni, ni + A->rmap->nlocal);
	    for (i = 0, nnz = 0; i < A->rmap->nlocal; i++)
		nnz += ni[A->rmap->nlocal + i];
#if USE_MPI
	    dnz1 = nnz;
	    MPI_Reduce(&dnz1, &dnz, 1, MPI_DOUBLE, MPI_SUM, 0, g->comm);
#else
	    dnz = nnz;
#endif

	    HYPRE_ParCSRMatrixMatvec(1.0, par_ma, par_va, 0.0, par_vb);
	    phgPerfGetMflops(g, NULL, NULL);	/* reset flops counter */
	    t0 = phgGetTime(NULL);
	    for (i = 0; i < loop_count; i++) {
		HYPRE_ParCSRMatrixMatvec(1.0, par_ma, par_va, 0.0, par_vb);
	    }
	    t1 = phgGetTime(NULL);
	    mflops = phgPerfGetMflops(g, NULL, NULL);
	    HYPRE_IJVectorGetValues(vb, A->rmap->nlocal, ni, (double*)y1->data);
	    /*phgPrintf("    --------------------------------------------"
		      "-------------------------\n");*/
	    phgPrintf("\n");
	    t1 -= t0;
	    phgPrintf(" HYPRE:  time %0.4lf, nnz %0.16lg, %0.2lfMF (%0.2lfMF), "
		      "err: %le\n", t1, dnz, mop / (t1==0 ? 1.:t1), mflops,
		(double)phgVecNorm2(phgVecAXPBY(-1.0, y0, 1.0, &y1), 0, NULL));

	    phgPerfGetMflops(g, NULL, NULL);	/* reset flops counter */
	    t0 = phgGetTime(NULL);
	    for (i = 0; i < loop_count; i++) {
		HYPRE_ParCSRMatrixMatvecT(1.0, par_ma, par_va, 0.0, par_vb);
	    }
	    t1 = phgGetTime(NULL);
	    mflops = phgPerfGetMflops(g, NULL, NULL);
	    HYPRE_IJVectorGetValues(vb, A->rmap->nlocal, ni, (double*)y1->data);
	    t1 -= t0;
	    phgPrintf("  A'*x:  time %0.4lf, nnz %0.16lg, %0.2lfMF (%0.2lfMF), "
		      "err: %le\n", t1, dnz, mop / (t1==0 ? 1.:t1), mflops,
		(double)phgVecNorm2(phgVecAXPBY(-1.0, y0, 1.0, &y1), 0, NULL));

	    phgPerfGetMflops(g, NULL, NULL);	/* reset flops counter */
	    t0 = phgGetTime(NULL);
	    /* Note: 'HYPRE_ParCSRMatrix' is currently typedef'ed to
	     *	     'hypre_ParCSRMatrix *' */
	    par_mb = hypre_ParMatmul((hypre_ParCSRMatrix *)par_ma,
					(hypre_ParCSRMatrix *)par_ma);
	    t1 = phgGetTime(NULL);
	    mflops = phgPerfGetMflops(g, NULL, NULL);
	    start = hypre_ParCSRMatrixFirstRowIndex(par_mb);
	    end = hypre_ParCSRMatrixLastRowIndex(par_mb) + 1;
	    for (i = start, nnz = 0; i < end; i++) {
		HYPRE_Int ncols;
		hypre_ParCSRMatrixGetRow(par_mb, i, &ncols, NULL, NULL);
		hypre_ParCSRMatrixRestoreRow(par_mb, i, &ncols, NULL, NULL);
		nnz += ncols;
	    }
#if USE_MPI
	    dnz1 = nnz;
	    MPI_Reduce(&dnz1, &dnz, 1, MPI_DOUBLE, MPI_SUM, 0, g->comm);
#else
	    dnz = nnz;
#endif
	    /* compare B*x <--> A*A*x */
	    HYPRE_ParCSRMatrixMatvec(1.0, par_ma, par_vb, 0.0, par_vc);
	    HYPRE_ParCSRMatrixMatvec(1.0, (void *)par_mb, par_va, 0.0, par_vb);
	    HYPRE_IJVectorGetValues(vb, A->rmap->nlocal, ni, (double*)y1->data);
	    HYPRE_IJVectorGetValues(vc, A->rmap->nlocal, ni, (double*)y2->data);
	    hypre_ParCSRMatrixDestroy((par_mb));
	    t1 -= t0;
	    phgPrintf("   A*A:  time %0.4lf, nnz %0.16lg, %0.2lfMF, err: %le\n",
		  t1, dnz, mflops,
		 (double)phgVecNorm2(phgVecAXPBY(-1.0, y1, 1.0, &y2), 0, NULL));

	    phgFree(ni);
	    HYPRE_IJMatrixDestroy(ma);
	    HYPRE_IJVectorDestroy(va);
	    HYPRE_IJVectorDestroy(vb);
	    HYPRE_IJVectorDestroy(vc);
	}
#endif	/* USE_HYPRE */

	if (A0 != A)
	    phgMatDestroy(&A0);
#if 0
if (A->rmap->nglobal > 1000) {
    VEC *v = phgMapCreateVec(A->rmap, 3);
    for (i = 0; i < v->map->nlocal; i++) {
	v->data[i + 0 * v->map->nlocal] = 1 * (i + v->map->partition[g->rank]);
	v->data[i + 1 * v->map->nlocal] = 2 * (i + v->map->partition[g->rank]);
	v->data[i + 2 * v->map->nlocal] = 3 * (i + v->map->partition[g->rank]);
    }
    phgMatDumpMATLAB(A, "A", "A.m");
    phgVecDumpMATLAB(v, "v", "v.m");
    phgFinalize();
    exit(0);
}
#endif
	phgMatDestroy(&A);
	phgVecDestroy(&x);
	phgVecDestroy(&y0);
	phgVecDestroy(&y1);
	phgVecDestroy(&y2);
	phgMapDestroy(&map);
	mem = phgMemoryUsage(g, &mem_peak);
	dnz = mem / (1024.0 * 1024.0);
	dnz1 = mem_peak / (1024.0 * 1024.0);
	/*phgPrintf("    --------------------------------------------"
		  "-------------------------\n");*/
	phgPrintf("\n");
	phgPrintf("  Memory: current %0.4lgMB, peak %0.4lgMB\n", dnz, dnz1);
#if 0
{
    static int loop_count = 0;
    if (++loop_count == 4)
	break;
}
#endif
	if (mem_peak > 1024 * (size_t)1024 * mem_max)
	    break;
	phgRefineAllElements(g, 1);
    }
    phgDofFree(&u_h);
    phgFreeGrid(&g);
    phgFinalize();

    return 0;
}