/*@
MatColoringSetFromOptions - Sets MatColoring options from user parameters
Collective on MatColoring
Input Parameters:
. mc - MatColoring context
Options Database Keys:
+ -mat_coloring_type - the type of coloring algorithm used
. -mat_coloring_maxcolors - the maximum number of relevant colors, all nodes not in a color are in maxcolors+1
. -mat_coloring_distance - compute a distance 1,2,... coloring.
. -mat_coloring_view - print information about the coloring and the produced index sets
Level: beginner
.keywords: Coloring, Matrix
.seealso: MatColoring, MatColoringApply()
@*/
PetscErrorCode MatColoringSetFromOptions(MatColoring mc)
{
PetscBool flg;
MatColoringType deft = MATCOLORINGSL;
char type[256];
PetscErrorCode ierr;
PetscInt dist,maxcolors;
PetscFunctionBegin;
PetscValidHeaderSpecific(mc,MAT_COLORING_CLASSID,1);
ierr = MatColoringGetDistance(mc,&dist);CHKERRQ(ierr);
ierr = MatColoringGetMaxColors(mc,&maxcolors);CHKERRQ(ierr);
if (!MatColoringRegisterAllCalled) {ierr = MatColoringRegisterAll();CHKERRQ(ierr);}
ierr = PetscObjectOptionsBegin((PetscObject)mc);CHKERRQ(ierr);
if (((PetscObject)mc)->type_name) deft = ((PetscObject)mc)->type_name;
ierr = PetscOptionsFList("-mat_coloring_type","The coloring method used","MatColoringSetType",MatColoringList,deft,type,256,&flg);CHKERRQ(ierr);
if (flg) {
ierr = MatColoringSetType(mc,type);CHKERRQ(ierr);
} else if (!((PetscObject)mc)->type_name) {
ierr = MatColoringSetType(mc,deft);CHKERRQ(ierr);
}
ierr = PetscOptionsInt("-mat_coloring_distance","Distance of the coloring","MatColoringSetDistance",dist,&dist,&flg);CHKERRQ(ierr);
if (flg) {ierr = MatColoringSetDistance(mc,dist);CHKERRQ(ierr);}
ierr = PetscOptionsInt("-mat_coloring_maxcolors","Maximum colors returned at the end. 1 returns an independent set","MatColoringSetMaxColors",maxcolors,&maxcolors,&flg);CHKERRQ(ierr);
if (flg) {ierr = MatColoringSetMaxColors(mc,maxcolors);CHKERRQ(ierr);}
if (mc->ops->setfromoptions) {
ierr = (*mc->ops->setfromoptions)(mc);CHKERRQ(ierr);
}
ierr = PetscOptionsBool("-mat_coloring_valid","Check that a valid coloring has been produced","",mc->valid,&mc->valid,NULL);CHKERRQ(ierr);
ierr = PetscOptionsEnum("-mat_coloring_weight_type","Sets the type of vertex weighting used","MatColoringSetWeightType",MatColoringWeightTypes,(PetscEnum)mc->weight_type,(PetscEnum*)&mc->weight_type,NULL);CHKERRQ(ierr);
ierr = PetscObjectProcessOptionsHandlers((PetscObject)mc);CHKERRQ(ierr);
ierr = PetscOptionsEnd();CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PETSC_EXTERN PetscErrorCode MatColoringApply_Power(MatColoring mc,ISColoring *iscoloring)
{
PetscErrorCode ierr;
Mat m = mc->mat,mp,ms;
MatColoring imc;
PetscInt i;
const char *optionsprefix;
PetscFunctionBegin;
/* square the matrix repeatedly if necessary */
if (mc->dist == 1) {
mp = m;
} else {
ierr = MatMatMult(m,m,MAT_INITIAL_MATRIX,2.0,&mp);CHKERRQ(ierr);
for (i=2;i<mc->dist;i++) {
ms = mp;
ierr = MatMatMult(m,ms,MAT_INITIAL_MATRIX,2.0,&mp);CHKERRQ(ierr);
ierr = MatDestroy(&ms);CHKERRQ(ierr);
}
}
ierr = MatColoringCreate(mp,&imc);CHKERRQ(ierr);
ierr = PetscObjectGetOptionsPrefix((PetscObject)mc,&optionsprefix);CHKERRQ(ierr);
ierr = PetscObjectSetOptionsPrefix((PetscObject)imc,optionsprefix);CHKERRQ(ierr);
ierr = PetscObjectAppendOptionsPrefix((PetscObject)imc,"power_");CHKERRQ(ierr);
ierr = MatColoringSetType(imc,MATCOLORINGGREEDY);CHKERRQ(ierr);
ierr = MatColoringSetDistance(imc,1);CHKERRQ(ierr);
ierr = MatColoringSetWeightType(imc,mc->weight_type);CHKERRQ(ierr);
ierr = MatColoringSetFromOptions(imc);CHKERRQ(ierr);
ierr = MatColoringApply(imc,iscoloring);CHKERRQ(ierr);
ierr = MatColoringDestroy(&imc);CHKERRQ(ierr);
if (mp != m) {ierr = MatDestroy(&mp);CHKERRQ(ierr);}
PetscFunctionReturn(0);
}
PetscErrorCode SNESComputeJacobianDefaultColor(SNES snes,Vec x1,Mat J,Mat B,void *ctx)
{
MatFDColoring color = (MatFDColoring)ctx;
PetscErrorCode ierr;
DM dm;
MatColoring mc;
ISColoring iscoloring;
PetscBool hascolor;
PetscBool solvec,matcolor = PETSC_FALSE;
PetscFunctionBegin;
if (color) PetscValidHeaderSpecific(color,MAT_FDCOLORING_CLASSID,6);
if (!color) {ierr = PetscObjectQuery((PetscObject)B,"SNESMatFDColoring",(PetscObject*)&color);CHKERRQ(ierr);}
if (!color) {
ierr = SNESGetDM(snes,&dm);CHKERRQ(ierr);
ierr = DMHasColoring(dm,&hascolor);CHKERRQ(ierr);
matcolor = PETSC_FALSE;
ierr = PetscOptionsGetBool(((PetscObject)snes)->options,((PetscObject)snes)->prefix,"-snes_fd_color_use_mat",&matcolor,NULL);CHKERRQ(ierr);
if (hascolor && !matcolor) {
ierr = DMCreateColoring(dm,IS_COLORING_GLOBAL,&iscoloring);CHKERRQ(ierr);
ierr = MatFDColoringCreate(B,iscoloring,&color);CHKERRQ(ierr);
ierr = MatFDColoringSetFunction(color,(PetscErrorCode (*)(void))SNESComputeFunctionCtx,NULL);CHKERRQ(ierr);
ierr = MatFDColoringSetFromOptions(color);CHKERRQ(ierr);
ierr = MatFDColoringSetUp(B,iscoloring,color);CHKERRQ(ierr);
ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
} else {
ierr = MatColoringCreate(B,&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 = MatFDColoringCreate(B,iscoloring,&color);CHKERRQ(ierr);
ierr = MatFDColoringSetFunction(color,(PetscErrorCode (*)(void))SNESComputeFunctionCtx,NULL);CHKERRQ(ierr);
ierr = MatFDColoringSetFromOptions(color);CHKERRQ(ierr);
ierr = MatFDColoringSetUp(B,iscoloring,color);CHKERRQ(ierr);
ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
}
ierr = PetscObjectCompose((PetscObject)B,"SNESMatFDColoring",(PetscObject)color);CHKERRQ(ierr);
ierr = PetscObjectDereference((PetscObject)color);CHKERRQ(ierr);
}
/* F is only usable if there is no RHS on the SNES and the full solution corresponds to x1 */
ierr = VecEqual(x1,snes->vec_sol,&solvec);CHKERRQ(ierr);
if (!snes->vec_rhs && solvec) {
Vec F;
ierr = SNESGetFunction(snes,&F,NULL,NULL);CHKERRQ(ierr);
ierr = MatFDColoringSetF(color,F);CHKERRQ(ierr);
}
ierr = MatFDColoringApply(B,color,x1,snes);CHKERRQ(ierr);
if (J != B) {
ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
PetscErrorCode ierr;
PetscInt time_steps=100,iout,NOUT=1;
PetscMPIInt size;
Vec global;
PetscReal dt,ftime,ftime_original;
TS ts;
PetscViewer viewfile;
Mat J = 0;
Vec x;
Data data;
PetscInt mn;
PetscBool flg;
MatColoring mc;
ISColoring iscoloring;
MatFDColoring matfdcoloring = 0;
PetscBool fd_jacobian_coloring = PETSC_FALSE;
SNES snes;
KSP ksp;
PC pc;
PetscViewer viewer;
char pcinfo[120],tsinfo[120];
TSType tstype;
PetscBool sundials;
ierr = PetscInitialize(&argc,&argv,(char*)0,help);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
/* set data */
data.m = 9;
data.n = 9;
data.a = 1.0;
data.epsilon = 0.1;
data.dx = 1.0/(data.m+1.0);
data.dy = 1.0/(data.n+1.0);
mn = (data.m)*(data.n);
ierr = PetscOptionsGetInt(NULL,"-time",&time_steps,NULL);CHKERRQ(ierr);
/* set initial conditions */
ierr = VecCreate(PETSC_COMM_WORLD,&global);CHKERRQ(ierr);
ierr = VecSetSizes(global,PETSC_DECIDE,mn);CHKERRQ(ierr);
ierr = VecSetFromOptions(global);CHKERRQ(ierr);
ierr = Initial(global,&data);CHKERRQ(ierr);
ierr = VecDuplicate(global,&x);CHKERRQ(ierr);
/* create timestep context */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSMonitorSet(ts,Monitor,&data,NULL);CHKERRQ(ierr);
#if defined(PETSC_HAVE_SUNDIALS)
ierr = TSSetType(ts,TSSUNDIALS);CHKERRQ(ierr);
#else
ierr = TSSetType(ts,TSEULER);CHKERRQ(ierr);
#endif
dt = 0.1;
ftime_original = data.tfinal = 1.0;
ierr = TSSetInitialTimeStep(ts,0.0,dt);CHKERRQ(ierr);
ierr = TSSetDuration(ts,time_steps,ftime_original);CHKERRQ(ierr);
ierr = TSSetSolution(ts,global);CHKERRQ(ierr);
/* set user provided RHSFunction and RHSJacobian */
ierr = TSSetRHSFunction(ts,NULL,RHSFunction,&data);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&J);CHKERRQ(ierr);
ierr = MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,mn,mn);CHKERRQ(ierr);
ierr = MatSetFromOptions(J);CHKERRQ(ierr);
ierr = MatSeqAIJSetPreallocation(J,5,NULL);CHKERRQ(ierr);
ierr = MatMPIAIJSetPreallocation(J,5,NULL,5,NULL);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,"-ts_fd",&flg);CHKERRQ(ierr);
if (!flg) {
ierr = TSSetRHSJacobian(ts,J,J,RHSJacobian,&data);CHKERRQ(ierr);
} else {
ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,"-fd_color",&fd_jacobian_coloring);CHKERRQ(ierr);
if (fd_jacobian_coloring) { /* Use finite differences with coloring */
/* Get data structure of J */
PetscBool pc_diagonal;
ierr = PetscOptionsHasName(NULL,"-pc_diagonal",&pc_diagonal);CHKERRQ(ierr);
if (pc_diagonal) { /* the preconditioner of J is a diagonal matrix */
PetscInt rstart,rend,i;
PetscScalar zero=0.0;
ierr = MatGetOwnershipRange(J,&rstart,&rend);CHKERRQ(ierr);
for (i=rstart; i<rend; i++) {
ierr = MatSetValues(J,1,&i,1,&i,&zero,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
} else {
/* Fill the structure using the expensive SNESComputeJacobianDefault. Temporarily set up the TS so we can call this function */
ierr = TSSetType(ts,TSBEULER);CHKERRQ(ierr);
ierr = TSSetUp(ts);CHKERRQ(ierr);
ierr = SNESComputeJacobianDefault(snes,x,J,J,ts);CHKERRQ(ierr);
}
/* create coloring context */
ierr = MatColoringCreate(J,&mc);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 = MatFDColoringCreate(J,iscoloring,&matfdcoloring);CHKERRQ(ierr);
ierr = MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))SNESTSFormFunction,ts);CHKERRQ(ierr);
ierr = MatFDColoringSetFromOptions(matfdcoloring);CHKERRQ(ierr);
ierr = MatFDColoringSetUp(J,iscoloring,matfdcoloring);CHKERRQ(ierr);
ierr = SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring);CHKERRQ(ierr);
ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
} else { /* Use finite differences (slow) */
ierr = SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,NULL);CHKERRQ(ierr);
}
}
/* Pick up a Petsc preconditioner */
/* one can always set method or preconditioner during the run time */
ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
ierr = SNESGetKSP(snes,&ksp);CHKERRQ(ierr);
ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
ierr = PCSetType(pc,PCJACOBI);CHKERRQ(ierr);
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
ierr = TSSetUp(ts);CHKERRQ(ierr);
/* Test TSSetPostStep() */
ierr = PetscOptionsHasName(NULL,"-test_PostStep",&flg);CHKERRQ(ierr);
if (flg) {
ierr = TSSetPostStep(ts,PostStep);CHKERRQ(ierr);
}
ierr = PetscOptionsGetInt(NULL,"-NOUT",&NOUT,NULL);CHKERRQ(ierr);
for (iout=1; iout<=NOUT; iout++) {
ierr = TSSetDuration(ts,time_steps,iout*ftime_original/NOUT);CHKERRQ(ierr);
ierr = TSSolve(ts,global);CHKERRQ(ierr);
ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,ftime,dt);CHKERRQ(ierr);
}
/* Interpolate solution at tfinal */
ierr = TSGetSolution(ts,&global);CHKERRQ(ierr);
ierr = TSInterpolate(ts,ftime_original,global);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,"-matlab_view",&flg);CHKERRQ(ierr);
if (flg) { /* print solution into a MATLAB file */
ierr = PetscViewerASCIIOpen(PETSC_COMM_WORLD,"out.m",&viewfile);CHKERRQ(ierr);
ierr = PetscViewerSetFormat(viewfile,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
ierr = VecView(global,viewfile);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewfile);CHKERRQ(ierr);
}
/* display solver info for Sundials */
ierr = TSGetType(ts,&tstype);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)ts,TSSUNDIALS,&sundials);CHKERRQ(ierr);
if (sundials) {
ierr = PetscViewerStringOpen(PETSC_COMM_WORLD,tsinfo,120,&viewer);CHKERRQ(ierr);
ierr = TSView(ts,viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
ierr = PetscViewerStringOpen(PETSC_COMM_WORLD,pcinfo,120,&viewer);CHKERRQ(ierr);
ierr = PCView(pc,viewer);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"%d Procs,%s TSType, %s Preconditioner\n",size,tsinfo,pcinfo);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
}
/* free the memories */
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = VecDestroy(&global);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = MatDestroy(&J);CHKERRQ(ierr);
if (fd_jacobian_coloring) {ierr = MatFDColoringDestroy(&matfdcoloring);CHKERRQ(ierr);}
ierr = PetscFinalize();
return 0;
}
void
NonlinearSystem::setupColoringFiniteDifferencedPreconditioner()
{
#ifdef LIBMESH_HAVE_PETSC
// Make sure that libMesh isn't going to override our preconditioner
_transient_sys.nonlinear_solver->jacobian = nullptr;
PetscNonlinearSolver<Number> & petsc_nonlinear_solver =
dynamic_cast<PetscNonlinearSolver<Number> &>(*_transient_sys.nonlinear_solver);
// Pointer to underlying PetscMatrix type
PetscMatrix<Number> * petsc_mat = dynamic_cast<PetscMatrix<Number> *>(_transient_sys.matrix);
#if PETSC_VERSION_LESS_THAN(3, 2, 0)
// This variable is only needed for PETSC < 3.2.0
PetscVector<Number> * petsc_vec =
dynamic_cast<PetscVector<Number> *>(_transient_sys.solution.get());
#endif
Moose::compute_jacobian(*_transient_sys.current_local_solution, *petsc_mat, _transient_sys);
if (!petsc_mat)
mooseError("Could not convert to Petsc matrix.");
petsc_mat->close();
PetscErrorCode ierr = 0;
ISColoring iscoloring;
#if PETSC_VERSION_LESS_THAN(3, 2, 0)
// PETSc 3.2.x
ierr = MatGetColoring(petsc_mat->mat(), MATCOLORING_LF, &iscoloring);
CHKERRABORT(libMesh::COMM_WORLD, ierr);
#elif PETSC_VERSION_LESS_THAN(3, 5, 0)
// PETSc 3.3.x, 3.4.x
ierr = MatGetColoring(petsc_mat->mat(), MATCOLORINGLF, &iscoloring);
CHKERRABORT(_communicator.get(), ierr);
#else
// PETSc 3.5.x
MatColoring matcoloring;
ierr = MatColoringCreate(petsc_mat->mat(), &matcoloring);
CHKERRABORT(_communicator.get(), ierr);
ierr = MatColoringSetType(matcoloring, MATCOLORINGLF);
CHKERRABORT(_communicator.get(), ierr);
ierr = MatColoringSetFromOptions(matcoloring);
CHKERRABORT(_communicator.get(), ierr);
ierr = MatColoringApply(matcoloring, &iscoloring);
CHKERRABORT(_communicator.get(), ierr);
ierr = MatColoringDestroy(&matcoloring);
CHKERRABORT(_communicator.get(), ierr);
#endif
MatFDColoringCreate(petsc_mat->mat(), iscoloring, &_fdcoloring);
MatFDColoringSetFromOptions(_fdcoloring);
MatFDColoringSetFunction(_fdcoloring,
(PetscErrorCode(*)(void)) & libMesh::__libmesh_petsc_snes_fd_residual,
&petsc_nonlinear_solver);
#if !PETSC_RELEASE_LESS_THAN(3, 5, 0)
MatFDColoringSetUp(petsc_mat->mat(), iscoloring, _fdcoloring);
#endif
#if PETSC_VERSION_LESS_THAN(3, 4, 0)
SNESSetJacobian(petsc_nonlinear_solver.snes(),
petsc_mat->mat(),
petsc_mat->mat(),
SNESDefaultComputeJacobianColor,
_fdcoloring);
#else
SNESSetJacobian(petsc_nonlinear_solver.snes(),
petsc_mat->mat(),
petsc_mat->mat(),
SNESComputeJacobianDefaultColor,
_fdcoloring);
#endif
#if PETSC_VERSION_LESS_THAN(3, 2, 0)
Mat my_mat = petsc_mat->mat();
MatStructure my_struct;
SNESComputeJacobian(
petsc_nonlinear_solver.snes(), petsc_vec->vec(), &my_mat, &my_mat, &my_struct);
#endif
#if PETSC_VERSION_LESS_THAN(3, 2, 0)
ISColoringDestroy(iscoloring);
#else
// PETSc 3.3.0
ISColoringDestroy(&iscoloring);
#endif
#endif
}
PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ_colorrart(Mat A,Mat R,PetscReal fill,Mat *C)
{
PetscErrorCode ierr;
Mat P;
PetscInt *rti,*rtj;
Mat_RARt *rart;
MatColoring coloring;
MatTransposeColoring matcoloring;
ISColoring iscoloring;
Mat Rt_dense,RARt_dense;
Mat_SeqAIJ *c;
PetscFunctionBegin;
/* create symbolic P=Rt */
ierr = MatGetSymbolicTranspose_SeqAIJ(R,&rti,&rtj);CHKERRQ(ierr);
ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,R->cmap->n,R->rmap->n,rti,rtj,NULL,&P);CHKERRQ(ierr);
/* get symbolic C=Pt*A*P */
ierr = MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);CHKERRQ(ierr);
ierr = MatSetBlockSizes(*C,PetscAbs(R->rmap->bs),PetscAbs(R->rmap->bs));CHKERRQ(ierr);
(*C)->ops->rartnumeric = MatRARtNumeric_SeqAIJ_SeqAIJ_colorrart;
/* create a supporting struct */
ierr = PetscNew(&rart);CHKERRQ(ierr);
c = (Mat_SeqAIJ*)(*C)->data;
c->rart = rart;
/* ------ Use coloring ---------- */
/* inode causes memory problem, don't know why */
if (c->inode.use) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MAT_USE_INODES is not supported. Use '-mat_no_inode'");
/* Create MatTransposeColoring from symbolic C=R*A*R^T */
ierr = MatColoringCreate(*C,&coloring);CHKERRQ(ierr);
ierr = MatColoringSetDistance(coloring,2);CHKERRQ(ierr);
ierr = MatColoringSetType(coloring,MATCOLORINGSL);CHKERRQ(ierr);
ierr = MatColoringSetFromOptions(coloring);CHKERRQ(ierr);
ierr = MatColoringApply(coloring,&iscoloring);CHKERRQ(ierr);
ierr = MatColoringDestroy(&coloring);CHKERRQ(ierr);
ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
rart->matcoloring = matcoloring;
ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
/* Create Rt_dense */
ierr = MatCreate(PETSC_COMM_SELF,&Rt_dense);CHKERRQ(ierr);
ierr = MatSetSizes(Rt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
ierr = MatSetType(Rt_dense,MATSEQDENSE);CHKERRQ(ierr);
ierr = MatSeqDenseSetPreallocation(Rt_dense,NULL);CHKERRQ(ierr);
Rt_dense->assembled = PETSC_TRUE;
rart->Rt = Rt_dense;
/* Create RARt_dense = R*A*Rt_dense */
ierr = MatCreate(PETSC_COMM_SELF,&RARt_dense);CHKERRQ(ierr);
ierr = MatSetSizes(RARt_dense,(*C)->rmap->n,matcoloring->ncolors,(*C)->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
ierr = MatSetType(RARt_dense,MATSEQDENSE);CHKERRQ(ierr);
ierr = MatSeqDenseSetPreallocation(RARt_dense,NULL);CHKERRQ(ierr);
rart->RARt = RARt_dense;
/* Allocate work array to store columns of A*R^T used in MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqDense() */
ierr = PetscMalloc1(A->rmap->n*4,&rart->work);CHKERRQ(ierr);
rart->destroy = (*C)->ops->destroy;
(*C)->ops->destroy = MatDestroy_SeqAIJ_RARt;
/* clean up */
ierr = MatRestoreSymbolicTranspose_SeqAIJ(R,&rti,&rtj);CHKERRQ(ierr);
ierr = MatDestroy(&P);CHKERRQ(ierr);
#if defined(PETSC_USE_INFO)
{
PetscReal density= (PetscReal)(c->nz)/(RARt_dense->rmap->n*RARt_dense->cmap->n);
ierr = PetscInfo(*C,"C=R*(A*Rt) via coloring C - use sparse-dense inner products\n");CHKERRQ(ierr);
ierr = PetscInfo6(*C,"RARt_den %D %D; Rt %D %D (RARt->nz %D)/(m*ncolors)=%g\n",RARt_dense->rmap->n,RARt_dense->cmap->n,R->cmap->n,R->rmap->n,c->nz,density);CHKERRQ(ierr);
}
#endif
PetscFunctionReturn(0);
}
