PetscErrorCode StokesSetupMatBlock00(Stokes *s)
{
PetscInt row, start, end, size, i, j;
PetscInt cols[5];
PetscScalar vals[5];
PetscErrorCode ierr;
PetscFunctionBeginUser;
/* A[0] is 2N-by-2N */
ierr = MatCreate(PETSC_COMM_WORLD,&s->subA[0]);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(s->subA[0],"a00_");CHKERRQ(ierr);
ierr = MatSetSizes(s->subA[0],PETSC_DECIDE,PETSC_DECIDE,2*s->nx*s->ny,2*s->nx*s->ny);CHKERRQ(ierr);
ierr = MatSetType(s->subA[0],MATMPIAIJ);CHKERRQ(ierr);
ierr = MatMPIAIJSetPreallocation(s->subA[0],5,NULL,5,NULL);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(s->subA[0], &start, &end);CHKERRQ(ierr);
for (row = start; row < end; row++) {
ierr = StokesGetPosition(s, row, &i, &j);CHKERRQ(ierr);
/* first part: rows 0 to (nx*ny-1) */
ierr = StokesStencilLaplacian(s, i, j, &size, cols, vals);CHKERRQ(ierr);
/* second part: rows (nx*ny) to (2*nx*ny-1) */
if (row >= s->nx*s->ny) {
for (i = 0; i < 5; i++) cols[i] = cols[i] + s->nx*s->ny;
}
for (i = 0; i < 5; i++) vals[i] = -1.0*vals[i]; /* dynamic viscosity coef mu=-1 */
ierr = MatSetValues(s->subA[0], 1, &row, size, cols, vals, INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(s->subA[0], MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(s->subA[0], MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode StokesSetupMatBlock01(Stokes *s)
{
PetscInt row, start, end, size, i, j;
PetscInt cols[5];
PetscScalar vals[5];
PetscErrorCode ierr;
PetscFunctionBeginUser;
/* A[1] is 2N-by-N */
ierr = MatCreate(PETSC_COMM_WORLD, &s->subA[1]);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(s->subA[1],"a01_");
ierr = MatSetSizes(s->subA[1],PETSC_DECIDE,PETSC_DECIDE,2*s->nx*s->ny,s->nx*s->ny);CHKERRQ(ierr);
ierr = MatSetType(s->subA[1],MATMPIAIJ);CHKERRQ(ierr);
ierr = MatMPIAIJSetPreallocation(s->subA[1],5,NULL,5,NULL);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(s->subA[1],&start,&end);CHKERRQ(ierr);
ierr = MatSetOption(s->subA[1],MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
for (row = start; row < end; row++) {
ierr = StokesGetPosition(s, row, &i, &j);CHKERRQ(ierr);
/* first part: rows 0 to (nx*ny-1) */
if (row < s->nx*s->ny) {
ierr = StokesStencilGradientX(s, i, j, &size, cols, vals);CHKERRQ(ierr);
}
/* second part: rows (nx*ny) to (2*nx*ny-1) */
else {
ierr = StokesStencilGradientY(s, i, j, &size, cols, vals);CHKERRQ(ierr);
}
ierr = MatSetValues(s->subA[1], 1, &row, size, cols, vals, INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(s->subA[1], MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(s->subA[1], MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode StokesSetupMatFp(Stokes *s)
{
PetscInt row, start, end, size, i, j;
PetscInt cols[5];
PetscScalar vals[5];
PetscErrorCode ierr;
PetscFunctionBeginUser;
// Fp is N-by-N
ierr = MatCreate(PETSC_COMM_WORLD,&s->Fp);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(s->Fp,"Fp_");CHKERRQ(ierr);
ierr = MatSetSizes(s->Fp,PETSC_DECIDE,PETSC_DECIDE,s->nx*s->ny,s->nx*s->ny);CHKERRQ(ierr);
ierr = MatSetType(s->Fp,MATMPIAIJ);CHKERRQ(ierr);
ierr = MatMPIAIJSetPreallocation(s->Fp,5,NULL,5,NULL);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(s->Fp, &start, &end);CHKERRQ(ierr);
for (row = start; row < end; row++) {
ierr = StokesGetPosition(s, row, &i, &j);CHKERRQ(ierr);
ierr = StokesStencilLaplacian(s, i, j, &size, cols, vals);CHKERRQ(ierr);
for (i = 0; i < 5; i++) vals[i] = -1.0*vals[i]; //* dynamic viscosity coef mu=-1
ierr = MatSetValues(s->Fp, 1, &row, size, cols, vals, INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(s->Fp, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(s->Fp, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode MatSetLocalToGlobalMapping_IS(Mat A,ISLocalToGlobalMapping rmapping,ISLocalToGlobalMapping cmapping)
{
PetscErrorCode ierr;
PetscInt n,bs;
Mat_IS *is = (Mat_IS*)A->data;
IS from,to;
Vec global;
PetscFunctionBegin;
PetscCheckSameComm(A,1,rmapping,2);
if (rmapping != cmapping) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_INCOMP,"MATIS requires the row and column mappings to be identical");
if (is->mapping) { /* Currenly destroys the objects that will be created by this routine. Is there anything else that should be checked? */
ierr = ISLocalToGlobalMappingDestroy(&is->mapping);CHKERRQ(ierr);
ierr = VecDestroy(&is->x);CHKERRQ(ierr);
ierr = VecDestroy(&is->y);CHKERRQ(ierr);
ierr = VecScatterDestroy(&is->ctx);CHKERRQ(ierr);
ierr = MatDestroy(&is->A);CHKERRQ(ierr);
}
ierr = PetscObjectReference((PetscObject)rmapping);CHKERRQ(ierr);
ierr = ISLocalToGlobalMappingDestroy(&is->mapping);CHKERRQ(ierr);
is->mapping = rmapping;
/*
ierr = PetscLayoutSetISLocalToGlobalMapping(A->rmap,rmapping);CHKERRQ(ierr);
ierr = PetscLayoutSetISLocalToGlobalMapping(A->cmap,cmapping);CHKERRQ(ierr);
*/
/* Create the local matrix A */
ierr = ISLocalToGlobalMappingGetSize(rmapping,&n);CHKERRQ(ierr);
ierr = ISLocalToGlobalMappingGetBlockSize(rmapping,&bs);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_SELF,&is->A);CHKERRQ(ierr);
if (bs > 1) {
ierr = MatSetType(is->A,MATSEQBAIJ);CHKERRQ(ierr);
} else {
ierr = MatSetType(is->A,MATSEQAIJ);CHKERRQ(ierr);
}
ierr = MatSetSizes(is->A,n,n,n,n);CHKERRQ(ierr);
ierr = MatSetBlockSize(is->A,bs);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(is->A,((PetscObject)A)->prefix);CHKERRQ(ierr);
ierr = MatAppendOptionsPrefix(is->A,"is_");CHKERRQ(ierr);
ierr = MatSetFromOptions(is->A);CHKERRQ(ierr);
/* Create the local work vectors */
ierr = VecCreate(PETSC_COMM_SELF,&is->x);CHKERRQ(ierr);
ierr = VecSetBlockSize(is->x,bs);CHKERRQ(ierr);
ierr = VecSetSizes(is->x,n,n);CHKERRQ(ierr);
ierr = VecSetOptionsPrefix(is->x,((PetscObject)A)->prefix);CHKERRQ(ierr);
ierr = VecAppendOptionsPrefix(is->x,"is_");CHKERRQ(ierr);
ierr = VecSetFromOptions(is->x);CHKERRQ(ierr);
ierr = VecDuplicate(is->x,&is->y);CHKERRQ(ierr);
/* setup the global to local scatter */
ierr = ISCreateStride(PETSC_COMM_SELF,n,0,1,&to);CHKERRQ(ierr);
ierr = ISLocalToGlobalMappingApplyIS(rmapping,to,&from);CHKERRQ(ierr);
ierr = MatCreateVecs(A,&global,NULL);CHKERRQ(ierr);
ierr = VecScatterCreate(global,from,is->x,to,&is->ctx);CHKERRQ(ierr);
ierr = VecDestroy(&global);CHKERRQ(ierr);
ierr = ISDestroy(&to);CHKERRQ(ierr);
ierr = ISDestroy(&from);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc, char **argv)
{
Mat mat;
MatNullSpace nsp;
PetscBool prefix = PETSC_FALSE, flg;
PetscErrorCode ierr;
PetscInt zero = 0;
PetscScalar value = 0;
ierr = PetscInitialize(&argc, &argv, NULL, help); if (ierr) return ierr;
ierr = PetscOptionsGetBool(NULL, NULL, "-with_prefix",&prefix,NULL);CHKERRQ(ierr);
ierr = MatCreateDense(PETSC_COMM_WORLD, 1, 1, 1, 1, NULL, &mat);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(mat, prefix ? "prefix_" : NULL);CHKERRQ(ierr);
ierr = MatSetUp(mat);CHKERRQ(ierr);
ierr = MatSetValues(mat, 1, &zero, 1, &zero, &value, INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatNullSpaceCreate(PETSC_COMM_WORLD, PETSC_TRUE, 0, NULL, &nsp);CHKERRQ(ierr);
ierr = MatNullSpaceTest(nsp, mat, &flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_PLIB,"Null space test failed!");
ierr = MatNullSpaceDestroy(&nsp);CHKERRQ(ierr);
ierr = MatDestroy(&mat);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
PetscErrorCode StokesSetupMatBlock10(Stokes *s)
{
PetscErrorCode ierr;
PetscFunctionBeginUser;
/* A[2] is minus transpose of A[1] */
ierr = MatTranspose(s->subA[1], MAT_INITIAL_MATRIX, &s->subA[2]);CHKERRQ(ierr);
ierr = MatScale(s->subA[2], -1.0);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(s->subA[2], "a10_");CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode StokesSetupMatBlock11(Stokes *s)
{
PetscErrorCode ierr;
PetscFunctionBeginUser;
/* A[3] is N-by-N null matrix */
ierr = MatCreate(PETSC_COMM_WORLD, &s->subA[3]);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(s->subA[3], "a11_");CHKERRQ(ierr);
ierr = MatSetSizes(s->subA[3], PETSC_DECIDE, PETSC_DECIDE, s->nx*s->ny, s->nx*s->ny);CHKERRQ(ierr);
ierr = MatSetType(s->subA[3], MATMPIAIJ);CHKERRQ(ierr);
ierr = MatMPIAIJSetPreallocation(s->subA[3], 0, NULL, 0, NULL);CHKERRQ(ierr);
ierr = MatAssemblyBegin(s->subA[3], MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(s->subA[3], MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **args) {
PetscErrorCode ierr;
DM da;
KSP ksp;
Mat A;
Vec b,u,uexact;
PetscReal errnorm;
DMDALocalInfo info;
PetscInitialize(&argc,&args,(char*)0,help);
ierr = DMDACreate1d(PETSC_COMM_WORLD,
DM_BOUNDARY_NONE,
9,1,1,NULL,
&da); CHKERRQ(ierr);
ierr = DMSetFromOptions(da); CHKERRQ(ierr);
ierr = DMSetUp(da); CHKERRQ(ierr);
ierr = DMDASetUniformCoordinates(da,0.0,1.0,-1.0,-1.0,-1.0,-1.0); CHKERRQ(ierr);
ierr = DMCreateMatrix(da,&A);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(A,"a_"); CHKERRQ(ierr);
ierr = MatSetFromOptions(A); CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da,&b);CHKERRQ(ierr);
ierr = VecDuplicate(b,&u); CHKERRQ(ierr);
ierr = VecDuplicate(b,&uexact); CHKERRQ(ierr);
ierr = formExactAndRHS(da,uexact,b); CHKERRQ(ierr);
ierr = formdirichletlaplacian(da,A); CHKERRQ(ierr);
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp); CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,A,A); CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp); CHKERRQ(ierr);
ierr = KSPSolve(ksp,b,u); CHKERRQ(ierr);
ierr = VecAXPY(u,-1.0,uexact); CHKERRQ(ierr); // u <- u + (-1.0) uxact
ierr = VecNorm(u,NORM_INFINITY,&errnorm); CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(da,&info);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,
"on %d point grid: error |u-uexact|_inf = %g\n",
info.mx,errnorm); CHKERRQ(ierr);
VecDestroy(&u); VecDestroy(&uexact); VecDestroy(&b);
MatDestroy(&A); KSPDestroy(&ksp); DMDestroy(&da);
PetscFinalize();
return 0;
}
PETSC_EXTERN PetscErrorCode TaoCreate_BQNLS(Tao tao)
{
TAO_BNK *bnk;
TAO_BQNK *bqnk;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = TaoCreate_BQNK(tao);CHKERRQ(ierr);
ierr = KSPSetOptionsPrefix(tao->ksp, "unused");CHKERRQ(ierr);
tao->ops->solve = TaoSolve_BNLS;
tao->ops->setfromoptions = TaoSetFromOptions_BQNLS;
bnk = (TAO_BNK*)tao->data;
bnk->update_type = BNK_UPDATE_STEP;
bnk->computehessian = TaoBQNLSComputeHessian;
bnk->computestep = TaoBQNLSComputeStep;
bqnk = (TAO_BQNK*)bnk->ctx;
ierr = MatSetOptionsPrefix(bqnk->B, "tao_bqnls_");CHKERRQ(ierr);
ierr = MatSetType(bqnk->B, MATLMVMBFGS);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
PetscErrorCode ierr;
PetscInitialize(&argc,&argv,(char*)0,help);
const int d = 2; // d = DOF
Mat A, Aminus;
// these are dense d x d sequential matrices, unrelated to the grid
// (each processor owns whole matrix)
ierr = MatCreateSeqAIJ(PETSC_COMM_WORLD,d,d,d,NULL,&A); CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(A,"A_"); CHKERRQ(ierr);
ierr = MatSetFromOptions(A); CHKERRQ(ierr);
// fill A
double val[d][d], c = 3.0;
val[0][0] = 0.0; val[0][1] = c;
val[1][0] = c; val[1][1] = 0.0;
ierr = fillsmallmat(2,val,A); CHKERRQ(ierr);
// fill Aminus; see getAminus.m for computation of Aminus from A
ierr = MatDuplicate(A,MAT_SHARE_NONZERO_PATTERN,&Aminus); CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(Aminus,"Aminus_"); CHKERRQ(ierr);
val[0][0] = -1.5; val[0][1] = 1.5;
val[1][0] = 1.5; val[1][1] = -1.5;
ierr = fillsmallmat(2,val,Aminus); CHKERRQ(ierr);
// set up the grid
DM da;
ierr = DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC,
-50, // override with -da_grid_x or -da_refine
d, 1, NULL, // dof = 1 and stencil width = 1
&da); CHKERRQ(ierr);
// determine grid locations (cell-centered grid)
DMDALocalInfo info;
double L = 10.0, dx;
ierr = DMDAGetLocalInfo(da,&info); CHKERRQ(ierr);
dx = L / (double)(info.mx);
ierr = DMDASetUniformCoordinates(da,dx/2,L-dx/2,-1.0,-1.0,-1.0,-1.0);CHKERRQ(ierr);
// u = u(t_n), unew = u(t_n+1)
Vec u, unew, F;
ierr = DMCreateLocalVector(da,&u);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)u,"solution u"); CHKERRQ(ierr);
ierr = VecDuplicate(u,&F);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)F,"flux F"); CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da,&unew);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)unew,"updated solution unew"); CHKERRQ(ierr);
ierr = VecSet(unew,0.0); CHKERRQ(ierr);
// at each cell we will need to compute Fcell = A qleft + Aminus dq
Vec dq, qleft, tmp, Fcell;
ierr = VecCreateSeq(PETSC_COMM_WORLD,d,&dq); CHKERRQ(ierr);
ierr = VecDuplicate(dq,&qleft); CHKERRQ(ierr);
ierr = VecDuplicate(dq,&tmp); CHKERRQ(ierr);
ierr = VecDuplicate(dq,&Fcell); CHKERRQ(ierr);
// view the solution graphically; control with -draw_pause
PetscViewer viewer;
ierr = PetscViewerDrawOpen(PETSC_COMM_WORLD,NULL,"solution u",
PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,&viewer); CHKERRQ(ierr);
/* time-stepping loop */
double t = 0.0, tf = 10.0, dt, nu;
int n, NN = 10;
dt = tf / NN;
nu = dt / dx;
for (n = 0; n < NN; ++n) {
ierr = PetscPrintf(PETSC_COMM_WORLD, " time[%3d]=%6g: \n", n, t); CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(da,unew,INSERT_VALUES,u); CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,unew,INSERT_VALUES,u); CHKERRQ(ierr);
ierr = VecView(u,viewer); CHKERRQ(ierr);
double **au, **aunew, **aF;
int j, p;
ierr = DMDAVecGetArrayDOF(da, u, &au);CHKERRQ(ierr);
ierr = DMDAVecGetArrayDOF(da, F, &aF);CHKERRQ(ierr);
for (j=info.xs; j<info.xs+info.xm; j++) {
double *adq, *aqleft, *aFcell;
ierr = VecGetArray(dq,&adq); CHKERRQ(ierr);
ierr = VecGetArray(qleft,&aqleft); CHKERRQ(ierr);
for (p = 0; p < d; p++) {
adq[p] = au[j+1][p] - au[j][p];
aqleft[p] = au[j][p];
}
ierr = VecRestoreArray(dq,&adq); CHKERRQ(ierr);
ierr = VecRestoreArray(qleft,&aqleft); CHKERRQ(ierr);
// tmp = A qleft
// Fcell = tmp + Aminus dq
ierr = MatMult(A,qleft,tmp); CHKERRQ(ierr);
ierr = MatMultAdd(Aminus,dq,tmp,Fcell); CHKERRQ(ierr);
ierr = VecGetArray(Fcell,&aFcell); CHKERRQ(ierr);
for (p = 0; p < d; p++)
aF[j][p] = aFcell[p];
ierr = VecRestoreArray(Fcell,&aFcell); CHKERRQ(ierr);
}
ierr = DMDAVecRestoreArrayDOF(da, F, &aF);CHKERRQ(ierr);
ierr = DMLocalToLocalBegin(da,F,INSERT_VALUES,F); CHKERRQ(ierr);
ierr = DMLocalToLocalEnd(da,F,INSERT_VALUES,F); CHKERRQ(ierr);
ierr = DMDAVecGetArrayDOF(da, F, &aF);CHKERRQ(ierr);
ierr = DMDAVecGetArrayDOF(da, unew, &aunew);CHKERRQ(ierr);
for (j=info.xs; j<info.xs+info.xm; j++) {
for (p = 0; p < d; p++)
aunew[j][p] = au[j][p] - nu * (aF[j+1][p] - aF[j][p]);
}
ierr = DMDAVecRestoreArrayDOF(da, u, &au);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayDOF(da, F, &aF);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayDOF(da, unew, &aunew);CHKERRQ(ierr);
t += dt;
}
// clean up
ierr = VecDestroy(&u); CHKERRQ(ierr);
ierr = VecDestroy(&unew); CHKERRQ(ierr);
ierr = VecDestroy(&F); CHKERRQ(ierr);
ierr = VecDestroy(&dq); CHKERRQ(ierr);
ierr = VecDestroy(&qleft); CHKERRQ(ierr);
ierr = VecDestroy(&tmp); CHKERRQ(ierr);
ierr = VecDestroy(&Fcell); CHKERRQ(ierr);
ierr = MatDestroy(&A); CHKERRQ(ierr);
ierr = MatDestroy(&Aminus); CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer); CHKERRQ(ierr);
ierr = DMDestroy(&da); CHKERRQ(ierr);
ierr = PetscFinalize(); CHKERRQ(ierr);
return 0;
}
void PetscMatrix<T>::init (const numeric_index_type m_in,
const numeric_index_type n_in,
const numeric_index_type m_l,
const numeric_index_type n_l,
const numeric_index_type nnz,
const numeric_index_type noz,
const numeric_index_type blocksize_in)
{
// So compilers don't warn when !LIBMESH_ENABLE_BLOCKED_STORAGE
libmesh_ignore(blocksize_in);
// Clear initialized matrices
if (this->initialized())
this->clear();
this->_is_initialized = true;
PetscErrorCode ierr = 0;
PetscInt m_global = static_cast<PetscInt>(m_in);
PetscInt n_global = static_cast<PetscInt>(n_in);
PetscInt m_local = static_cast<PetscInt>(m_l);
PetscInt n_local = static_cast<PetscInt>(n_l);
PetscInt n_nz = static_cast<PetscInt>(nnz);
PetscInt n_oz = static_cast<PetscInt>(noz);
ierr = MatCreate(this->comm().get(), &_mat);
LIBMESH_CHKERRABORT(ierr);
ierr = MatSetSizes(_mat, m_local, n_local, m_global, n_global);
LIBMESH_CHKERRABORT(ierr);
#ifdef LIBMESH_ENABLE_BLOCKED_STORAGE
PetscInt blocksize = static_cast<PetscInt>(blocksize_in);
if (blocksize > 1)
{
// specified blocksize, bs>1.
// double check sizes.
libmesh_assert_equal_to (m_local % blocksize, 0);
libmesh_assert_equal_to (n_local % blocksize, 0);
libmesh_assert_equal_to (m_global % blocksize, 0);
libmesh_assert_equal_to (n_global % blocksize, 0);
libmesh_assert_equal_to (n_nz % blocksize, 0);
libmesh_assert_equal_to (n_oz % blocksize, 0);
ierr = MatSetType(_mat, MATBAIJ); // Automatically chooses seqbaij or mpibaij
LIBMESH_CHKERRABORT(ierr);
ierr = MatSetBlockSize(_mat, blocksize);
LIBMESH_CHKERRABORT(ierr);
ierr = MatSeqBAIJSetPreallocation(_mat, blocksize, n_nz/blocksize, PETSC_NULL);
LIBMESH_CHKERRABORT(ierr);
ierr = MatMPIBAIJSetPreallocation(_mat, blocksize,
n_nz/blocksize, PETSC_NULL,
n_oz/blocksize, PETSC_NULL);
LIBMESH_CHKERRABORT(ierr);
}
else
#endif
{
ierr = MatSetType(_mat, MATAIJ); // Automatically chooses seqaij or mpiaij
LIBMESH_CHKERRABORT(ierr);
ierr = MatSeqAIJSetPreallocation(_mat, n_nz, PETSC_NULL);
LIBMESH_CHKERRABORT(ierr);
ierr = MatMPIAIJSetPreallocation(_mat, n_nz, PETSC_NULL, n_oz, PETSC_NULL);
LIBMESH_CHKERRABORT(ierr);
}
// Make it an error for PETSc to allocate new nonzero entries during assembly
#if PETSC_VERSION_LESS_THAN(3,0,0)
ierr = MatSetOption(_mat, MAT_NEW_NONZERO_ALLOCATION_ERR);
#else
ierr = MatSetOption(_mat, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_TRUE);
#endif
LIBMESH_CHKERRABORT(ierr);
// Is prefix information available somewhere? Perhaps pass in the system name?
ierr = MatSetOptionsPrefix(_mat, "");
LIBMESH_CHKERRABORT(ierr);
ierr = MatSetFromOptions(_mat);
LIBMESH_CHKERRABORT(ierr);
this->zero ();
}
void PetscMatrix<T>::init ()
{
libmesh_assert(this->_dof_map);
// Clear initialized matrices
if (this->initialized())
this->clear();
this->_is_initialized = true;
const numeric_index_type my_m = this->_dof_map->n_dofs();
const numeric_index_type my_n = my_m;
const numeric_index_type n_l = this->_dof_map->n_dofs_on_processor(this->processor_id());
const numeric_index_type m_l = n_l;
const std::vector<numeric_index_type>& n_nz = this->_dof_map->get_n_nz();
const std::vector<numeric_index_type>& n_oz = this->_dof_map->get_n_oz();
// Make sure the sparsity pattern isn't empty unless the matrix is 0x0
libmesh_assert_equal_to (n_nz.size(), m_l);
libmesh_assert_equal_to (n_oz.size(), m_l);
PetscErrorCode ierr = 0;
PetscInt m_global = static_cast<PetscInt>(my_m);
PetscInt n_global = static_cast<PetscInt>(my_n);
PetscInt m_local = static_cast<PetscInt>(m_l);
PetscInt n_local = static_cast<PetscInt>(n_l);
ierr = MatCreate(this->comm().get(), &_mat);
LIBMESH_CHKERRABORT(ierr);
ierr = MatSetSizes(_mat, m_local, n_local, m_global, n_global);
LIBMESH_CHKERRABORT(ierr);
#ifdef LIBMESH_ENABLE_BLOCKED_STORAGE
PetscInt blocksize = static_cast<PetscInt>(this->_dof_map->block_size());
if (blocksize > 1)
{
// specified blocksize, bs>1.
// double check sizes.
libmesh_assert_equal_to (m_local % blocksize, 0);
libmesh_assert_equal_to (n_local % blocksize, 0);
libmesh_assert_equal_to (m_global % blocksize, 0);
libmesh_assert_equal_to (n_global % blocksize, 0);
ierr = MatSetType(_mat, MATBAIJ); // Automatically chooses seqbaij or mpibaij
LIBMESH_CHKERRABORT(ierr);
ierr = MatSetBlockSize(_mat, blocksize);
LIBMESH_CHKERRABORT(ierr);
// transform the per-entry n_nz and n_oz arrays into their block counterparts.
std::vector<numeric_index_type> b_n_nz, b_n_oz;
transform_preallocation_arrays (blocksize,
n_nz, n_oz,
b_n_nz, b_n_oz);
ierr = MatSeqBAIJSetPreallocation(_mat, blocksize, 0, (PetscInt*)(b_n_nz.empty()?NULL:&b_n_nz[0]));
LIBMESH_CHKERRABORT(ierr);
ierr = MatMPIBAIJSetPreallocation(_mat, blocksize,
0, (PetscInt*)(b_n_nz.empty()?NULL:&b_n_nz[0]),
0, (PetscInt*)(b_n_oz.empty()?NULL:&b_n_oz[0]));
LIBMESH_CHKERRABORT(ierr);
}
else
#endif
{
// no block storage case
ierr = MatSetType(_mat, MATAIJ); // Automatically chooses seqaij or mpiaij
LIBMESH_CHKERRABORT(ierr);
ierr = MatSeqAIJSetPreallocation(_mat, 0, (PetscInt*)(n_nz.empty()?NULL:&n_nz[0]));
LIBMESH_CHKERRABORT(ierr);
ierr = MatMPIAIJSetPreallocation(_mat,
0, (PetscInt*)(n_nz.empty()?NULL:&n_nz[0]),
0, (PetscInt*)(n_oz.empty()?NULL:&n_oz[0]));
LIBMESH_CHKERRABORT(ierr);
}
// Is prefix information available somewhere? Perhaps pass in the system name?
ierr = MatSetOptionsPrefix(_mat, "");
LIBMESH_CHKERRABORT(ierr);
ierr = MatSetFromOptions(_mat);
LIBMESH_CHKERRABORT(ierr);
this->zero();
}
int main(int argc,char **argv)
{
Mat A,R,C,C_dense,C_sparse,Rt_dense,P,PtAP;
PetscInt row,col,m,n;
PetscErrorCode ierr;
MatScalar one =1.0,val;
MatColoring mc;
MatTransposeColoring matcoloring = 0;
ISColoring iscoloring;
PetscBool equal;
PetscMPIInt size;
ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This is a uniprocessor example only!");
/* Create seqaij A */
ierr = MatCreate(PETSC_COMM_SELF,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,4,4,4,4);CHKERRQ(ierr);
ierr = MatSetType(A,MATSEQAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
row = 0; col=0; val=1.0; ierr = MatSetValues(A,1,&row,1,&col,&val,ADD_VALUES);CHKERRQ(ierr);
row = 1; col=3; val=2.0; ierr = MatSetValues(A,1,&row,1,&col,&val,ADD_VALUES);CHKERRQ(ierr);
row = 2; col=2; val=3.0; ierr = MatSetValues(A,1,&row,1,&col,&val,ADD_VALUES);CHKERRQ(ierr);
row = 3; col=0; val=4.0; ierr = MatSetValues(A,1,&row,1,&col,&val,ADD_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(A,"A_");CHKERRQ(ierr);
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"\n");CHKERRQ(ierr);
/* Create seqaij R */
ierr = MatCreate(PETSC_COMM_SELF,&R);CHKERRQ(ierr);
ierr = MatSetSizes(R,2,4,2,4);CHKERRQ(ierr);
ierr = MatSetType(R,MATSEQAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(R);CHKERRQ(ierr);
ierr = MatSetUp(R);CHKERRQ(ierr);
row = 0; col=0; ierr = MatSetValues(R,1,&row,1,&col,&one,ADD_VALUES);CHKERRQ(ierr);
row = 0; col=1; ierr = MatSetValues(R,1,&row,1,&col,&one,ADD_VALUES);CHKERRQ(ierr);
row = 1; col=1; ierr = MatSetValues(R,1,&row,1,&col,&one,ADD_VALUES);CHKERRQ(ierr);
row = 1; col=2; ierr = MatSetValues(R,1,&row,1,&col,&one,ADD_VALUES);CHKERRQ(ierr);
row = 1; col=3; ierr = MatSetValues(R,1,&row,1,&col,&one,ADD_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(R,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(R,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(R,"R_");CHKERRQ(ierr);
ierr = MatView(R,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"\n");CHKERRQ(ierr);
/* C = A*R^T */
ierr = MatMatTransposeMult(A,R,MAT_INITIAL_MATRIX,2.0,&C);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(C,"ARt_");CHKERRQ(ierr);
ierr = MatView(C,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"\n");CHKERRQ(ierr);
/* Create MatTransposeColoring from symbolic C=A*R^T */
ierr = MatColoringCreate(C,&mc);CHKERRQ(ierr);
ierr = MatColoringSetDistance(mc,2);CHKERRQ(ierr);
/* ierr = MatColoringSetType(mc,MATCOLORINGSL);CHKERRQ(ierr); */
ierr = MatColoringSetFromOptions(mc);CHKERRQ(ierr);
ierr = MatColoringApply(mc,&iscoloring);CHKERRQ(ierr);
ierr = MatColoringDestroy(&mc);CHKERRQ(ierr);
ierr = MatTransposeColoringCreate(C,iscoloring,&matcoloring);CHKERRQ(ierr);
ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
/* Create Rt_dense */
ierr = MatCreate(PETSC_COMM_WORLD,&Rt_dense);CHKERRQ(ierr);
ierr = MatSetSizes(Rt_dense,4,matcoloring->ncolors,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
ierr = MatSetType(Rt_dense,MATDENSE);CHKERRQ(ierr);
ierr = MatSeqDenseSetPreallocation(Rt_dense,NULL);CHKERRQ(ierr);
ierr = MatAssemblyBegin(Rt_dense,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Rt_dense,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatGetLocalSize(Rt_dense,&m,&n);CHKERRQ(ierr);
printf("Rt_dense: %d,%d\n",(int)m,(int)n);
/* Get Rt_dense by Apply MatTransposeColoring to R */
ierr = MatTransColoringApplySpToDen(matcoloring,R,Rt_dense);CHKERRQ(ierr);
/* C_dense = A*Rt_dense */
ierr = MatMatMult(A,Rt_dense,MAT_INITIAL_MATRIX,2.0,&C_dense);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(C_dense,"ARt_dense_");CHKERRQ(ierr);
/*ierr = MatView(C_dense,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); */
/*ierr = PetscPrintf(PETSC_COMM_SELF,"\n");CHKERRQ(ierr); */
/* Recover C from C_dense */
ierr = MatDuplicate(C,MAT_DO_NOT_COPY_VALUES,&C_sparse);CHKERRQ(ierr);
ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C_sparse);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(C_sparse,"ARt_color_");CHKERRQ(ierr);
ierr = MatView(C_sparse,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"\n");CHKERRQ(ierr);
ierr = MatDestroy(&C_dense);CHKERRQ(ierr);
ierr = MatDestroy(&C_sparse);CHKERRQ(ierr);
ierr = MatDestroy(&Rt_dense);CHKERRQ(ierr);
ierr = MatTransposeColoringDestroy(&matcoloring);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
/* Test PtAP = P^T*A*P, P = R^T */
ierr = MatTranspose(R,MAT_INITIAL_MATRIX,&P);CHKERRQ(ierr);
ierr = MatPtAP(A,P,MAT_INITIAL_MATRIX,2.0,&PtAP);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(PtAP,"PtAP_");CHKERRQ(ierr);
ierr = MatView(PtAP,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = MatDestroy(&P);CHKERRQ(ierr);
/* Test C = RARt */
ierr = MatRARt(A,R,MAT_INITIAL_MATRIX,2.0,&C);CHKERRQ(ierr);
ierr = MatRARt(A,R,MAT_REUSE_MATRIX,2.0,&C);CHKERRQ(ierr);
ierr = MatEqual(C,PtAP,&equal);CHKERRQ(ierr);
if (!equal) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: PtAP != RARt");CHKERRQ(ierr);
}
/* Free spaces */
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&R);CHKERRQ(ierr);
ierr = MatDestroy(&PtAP);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
/* Developer Notes: This should be implemented with a MatCreate_SchurComplement() as that is the standard design for new Mat classes. */
PetscErrorCode MatGetSchurComplement_Basic(Mat mat,IS isrow0,IS iscol0,IS isrow1,IS iscol1,MatReuse mreuse,Mat *newmat,MatReuse preuse,Mat *newpmat)
{
PetscErrorCode ierr;
Mat A=0,Ap=0,B=0,C=0,D=0;
PetscFunctionBegin;
PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
PetscValidHeaderSpecific(isrow0,IS_CLASSID,2);
PetscValidHeaderSpecific(iscol0,IS_CLASSID,3);
PetscValidHeaderSpecific(isrow1,IS_CLASSID,4);
PetscValidHeaderSpecific(iscol1,IS_CLASSID,5);
if (mreuse == MAT_REUSE_MATRIX) PetscValidHeaderSpecific(*newmat,MAT_CLASSID,7);
if (preuse == MAT_REUSE_MATRIX) PetscValidHeaderSpecific(*newpmat,MAT_CLASSID,9);
PetscValidType(mat,1);
if (mat->factortype) SETERRQ(((PetscObject)mat)->comm,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
if (mreuse != MAT_IGNORE_MATRIX) {
/* Use MatSchurComplement */
if (mreuse == MAT_REUSE_MATRIX) {
ierr = MatSchurComplementGetSubmatrices(*newmat,&A,&Ap,&B,&C,&D);CHKERRQ(ierr);
if (!A || !Ap || !B || !C) SETERRQ(((PetscObject)mat)->comm,PETSC_ERR_ARG_WRONGSTATE,"Attempting to reuse matrix but Schur complement matrices unset");
if (A != Ap) SETERRQ(((PetscObject)mat)->comm,PETSC_ERR_ARG_WRONGSTATE,"Preconditioning matrix does not match operator");
ierr = MatDestroy(&Ap);CHKERRQ(ierr); /* get rid of extra reference */
}
ierr = MatGetSubMatrix(mat,isrow0,iscol0,mreuse,&A);CHKERRQ(ierr);
ierr = MatGetSubMatrix(mat,isrow0,iscol1,mreuse,&B);CHKERRQ(ierr);
ierr = MatGetSubMatrix(mat,isrow1,iscol0,mreuse,&C);CHKERRQ(ierr);
ierr = MatGetSubMatrix(mat,isrow1,iscol1,mreuse,&D);CHKERRQ(ierr);
switch (mreuse) {
case MAT_INITIAL_MATRIX:
ierr = MatCreateSchurComplement(A,A,B,C,D,newmat);CHKERRQ(ierr);
break;
case MAT_REUSE_MATRIX:
ierr = MatSchurComplementUpdate(*newmat,A,A,B,C,D,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
break;
default:
SETERRQ(((PetscObject)mat)->comm,PETSC_ERR_SUP,"Unrecognized value of mreuse");
}
}
if (preuse != MAT_IGNORE_MATRIX) {
/* Use the diagonal part of A to form D - C inv(diag(A)) B */
Mat Ad,AdB,S;
Vec diag;
PetscInt i,m,n,mstart,mend;
PetscScalar *x;
/* We could compose these with newpmat so that the matrices can be reused. */
if (!A) {ierr = MatGetSubMatrix(mat,isrow0,iscol0,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);}
if (!B) {ierr = MatGetSubMatrix(mat,isrow0,iscol1,MAT_INITIAL_MATRIX,&B);CHKERRQ(ierr);}
if (!C) {ierr = MatGetSubMatrix(mat,isrow1,iscol0,MAT_INITIAL_MATRIX,&C);CHKERRQ(ierr);}
if (!D) {ierr = MatGetSubMatrix(mat,isrow1,iscol1,MAT_INITIAL_MATRIX,&D);CHKERRQ(ierr);}
ierr = MatGetVecs(A,&diag,PETSC_NULL);CHKERRQ(ierr);
ierr = MatGetDiagonal(A,diag);CHKERRQ(ierr);
ierr = VecReciprocal(diag);CHKERRQ(ierr);
ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
/* We need to compute S = D - C inv(diag(A)) B. For row-oriented formats, it is easy to scale the rows of B and
* for column-oriented formats the columns of C can be scaled. Would skip creating a silly diagonal matrix. */
ierr = MatCreate(((PetscObject)A)->comm,&Ad);CHKERRQ(ierr);
ierr = MatSetSizes(Ad,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(Ad,((PetscObject)mat)->prefix);CHKERRQ(ierr);
ierr = MatAppendOptionsPrefix(Ad,"diag_");CHKERRQ(ierr);
ierr = MatSetFromOptions(Ad);CHKERRQ(ierr);
ierr = MatSeqAIJSetPreallocation(Ad,1,PETSC_NULL);CHKERRQ(ierr);
ierr = MatMPIAIJSetPreallocation(Ad,1,PETSC_NULL,0,PETSC_NULL);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(Ad,&mstart,&mend);CHKERRQ(ierr);
ierr = VecGetArray(diag,&x);CHKERRQ(ierr);
for (i=mstart; i<mend; i++) {
ierr = MatSetValue(Ad,i,i,x[i-mstart],INSERT_VALUES);CHKERRQ(ierr);
}
ierr = VecRestoreArray(diag,&x);CHKERRQ(ierr);
ierr = MatAssemblyBegin(Ad,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Ad,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = VecDestroy(&diag);CHKERRQ(ierr);
ierr = MatMatMult(Ad,B,MAT_INITIAL_MATRIX,1,&AdB);CHKERRQ(ierr);
S = (preuse == MAT_REUSE_MATRIX) ? *newpmat : (Mat)0;
ierr = MatMatMult(C,AdB,preuse,PETSC_DEFAULT,&S);CHKERRQ(ierr);
ierr = MatAYPX(S,-1,D,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
*newpmat = S;
ierr = MatDestroy(&Ad);CHKERRQ(ierr);
ierr = MatDestroy(&AdB);CHKERRQ(ierr);
}
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatDestroy(&D);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **args)
{
Mat A,Asp;
PetscViewer fd; /* viewer */
char file[PETSC_MAX_PATH_LEN]; /* input file name */
PetscErrorCode ierr;
PetscInt m,n,rstart,rend;
PetscBool flg;
PetscInt row,ncols,j,nrows,nnzA=0,nnzAsp=0;
const PetscInt *cols;
const PetscScalar *vals;
PetscReal norm,percent,val,dtol=1.e-16;
PetscMPIInt rank;
MatInfo matinfo;
PetscInt Dnnz,Onnz;
PetscInitialize(&argc,&args,(char *)0,help);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
/* Determine files from which we read the linear systems. */
ierr = PetscOptionsGetString(PETSC_NULL,"-f",file,PETSC_MAX_PATH_LEN,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_WORLD,1,"Must indicate binary file with the -f option");
/* Open binary file. Note that we use FILE_MODE_READ to indicate
reading from this file. */
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,file,FILE_MODE_READ,&fd);CHKERRQ(ierr);
/* Load the matrix; then destroy the viewer. */
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(A,"a_");CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatLoad(A,fd);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&fd);CHKERRQ(ierr);
ierr = MatGetSize(A,&m,&n);CHKERRQ(ierr);
ierr = MatGetInfo(A,MAT_LOCAL,&matinfo);CHKERRQ(ierr);
//printf("matinfo.nz_used %g\n",matinfo.nz_used);
/* Get a sparse matrix Asp by dumping zero entries of A */
ierr = MatCreate(PETSC_COMM_WORLD,&Asp);CHKERRQ(ierr);
ierr = MatSetSizes(Asp,m,n,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(Asp,"asp_");CHKERRQ(ierr);
ierr = MatSetFromOptions(Asp);CHKERRQ(ierr);
Dnnz = (PetscInt)matinfo.nz_used/m + 1;
Onnz = Dnnz/2;
printf("Dnnz %d %d\n",Dnnz,Onnz);
ierr = MatSeqAIJSetPreallocation(Asp,Dnnz,PETSC_NULL);CHKERRQ(ierr);
ierr = MatMPIAIJSetPreallocation(Asp,Dnnz,PETSC_NULL,Onnz,PETSC_NULL);CHKERRQ(ierr);
/* Check zero rows */
ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
nrows = 0;
for (row=rstart; row<rend; row++){
ierr = MatGetRow(A,row,&ncols,&cols,&vals);CHKERRQ(ierr);
nnzA += ncols;
norm = 0.0;
for (j=0; j<ncols; j++){
val = PetscAbsScalar(vals[j]);
if (norm < val) norm = norm;
if (val > dtol){
ierr = MatSetValues(Asp,1,&row,1,&cols[j],&vals[j],INSERT_VALUES);CHKERRQ(ierr);
nnzAsp++;
}
}
if (!norm) nrows++;
ierr = MatRestoreRow(A,row,&ncols,&cols,&vals);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(Asp,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Asp,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
percent=(PetscReal)nnzA*100/(m*n);
ierr = PetscPrintf(PETSC_COMM_SELF," [%d] Matrix A local size %d,%d; nnzA %d, %g percent; No. of zero rows: %d\n",rank,m,n,nnzA,percent,nrows);
percent=(PetscReal)nnzAsp*100/(m*n);
ierr = PetscPrintf(PETSC_COMM_SELF," [%d] Matrix Asp nnzAsp %d, %g percent\n",rank,nnzAsp,percent);
/* investigate matcoloring for Asp */
PetscBool Asp_coloring = PETSC_FALSE;
ierr = PetscOptionsHasName(PETSC_NULL,"-Asp_color",&Asp_coloring);CHKERRQ(ierr);
if (Asp_coloring){
ISColoring iscoloring;
MatFDColoring matfdcoloring;
ierr = PetscPrintf(PETSC_COMM_WORLD," Create coloring of Asp...\n");
ierr = MatGetColoring(Asp,MATCOLORINGSL,&iscoloring);CHKERRQ(ierr);
ierr = MatFDColoringCreate(Asp,iscoloring,&matfdcoloring);CHKERRQ(ierr);
ierr = MatFDColoringSetFromOptions(matfdcoloring);CHKERRQ(ierr);
//ierr = MatFDColoringView(matfdcoloring,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
ierr = MatFDColoringDestroy(&matfdcoloring);CHKERRQ(ierr);
}
/* Write Asp in binary for study - see ~petsc/src/mat/examples/tests/ex124.c */
PetscBool Asp_write = PETSC_FALSE;
ierr = PetscOptionsHasName(PETSC_NULL,"-Asp_write",&Asp_write);CHKERRQ(ierr);
if (Asp_write){
PetscViewer viewer;
ierr = PetscPrintf(PETSC_COMM_SELF,"Write Asp into file Asp.dat ...\n");
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,"Asp.dat",FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
ierr = MatView(Asp,viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
}
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&Asp);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
PetscErrorCode MatSetLocalToGlobalMapping_IS(Mat A,ISLocalToGlobalMapping rmapping,ISLocalToGlobalMapping cmapping)
{
PetscErrorCode ierr;
PetscInt nr,rbs,nc,cbs;
Mat_IS *is = (Mat_IS*)A->data;
IS from,to;
Vec cglobal,rglobal;
PetscFunctionBegin;
PetscCheckSameComm(A,1,rmapping,2);
PetscCheckSameComm(A,1,cmapping,3);
/* Destroy any previous data */
ierr = VecDestroy(&is->x);CHKERRQ(ierr);
ierr = VecDestroy(&is->y);CHKERRQ(ierr);
ierr = VecScatterDestroy(&is->rctx);CHKERRQ(ierr);
ierr = VecScatterDestroy(&is->cctx);CHKERRQ(ierr);
ierr = MatDestroy(&is->A);CHKERRQ(ierr);
ierr = PetscSFDestroy(&is->sf);CHKERRQ(ierr);
ierr = PetscFree2(is->sf_rootdata,is->sf_leafdata);CHKERRQ(ierr);
/* Setup Layout and set local to global maps */
ierr = PetscLayoutSetUp(A->rmap);CHKERRQ(ierr);
ierr = PetscLayoutSetUp(A->cmap);CHKERRQ(ierr);
ierr = PetscLayoutSetISLocalToGlobalMapping(A->rmap,rmapping);CHKERRQ(ierr);
ierr = PetscLayoutSetISLocalToGlobalMapping(A->cmap,cmapping);CHKERRQ(ierr);
/* Create the local matrix A */
ierr = ISLocalToGlobalMappingGetSize(rmapping,&nr);CHKERRQ(ierr);
ierr = ISLocalToGlobalMappingGetBlockSize(rmapping,&rbs);CHKERRQ(ierr);
ierr = ISLocalToGlobalMappingGetSize(cmapping,&nc);CHKERRQ(ierr);
ierr = ISLocalToGlobalMappingGetBlockSize(cmapping,&cbs);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_SELF,&is->A);CHKERRQ(ierr);
ierr = MatSetType(is->A,MATAIJ);CHKERRQ(ierr);
ierr = MatSetSizes(is->A,nr,nc,nr,nc);CHKERRQ(ierr);
ierr = MatSetBlockSizes(is->A,rbs,cbs);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(is->A,((PetscObject)A)->prefix);CHKERRQ(ierr);
ierr = MatAppendOptionsPrefix(is->A,"is_");CHKERRQ(ierr);
ierr = MatSetFromOptions(is->A);CHKERRQ(ierr);
/* Create the local work vectors */
ierr = MatCreateVecs(is->A,&is->x,&is->y);CHKERRQ(ierr);
/* setup the global to local scatters */
ierr = MatCreateVecs(A,&cglobal,&rglobal);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF,nr,0,1,&to);CHKERRQ(ierr);
ierr = ISLocalToGlobalMappingApplyIS(rmapping,to,&from);CHKERRQ(ierr);
ierr = VecScatterCreate(rglobal,from,is->y,to,&is->rctx);CHKERRQ(ierr);
if (rmapping != cmapping) {
ierr = ISDestroy(&to);CHKERRQ(ierr);
ierr = ISDestroy(&from);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF,nc,0,1,&to);CHKERRQ(ierr);
ierr = ISLocalToGlobalMappingApplyIS(cmapping,to,&from);CHKERRQ(ierr);
ierr = VecScatterCreate(cglobal,from,is->x,to,&is->cctx);CHKERRQ(ierr);
} else {
ierr = PetscObjectReference((PetscObject)is->rctx);CHKERRQ(ierr);
is->cctx = is->rctx;
}
ierr = VecDestroy(&rglobal);CHKERRQ(ierr);
ierr = VecDestroy(&cglobal);CHKERRQ(ierr);
ierr = ISDestroy(&to);CHKERRQ(ierr);
ierr = ISDestroy(&from);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **argv) {
Mat A,B,C,D;
PetscScalar a[]= {1.,1.,0.,0.,1.,1.,0.,0.,1.};
PetscInt ij[]= {0,1,2};
PetscScalar none=-1.;
PetscErrorCode ierr;
PetscReal fill=4;
PetscReal norm;
PetscInitialize(&argc,&argv,(char *)0,help);
ierr = MatCreate(PETSC_COMM_SELF,&A);
CHKERRQ(ierr);
ierr = MatSetSizes(A,3,3,3,3);
CHKERRQ(ierr);
ierr = MatSetType(A,MATSEQAIJ);
CHKERRQ(ierr);
ierr = MatSetUp(A);
CHKERRQ(ierr);
ierr = MatSetOption(A,MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE);
CHKERRQ(ierr);
ierr = MatSetValues(A,3,ij,3,ij,a,ADD_VALUES);
CHKERRQ(ierr);
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(A,"A_");
CHKERRQ(ierr);
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);
CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"\n");
CHKERRQ(ierr);
/* Test MatMatMult() */
ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&B);
CHKERRQ(ierr); /* B = A^T */
ierr = MatMatMult(B,A,MAT_INITIAL_MATRIX,fill,&C);
CHKERRQ(ierr); /* C = B*A */
ierr = MatSetOptionsPrefix(C,"C=B*A=A^T*A_");
CHKERRQ(ierr);
ierr = MatView(C,PETSC_VIEWER_STDOUT_WORLD);
CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"\n");
CHKERRQ(ierr);
ierr = MatMatMultSymbolic(C,A,fill,&D);
CHKERRQ(ierr);
ierr = MatMatMultNumeric(C,A,D);
CHKERRQ(ierr); /* D = C*A = (A^T*A)*A */
ierr = MatSetOptionsPrefix(D,"D=C*A=(A^T*A)*A_");
CHKERRQ(ierr);
ierr = MatView(D,PETSC_VIEWER_STDOUT_WORLD);
CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"\n");
CHKERRQ(ierr);
/* Repeat the numeric product to test reuse of the previous symbolic product */
ierr = MatMatMultNumeric(C,A,D);
CHKERRQ(ierr);
ierr = MatView(D,PETSC_VIEWER_STDOUT_WORLD);
CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"\n");
CHKERRQ(ierr);
ierr = MatDestroy(&B);
CHKERRQ(ierr);
ierr = MatDestroy(&C);
CHKERRQ(ierr);
/* Test PtAP routine. */
ierr = MatDuplicate(A,MAT_COPY_VALUES,&B);
CHKERRQ(ierr); /* B = A */
ierr = MatPtAP(A,B,MAT_INITIAL_MATRIX,fill,&C);
CHKERRQ(ierr); /* C = B^T*A*B */
ierr = MatAXPY(D,none,C,DIFFERENT_NONZERO_PATTERN);
CHKERRQ(ierr);
ierr = MatNorm(D,NORM_FROBENIUS,&norm);
if (norm > 1.e-15) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error in MatPtAP: %g\n",norm);
}
ierr = MatDestroy(&C);
CHKERRQ(ierr);
ierr = MatDestroy(&D);
CHKERRQ(ierr);
/* Repeat PtAP to test symbolic/numeric separation for reuse of the symbolic product */
ierr = MatPtAP(A,B,MAT_INITIAL_MATRIX,fill,&C);
CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(C,"C=BtAB_");
CHKERRQ(ierr);
ierr = MatView(C,PETSC_VIEWER_STDOUT_WORLD);
CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"\n");
CHKERRQ(ierr);
ierr = MatPtAPSymbolic(A,B,fill,&D);
CHKERRQ(ierr);
ierr = MatPtAPNumeric(A,B,D);
CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(D,"D=BtAB_");
CHKERRQ(ierr);
ierr = MatView(D,PETSC_VIEWER_STDOUT_WORLD);
CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"\n");
CHKERRQ(ierr);
/* Repeat numeric product to test reuse of the previous symbolic product */
ierr = MatPtAPNumeric(A,B,D);
CHKERRQ(ierr);
ierr = MatAXPY(D,none,C,DIFFERENT_NONZERO_PATTERN);
CHKERRQ(ierr);
ierr = MatNorm(D,NORM_FROBENIUS,&norm);
if (norm > 1.e-15) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error in symbolic/numeric MatPtAP: %g\n",norm);
}
ierr = MatDestroy(&B);
ierr = MatDestroy(&C);
ierr = MatDestroy(&D);
/* A test contributed by Tobias Neckel <*****@*****.**> */
ierr = testPTAPRectangular();
CHKERRQ(ierr);
/* test MatMatTransposeMult(): A*B^T */
ierr = MatMatTransposeMult(A,A,MAT_INITIAL_MATRIX,fill,&D);
CHKERRQ(ierr); /* D = A*A^T */
ierr = MatSetOptionsPrefix(D,"D=A*A^T_");
CHKERRQ(ierr);
ierr = MatView(D,PETSC_VIEWER_STDOUT_WORLD);
CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"\n");
CHKERRQ(ierr);
ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&B);
CHKERRQ(ierr); /* B = A^T */
ierr = MatMatMult(A,B,MAT_INITIAL_MATRIX,fill,&C);
CHKERRQ(ierr); /* C=A*B */
ierr = MatSetOptionsPrefix(C,"D=A*B=A*A^T_");
CHKERRQ(ierr);
ierr = MatView(C,PETSC_VIEWER_STDOUT_WORLD);
CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"\n");
CHKERRQ(ierr);
ierr = MatDestroy(&A);
ierr = MatDestroy(&B);
ierr = MatDestroy(&C);
ierr = MatDestroy(&D);
PetscFinalize();
return(0);
}
static PetscErrorCode ComputeSubdomainMatrix(DomainData dd, GLLData glldata, Mat *local_mat)
{
PetscErrorCode ierr;
PetscInt localsize,zloc,yloc,xloc,auxnex,auxney,auxnez;
PetscInt ie,je,ke,i,j,k,ig,jg,kg,ii,ming;
PetscInt *indexg,*cols,*colsg;
PetscScalar *vals;
Mat temp_local_mat,elem_mat_DBC=0,*usedmat;
IS submatIS;
PetscFunctionBeginUser;
ierr = MatGetSize(glldata.elem_mat,&i,&j);CHKERRQ(ierr);
ierr = PetscMalloc1(i,&indexg);CHKERRQ(ierr);
ierr = PetscMalloc1(i,&colsg);CHKERRQ(ierr);
/* get submatrix of elem_mat without dirichlet nodes */
if (!dd.pure_neumann && !dd.DBC_zerorows && !dd.ipx) {
xloc = dd.p+1;
yloc = 1;
zloc = 1;
if (dd.dim>1) yloc = dd.p+1;
if (dd.dim>2) zloc = dd.p+1;
ii = 0;
for (k=0;k<zloc;k++) {
for (j=0;j<yloc;j++) {
for (i=1;i<xloc;i++) {
indexg[ii]=k*xloc*yloc+j*xloc+i;
ii++;
}
}
}
ierr = ISCreateGeneral(PETSC_COMM_SELF,ii,indexg,PETSC_COPY_VALUES,&submatIS);CHKERRQ(ierr);
ierr = MatGetSubMatrix(glldata.elem_mat,submatIS,submatIS,MAT_INITIAL_MATRIX,&elem_mat_DBC);CHKERRQ(ierr);
ierr = ISDestroy(&submatIS);CHKERRQ(ierr);
}
/* Assemble subdomain matrix */
localsize = dd.xm_l*dd.ym_l*dd.zm_l;
ierr = MatCreate(PETSC_COMM_SELF,&temp_local_mat);CHKERRQ(ierr);
ierr = MatSetSizes(temp_local_mat,localsize,localsize,localsize,localsize);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(temp_local_mat,"subdomain_");CHKERRQ(ierr);
/* set local matrices type: here we use SEQSBAIJ primarily for testing purpose */
/* in order to avoid conversions inside the BDDC code, use SeqAIJ if possible */
if (dd.DBC_zerorows && !dd.ipx) { /* in this case, we need to zero out some of the rows, so use seqaij */
ierr = MatSetType(temp_local_mat,MATSEQAIJ);CHKERRQ(ierr);
} else {
ierr = MatSetType(temp_local_mat,MATSEQSBAIJ);CHKERRQ(ierr);
}
ierr = MatSetFromOptions(temp_local_mat);CHKERRQ(ierr);
i = PetscPowRealInt(3.0*(dd.p+1.0),dd.dim);
ierr = MatSeqAIJSetPreallocation(temp_local_mat,i,NULL);CHKERRQ(ierr); /* very overestimated */
ierr = MatSeqSBAIJSetPreallocation(temp_local_mat,1,i,NULL);CHKERRQ(ierr); /* very overestimated */
ierr = MatSetOption(temp_local_mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);CHKERRQ(ierr);
yloc = dd.p+1;
zloc = dd.p+1;
if (dd.dim < 3) zloc = 1;
if (dd.dim < 2) yloc = 1;
auxnez = dd.nez_l;
auxney = dd.ney_l;
auxnex = dd.nex_l;
if (dd.dim < 3) auxnez = 1;
if (dd.dim < 2) auxney = 1;
for (ke=0; ke<auxnez; ke++) {
for (je=0; je<auxney; je++) {
for (ie=0; ie<auxnex; ie++) {
/* customize element accounting for BC */
xloc = dd.p+1;
ming = 0;
usedmat = &glldata.elem_mat;
if (!dd.pure_neumann && !dd.DBC_zerorows && !dd.ipx) {
if (ie == 0) {
xloc = dd.p;
usedmat = &elem_mat_DBC;
} else {
ming = -1;
usedmat = &glldata.elem_mat;
}
}
/* local to the element/global to the subdomain indexing */
for (k=0; k<zloc; k++) {
kg = ke*dd.p+k;
for (j=0; j<yloc; j++) {
jg = je*dd.p+j;
for (i=0; i<xloc; i++) {
ig = ie*dd.p+i+ming;
ii = k*xloc*yloc+j*xloc+i;
indexg[ii] = kg*dd.xm_l*dd.ym_l+jg*dd.xm_l+ig;
}
}
}
/* Set values */
for (i=0; i<xloc*yloc*zloc; i++) {
ierr = MatGetRow(*usedmat,i,&j,(const PetscInt**)&cols,(const PetscScalar**)&vals);CHKERRQ(ierr);
for (k=0; k<j; k++) colsg[k] = indexg[cols[k]];
ierr = MatSetValues(temp_local_mat,1,&indexg[i],j,colsg,vals,ADD_VALUES);CHKERRQ(ierr);
ierr = MatRestoreRow(*usedmat,i,&j,(const PetscInt**)&cols,(const PetscScalar**)&vals);CHKERRQ(ierr);
}
}
}
}
ierr = PetscFree(indexg);CHKERRQ(ierr);
ierr = PetscFree(colsg);CHKERRQ(ierr);
ierr = MatAssemblyBegin(temp_local_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd (temp_local_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
#if DEBUG
{
Vec lvec,rvec;
PetscReal norm;
ierr = MatCreateVecs(temp_local_mat,&lvec,&rvec);CHKERRQ(ierr);
ierr = VecSet(lvec,1.0);CHKERRQ(ierr);
ierr = MatMult(temp_local_mat,lvec,rvec);CHKERRQ(ierr);
ierr = VecNorm(rvec,NORM_INFINITY,&norm);CHKERRQ(ierr);
printf("Test null space of local mat % 1.14e\n",norm);
ierr = VecDestroy(&lvec);CHKERRQ(ierr);
ierr = VecDestroy(&rvec);CHKERRQ(ierr);
}
#endif
*local_mat = temp_local_mat;
ierr = MatDestroy(&elem_mat_DBC);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **args) {
PetscErrorCode ierr;
Vec x, b, xexact;
Mat A;
KSP ksp;
int m = 4, i, Istart, Iend, j[3];
double v[3], xval, errnorm;
PetscInitialize(&argc,&args,NULL,help);
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,"tri_","options for tri",""); CHKERRQ(ierr);
ierr = PetscOptionsInt("-m","dimension of linear system","tri.c",m,&m,NULL); CHKERRQ(ierr);
ierr = PetscOptionsEnd(); CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&x); CHKERRQ(ierr);
ierr = VecSetSizes(x,PETSC_DECIDE,m); CHKERRQ(ierr);
ierr = VecSetFromOptions(x); CHKERRQ(ierr);
ierr = VecDuplicate(x,&b); CHKERRQ(ierr);
ierr = VecDuplicate(x,&xexact); CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&A); CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m,m); CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(A,"a_"); CHKERRQ(ierr);
ierr = MatSetFromOptions(A); CHKERRQ(ierr);
ierr = MatSetUp(A); CHKERRQ(ierr);
//ENDSETUP
ierr = MatGetOwnershipRange(A,&Istart,&Iend); CHKERRQ(ierr);
for (i=Istart; i<Iend; i++) {
if (i == 0) {
v[0] = 3.0; v[1] = -1.0;
j[0] = 0; j[1] = 1;
ierr = MatSetValues(A,1,&i,2,j,v,INSERT_VALUES); CHKERRQ(ierr);
} else {
v[0] = -1.0; v[1] = 3.0; v[2] = -1.0;
j[0] = i-1; j[1] = i; j[2] = i+1;
if (i == m-1) {
ierr = MatSetValues(A,1,&i,2,j,v,INSERT_VALUES); CHKERRQ(ierr);
} else {
ierr = MatSetValues(A,1,&i,3,j,v,INSERT_VALUES); CHKERRQ(ierr);
}
}
xval = exp(cos(i));
ierr = VecSetValues(xexact,1,&i,&xval,INSERT_VALUES); CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
ierr = VecAssemblyBegin(xexact); CHKERRQ(ierr);
ierr = VecAssemblyEnd(xexact); CHKERRQ(ierr);
ierr = MatMult(A,xexact,b); CHKERRQ(ierr);
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp); CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,A,A); CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp); CHKERRQ(ierr);
ierr = KSPSolve(ksp,b,x); CHKERRQ(ierr);
ierr = VecAXPY(x,-1.0,xexact); CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&errnorm); CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,
"error for m = %d system is |x-xexact|_2 = %.1e\n",m,errnorm); CHKERRQ(ierr);
KSPDestroy(&ksp); MatDestroy(&A);
VecDestroy(&x); VecDestroy(&b); VecDestroy(&xexact);
PetscFinalize();
return 0;
}