static PetscErrorCode TestMatrix(Mat A,Vec X,Vec Y,Vec Z)
{
PetscErrorCode ierr;
Vec W1,W2;
Mat E;
const char *mattypename;
PetscViewer viewer = PETSC_VIEWER_STDOUT_WORLD;
PetscFunctionBegin;
ierr = VecDuplicate(X,&W1);
CHKERRQ(ierr);
ierr = VecDuplicate(X,&W2);
CHKERRQ(ierr);
ierr = MatScale(A,31);
CHKERRQ(ierr);
ierr = MatShift(A,37);
CHKERRQ(ierr);
ierr = MatDiagonalScale(A,X,Y);
CHKERRQ(ierr);
ierr = MatScale(A,41);
CHKERRQ(ierr);
ierr = MatDiagonalScale(A,Y,Z);
CHKERRQ(ierr);
ierr = MatComputeExplicitOperator(A,&E);
CHKERRQ(ierr);
ierr = PetscObjectGetType((PetscObject)A,&mattypename);
CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"Matrix of type: %s\n",mattypename);
CHKERRQ(ierr);
ierr = MatView(E,viewer);
CHKERRQ(ierr);
ierr = MatMult(A,Z,W1);
CHKERRQ(ierr);
ierr = MatMultTranspose(A,W1,W2);
CHKERRQ(ierr);
ierr = VecView(W2,viewer);
CHKERRQ(ierr);
ierr = MatGetDiagonal(A,W2);
CHKERRQ(ierr);
ierr = VecView(W2,viewer);
CHKERRQ(ierr);
ierr = MatDestroy(&E);
CHKERRQ(ierr);
ierr = VecDestroy(&W1);
CHKERRQ(ierr);
ierr = VecDestroy(&W2);
CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode StokesSetupApproxSchur(Stokes *s)
{
Vec diag;
PetscErrorCode ierr;
PetscFunctionBeginUser;
/* Schur complement approximation: myS = A11 - A10 diag(A00)^(-1) A01 */
/* note: A11 is zero */
/* note: in real life this matrix would be build directly, */
/* i.e. without MatMatMult */
/* inverse of diagonal of A00 */
ierr = VecCreate(PETSC_COMM_WORLD,&diag);CHKERRQ(ierr);
ierr = VecSetSizes(diag,PETSC_DECIDE,2*s->nx*s->ny);CHKERRQ(ierr);
ierr = VecSetType(diag,VECMPI);CHKERRQ(ierr);
ierr = MatGetDiagonal(s->subA[0],diag);
ierr = VecReciprocal(diag);
/* compute: - A10 diag(A00)^(-1) A01 */
ierr = MatDiagonalScale(s->subA[1],diag,NULL); /* (*warning* overwrites subA[1]) */
ierr = MatMatMult(s->subA[2],s->subA[1],MAT_INITIAL_MATRIX,PETSC_DEFAULT,&s->myS);CHKERRQ(ierr);
ierr = MatScale(s->myS,-1.0);CHKERRQ(ierr);
/* restore A10 */
ierr = MatGetDiagonal(s->subA[0],diag);
ierr = MatDiagonalScale(s->subA[1],diag,NULL);
ierr = VecDestroy(&diag);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
// Create a translation matrix
static void MatTranslate(Matrix44 &dest,sF32 tx,sF32 ty,sF32 tz)
{
MatScale(dest,1.0f,1.0f,1.0f);
dest[3][0] = tx;
dest[3][1] = ty;
dest[3][2] = tz;
}
PetscErrorCode TSPrecond_Sundials(realtype tn,N_Vector y,N_Vector fy,booleantype jok,booleantype *jcurPtr,
realtype _gamma,void *P_data,N_Vector vtemp1,N_Vector vtemp2,N_Vector vtemp3)
{
TS ts = (TS) P_data;
TS_Sundials *cvode = (TS_Sundials*)ts->data;
PC pc;
PetscErrorCode ierr;
Mat J,P;
Vec yy = cvode->w1,yydot = cvode->ydot;
PetscReal gm = (PetscReal)_gamma;
MatStructure str = DIFFERENT_NONZERO_PATTERN;
PetscScalar *y_data;
PetscFunctionBegin;
ierr = TSGetIJacobian(ts,&J,&P,NULL,NULL);CHKERRQ(ierr);
y_data = (PetscScalar*) N_VGetArrayPointer(y);
ierr = VecPlaceArray(yy,y_data);CHKERRQ(ierr);
ierr = VecZeroEntries(yydot);CHKERRQ(ierr); /* The Jacobian is independent of Ydot for ODE which is all that CVode works for */
/* compute the shifted Jacobian (1/gm)*I + Jrest */
ierr = TSComputeIJacobian(ts,ts->ptime,yy,yydot,1/gm,&J,&P,&str,PETSC_FALSE);CHKERRQ(ierr);
ierr = VecResetArray(yy);CHKERRQ(ierr);
ierr = MatScale(P,gm);CHKERRQ(ierr); /* turn into I-gm*Jrest, J is not used by Sundials */
*jcurPtr = TRUE;
ierr = TSSundialsGetPC(ts,&pc);CHKERRQ(ierr);
ierr = PCSetOperators(pc,J,P,str);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
void Field_solver::construct_equation_matrix_in_full_domain( Mat *A,
int nx, int ny, int nz,
double dx, double dy, double dz,
PetscInt nlocal, PetscInt rstart, PetscInt rend )
{
PetscErrorCode ierr;
Mat d2dy2, d2dz2;
int nrow = ( nx - 2 ) * ( ny - 2 ) * ( nz - 2 );
int ncol = nrow;
PetscInt nonzero_per_row = 7; // approx
construct_d2dx2_in_3d( A, nx, ny, nz, rstart, rend );
ierr = MatScale( *A, dy * dy * dz * dz ); CHKERRXX( ierr );
alloc_petsc_matrix( &d2dy2, nlocal, nlocal, nrow, ncol, nonzero_per_row );
construct_d2dy2_in_3d( &d2dy2, nx, ny, nz, rstart, rend );
ierr = MatAXPY( *A, dx * dx * dz * dz, d2dy2, DIFFERENT_NONZERO_PATTERN ); CHKERRXX( ierr );
ierr = MatDestroy( &d2dy2 ); CHKERRXX( ierr );
alloc_petsc_matrix( &d2dz2, nlocal, nlocal, nrow, ncol, nonzero_per_row );
construct_d2dz2_in_3d( &d2dz2, nx, ny, nz, rstart, rend );
ierr = MatAXPY( *A, dx * dx * dy * dy, d2dz2, DIFFERENT_NONZERO_PATTERN ); CHKERRXX( ierr );
ierr = MatDestroy( &d2dz2 ); CHKERRXX( ierr );
return;
}
PetscErrorCode CalcMat(FEMInf fem, int L, Mat *H, Mat *S) {
PetscErrorCode ierr;
char label[10]; sprintf(label, "L+%d", L);
PrintTimeStamp(fem->comm, label, NULL);
FEMInfCreateMat(fem, 1, H);
FEMInfCreateMat(fem, 1, S);
PetscBool s_is_id; FEMInfGetOverlapIsId(fem, &s_is_id);
if(s_is_id)
S = NULL;
else {
ierr = FEMInfSR1Mat(fem, *S); CHKERRQ(ierr); CHKERRQ(ierr);
}
ierr = FEMInfD2R1Mat(fem, *H); CHKERRQ(ierr);
MatScale(*H, -0.5);
if(L != 0) {
Mat A;
FEMInfCreateMat(fem, 1, &A);
ierr = FEMInfR2invR1Mat(fem, A); CHKERRQ(ierr);
MatAXPY(*H, 0.5*L*(L+1), A, DIFFERENT_NONZERO_PATTERN);
}
Mat V;
FEMInfCreateMat(fem, 1, &V);
FEMInfENR1Mat(fem, 0, 0.0, V);
MatAXPY(*H, -1.0, V, DIFFERENT_NONZERO_PATTERN);
return 0;
}
static PetscErrorCode CheckMatrices(Mat A,Mat B,Vec left,Vec right,Vec X,Vec Y,Vec X1,Vec Y1)
{
PetscErrorCode ierr;
Vec *ltmp,*rtmp;
PetscFunctionBegin;
ierr = VecDuplicateVecs(right,2,&rtmp);CHKERRQ(ierr);
ierr = VecDuplicateVecs(left,2,<mp);CHKERRQ(ierr);
ierr = MatScale(A,PETSC_PI);CHKERRQ(ierr);
ierr = MatScale(B,PETSC_PI);CHKERRQ(ierr);
ierr = MatDiagonalScale(A,left,right);CHKERRQ(ierr);
ierr = MatDiagonalScale(B,left,right);CHKERRQ(ierr);
ierr = MatMult(A,X,ltmp[0]);CHKERRQ(ierr);
ierr = MatMult(B,X,ltmp[1]);CHKERRQ(ierr);
ierr = Compare2(ltmp,"MatMult");CHKERRQ(ierr);
ierr = MatMultTranspose(A,Y,rtmp[0]);CHKERRQ(ierr);
ierr = MatMultTranspose(B,Y,rtmp[1]);CHKERRQ(ierr);
ierr = Compare2(rtmp,"MatMultTranspose");CHKERRQ(ierr);
ierr = VecCopy(Y1,ltmp[0]);CHKERRQ(ierr);
ierr = VecCopy(Y1,ltmp[1]);CHKERRQ(ierr);
ierr = MatMultAdd(A,X,ltmp[0],ltmp[0]);CHKERRQ(ierr);
ierr = MatMultAdd(B,X,ltmp[1],ltmp[1]);CHKERRQ(ierr);
ierr = Compare2(ltmp,"MatMultAdd v2==v3");CHKERRQ(ierr);
ierr = MatMultAdd(A,X,Y1,ltmp[0]);CHKERRQ(ierr);
ierr = MatMultAdd(B,X,Y1,ltmp[1]);CHKERRQ(ierr);
ierr = Compare2(ltmp,"MatMultAdd v2!=v3");CHKERRQ(ierr);
ierr = VecCopy(X1,rtmp[0]);CHKERRQ(ierr);
ierr = VecCopy(X1,rtmp[1]);CHKERRQ(ierr);
ierr = MatMultTransposeAdd(A,Y,rtmp[0],rtmp[0]);CHKERRQ(ierr);
ierr = MatMultTransposeAdd(B,Y,rtmp[1],rtmp[1]);CHKERRQ(ierr);
ierr = Compare2(rtmp,"MatMultTransposeAdd v2==v3");CHKERRQ(ierr);
ierr = MatMultTransposeAdd(A,Y,X1,rtmp[0]);CHKERRQ(ierr);
ierr = MatMultTransposeAdd(B,Y,X1,rtmp[1]);CHKERRQ(ierr);
ierr = Compare2(rtmp,"MatMultTransposeAdd v2!=v3");CHKERRQ(ierr);
ierr = VecDestroyVecs(2,<mp);CHKERRQ(ierr);
ierr = VecDestroyVecs(2,&rtmp);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode NEPSolve_Interpol(NEP nep)
{
PetscErrorCode ierr;
NEP_INTERPOL *ctx = (NEP_INTERPOL*)nep->data;
Mat *A; /*T=nep->function,Tp=nep->jacobian;*/
PetscScalar *x,*fx,t;
PetscReal *cs,a,b,s;
PetscInt i,j,k,deg=ctx->deg;
PetscFunctionBegin;
ierr = PetscMalloc4(deg+1,&A,(deg+1)*(deg+1),&cs,deg+1,&x,(deg+1)*nep->nt,&fx);CHKERRQ(ierr);
ierr = RGIntervalGetEndpoints(nep->rg,&a,&b,NULL,NULL);CHKERRQ(ierr);
ierr = ChebyshevNodes(deg,a,b,x,cs);CHKERRQ(ierr);
for (j=0;j<nep->nt;j++) {
for (i=0;i<=deg;i++) {
ierr = FNEvaluateFunction(nep->f[j],x[i],&fx[i+j*(deg+1)]);CHKERRQ(ierr);
}
}
/* Polynomial coefficients */
for (k=0;k<=deg;k++) {
ierr = MatDuplicate(nep->A[0],MAT_COPY_VALUES,&A[k]);CHKERRQ(ierr);
t = 0.0;
for (i=0;i<deg+1;i++) t += fx[i]*cs[i*(deg+1)+k];
t *= 2.0/(deg+1);
if (k==0) t /= 2.0;
ierr = MatScale(A[k],t);CHKERRQ(ierr);
for (j=1;j<nep->nt;j++) {
t = 0.0;
for (i=0;i<deg+1;i++) t += fx[i+j*(deg+1)]*cs[i*(deg+1)+k];
t *= 2.0/(deg+1);
if (k==0) t /= 2.0;
ierr = MatAXPY(A[k],t,nep->A[j],SUBSET_NONZERO_PATTERN);CHKERRQ(ierr);
}
}
ierr = PEPSetOperators(ctx->pep,deg+1,A);CHKERRQ(ierr);
for (k=0;k<=deg;k++) {
ierr = MatDestroy(&A[k]);CHKERRQ(ierr);
}
ierr = PetscFree4(A,cs,x,fx);CHKERRQ(ierr);
/* Solve polynomial eigenproblem */
ierr = PEPSolve(ctx->pep);CHKERRQ(ierr);
ierr = PEPGetConverged(ctx->pep,&nep->nconv);CHKERRQ(ierr);
ierr = PEPGetIterationNumber(ctx->pep,&nep->its);CHKERRQ(ierr);
ierr = PEPGetConvergedReason(ctx->pep,(PEPConvergedReason*)&nep->reason);CHKERRQ(ierr);
s = 2.0/(b-a);
for (i=0;i<nep->nconv;i++) {
ierr = PEPGetEigenpair(ctx->pep,i,&nep->eigr[i],&nep->eigi[i],NULL,NULL);CHKERRQ(ierr);
nep->eigr[i] /= s;
nep->eigr[i] += (a+b)/2.0;
nep->eigi[i] /= s;
}
nep->state = NEP_STATE_EIGENVECTORS;
PetscFunctionReturn(0);
}
PetscErrorCode MatScale_IS(Mat A,PetscScalar a)
{
Mat_IS *is = (Mat_IS*)A->data;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = MatScale(is->A,a);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode MatScale_SMF(Mat mat, PetscReal a)
{
PetscErrorCode ierr;
MatSubMatFreeCtx ctx;
PetscFunctionBegin;
ierr = MatShellGetContext(mat,(void **)&ctx);CHKERRQ(ierr);
ierr = MatScale(ctx->A,a);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
// Create a z-axis rotation matrix
static void MatRotateZ(Matrix44 &dest,sF32 angle)
{
sF32 s = sFSin(angle);
sF32 c = sFCos(angle);
MatScale(dest,1.0f,1.0f,1.0f);
dest[0][0] = c;
dest[0][1] = s;
dest[1][0] = -s;
dest[1][1] = c;
}
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);
}
int main(int argc,char **args)
{
const PetscScalar xvals[] = {11,13},yvals[] = {17,19};
const PetscInt inds[] = {0,1};
PetscScalar avals[] = {2,3,5,7};
Mat S1,S2;
Vec X,Y;
User user;
PetscErrorCode ierr;
ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
ierr = PetscNew(&user);CHKERRQ(ierr);
ierr = MatCreateSeqAIJ(PETSC_COMM_WORLD,2,2,2,NULL,&user->A);CHKERRQ(ierr);
ierr = MatSetUp(user->A);CHKERRQ(ierr);
ierr = MatSetValues(user->A,2,inds,2,inds,avals,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(user->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(user->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_WORLD,2,&X);CHKERRQ(ierr);
ierr = VecSetValues(X,2,inds,xvals,INSERT_VALUES);CHKERRQ(ierr);
ierr = VecAssemblyBegin(X);CHKERRQ(ierr);
ierr = VecAssemblyEnd(X);CHKERRQ(ierr);
ierr = VecDuplicate(X,&Y);CHKERRQ(ierr);
ierr = VecSetValues(Y,2,inds,yvals,INSERT_VALUES);CHKERRQ(ierr);
ierr = VecAssemblyBegin(Y);CHKERRQ(ierr);
ierr = VecAssemblyEnd(Y);CHKERRQ(ierr);
ierr = MatCreateShell(PETSC_COMM_WORLD,2,2,2,2,user,&S1);CHKERRQ(ierr);
ierr = MatSetUp(S1);CHKERRQ(ierr);
ierr = MatShellSetOperation(S1,MATOP_MULT,(void (*)(void))MatMult_User);CHKERRQ(ierr);
ierr = MatShellSetOperation(S1,MATOP_COPY,(void (*)(void))MatCopy_User);CHKERRQ(ierr);
ierr = MatShellSetOperation(S1,MATOP_DESTROY,(void (*)(void))MatDestroy_User);CHKERRQ(ierr);
ierr = MatCreateShell(PETSC_COMM_WORLD,2,2,2,2,NULL,&S2);CHKERRQ(ierr);
ierr = MatSetUp(S2);CHKERRQ(ierr);
ierr = MatShellSetOperation(S2,MATOP_MULT,(void (*)(void))MatMult_User);CHKERRQ(ierr);
ierr = MatShellSetOperation(S2,MATOP_COPY,(void (*)(void))MatCopy_User);CHKERRQ(ierr);
ierr = MatShellSetOperation(S2,MATOP_DESTROY,(void (*)(void))MatDestroy_User);CHKERRQ(ierr);
ierr = MatScale(S1,31);CHKERRQ(ierr);
ierr = MatShift(S1,37);CHKERRQ(ierr);
ierr = MatDiagonalScale(S1,X,Y);CHKERRQ(ierr);
ierr = MatCopy(S1,S2,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatMult(S1,X,Y);CHKERRQ(ierr);
ierr = VecView(Y,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = MatMult(S2,X,Y);CHKERRQ(ierr);
ierr = VecView(Y,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = MatDestroy(&S1);CHKERRQ(ierr);
ierr = MatDestroy(&S2);CHKERRQ(ierr);
ierr = VecDestroy(&X);CHKERRQ(ierr);
ierr = VecDestroy(&Y);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int testSlaterPotWithECS() {
PrintTimeStamp(PETSC_COMM_SELF, "ECS", NULL);
MPI_Comm comm = PETSC_COMM_SELF;
BPS bps; BPSCreate(comm, &bps); BPSSetLine(bps, 100.0, 101);
CScaling scaler; CScalingCreate(comm, &scaler);
CScalingSetSharpECS(scaler, 60.0, 20.0*M_PI/180.0);
int order = 5;
BSS bss; BSSCreate(comm, &bss); BSSSetKnots(bss, order, bps);
BSSSetCScaling(bss, scaler); BSSSetUp(bss);
Pot slater; PotCreate(comm, &slater); PotSetSlater(slater, 7.5, 2, 1.0);
if(getenv("SHOW_DEBUG"))
BSSView(bss, PETSC_VIEWER_STDOUT_SELF);
Mat H; BSSCreateR1Mat(bss, &H);
Mat V; BSSCreateR1Mat(bss, &V); BSSPotR1Mat(bss, slater, V);
Mat S; BSSCreateR1Mat(bss, &S); BSSSR1Mat(bss, S);
BSSD2R1Mat(bss, H);
MatScale(H, -0.5);
MatAXPY(H, 1.0, V, DIFFERENT_NONZERO_PATTERN);
EEPS eps; EEPSCreate(comm, &eps);
EEPSSetOperators(eps, H, S);
EEPSSetTarget(eps, 3.4);
EPSSetDimensions(eps->eps, 10, PETSC_DEFAULT, PETSC_DEFAULT);
EPSSetTolerances(eps->eps, PETSC_DEFAULT, 1000);
// EPSSetType(eps, EPSARNOLDI);
EEPSSolve(eps);
PetscInt nconv;
PetscScalar kr;
EPSGetConverged(eps->eps, &nconv);
ASSERT_TRUE(nconv > 0);
if(getenv("SHOW_DEBUG"))
for(int i = 0; i < nconv; i++) {
EPSGetEigenpair(eps->eps, i, &kr, NULL, NULL, NULL);
PetscPrintf(comm, "%f, %f\n", PetscRealPart(kr), PetscImaginaryPart(kr));
}
EPSGetEigenpair(eps->eps, 0, &kr, NULL, NULL, NULL);
PFDestroy(&slater); BSSDestroy(&bss); EEPSDestroy(&eps);
MatDestroy(&H); MatDestroy(&V); MatDestroy(&S);
// ASSERT_DOUBLE_NEAR(-0.0127745, PetscImaginaryPart(kr), pow(10.0, -4.0));
// ASSERT_DOUBLE_NEAR(3.4263903, PetscRealPart(kr), pow(10.0, -4.0));
return 0;
}
/*@
MatSchurComplementComputeExplicitOperator - Compute the Schur complement matrix explicitly
Collective on Mat
Input Parameter:
. M - the matrix obtained with MatCreateSchurComplement()
Output Parameter:
. S - the Schur complement matrix
Note: This can be expensive, so it is mainly for testing
Level: advanced
.seealso: MatCreateSchurComplement(), MatSchurComplementUpdate()
@*/
PetscErrorCode MatSchurComplementComputeExplicitOperator(Mat M, Mat *S)
{
Mat B, C, D;
KSP ksp;
PC pc;
PetscBool isLU, isILU;
PetscReal fill = 2.0;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = MatSchurComplementGetSubMatrices(M, NULL, NULL, &B, &C, &D);CHKERRQ(ierr);
ierr = MatSchurComplementGetKSP(M, &ksp);CHKERRQ(ierr);
ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject) pc, PCLU, &isLU);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject) pc, PCILU, &isILU);CHKERRQ(ierr);
if (isLU || isILU) {
Mat fact, Bd, AinvB, AinvBd;
PetscReal eps = 1.0e-10;
/* This can be sped up for banded LU */
ierr = KSPSetUp(ksp);CHKERRQ(ierr);
ierr = PCFactorGetMatrix(pc, &fact);CHKERRQ(ierr);
ierr = MatConvert(B, MATDENSE, MAT_INITIAL_MATRIX, &Bd);CHKERRQ(ierr);
ierr = MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);CHKERRQ(ierr);
ierr = MatMatSolve(fact, Bd, AinvBd);CHKERRQ(ierr);
ierr = MatDestroy(&Bd);CHKERRQ(ierr);
ierr = MatChop(AinvBd, eps);CHKERRQ(ierr);
ierr = MatConvert(AinvBd, MATAIJ, MAT_INITIAL_MATRIX, &AinvB);CHKERRQ(ierr);
ierr = MatDestroy(&AinvBd);CHKERRQ(ierr);
ierr = MatMatMult(C, AinvB, MAT_INITIAL_MATRIX, fill, S);CHKERRQ(ierr);
ierr = MatDestroy(&AinvB);CHKERRQ(ierr);
} else {
Mat Ainvd, Ainv;
ierr = PCComputeExplicitOperator(pc, &Ainvd);CHKERRQ(ierr);
ierr = MatConvert(Ainvd, MATAIJ, MAT_INITIAL_MATRIX, &Ainv);CHKERRQ(ierr);
ierr = MatDestroy(&Ainvd);CHKERRQ(ierr);
#if 0
/* Symmetric version */
ierr = MatPtAP(Ainv, B, MAT_INITIAL_MATRIX, fill, S);CHKERRQ(ierr);
#else
/* Nonsymmetric version */
ierr = MatMatMatMult(C, Ainv, B, MAT_INITIAL_MATRIX, fill, S);CHKERRQ(ierr);
#endif
ierr = MatDestroy(&Ainv);CHKERRQ(ierr);
}
if (D) {
ierr = MatAXPY(*S, -1.0, D, DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
}
ierr = MatScale(*S,-1.0);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*@
MatCreateSchurComplementPmat - create a preconditioning matrix for the Schur complement by assembling Sp = A11 - A10 inv(diag(A00)) A01
Collective on Mat
Input Parameters:
+ A00,A01,A10,A11 - the four parts of the original matrix A = [A00 A01; A10 A11] (A01,A10, and A11 are optional, implying zero matrices)
. ainvtype - type of approximation for inv(A00) used when forming Sp = A11 - A10 inv(A00) A01
- preuse - MAT_INITIAL_MATRIX for a new Sp, or MAT_REUSE_MATRIX to reuse an existing Sp, or MAT_IGNORE_MATRIX to put nothing in Sp
Output Parameter:
- Spmat - approximate Schur complement suitable for preconditioning S = A11 - A10 inv(diag(A00)) A01
Note:
Since the real Schur complement is usually dense, providing a good approximation to newpmat usually requires
application-specific information. The default for assembled matrices is to use the inverse of the diagonal of
the (0,0) block A00 in place of A00^{-1}. This rarely produce a scalable algorithm. Optionally, A00 can be lumped
before forming inv(diag(A00)).
Level: advanced
Concepts: matrices^submatrices
.seealso: MatCreateSchurComplement(), MatGetSchurComplement(), MatSchurComplementGetPmat(), MatSchurComplementAinvType
@*/
PetscErrorCode MatCreateSchurComplementPmat(Mat A00,Mat A01,Mat A10,Mat A11,MatSchurComplementAinvType ainvtype,MatReuse preuse,Mat *Spmat)
{
PetscErrorCode ierr;
PetscInt N00;
PetscFunctionBegin;
/* Use an appropriate approximate inverse of A00 to form A11 - A10 inv(diag(A00)) A01; a NULL A01, A10 or A11 indicates a zero matrix. */
/* TODO: Perhaps should create an appropriately-sized zero matrix of the same type as A00? */
if ((!A01 || !A10) & !A11) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot assemble Spmat: A01, A10 and A11 are all NULL.");
if (preuse == MAT_IGNORE_MATRIX) PetscFunctionReturn(0);
/* A zero size A00 or empty A01 or A10 imply S = A11. */
ierr = MatGetSize(A00,&N00,NULL);CHKERRQ(ierr);
if (!A01 || !A10 || !N00) {
if (preuse == MAT_INITIAL_MATRIX) {
ierr = MatDuplicate(A11,MAT_COPY_VALUES,Spmat);CHKERRQ(ierr);
} else { /* MAT_REUSE_MATRIX */
/* TODO: when can we pass SAME_NONZERO_PATTERN? */
ierr = MatCopy(A11,*Spmat,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
}
} else {
Mat AdB;
Vec diag;
ierr = MatCreateVecs(A00,&diag,NULL);CHKERRQ(ierr);
if (ainvtype == MAT_SCHUR_COMPLEMENT_AINV_LUMP) {
ierr = MatGetRowSum(A00,diag);CHKERRQ(ierr);
} else if (ainvtype == MAT_SCHUR_COMPLEMENT_AINV_DIAG) {
ierr = MatGetDiagonal(A00,diag);CHKERRQ(ierr);
} else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Unknown MatSchurComplementAinvType: %D", ainvtype);
ierr = VecReciprocal(diag);CHKERRQ(ierr);
ierr = MatDuplicate(A01,MAT_COPY_VALUES,&AdB);CHKERRQ(ierr);
ierr = MatDiagonalScale(AdB,diag,NULL);CHKERRQ(ierr);
ierr = VecDestroy(&diag);CHKERRQ(ierr);
/* Cannot really reuse Spmat in MatMatMult() because of MatAYPX() -->
MatAXPY() --> MatHeaderReplace() --> MatDestroy_XXX_MatMatMult() */
ierr = MatDestroy(Spmat);CHKERRQ(ierr);
ierr = MatMatMult(A10,AdB,MAT_INITIAL_MATRIX,PETSC_DEFAULT,Spmat);CHKERRQ(ierr);
if (!A11) {
ierr = MatScale(*Spmat,-1.0);CHKERRQ(ierr);
} else {
/* TODO: when can we pass SAME_NONZERO_PATTERN? */
ierr = MatAYPX(*Spmat,-1,A11,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
}
ierr = MatDestroy(&AdB);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
PetscErrorCode TSPrecond_Sundials(realtype tn,N_Vector y,N_Vector fy,
booleantype jok,booleantype *jcurPtr,
realtype _gamma,void *P_data,
N_Vector vtemp1,N_Vector vtemp2,N_Vector vtemp3)
{
TS ts = (TS) P_data;
TS_Sundials *cvode = (TS_Sundials*)ts->data;
PC pc = cvode->pc;
PetscErrorCode ierr;
Mat Jac = ts->B;
Vec yy = cvode->w1;
PetscScalar one = 1.0,gm;
MatStructure str = DIFFERENT_NONZERO_PATTERN;
PetscScalar *y_data;
PetscFunctionBegin;
/* This allows us to construct preconditioners in-place if we like */
ierr = MatSetUnfactored(Jac);CHKERRQ(ierr);
/* jok - TRUE means reuse current Jacobian else recompute Jacobian */
if (jok) {
ierr = MatCopy(cvode->pmat,Jac,str);CHKERRQ(ierr);
*jcurPtr = FALSE;
} else {
/* make PETSc vector yy point to SUNDIALS vector y */
y_data = (PetscScalar *) N_VGetArrayPointer(y);
ierr = VecPlaceArray(yy,y_data); CHKERRQ(ierr);
/* compute the Jacobian */
ierr = TSComputeRHSJacobian(ts,ts->ptime,yy,&Jac,&Jac,&str);CHKERRQ(ierr);
ierr = VecResetArray(yy); CHKERRQ(ierr);
/* copy the Jacobian matrix */
if (!cvode->pmat) {
ierr = MatDuplicate(Jac,MAT_COPY_VALUES,&cvode->pmat);CHKERRQ(ierr);
ierr = PetscLogObjectParent(ts,cvode->pmat);CHKERRQ(ierr);
} else {
ierr = MatCopy(Jac,cvode->pmat,str);CHKERRQ(ierr);
}
*jcurPtr = TRUE;
}
/* construct I-gamma*Jac */
gm = -_gamma;
ierr = MatScale(Jac,gm);CHKERRQ(ierr);
ierr = MatShift(Jac,one);CHKERRQ(ierr);
ierr = PCSetOperators(pc,Jac,Jac,str);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
Mat A,B;
MatScalar a[1],alpha;
PetscMPIInt size,rank;
PetscInt m,n,i,col, prid;
PetscErrorCode ierr;
PetscInitialize(&argc,&argv,(char *)0,help);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
prid = size;
ierr = PetscOptionsGetInt(PETSC_NULL,"-prid",&prid,PETSC_NULL);CHKERRQ(ierr);
m = n = 10*size;
ierr = MatCreate(PETSC_COMM_SELF,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DETERMINE,PETSC_DETERMINE,m,n);CHKERRQ(ierr);
ierr = MatSetType(A,MATSEQAIJ);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
a[0] = rank+1;
for (i=0; i<m-rank; i++){
col = i+rank;
ierr = MatSetValues(A,1,&i,1,&col,a,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
if (rank == prid){
ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] A: \n",rank);
ierr = MatView(A,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
}
/* Test MatCreateMPIAIJSumSeqAIJ */
ierr = MatCreateMPIAIJSumSeqAIJ(PETSC_COMM_WORLD,A,PETSC_DECIDE,PETSC_DECIDE,MAT_INITIAL_MATRIX,&B);CHKERRQ(ierr);
/* Test MAT_REUSE_MATRIX */
alpha = 0.1;
for (i=0; i<3; i++){
ierr = MatScale(A,alpha);CHKERRQ(ierr);
ierr = MatCreateMPIAIJSumSeqAIJ(PETSC_COMM_WORLD,A,PETSC_DECIDE,PETSC_DECIDE,MAT_REUSE_MATRIX,&B);CHKERRQ(ierr);
}
ierr = MatView(B, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
PetscFinalize();
return(0);
}
static void make_transform_matrix(
int transform_order, int rotate_order,
double tx, double ty, double tz,
double rx, double ry, double rz,
double sx, double sy, double sz,
double *transform)
{
int i;
double T[16], R[16], S[16], RX[16], RY[16], RZ[16];
double *queue[3];
MatTranslate(T, tx, ty, tz);
MatRotateX(RX, rx);
MatRotateY(RY, ry);
MatRotateZ(RZ, rz);
MatScale(S, sx, sy, sz);
switch (rotate_order) {
case ORDER_XYZ: VEC3_SET(queue, RX, RY, RZ); break;
case ORDER_XZY: VEC3_SET(queue, RX, RZ, RY); break;
case ORDER_YXZ: VEC3_SET(queue, RY, RX, RZ); break;
case ORDER_YZX: VEC3_SET(queue, RY, RZ, RX); break;
case ORDER_ZXY: VEC3_SET(queue, RZ, RX, RY); break;
case ORDER_ZYX: VEC3_SET(queue, RZ, RY, RX); break;
default:
assert(!"invalid rotate order");
break;
}
MatIdentity(R);
for (i = 0; i < 3; i++)
MatMultiply(R, queue[i], R);
switch (transform_order) {
case ORDER_SRT: VEC3_SET(queue, S, R, T); break;
case ORDER_STR: VEC3_SET(queue, S, T, R); break;
case ORDER_RST: VEC3_SET(queue, R, S, T); break;
case ORDER_RTS: VEC3_SET(queue, R, T, S); break;
case ORDER_TRS: VEC3_SET(queue, T, R, S); break;
case ORDER_TSR: VEC3_SET(queue, T, S, R); break;
default:
assert(!"invalid transform order order");
break;
}
MatIdentity(transform);
for (i = 0; i < 3; i++)
MatMultiply(transform, queue[i], transform);
}
/*@
MatAYPX - Computes Y = a*Y + X.
Logically on Mat
Input Parameters:
+ a - the PetscScalar multiplier
. Y - the first matrix
. X - the second matrix
- str - either SAME_NONZERO_PATTERN, DIFFERENT_NONZERO_PATTERN or SUBSET_NONZERO_PATTERN
Level: intermediate
.keywords: matrix, add
.seealso: MatAXPY()
@*/
PetscErrorCode MatAYPX(Mat Y,PetscScalar a,Mat X,MatStructure str)
{
PetscScalar one = 1.0;
PetscErrorCode ierr;
PetscInt mX,mY,nX,nY;
PetscFunctionBegin;
PetscValidHeaderSpecific(X,MAT_CLASSID,3);
PetscValidHeaderSpecific(Y,MAT_CLASSID,1);
PetscValidLogicalCollectiveScalar(Y,a,2);
ierr = MatGetSize(X,&mX,&nX);CHKERRQ(ierr);
ierr = MatGetSize(X,&mY,&nY);CHKERRQ(ierr);
if (mX != mY || nX != nY) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Non conforming matrices: %D %D first %D %D second",mX,mY,nX,nY);
ierr = MatScale(Y,a);CHKERRQ(ierr);
ierr = MatAXPY(Y,one,X,str);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*@C
MatCompositeMerge - Given a composite matrix, replaces it with a "regular" matrix
by summing all the matrices inside the composite matrix.
Collective on MPI_Comm
Input Parameters:
. mat - the composite matrix
Options Database:
. -mat_composite_merge (you must call MatAssemblyBegin()/MatAssemblyEnd() to have this checked)
Level: advanced
Notes:
The MatType of the resulting matrix will be the same as the MatType of the FIRST
matrix in the composite matrix.
.seealso: MatDestroy(), MatMult(), MatCompositeAddMat(), MatCreateComposite(), MATCOMPOSITE
@*/
PetscErrorCode MatCompositeMerge(Mat mat)
{
Mat_Composite *shell = (Mat_Composite*)mat->data;
Mat_CompositeLink next = shell->head, prev = shell->tail;
PetscErrorCode ierr;
Mat tmat,newmat;
Vec left,right;
PetscScalar scale;
PetscFunctionBegin;
if (!next) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must provide at least one matrix with MatCompositeAddMat()");
PetscFunctionBegin;
if (shell->type == MAT_COMPOSITE_ADDITIVE) {
ierr = MatDuplicate(next->mat,MAT_COPY_VALUES,&tmat);CHKERRQ(ierr);
while ((next = next->next)) {
ierr = MatAXPY(tmat,1.0,next->mat,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
}
} else {
ierr = MatDuplicate(next->mat,MAT_COPY_VALUES,&tmat);CHKERRQ(ierr);
while ((prev = prev->prev)) {
ierr = MatMatMult(tmat,prev->mat,MAT_INITIAL_MATRIX,PETSC_DECIDE,&newmat);CHKERRQ(ierr);
ierr = MatDestroy(&tmat);CHKERRQ(ierr);
tmat = newmat;
}
}
scale = shell->scale;
if ((left = shell->left)) {ierr = PetscObjectReference((PetscObject)left);CHKERRQ(ierr);}
if ((right = shell->right)) {ierr = PetscObjectReference((PetscObject)right);CHKERRQ(ierr);}
ierr = MatHeaderReplace(mat,&tmat);CHKERRQ(ierr);
ierr = MatDiagonalScale(mat,left,right);CHKERRQ(ierr);
ierr = MatScale(mat,scale);CHKERRQ(ierr);
ierr = VecDestroy(&left);CHKERRQ(ierr);
ierr = VecDestroy(&right);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
K is the discretiziation of the Laplacian
G is the discretization of the gradient
Computes Jacobian of K u + diag(u) G u which is given by
K + diag(u)G + diag(Gu)
*/
PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec globalin,Mat A, Mat B,void *ctx)
{
PetscErrorCode ierr;
AppCtx *appctx = (AppCtx*)ctx;
Vec Gglobalin;
PetscFunctionBegin;
/* A = diag(u) G */
ierr = MatCopy(appctx->SEMop.grad,A,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatDiagonalScale(A,globalin,NULL);CHKERRQ(ierr);
/* A = A + diag(Gu) */
ierr = VecDuplicate(globalin,&Gglobalin);CHKERRQ(ierr);
ierr = MatMult(appctx->SEMop.grad,globalin,Gglobalin);CHKERRQ(ierr);
ierr = MatDiagonalSet(A,Gglobalin,ADD_VALUES);CHKERRQ(ierr);
ierr = VecDestroy(&Gglobalin);CHKERRQ(ierr);
/* A = K - A */
ierr = MatScale(A,-1.0);CHKERRQ(ierr);
ierr = MatAXPY(A,0.0,appctx->SEMop.keptstiff,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode PCBDDCNullSpaceAssembleCorrection(PC pc, PetscBool isdir, IS local_dofs)
{
PC_BDDC *pcbddc = (PC_BDDC*)pc->data;
PC_IS *pcis = (PC_IS*)pc->data;
Mat_IS* matis = (Mat_IS*)pc->pmat->data;
KSP local_ksp;
PC newpc;
NullSpaceCorrection_ctx shell_ctx;
Mat local_mat,local_pmat,small_mat,inv_small_mat;
Vec work1,work2;
const Vec *nullvecs;
VecScatter scatter_ctx;
IS is_aux;
MatFactorInfo matinfo;
PetscScalar *basis_mat,*Kbasis_mat,*array,*array_mat;
PetscScalar one = 1.0,zero = 0.0, m_one = -1.0;
PetscInt basis_dofs,basis_size,nnsp_size,i,k;
PetscBool nnsp_has_cnst;
PetscErrorCode ierr;
PetscFunctionBegin;
/* Infer the local solver */
ierr = ISGetSize(local_dofs,&basis_dofs);CHKERRQ(ierr);
if (isdir) {
/* Dirichlet solver */
local_ksp = pcbddc->ksp_D;
} else {
/* Neumann solver */
local_ksp = pcbddc->ksp_R;
}
ierr = KSPGetOperators(local_ksp,&local_mat,&local_pmat);CHKERRQ(ierr);
/* Get null space vecs */
ierr = MatNullSpaceGetVecs(pcbddc->NullSpace,&nnsp_has_cnst,&nnsp_size,&nullvecs);CHKERRQ(ierr);
basis_size = nnsp_size;
if (nnsp_has_cnst) {
basis_size++;
}
if (basis_dofs) {
/* Create shell ctx */
ierr = PetscNew(&shell_ctx);CHKERRQ(ierr);
/* Create work vectors in shell context */
ierr = VecCreate(PETSC_COMM_SELF,&shell_ctx->work_small_1);CHKERRQ(ierr);
ierr = VecSetSizes(shell_ctx->work_small_1,basis_size,basis_size);CHKERRQ(ierr);
ierr = VecSetType(shell_ctx->work_small_1,VECSEQ);CHKERRQ(ierr);
ierr = VecDuplicate(shell_ctx->work_small_1,&shell_ctx->work_small_2);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_SELF,&shell_ctx->work_full_1);CHKERRQ(ierr);
ierr = VecSetSizes(shell_ctx->work_full_1,basis_dofs,basis_dofs);CHKERRQ(ierr);
ierr = VecSetType(shell_ctx->work_full_1,VECSEQ);CHKERRQ(ierr);
ierr = VecDuplicate(shell_ctx->work_full_1,&shell_ctx->work_full_2);CHKERRQ(ierr);
/* Allocate workspace */
ierr = MatCreateSeqDense(PETSC_COMM_SELF,basis_dofs,basis_size,NULL,&shell_ctx->basis_mat );CHKERRQ(ierr);
ierr = MatCreateSeqDense(PETSC_COMM_SELF,basis_dofs,basis_size,NULL,&shell_ctx->Kbasis_mat);CHKERRQ(ierr);
ierr = MatDenseGetArray(shell_ctx->basis_mat,&basis_mat);CHKERRQ(ierr);
ierr = MatDenseGetArray(shell_ctx->Kbasis_mat,&Kbasis_mat);CHKERRQ(ierr);
/* Restrict local null space on selected dofs (Dirichlet or Neumann)
and compute matrices N and K*N */
ierr = VecDuplicate(shell_ctx->work_full_1,&work1);CHKERRQ(ierr);
ierr = VecDuplicate(shell_ctx->work_full_1,&work2);CHKERRQ(ierr);
ierr = VecScatterCreate(pcis->vec1_N,local_dofs,work1,(IS)0,&scatter_ctx);CHKERRQ(ierr);
}
for (k=0;k<nnsp_size;k++) {
ierr = VecScatterBegin(matis->rctx,nullvecs[k],pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterEnd(matis->rctx,nullvecs[k],pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
if (basis_dofs) {
ierr = VecPlaceArray(work1,(const PetscScalar*)&basis_mat[k*basis_dofs]);CHKERRQ(ierr);
ierr = VecScatterBegin(scatter_ctx,pcis->vec1_N,work1,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterEnd(scatter_ctx,pcis->vec1_N,work1,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecPlaceArray(work2,(const PetscScalar*)&Kbasis_mat[k*basis_dofs]);CHKERRQ(ierr);
ierr = MatMult(local_mat,work1,work2);CHKERRQ(ierr);
ierr = VecResetArray(work1);CHKERRQ(ierr);
ierr = VecResetArray(work2);CHKERRQ(ierr);
}
}
if (basis_dofs) {
if (nnsp_has_cnst) {
ierr = VecPlaceArray(work1,(const PetscScalar*)&basis_mat[k*basis_dofs]);CHKERRQ(ierr);
ierr = VecSet(work1,one);CHKERRQ(ierr);
ierr = VecPlaceArray(work2,(const PetscScalar*)&Kbasis_mat[k*basis_dofs]);CHKERRQ(ierr);
ierr = MatMult(local_mat,work1,work2);CHKERRQ(ierr);
ierr = VecResetArray(work1);CHKERRQ(ierr);
ierr = VecResetArray(work2);CHKERRQ(ierr);
}
ierr = VecDestroy(&work1);CHKERRQ(ierr);
ierr = VecDestroy(&work2);CHKERRQ(ierr);
ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
ierr = MatDenseRestoreArray(shell_ctx->basis_mat,&basis_mat);CHKERRQ(ierr);
ierr = MatDenseRestoreArray(shell_ctx->Kbasis_mat,&Kbasis_mat);CHKERRQ(ierr);
/* Assemble another Mat object in shell context */
ierr = MatTransposeMatMult(shell_ctx->basis_mat,shell_ctx->Kbasis_mat,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&small_mat);CHKERRQ(ierr);
ierr = MatFactorInfoInitialize(&matinfo);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF,basis_size,0,1,&is_aux);CHKERRQ(ierr);
ierr = MatLUFactor(small_mat,is_aux,is_aux,&matinfo);CHKERRQ(ierr);
ierr = ISDestroy(&is_aux);CHKERRQ(ierr);
ierr = PetscMalloc1(basis_size*basis_size,&array_mat);CHKERRQ(ierr);
for (k=0;k<basis_size;k++) {
ierr = VecSet(shell_ctx->work_small_1,zero);CHKERRQ(ierr);
ierr = VecSetValue(shell_ctx->work_small_1,k,one,INSERT_VALUES);CHKERRQ(ierr);
ierr = VecAssemblyBegin(shell_ctx->work_small_1);CHKERRQ(ierr);
ierr = VecAssemblyEnd(shell_ctx->work_small_1);CHKERRQ(ierr);
ierr = MatSolve(small_mat,shell_ctx->work_small_1,shell_ctx->work_small_2);CHKERRQ(ierr);
ierr = VecGetArrayRead(shell_ctx->work_small_2,(const PetscScalar**)&array);CHKERRQ(ierr);
for (i=0;i<basis_size;i++) {
array_mat[i*basis_size+k]=array[i];
}
ierr = VecRestoreArrayRead(shell_ctx->work_small_2,(const PetscScalar**)&array);CHKERRQ(ierr);
}
ierr = MatCreateSeqDense(PETSC_COMM_SELF,basis_size,basis_size,array_mat,&inv_small_mat);CHKERRQ(ierr);
ierr = MatMatMult(shell_ctx->basis_mat,inv_small_mat,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&shell_ctx->Lbasis_mat);CHKERRQ(ierr);
ierr = PetscFree(array_mat);CHKERRQ(ierr);
ierr = MatDestroy(&inv_small_mat);CHKERRQ(ierr);
ierr = MatDestroy(&small_mat);CHKERRQ(ierr);
ierr = MatScale(shell_ctx->Kbasis_mat,m_one);CHKERRQ(ierr);
/* Rebuild local PC */
ierr = KSPGetPC(local_ksp,&shell_ctx->local_pc);CHKERRQ(ierr);
ierr = PetscObjectReference((PetscObject)shell_ctx->local_pc);CHKERRQ(ierr);
ierr = PCCreate(PETSC_COMM_SELF,&newpc);CHKERRQ(ierr);
ierr = PCSetOperators(newpc,local_mat,local_mat);CHKERRQ(ierr);
ierr = PCSetType(newpc,PCSHELL);CHKERRQ(ierr);
ierr = PCShellSetContext(newpc,shell_ctx);CHKERRQ(ierr);
ierr = PCShellSetApply(newpc,PCBDDCApplyNullSpaceCorrectionPC);CHKERRQ(ierr);
ierr = PCShellSetDestroy(newpc,PCBDDCDestroyNullSpaceCorrectionPC);CHKERRQ(ierr);
ierr = PCSetUp(newpc);CHKERRQ(ierr);
ierr = KSPSetPC(local_ksp,newpc);CHKERRQ(ierr);
ierr = PCDestroy(&newpc);CHKERRQ(ierr);
ierr = KSPSetUp(local_ksp);CHKERRQ(ierr);
}
/* test */
if (pcbddc->dbg_flag && basis_dofs) {
KSP check_ksp;
PC check_pc;
Mat test_mat;
Vec work3;
PetscReal test_err,lambda_min,lambda_max;
PetscBool setsym,issym=PETSC_FALSE;
PetscInt tabs;
ierr = PetscViewerASCIIGetTab(pcbddc->dbg_viewer,&tabs);CHKERRQ(ierr);
ierr = KSPGetPC(local_ksp,&check_pc);CHKERRQ(ierr);
ierr = VecDuplicate(shell_ctx->work_full_1,&work1);CHKERRQ(ierr);
ierr = VecDuplicate(shell_ctx->work_full_1,&work2);CHKERRQ(ierr);
ierr = VecDuplicate(shell_ctx->work_full_1,&work3);CHKERRQ(ierr);
ierr = VecSetRandom(shell_ctx->work_small_1,NULL);CHKERRQ(ierr);
ierr = MatMult(shell_ctx->basis_mat,shell_ctx->work_small_1,work1);CHKERRQ(ierr);
ierr = VecCopy(work1,work2);CHKERRQ(ierr);
ierr = MatMult(local_mat,work1,work3);CHKERRQ(ierr);
ierr = PCApply(check_pc,work3,work1);CHKERRQ(ierr);
ierr = VecAXPY(work1,m_one,work2);CHKERRQ(ierr);
ierr = VecNorm(work1,NORM_INFINITY,&test_err);CHKERRQ(ierr);
ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d error for nullspace correction for ",PetscGlobalRank);CHKERRQ(ierr);
ierr = PetscViewerASCIIUseTabs(pcbddc->dbg_viewer,PETSC_FALSE);CHKERRQ(ierr);
if (isdir) {
ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Dirichlet ");CHKERRQ(ierr);
} else {
ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Neumann ");CHKERRQ(ierr);
}
ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"solver is :%1.14e\n",test_err);CHKERRQ(ierr);
ierr = PetscViewerASCIISetTab(pcbddc->dbg_viewer,tabs);CHKERRQ(ierr);
ierr = PetscViewerASCIIUseTabs(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatTransposeMatMult(shell_ctx->Lbasis_mat,shell_ctx->Kbasis_mat,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&test_mat);CHKERRQ(ierr);
ierr = MatShift(test_mat,one);CHKERRQ(ierr);
ierr = MatNorm(test_mat,NORM_INFINITY,&test_err);CHKERRQ(ierr);
ierr = MatDestroy(&test_mat);CHKERRQ(ierr);
ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d error for nullspace matrices is :%1.14e\n",PetscGlobalRank,test_err);CHKERRQ(ierr);
/* Create ksp object suitable for extreme eigenvalues' estimation */
ierr = KSPCreate(PETSC_COMM_SELF,&check_ksp);CHKERRQ(ierr);
ierr = KSPSetErrorIfNotConverged(check_ksp,pc->erroriffailure);CHKERRQ(ierr);
ierr = KSPSetOperators(check_ksp,local_mat,local_mat);CHKERRQ(ierr);
ierr = KSPSetTolerances(check_ksp,1.e-8,1.e-8,PETSC_DEFAULT,basis_dofs);CHKERRQ(ierr);
ierr = KSPSetComputeSingularValues(check_ksp,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatIsSymmetricKnown(pc->pmat,&setsym,&issym);CHKERRQ(ierr);
if (issym) {
ierr = KSPSetType(check_ksp,KSPCG);CHKERRQ(ierr);
}
ierr = KSPSetPC(check_ksp,check_pc);CHKERRQ(ierr);
ierr = KSPSetUp(check_ksp);CHKERRQ(ierr);
ierr = VecSetRandom(work1,NULL);CHKERRQ(ierr);
ierr = MatMult(local_mat,work1,work2);CHKERRQ(ierr);
ierr = KSPSolve(check_ksp,work2,work2);CHKERRQ(ierr);
ierr = VecAXPY(work2,m_one,work1);CHKERRQ(ierr);
ierr = VecNorm(work2,NORM_INFINITY,&test_err);CHKERRQ(ierr);
ierr = KSPComputeExtremeSingularValues(check_ksp,&lambda_max,&lambda_min);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(check_ksp,&k);CHKERRQ(ierr);
ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d error for adapted KSP %1.14e (it %d, eigs %1.6e %1.6e)\n",PetscGlobalRank,test_err,k,lambda_min,lambda_max);CHKERRQ(ierr);
ierr = KSPDestroy(&check_ksp);CHKERRQ(ierr);
ierr = VecDestroy(&work1);CHKERRQ(ierr);
ierr = VecDestroy(&work2);CHKERRQ(ierr);
ierr = VecDestroy(&work3);CHKERRQ(ierr);
}
/* all processes shoud call this, even the void ones */
if (pcbddc->dbg_flag) {
ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
int main(int Argc,char **Args)
{
PetscBool flg;
PetscInt n = -6;
PetscScalar rho = 1.0;
PetscReal h;
PetscReal beta = 1.0;
DM da;
PetscRandom rctx;
PetscMPIInt comm_size;
Mat H,HtH;
PetscInt x, y, xs, ys, xm, ym;
PetscReal r1, r2;
PetscScalar uxy1, uxy2;
MatStencil sxy, sxy_m;
PetscScalar val, valconj;
Vec b, Htb,xvec;
KSP kspmg;
PC pcmg;
PetscErrorCode ierr;
PetscInt ix[1] = {0};
PetscScalar vals[1] = {1.0};
PetscInitialize(&Argc,&Args,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-size",&n,&flg);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,"-beta",&beta,&flg);CHKERRQ(ierr);
ierr = PetscOptionsGetScalar(NULL,"-rho",&rho,&flg);CHKERRQ(ierr);
/* Set the fudge parameters, we scale the whole thing by 1/(2*h) later */
h = 1.;
rho *= 1./(2.*h);
/* Geometry info */
ierr = DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_PERIODIC,DMDA_BOUNDARY_PERIODIC, DMDA_STENCIL_STAR, n, n,
PETSC_DECIDE, PETSC_DECIDE, 2 /* this is the # of dof's */,
1, NULL, NULL, &da);CHKERRQ(ierr);
/* Random numbers */
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
/* Single or multi processor ? */
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&comm_size);CHKERRQ(ierr);
/* construct matrix */
ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr);
ierr = DMCreateMatrix(da, &H);CHKERRQ(ierr);
/* get local corners for this processor */
ierr = DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);CHKERRQ(ierr);
/* Assemble the matrix */
for (x=xs; x<xs+xm; x++) {
for (y=ys; y<ys+ym; y++) {
/* each lattice point sets only the *forward* pointing parameters (right, down),
i.e. Nabla_1^+ and Nabla_2^+.
In this way we can use only local random number creation. That means
we also have to set the corresponding backward pointing entries. */
/* Compute some normally distributed random numbers via Box-Muller */
ierr = PetscRandomGetValueReal(rctx, &r1);CHKERRQ(ierr);
r1 = 1.-r1; /* to change from [0,1) to (0,1], which we need for the log */
ierr = PetscRandomGetValueReal(rctx, &r2);CHKERRQ(ierr);
PetscReal R = PetscSqrtReal(-2.*PetscLogReal(r1));
PetscReal c = PetscCosReal(2.*PETSC_PI*r2);
PetscReal s = PetscSinReal(2.*PETSC_PI*r2);
/* use those to set the field */
uxy1 = PetscExpScalar(((PetscScalar) (R*c/beta))*PETSC_i);
uxy2 = PetscExpScalar(((PetscScalar) (R*s/beta))*PETSC_i);
sxy.i = x; sxy.j = y; /* the point where we are */
/* center action */
sxy.c = 0; /* spin 0, 0 */
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy, &rho, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 1; /* spin 1, 1 */
val = -rho;
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
sxy_m.i = x+1; sxy_m.j = y; /* right action */
sxy.c = 0; sxy_m.c = 0; /* spin 0, 0 */
val = -uxy1; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 0; sxy_m.c = 1; /* spin 0, 1 */
val = -uxy1; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 1; sxy_m.c = 0; /* spin 1, 0 */
val = uxy1; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 1; sxy_m.c = 1; /* spin 1, 1 */
val = uxy1; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy_m.i = x; sxy_m.j = y+1; /* down action */
sxy.c = 0; sxy_m.c = 0; /* spin 0, 0 */
val = -uxy2; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 0; sxy_m.c = 1; /* spin 0, 1 */
val = -PETSC_i*uxy2; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 1; sxy_m.c = 0; /* spin 1, 0 */
val = -PETSC_i*uxy2; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 1; sxy_m.c = 1; /* spin 1, 1 */
val = PetscConj(uxy2); valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* scale H */
ierr = MatScale(H, 1./(2.*h));CHKERRQ(ierr);
/* it looks like H is Hermetian */
/* construct normal equations */
ierr = MatMatMult(H, H, MAT_INITIAL_MATRIX, 1., &HtH);CHKERRQ(ierr);
/* permutation matrix to check whether H and HtH are identical to the ones in the paper */
/* Mat perm; */
/* ierr = DMCreateMatrix(da, &perm);CHKERRQ(ierr); */
/* PetscInt row, col; */
/* PetscScalar one = 1.0; */
/* for (PetscInt i=0; i<n; i++) { */
/* for (PetscInt j=0; j<n; j++) { */
/* row = (i*n+j)*2; col = i*n+j; */
/* ierr = MatSetValues(perm, 1, &row, 1, &col, &one, INSERT_VALUES);CHKERRQ(ierr); */
/* row = (i*n+j)*2+1; col = i*n+j + n*n; */
/* ierr = MatSetValues(perm, 1, &row, 1, &col, &one, INSERT_VALUES);CHKERRQ(ierr); */
/* } */
/* } */
/* ierr = MatAssemblyBegin(perm, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); */
/* ierr = MatAssemblyEnd(perm, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); */
/* Mat Hperm; */
/* ierr = MatPtAP(H, perm, MAT_INITIAL_MATRIX, 1.0, &Hperm);CHKERRQ(ierr); */
/* ierr = PetscPrintf(PETSC_COMM_WORLD, "Matrix H after construction\n");CHKERRQ(ierr); */
/* ierr = MatView(Hperm, PETSC_VIEWER_STDOUT_(PETSC_COMM_WORLD));CHKERRQ(ierr); */
/* Mat HtHperm; */
/* ierr = MatPtAP(HtH, perm, MAT_INITIAL_MATRIX, 1.0, &HtHperm);CHKERRQ(ierr); */
/* ierr = PetscPrintf(PETSC_COMM_WORLD, "Matrix HtH:\n");CHKERRQ(ierr); */
/* ierr = MatView(HtHperm, PETSC_VIEWER_STDOUT_(PETSC_COMM_WORLD));CHKERRQ(ierr); */
/* right hand side */
ierr = DMCreateGlobalVector(da, &b);CHKERRQ(ierr);
ierr = VecSet(b,0.0);CHKERRQ(ierr);
ierr = VecSetValues(b, 1, ix, vals, INSERT_VALUES);CHKERRQ(ierr);
ierr = VecAssemblyBegin(b);CHKERRQ(ierr);
ierr = VecAssemblyEnd(b);CHKERRQ(ierr);
/* ierr = VecSetRandom(b, rctx);CHKERRQ(ierr); */
ierr = VecDuplicate(b, &Htb);CHKERRQ(ierr);
ierr = MatMultTranspose(H, b, Htb);CHKERRQ(ierr);
/* construct solver */
ierr = KSPCreate(PETSC_COMM_WORLD,&kspmg);CHKERRQ(ierr);
ierr = KSPSetType(kspmg, KSPCG);CHKERRQ(ierr);
ierr = KSPGetPC(kspmg,&pcmg);CHKERRQ(ierr);
ierr = PCSetType(pcmg,PCASA);CHKERRQ(ierr);
/* maybe user wants to override some of the choices */
ierr = KSPSetFromOptions(kspmg);CHKERRQ(ierr);
ierr = KSPSetOperators(kspmg, HtH, HtH, DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = DMDASetRefinementFactor(da, 3, 3, 3);CHKERRQ(ierr);
ierr = PCSetDM(pcmg,da);CHKERRQ(ierr);
ierr = PCASASetTolerances(pcmg, 1.e-6, 1.e-10,PETSC_DEFAULT,PETSC_DEFAULT);CHKERRQ(ierr);
ierr = VecDuplicate(b, &xvec);CHKERRQ(ierr);
ierr = VecSet(xvec, 0.0);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve the linear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = KSPSolve(kspmg, Htb, xvec);CHKERRQ(ierr);
/* ierr = VecView(xvec, PETSC_VIEWER_STDOUT_(PETSC_COMM_WORLD));CHKERRQ(ierr); */
ierr = KSPDestroy(&kspmg);CHKERRQ(ierr);
ierr = VecDestroy(&xvec);CHKERRQ(ierr);
/* seems to be destroyed by KSPDestroy */
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = VecDestroy(&Htb);CHKERRQ(ierr);
ierr = MatDestroy(&HtH);CHKERRQ(ierr);
ierr = MatDestroy(&H);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **argv)
{
PetscErrorCode ierr;
KSP ksp;
PC pc;
Vec x,b;
DA da;
Mat A,Atrans;
PetscInt dof=1,M=-8;
PetscTruth flg,trans=PETSC_FALSE;
PetscInitialize(&argc,&argv,(char *)0,help);
ierr = PetscOptionsGetInt(PETSC_NULL,"-dof",&dof,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-M",&M,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetTruth(PETSC_NULL,"-trans",&trans,PETSC_NULL);CHKERRQ(ierr);
ierr = DACreate(PETSC_COMM_WORLD,&da);CHKERRQ(ierr);
ierr = DASetDim(da,3);CHKERRQ(ierr);
ierr = DASetPeriodicity(da,DA_NONPERIODIC);CHKERRQ(ierr);
ierr = DASetStencilType(da,DA_STENCIL_STAR);CHKERRQ(ierr);
ierr = DASetSizes(da,M,M,M);CHKERRQ(ierr);
ierr = DASetNumProcs(da,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
ierr = DASetDof(da,dof);CHKERRQ(ierr);
ierr = DASetStencilWidth(da,1);CHKERRQ(ierr);
ierr = DASetVertexDivision(da,PETSC_NULL,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
ierr = DASetFromOptions(da);CHKERRQ(ierr);
ierr = DACreateGlobalVector(da,&x);CHKERRQ(ierr);
ierr = DACreateGlobalVector(da,&b);CHKERRQ(ierr);
ierr = ComputeRHS(da,b);CHKERRQ(ierr);
ierr = DAGetMatrix(da,MATBAIJ,&A);CHKERRQ(ierr);
ierr = ComputeMatrix(da,A);CHKERRQ(ierr);
/* A is non-symmetric. Make A = 0.5*(A + Atrans) symmetric for testing icc and cholesky */
ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&Atrans);CHKERRQ(ierr);
ierr = MatAXPY(A,1.0,Atrans,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatScale(A,0.5);CHKERRQ(ierr);
ierr = MatDestroy(Atrans);CHKERRQ(ierr);
/* Test sbaij matrix */
flg = PETSC_FALSE;
ierr = PetscOptionsGetTruth(PETSC_NULL, "-test_sbaij1", &flg,PETSC_NULL);CHKERRQ(ierr);
if (flg){
Mat sA;
ierr = MatConvert(A,MATSBAIJ,MAT_INITIAL_MATRIX,&sA);CHKERRQ(ierr);
ierr = MatDestroy(A);CHKERRQ(ierr);
A = sA;
}
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,A,A,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
ierr = PCSetDA(pc,da);CHKERRQ(ierr);
if (trans) {
ierr = KSPSolveTranspose(ksp,b,x);CHKERRQ(ierr);
} else {
ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
}
/* check final residual */
flg = PETSC_FALSE;
ierr = PetscOptionsGetTruth(PETSC_NULL, "-check_final_residual", &flg,PETSC_NULL);CHKERRQ(ierr);
if (flg){
Vec b1;
PetscReal norm;
ierr = KSPGetSolution(ksp,&x);CHKERRQ(ierr);
ierr = VecDuplicate(b,&b1);CHKERRQ(ierr);
ierr = MatMult(A,x,b1);CHKERRQ(ierr);
ierr = VecAXPY(b1,-1.0,b);CHKERRQ(ierr);
ierr = VecNorm(b1,NORM_2,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Final residual %g\n",norm);CHKERRQ(ierr);
ierr = VecDestroy(b1);CHKERRQ(ierr);
}
ierr = KSPDestroy(ksp);CHKERRQ(ierr);
ierr = VecDestroy(x);CHKERRQ(ierr);
ierr = VecDestroy(b);CHKERRQ(ierr);
ierr = MatDestroy(A);CHKERRQ(ierr);
ierr = DADestroy(da);CHKERRQ(ierr);
ierr = PetscFinalize();CHKERRQ(ierr);
return 0;
}
int main(int argc,char **args)
{
Vec x,y,u,s1,s2;
Mat A,sA,sB;
PetscRandom rctx;
PetscReal r1,r2,rnorm,tol = PETSC_SQRT_MACHINE_EPSILON;
PetscScalar one=1.0, neg_one=-1.0, value[3], four=4.0,alpha=0.1;
PetscInt n,col[3],n1,block,row,i,j,i2,j2,Ii,J,rstart,rend,bs=1,mbs=16,d_nz=3,o_nz=3,prob=2;
PetscErrorCode ierr;
PetscMPIInt size,rank;
PetscBool flg;
MatType type;
ierr = PetscInitialize(&argc,&args,(char*)0,help);
if (ierr) return ierr;
ierr = PetscOptionsGetInt(NULL,NULL,"-mbs",&mbs,NULL);
CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-bs",&bs,NULL);
CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);
CHKERRQ(ierr);
n = mbs*bs;
/* Assemble MPISBAIJ matrix sA */
ierr = MatCreate(PETSC_COMM_WORLD,&sA);
CHKERRQ(ierr);
ierr = MatSetSizes(sA,PETSC_DECIDE,PETSC_DECIDE,n,n);
CHKERRQ(ierr);
ierr = MatSetType(sA,MATSBAIJ);
CHKERRQ(ierr);
ierr = MatSetFromOptions(sA);
CHKERRQ(ierr);
ierr = MatGetType(sA,&type);
CHKERRQ(ierr);
ierr = MatMPISBAIJSetPreallocation(sA,bs,d_nz,NULL,o_nz,NULL);
CHKERRQ(ierr);
ierr = MatSeqSBAIJSetPreallocation(sA,bs,d_nz,NULL);
CHKERRQ(ierr);
ierr = MatSetOption(sA,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
CHKERRQ(ierr);
if (bs == 1) {
if (prob == 1) { /* tridiagonal matrix */
value[0] = -1.0;
value[1] = 2.0;
value[2] = -1.0;
for (i=1; i<n-1; i++) {
col[0] = i-1;
col[1] = i;
col[2] = i+1;
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
i = n - 1;
col[0]=0;
col[1] = n - 2;
col[2] = n - 1;
value[0]= 0.1;
value[1]=-1;
value[2]=2;
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
i = 0;
col[0] = 0;
col[1] = 1;
col[2]=n-1;
value[0] = 2.0;
value[1] = -1.0;
value[2]=0.1;
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
} else if (prob ==2) { /* matrix for the five point stencil */
n1 = (int) PetscSqrtReal((PetscReal)n);
if (n1*n1 != n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"n must be a perfect square of n1");
for (i=0; i<n1; i++) {
for (j=0; j<n1; j++) {
Ii = j + n1*i;
if (i>0) {
J = Ii - n1;
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
if (i<n1-1) {
J = Ii + n1;
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
if (j>0) {
J = Ii - 1;
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
if (j<n1-1) {
J = Ii + 1;
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
ierr = MatSetValues(sA,1,&Ii,1,&Ii,&four,INSERT_VALUES);
CHKERRQ(ierr);
}
}
}
/* end of if (bs == 1) */
} else { /* bs > 1 */
for (block=0; block<n/bs; block++) {
/* diagonal blocks */
value[0] = -1.0;
value[1] = 4.0;
value[2] = -1.0;
for (i=1+block*bs; i<bs-1+block*bs; i++) {
col[0] = i-1;
col[1] = i;
col[2] = i+1;
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
i = bs - 1+block*bs;
col[0] = bs - 2+block*bs;
col[1] = bs - 1+block*bs;
value[0]=-1.0;
value[1]=4.0;
ierr = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);
CHKERRQ(ierr);
i = 0+block*bs;
col[0] = 0+block*bs;
col[1] = 1+block*bs;
value[0]=4.0;
value[1] = -1.0;
ierr = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
/* off-diagonal blocks */
value[0]=-1.0;
for (i=0; i<(n/bs-1)*bs; i++) {
col[0]=i+bs;
ierr = MatSetValues(sA,1,&i,1,col,value,INSERT_VALUES);
CHKERRQ(ierr);
col[0]=i;
row=i+bs;
ierr = MatSetValues(sA,1,&row,1,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(sA,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = MatAssemblyEnd(sA,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
/* Test MatView() */
ierr = MatCreateBAIJ(PETSC_COMM_WORLD,bs,PETSC_DECIDE,PETSC_DECIDE,n,n,d_nz,NULL,o_nz,NULL,&A);
CHKERRQ(ierr);
ierr = MatSetOption(A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
CHKERRQ(ierr);
if (bs == 1) {
if (prob == 1) { /* tridiagonal matrix */
value[0] = -1.0;
value[1] = 2.0;
value[2] = -1.0;
for (i=1; i<n-1; i++) {
col[0] = i-1;
col[1] = i;
col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
i = n - 1;
col[0]=0;
col[1] = n - 2;
col[2] = n - 1;
value[0]= 0.1;
value[1]=-1;
value[2]=2;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
i = 0;
col[0] = 0;
col[1] = 1;
col[2]=n-1;
value[0] = 2.0;
value[1] = -1.0;
value[2]=0.1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
} else if (prob ==2) { /* matrix for the five point stencil */
n1 = (int) PetscSqrtReal((PetscReal)n);
for (i=0; i<n1; i++) {
for (j=0; j<n1; j++) {
Ii = j + n1*i;
if (i>0) {
J = Ii - n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
if (i<n1-1) {
J = Ii + n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
if (j>0) {
J = Ii - 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
if (j<n1-1) {
J = Ii + 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
ierr = MatSetValues(A,1,&Ii,1,&Ii,&four,INSERT_VALUES);
CHKERRQ(ierr);
}
}
}
/* end of if (bs == 1) */
} else { /* bs > 1 */
for (block=0; block<n/bs; block++) {
/* diagonal blocks */
value[0] = -1.0;
value[1] = 4.0;
value[2] = -1.0;
for (i=1+block*bs; i<bs-1+block*bs; i++) {
col[0] = i-1;
col[1] = i;
col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
i = bs - 1+block*bs;
col[0] = bs - 2+block*bs;
col[1] = bs - 1+block*bs;
value[0]=-1.0;
value[1]=4.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
CHKERRQ(ierr);
i = 0+block*bs;
col[0] = 0+block*bs;
col[1] = 1+block*bs;
value[0]=4.0;
value[1] = -1.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
/* off-diagonal blocks */
value[0]=-1.0;
for (i=0; i<(n/bs-1)*bs; i++) {
col[0]=i+bs;
ierr = MatSetValues(A,1,&i,1,col,value,INSERT_VALUES);
CHKERRQ(ierr);
col[0]=i;
row=i+bs;
ierr = MatSetValues(A,1,&row,1,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
/* Test MatGetSize(), MatGetLocalSize() */
ierr = MatGetSize(sA, &i,&j);
CHKERRQ(ierr);
ierr = MatGetSize(A, &i2,&j2);
CHKERRQ(ierr);
i -= i2;
j -= j2;
if (i || j) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatGetSize()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
ierr = MatGetLocalSize(sA, &i,&j);
CHKERRQ(ierr);
ierr = MatGetLocalSize(A, &i2,&j2);
CHKERRQ(ierr);
i2 -= i;
j2 -= j;
if (i2 || j2) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatGetLocalSize()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
/* vectors */
/*--------------------*/
/* i is obtained from MatGetLocalSize() */
ierr = VecCreate(PETSC_COMM_WORLD,&x);
CHKERRQ(ierr);
ierr = VecSetSizes(x,i,PETSC_DECIDE);
CHKERRQ(ierr);
ierr = VecSetFromOptions(x);
CHKERRQ(ierr);
ierr = VecDuplicate(x,&y);
CHKERRQ(ierr);
ierr = VecDuplicate(x,&u);
CHKERRQ(ierr);
ierr = VecDuplicate(x,&s1);
CHKERRQ(ierr);
ierr = VecDuplicate(x,&s2);
CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);
CHKERRQ(ierr);
ierr = VecSetRandom(x,rctx);
CHKERRQ(ierr);
ierr = VecSet(u,one);
CHKERRQ(ierr);
/* Test MatNorm() */
ierr = MatNorm(A,NORM_FROBENIUS,&r1);
CHKERRQ(ierr);
ierr = MatNorm(sA,NORM_FROBENIUS,&r2);
CHKERRQ(ierr);
rnorm = PetscAbsReal(r1-r2)/r2;
if (rnorm > tol && !rank) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_FROBENIUS(), Anorm=%16.14e, sAnorm=%16.14e bs=%D\n",r1,r2,bs);
CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_INFINITY,&r1);
CHKERRQ(ierr);
ierr = MatNorm(sA,NORM_INFINITY,&r2);
CHKERRQ(ierr);
rnorm = PetscAbsReal(r1-r2)/r2;
if (rnorm > tol && !rank) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Error: MatNorm_INFINITY(), Anorm=%16.14e, sAnorm=%16.14e bs=%D\n",r1,r2,bs);
CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_1,&r1);
CHKERRQ(ierr);
ierr = MatNorm(sA,NORM_1,&r2);
CHKERRQ(ierr);
rnorm = PetscAbsReal(r1-r2)/r2;
if (rnorm > tol && !rank) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Error: MatNorm_1(), Anorm=%16.14e, sAnorm=%16.14e bs=%D\n",r1,r2,bs);
CHKERRQ(ierr);
}
/* Test MatGetOwnershipRange() */
ierr = MatGetOwnershipRange(sA,&rstart,&rend);
CHKERRQ(ierr);
ierr = MatGetOwnershipRange(A,&i2,&j2);
CHKERRQ(ierr);
i2 -= rstart;
j2 -= rend;
if (i2 || j2) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MaGetOwnershipRange()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
/* Test MatDiagonalScale() */
ierr = MatDiagonalScale(A,x,x);
CHKERRQ(ierr);
ierr = MatDiagonalScale(sA,x,x);
CHKERRQ(ierr);
ierr = MatMultEqual(A,sA,10,&flg);
CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NOTSAMETYPE,"Error in MatDiagonalScale");
/* Test MatGetDiagonal(), MatScale() */
ierr = MatGetDiagonal(A,s1);
CHKERRQ(ierr);
ierr = MatGetDiagonal(sA,s2);
CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&r1);
CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&r2);
CHKERRQ(ierr);
r1 -= r2;
if (r1<-tol || r1>tol) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatDiagonalScale() or MatGetDiagonal(), r1=%g \n",rank,(double)r1);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
ierr = MatScale(A,alpha);
CHKERRQ(ierr);
ierr = MatScale(sA,alpha);
CHKERRQ(ierr);
/* Test MatGetRowMaxAbs() */
ierr = MatGetRowMaxAbs(A,s1,NULL);
CHKERRQ(ierr);
ierr = MatGetRowMaxAbs(sA,s2,NULL);
CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&r1);
CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&r2);
CHKERRQ(ierr);
r1 -= r2;
if (r1<-tol || r1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetRowMaxAbs() \n");
CHKERRQ(ierr);
}
/* Test MatMult(), MatMultAdd() */
ierr = MatMultEqual(A,sA,10,&flg);
CHKERRQ(ierr);
if (!flg) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatMult() or MatScale()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
ierr = MatMultAddEqual(A,sA,10,&flg);
CHKERRQ(ierr);
if (!flg) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatMultAdd()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
/* Test MatMultTranspose(), MatMultTransposeAdd() */
for (i=0; i<10; i++) {
ierr = VecSetRandom(x,rctx);
CHKERRQ(ierr);
ierr = MatMultTranspose(A,x,s1);
CHKERRQ(ierr);
ierr = MatMultTranspose(sA,x,s2);
CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&r1);
CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&r2);
CHKERRQ(ierr);
r1 -= r2;
if (r1<-tol || r1>tol) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatMult() or MatScale(), err=%g\n",rank,(double)r1);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
}
for (i=0; i<10; i++) {
ierr = VecSetRandom(x,rctx);
CHKERRQ(ierr);
ierr = VecSetRandom(y,rctx);
CHKERRQ(ierr);
ierr = MatMultTransposeAdd(A,x,y,s1);
CHKERRQ(ierr);
ierr = MatMultTransposeAdd(sA,x,y,s2);
CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&r1);
CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&r2);
CHKERRQ(ierr);
r1 -= r2;
if (r1<-tol || r1>tol) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatMultAdd(), err=%g \n",rank,(double)r1);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
}
/* Test MatDuplicate() */
ierr = MatDuplicate(sA,MAT_COPY_VALUES,&sB);
CHKERRQ(ierr);
ierr = MatEqual(sA,sB,&flg);
CHKERRQ(ierr);
if (!flg) {
ierr = PetscPrintf(PETSC_COMM_WORLD," Error in MatDuplicate(), sA != sB \n");
CHKERRQ(ierr);
CHKERRQ(ierr);
}
ierr = MatMultEqual(sA,sB,5,&flg);
CHKERRQ(ierr);
if (!flg) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatDuplicate() or MatMult()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
ierr = MatMultAddEqual(sA,sB,5,&flg);
CHKERRQ(ierr);
if (!flg) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatDuplicate() or MatMultAdd(()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
ierr = MatDestroy(&sB);
CHKERRQ(ierr);
ierr = VecDestroy(&u);
CHKERRQ(ierr);
ierr = VecDestroy(&x);
CHKERRQ(ierr);
ierr = VecDestroy(&y);
CHKERRQ(ierr);
ierr = VecDestroy(&s1);
CHKERRQ(ierr);
ierr = VecDestroy(&s2);
CHKERRQ(ierr);
ierr = MatDestroy(&sA);
CHKERRQ(ierr);
ierr = MatDestroy(&A);
CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rctx);
CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **args)
{
PetscMPIInt size;
PetscErrorCode ierr;
Vec x,y,b,s1,s2;
Mat A; /* linear system matrix */
Mat sA,sB,sC; /* symmetric part of the matrices */
PetscInt n,mbs=16,bs=1,nz=3,prob=1,i,j,k1,k2,col[3],lf,block, row,Ii,J,n1,inc;
PetscReal norm1,norm2,rnorm,tol=PETSC_SMALL;
PetscScalar neg_one = -1.0,four=4.0,value[3];
IS perm, iscol;
PetscRandom rdm;
PetscBool doIcc=PETSC_TRUE,equal;
MatInfo minfo1,minfo2;
MatFactorInfo factinfo;
MatType type;
PetscInitialize(&argc,&args,(char*)0,help);
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!");
ierr = PetscOptionsGetInt(NULL,"-bs",&bs,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-mbs",&mbs,NULL);CHKERRQ(ierr);
n = mbs*bs;
ierr = MatCreate(PETSC_COMM_SELF,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetType(A,MATSEQBAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSeqBAIJSetPreallocation(A,bs,nz,NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_SELF,&sA);CHKERRQ(ierr);
ierr = MatSetSizes(sA,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetType(sA,MATSEQSBAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(sA);CHKERRQ(ierr);
ierr = MatGetType(sA,&type);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)sA,MATSEQSBAIJ,&doIcc);CHKERRQ(ierr);
ierr = MatSeqSBAIJSetPreallocation(sA,bs,nz,NULL);CHKERRQ(ierr);
ierr = MatSetOption(sA,MAT_IGNORE_LOWER_TRIANGULAR,PETSC_TRUE);CHKERRQ(ierr);
/* Test MatGetOwnershipRange() */
ierr = MatGetOwnershipRange(A,&Ii,&J);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(sA,&i,&j);CHKERRQ(ierr);
if (i-Ii || j-J) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetOwnershipRange() in MatSBAIJ format\n");CHKERRQ(ierr);
}
/* Assemble matrix */
if (bs == 1) {
ierr = PetscOptionsGetInt(NULL,"-test_problem",&prob,NULL);CHKERRQ(ierr);
if (prob == 1) { /* tridiagonal matrix */
value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
for (i=1; i<n-1; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
i = n - 1; col[0]=0; col[1] = n - 2; col[2] = n - 1;
value[0]= 0.1; value[1]=-1; value[2]=2;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
i = 0;
col[0] = n-1; col[1] = 1; col[2] = 0;
value[0] = 0.1; value[1] = -1.0; value[2] = 2;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
} else if (prob ==2) { /* matrix for the five point stencil */
n1 = (PetscInt) (PetscSqrtReal((PetscReal)n) + 0.001);
if (n1*n1 - n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"sqrt(n) must be a positive interger!");
for (i=0; i<n1; i++) {
for (j=0; j<n1; j++) {
Ii = j + n1*i;
if (i>0) {
J = Ii - n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (i<n1-1) {
J = Ii + n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (j>0) {
J = Ii - 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (j<n1-1) {
J = Ii + 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatSetValues(A,1,&Ii,1,&Ii,&four,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&Ii,&four,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
} else { /* bs > 1 */
for (block=0; block<n/bs; block++) {
/* diagonal blocks */
value[0] = -1.0; value[1] = 4.0; value[2] = -1.0;
for (i=1+block*bs; i<bs-1+block*bs; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
i = bs - 1+block*bs; col[0] = bs - 2+block*bs; col[1] = bs - 1+block*bs;
value[0]=-1.0; value[1]=4.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
i = 0+block*bs; col[0] = 0+block*bs; col[1] = 1+block*bs;
value[0]=4.0; value[1] = -1.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
/* off-diagonal blocks */
value[0]=-1.0;
for (i=0; i<(n/bs-1)*bs; i++) {
col[0]=i+bs;
ierr = MatSetValues(A,1,&i,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
col[0]=i; row=i+bs;
ierr = MatSetValues(A,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(sA,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(sA,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Test MatGetInfo() of A and sA */
ierr = MatGetInfo(A,MAT_LOCAL,&minfo1);CHKERRQ(ierr);
ierr = MatGetInfo(sA,MAT_LOCAL,&minfo2);CHKERRQ(ierr);
/*
printf("A matrix nonzeros (BAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo1.nz_used,(int)minfo1.nz_allocated);
printf("sA matrix nonzeros(SBAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo2.nz_used,(int)minfo2.nz_allocated);
*/
i = (int) (minfo1.nz_used - minfo2.nz_used);
j = (int) (minfo1.nz_allocated - minfo2.nz_allocated);
k1 = (int) (minfo1.nz_allocated - minfo1.nz_used);
k2 = (int) (minfo2.nz_allocated - minfo2.nz_used);
if (i < 0 || j < 0 || k1 < 0 || k2 < 0) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error (compare A and sA): MatGetInfo()\n");CHKERRQ(ierr);
}
/* Test MatDuplicate() */
ierr = MatNorm(A,NORM_FROBENIUS,&norm1);CHKERRQ(ierr);
ierr = MatDuplicate(sA,MAT_COPY_VALUES,&sB);CHKERRQ(ierr);
ierr = MatEqual(sA,sB,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NOTSAMETYPE,"Error in MatDuplicate()");
/* Test MatNorm() */
ierr = MatNorm(A,NORM_FROBENIUS,&norm1);CHKERRQ(ierr);
ierr = MatNorm(sB,NORM_FROBENIUS,&norm2);CHKERRQ(ierr);
rnorm = PetscAbsReal(norm1-norm2)/norm2;
if (rnorm > tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_FROBENIUS, NormA=%16.14e NormsB=%16.14e\n",norm1,norm2);CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_INFINITY,&norm1);CHKERRQ(ierr);
ierr = MatNorm(sB,NORM_INFINITY,&norm2);CHKERRQ(ierr);
rnorm = PetscAbsReal(norm1-norm2)/norm2;
if (rnorm > tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_INFINITY(), NormA=%16.14e NormsB=%16.14e\n",norm1,norm2);CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_1,&norm1);CHKERRQ(ierr);
ierr = MatNorm(sB,NORM_1,&norm2);CHKERRQ(ierr);
rnorm = PetscAbsReal(norm1-norm2)/norm2;
if (rnorm > tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_INFINITY(), NormA=%16.14e NormsB=%16.14e\n",norm1,norm2);CHKERRQ(ierr);
}
/* Test MatGetInfo(), MatGetSize(), MatGetBlockSize() */
ierr = MatGetInfo(A,MAT_LOCAL,&minfo1);CHKERRQ(ierr);
ierr = MatGetInfo(sB,MAT_LOCAL,&minfo2);CHKERRQ(ierr);
/*
printf("matrix nonzeros (BAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo1.nz_used,(int)minfo1.nz_allocated);
printf("matrix nonzeros(SBAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo2.nz_used,(int)minfo2.nz_allocated);
*/
i = (int) (minfo1.nz_used - minfo2.nz_used);
j = (int) (minfo1.nz_allocated - minfo2.nz_allocated);
k1 = (int) (minfo1.nz_allocated - minfo1.nz_used);
k2 = (int) (minfo2.nz_allocated - minfo2.nz_used);
if (i < 0 || j < 0 || k1 < 0 || k2 < 0) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error(compare A and sB): MatGetInfo()\n");CHKERRQ(ierr);
}
ierr = MatGetSize(A,&Ii,&J);CHKERRQ(ierr);
ierr = MatGetSize(sB,&i,&j);CHKERRQ(ierr);
if (i-Ii || j-J) {
PetscPrintf(PETSC_COMM_SELF,"Error: MatGetSize()\n");CHKERRQ(ierr);
}
ierr = MatGetBlockSize(A, &Ii);CHKERRQ(ierr);
ierr = MatGetBlockSize(sB, &i);CHKERRQ(ierr);
if (i-Ii) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetBlockSize()\n");CHKERRQ(ierr);
}
ierr = PetscRandomCreate(PETSC_COMM_SELF,&rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,n,&x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&s1);CHKERRQ(ierr);
ierr = VecDuplicate(x,&s2);CHKERRQ(ierr);
ierr = VecDuplicate(x,&y);CHKERRQ(ierr);
ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
/* Test MatDiagonalScale(), MatGetDiagonal(), MatScale() */
#if !defined(PETSC_USE_COMPLEX)
/* Scaling matrix with complex numbers results non-spd matrix,
causing crash of MatForwardSolve() and MatBackwardSolve() */
ierr = MatDiagonalScale(A,x,x);CHKERRQ(ierr);
ierr = MatDiagonalScale(sB,x,x);CHKERRQ(ierr);
ierr = MatMultEqual(A,sB,10,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NOTSAMETYPE,"Error in MatDiagonalScale");
ierr = MatGetDiagonal(A,s1);CHKERRQ(ierr);
ierr = MatGetDiagonal(sB,s2);CHKERRQ(ierr);
ierr = VecAXPY(s2,neg_one,s1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm1);CHKERRQ(ierr);
if (norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatGetDiagonal(), ||s1-s2||=%G\n",norm1);CHKERRQ(ierr);
}
{
PetscScalar alpha=0.1;
ierr = MatScale(A,alpha);CHKERRQ(ierr);
ierr = MatScale(sB,alpha);CHKERRQ(ierr);
}
#endif
/* Test MatGetRowMaxAbs() */
ierr = MatGetRowMaxAbs(A,s1,NULL);CHKERRQ(ierr);
ierr = MatGetRowMaxAbs(sB,s2,NULL);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
norm1 -= norm2;
if (norm1<-tol || norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatGetRowMaxAbs() \n");CHKERRQ(ierr);
}
/* Test MatMult() */
for (i=0; i<40; i++) {
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
ierr = MatMult(A,x,s1);CHKERRQ(ierr);
ierr = MatMult(sB,x,s2);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
norm1 -= norm2;
if (norm1<-tol || norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMult(), norm1-norm2: %G\n",norm1);CHKERRQ(ierr);
}
}
/* MatMultAdd() */
for (i=0; i<40; i++) {
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
ierr = VecSetRandom(y,rdm);CHKERRQ(ierr);
ierr = MatMultAdd(A,x,y,s1);CHKERRQ(ierr);
ierr = MatMultAdd(sB,x,y,s2);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
norm1 -= norm2;
if (norm1<-tol || norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatMultAdd(), norm1-norm2: %G\n",norm1);CHKERRQ(ierr);
}
}
/* Test MatCholeskyFactor(), MatICCFactor() with natural ordering */
ierr = MatGetOrdering(A,MATORDERINGNATURAL,&perm,&iscol);CHKERRQ(ierr);
ierr = ISDestroy(&iscol);CHKERRQ(ierr);
norm1 = tol;
inc = bs;
/* initialize factinfo */
ierr = PetscMemzero(&factinfo,sizeof(MatFactorInfo));CHKERRQ(ierr);
for (lf=-1; lf<10; lf += inc) {
if (lf==-1) { /* Cholesky factor of sB (duplicate sA) */
factinfo.fill = 5.0;
ierr = MatGetFactor(sB,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&sC);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(sC,sB,perm,&factinfo);CHKERRQ(ierr);
} else if (!doIcc) break;
else { /* incomplete Cholesky factor */
factinfo.fill = 5.0;
factinfo.levels = lf;
ierr = MatGetFactor(sB,MATSOLVERPETSC,MAT_FACTOR_ICC,&sC);CHKERRQ(ierr);
ierr = MatICCFactorSymbolic(sC,sB,perm,&factinfo);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorNumeric(sC,sB,&factinfo);CHKERRQ(ierr);
/* MatView(sC, PETSC_VIEWER_DRAW_WORLD); */
/* test MatGetDiagonal on numeric factor */
/*
if (lf == -1) {
ierr = MatGetDiagonal(sC,s1);CHKERRQ(ierr);
printf(" in ex74.c, diag: \n");
ierr = VecView(s1,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
}
*/
ierr = MatMult(sB,x,b);CHKERRQ(ierr);
/* test MatForwardSolve() and MatBackwardSolve() */
if (lf == -1) {
ierr = MatForwardSolve(sC,b,s1);CHKERRQ(ierr);
ierr = MatBackwardSolve(sC,s1,s2);CHKERRQ(ierr);
ierr = VecAXPY(s2,neg_one,x);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&norm2);CHKERRQ(ierr);
if (10*norm1 < norm2) {
ierr = PetscPrintf(PETSC_COMM_SELF,"MatForwardSolve and BackwardSolve: Norm of error=%G, bs=%d\n",norm2,bs);CHKERRQ(ierr);
}
}
/* test MatSolve() */
ierr = MatSolve(sC,b,y);CHKERRQ(ierr);
ierr = MatDestroy(&sC);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(y,neg_one,x);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm2);CHKERRQ(ierr);
/* printf("lf: %d, error: %G\n", lf,norm2); */
if (10*norm1 < norm2 && lf-inc != -1) {
ierr = PetscPrintf(PETSC_COMM_SELF,"lf=%D, %D, Norm of error=%G, %G\n",lf-inc,lf,norm1,norm2);CHKERRQ(ierr);
}
norm1 = norm2;
if (norm2 < tol && lf != -1) break;
}
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&sB);CHKERRQ(ierr);
ierr = MatDestroy(&sA);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&s1);CHKERRQ(ierr);
ierr = VecDestroy(&s2);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **argv)
{
PetscErrorCode ierr;
KSP ksp;
PC pc;
Vec x,b;
DM da;
Mat A,Atrans;
PetscInt dof=1,M=8;
PetscBool flg,trans=PETSC_FALSE;
ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
ierr = PetscOptionsGetInt(NULL,NULL,"-dof",&dof,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-M",&M,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-trans",&trans,NULL);CHKERRQ(ierr);
ierr = DMDACreate(PETSC_COMM_WORLD,&da);CHKERRQ(ierr);
ierr = DMSetDimension(da,3);CHKERRQ(ierr);
ierr = DMDASetBoundaryType(da,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE);CHKERRQ(ierr);
ierr = DMDASetStencilType(da,DMDA_STENCIL_STAR);CHKERRQ(ierr);
ierr = DMDASetSizes(da,M,M,M);CHKERRQ(ierr);
ierr = DMDASetNumProcs(da,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
ierr = DMDASetDof(da,dof);CHKERRQ(ierr);
ierr = DMDASetStencilWidth(da,1);CHKERRQ(ierr);
ierr = DMDASetOwnershipRanges(da,NULL,NULL,NULL);CHKERRQ(ierr);
ierr = DMSetFromOptions(da);CHKERRQ(ierr);
ierr = DMSetUp(da);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da,&x);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da,&b);CHKERRQ(ierr);
ierr = ComputeRHS(da,b);CHKERRQ(ierr);
ierr = DMSetMatType(da,MATBAIJ);CHKERRQ(ierr);
ierr = DMSetFromOptions(da);CHKERRQ(ierr);
ierr = DMCreateMatrix(da,&A);CHKERRQ(ierr);
ierr = ComputeMatrix(da,A);CHKERRQ(ierr);
/* A is non-symmetric. Make A = 0.5*(A + Atrans) symmetric for testing icc and cholesky */
ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&Atrans);CHKERRQ(ierr);
ierr = MatAXPY(A,1.0,Atrans,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatScale(A,0.5);CHKERRQ(ierr);
ierr = MatDestroy(&Atrans);CHKERRQ(ierr);
/* Test sbaij matrix */
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,NULL, "-test_sbaij1", &flg,NULL);CHKERRQ(ierr);
if (flg) {
Mat sA;
PetscBool issymm;
ierr = MatIsTranspose(A,A,0.0,&issymm);CHKERRQ(ierr);
if (issymm) {
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
} else {ierr = PetscPrintf(PETSC_COMM_WORLD,"Warning: A is non-symmetric\n");CHKERRQ(ierr);}
ierr = MatConvert(A,MATSBAIJ,MAT_INITIAL_MATRIX,&sA);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
A = sA;
}
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,A,A);CHKERRQ(ierr);
ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
ierr = PCSetDM(pc,(DM)da);CHKERRQ(ierr);
if (trans) {
ierr = KSPSolveTranspose(ksp,b,x);CHKERRQ(ierr);
} else {
ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
}
/* check final residual */
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,NULL, "-check_final_residual", &flg,NULL);CHKERRQ(ierr);
if (flg) {
Vec b1;
PetscReal norm;
ierr = KSPGetSolution(ksp,&x);CHKERRQ(ierr);
ierr = VecDuplicate(b,&b1);CHKERRQ(ierr);
ierr = MatMult(A,x,b1);CHKERRQ(ierr);
ierr = VecAXPY(b1,-1.0,b);CHKERRQ(ierr);
ierr = VecNorm(b1,NORM_2,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Final residual %g\n",norm);CHKERRQ(ierr);
ierr = VecDestroy(&b1);CHKERRQ(ierr);
}
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
PetscErrorCode BearQueryMat(PetscInt s, PetscScalar c, Mat invL1, Mat invU1, Mat invL2, Mat invU2, Mat H12, Mat H21, Vec order){
PetscErrorCode err;
PetscInt n1, n2, n, M, N;
PetscInt oseed;
PetscScalar val, one = 1.0;
PetscMPIInt size;
PetscLogDouble tic, toc;
Mat r = NULL;
Mat r1 = NULL, q1 = NULL, t1_1 = NULL, t1_2 = NULL, t1_3 = NULL, t1_4 = NULL, t1_5 = NULL; // dimension: n1
Mat r2 = NULL, q2 = NULL, q_tilda = NULL, t2_1 = NULL, t2_2 = NULL, t2_3 = NULL; // dimension: n2_idx
Vec vr=NULL, vr1=NULL, vr2=NULL;
PetscInt col = 0;
err = MPI_Comm_size(PETSC_COMM_WORLD, &size); CHKERRQ(err);
err = MatGetSize(H12, &n1, &n2); CHKERRQ(err);
n = n1 + n2;
err = PetscPrintf(PETSC_COMM_WORLD, "n1: %d, n2: %d\n", n1, n2); CHKERRQ(err);
err = MatCreateAIJ(PETSC_COMM_WORLD, PETSC_DECIDE, 1, n, size, 1, NULL, 1, NULL, &r); CHKERRQ(err);
err = MatCreateAIJ(PETSC_COMM_WORLD, PETSC_DECIDE, 1, n1, size, 1, NULL, 1, NULL, &q1); CHKERRQ(err);
err = MatCreateAIJ(PETSC_COMM_WORLD, PETSC_DECIDE, 1, n2, size, 1, NULL, 1, NULL, &q2); CHKERRQ(err);
// err = MatCreate(PETSC_COMM_WORLD, &q2); CHKERRQ(err);
// err = MatSetSizes(q2, PETSC_DECIDE, PETSC_DECIDE, n2, 1); CHKERRQ(err);
// err = MatSetType(q2, MATAIJ); CHKERRQ(err);
// err = MatSetUp(q2);
s = s - 1; // shift -1 for zero-based index
err = VecGetValues(order, 1, &s, &val); CHKERRQ(err);
oseed = (PetscInt) val;
// err = PetscPrintf(PETSC_COMM_WORLD, "Given seed: %d, Reorered seed: %d (0 ~ n-1)\n", s, oseed); CHKERRQ(err);
if(oseed < n1){
//err = MatSetValues(q1, 1, &oseed, 1, &col, &one, INSERT_VALUES); CHKERRQ(err);
err = MatSetValue(q1, oseed, col, one, INSERT_VALUES); CHKERRQ(err);
}else{
oseed = oseed - n1;
//err = MatSetValues(q2, 1, &oseed, 1, &col, &one, INSERT_VALUES); CHKERRQ(err);
err = MatSetValue(q2, oseed, col, one, INSERT_VALUES); CHKERRQ(err);
//err = printVecSum(q2);
}
err = MatAssemblyBegin(q1, MAT_FINAL_ASSEMBLY); CHKERRQ(err);
err = MatAssemblyEnd(q1, MAT_FINAL_ASSEMBLY); CHKERRQ(err);
err = MatAssemblyBegin(q2, MAT_FINAL_ASSEMBLY); CHKERRQ(err);
err = MatAssemblyEnd(q2, MAT_FINAL_ASSEMBLY); CHKERRQ(err);
err = printMatInfo("q1", q1);
err = printMatInfo("q2", q2);
//err = MatView(q1, PETSC_VIEWER_STDOUT_WORLD);
//err = MatView(q2, PETSC_VIEWER_STDOUT_WORLD);
err = MatDuplicate(q1, MAT_DO_NOT_COPY_VALUES, &r1); CHKERRQ(err);
err = MatDuplicate(q1, MAT_DO_NOT_COPY_VALUES, &t1_1); CHKERRQ(err);
err = MatDuplicate(q1, MAT_DO_NOT_COPY_VALUES, &t1_2); CHKERRQ(err);
err = MatDuplicate(q1, MAT_DO_NOT_COPY_VALUES, &t1_3); CHKERRQ(err);
err = MatDuplicate(q1, MAT_DO_NOT_COPY_VALUES, &t1_4); CHKERRQ(err);
err = MatDuplicate(q1, MAT_DO_NOT_COPY_VALUES, &t1_5); CHKERRQ(err);
err = MatDuplicate(q2, MAT_DO_NOT_COPY_VALUES, &r2); CHKERRQ(err);
err = MatDuplicate(q2, MAT_DO_NOT_COPY_VALUES, &q_tilda); CHKERRQ(err);
err = MatDuplicate(q2, MAT_DO_NOT_COPY_VALUES, &t2_1); CHKERRQ(err);
err = MatDuplicate(q2, MAT_DO_NOT_COPY_VALUES, &t2_2); CHKERRQ(err);
err = MatDuplicate(q2, MAT_DO_NOT_COPY_VALUES, &t2_3); CHKERRQ(err);
err = MatMatMult(invL1, q1, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &t1_1); CHKERRQ(err);
err = MatMatMult(invU1, t1_1, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &t1_2); CHKERRQ(err);
err = MatMatMult(H21, t1_2, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &t2_1); CHKERRQ(err);
err = MatScale(t2_1, -1.0); CHKERRQ(err);
err = MatAXPY(t2_1, 1.0, q2, DIFFERENT_NONZERO_PATTERN); CHKERRQ(err);
//MatView(t1_1, PETSC_VIEWER_STDOUT_WORLD);
err = PetscTime(&tic);
err = MatMatMult(invL2, t2_1, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &t2_2); CHKERRQ(err);
err = MatMatMult(invU2, t2_2, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &r2); CHKERRQ(err);
err = PetscTime(&toc);
err = PetscPrintf(PETSC_COMM_WORLD, "running time: %f sec\n", toc-tic); CHKERRQ(err);
err = MatMatMult(H12, r2, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &t1_3); CHKERRQ(err);
err = MatScale(t1_3, -1.0); CHKERRQ(err);
err = MatAXPY(t1_3, 1.0, q1, DIFFERENT_NONZERO_PATTERN); CHKERRQ(err);
err = MatMatMult(invL1, t1_3, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &t1_5); CHKERRQ(err);
err = MatMatMult(invU1, t1_5, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &r1); CHKERRQ(err);
//MatView(r1, PETSC_VIEWER_STDOUT_WORLD);
MatGetSize(r1, &M, &N);
PetscPrintf(PETSC_COMM_WORLD, "%d %d\n", M, N);
err = VecCreateMPI(PETSC_COMM_WORLD, PETSC_DECIDE, n1, &vr1);
err = MatGetColumnVector(r1, vr1, 0);
err = VecCreateMPI(PETSC_COMM_WORLD, PETSC_DECIDE, n2, &vr2);
err = MatGetColumnVector(r2, vr2, 0);
err = printMatInfo("r2", r2);
/*
// Start matrix-vec multiplications
err = MatMult(invU2, t2_2, r2); CHKERRQ(err);
err = MatMult(H12, r2, t1_3); CHKERRQ(err);
err = VecAXPBYPCZ(t1_4, 1.0, -1.0, 0.0, q1, t1_3); CHKERRQ(err);
err = MatMult(invL1, t1_4, t1_5); CHKERRQ(err);
err = MatMult(invU1, t1_5, r1); CHKERRQ(err);
//err = printVecSum(r1);
//err = VecView(r2, PETSC_VIEWER_STDOUT_WORLD);
// Concatenate r1 and r2
err = VecMerge(r1, r2, r); CHKERRQ(err);
err = VecScale(r, c); CHKERRQ(err);
//err = VecView(r, PETSC_VIEWER_STDOUT_WORLD);
//err = VecDuplicate(r, &or); CHKERRQ(err);
err = VecReorder(r, order, or); CHKERRQ(err);
//err = VecView(or, PETSC_VIEWER_STDOUT_WORLD);
*/
err = MatDestroy(&r); CHKERRQ(err);
err = MatDestroy(&r1); CHKERRQ(err);
err = MatDestroy(&q1); CHKERRQ(err);
err = MatDestroy(&t1_1); CHKERRQ(err);
err = MatDestroy(&t1_2); CHKERRQ(err);
err = MatDestroy(&t1_3); CHKERRQ(err);
err = MatDestroy(&t1_4); CHKERRQ(err);
err = MatDestroy(&t1_5); CHKERRQ(err);
err = MatDestroy(&r2); CHKERRQ(err);
err = MatDestroy(&q2); CHKERRQ(err);
err = MatDestroy(&q_tilda); CHKERRQ(err);
err = MatDestroy(&t2_1); CHKERRQ(err);
err = MatDestroy(&t2_2); CHKERRQ(err);
err = MatDestroy(&t2_3); CHKERRQ(err);
return err;
}
void _Stokes_SLE_PenaltySolver_Solve( void* solver,void* stokesSLE ) {
Stokes_SLE_PenaltySolver* self = (Stokes_SLE_PenaltySolver*)solver;
Stokes_SLE* sle = (Stokes_SLE*)stokesSLE;
/* Create shortcuts to stuff needed on sle */
Mat kMatrix = sle->kStiffMat->matrix;
Mat gradMat = sle->gStiffMat->matrix;
Mat divMat = NULL;
Mat C_Mat = sle->cStiffMat->matrix;
Vec uVec = sle->uSolnVec->vector;
Vec pVec = sle->pSolnVec->vector;
Vec fVec = sle->fForceVec->vector;
Vec hVec = sle->hForceVec->vector;
Vec hTempVec;
Vec fTempVec;
Vec penalty;
Mat GTrans, kHat;
KSP ksp_v;
double negOne=-1.0;
double one=1.0;
Mat C_InvMat;
Vec diagC;
PC pc;
int rank;
MPI_Comm_rank( MPI_COMM_WORLD, &rank );
Journal_DPrintf( self->debug, "In %s():\n", __func__ );
VecDuplicate( hVec, &hTempVec );
VecDuplicate( fVec, &fTempVec );
VecDuplicate( pVec, &diagC );
if( sle->dStiffMat == NULL ) {
Journal_DPrintf( self->debug, "Div matrix == NULL : Problem is assumed to be symmetric. ie Div = GTrans \n");
#if( PETSC_VERSION_MAJOR <= 2 )
MatTranspose( gradMat, >rans );
#else
MatTranspose( gradMat, MAT_INITIAL_MATRIX, >rans );
#endif
divMat = GTrans;
}
else {
MatType type;
PetscInt size[2];
MatGetType( sle->dStiffMat->matrix, &type );
MatGetLocalSize( sle->dStiffMat->matrix, size + 0, size + 1 );
/* make a copy we can play with */
MatCreate( sle->comm, >rans );
MatSetSizes( GTrans, size[0], size[1], PETSC_DECIDE, PETSC_DECIDE );
MatSetType( GTrans, type );
#if (((PETSC_VERSION_MAJOR==3) && (PETSC_VERSION_MINOR>=3)) || (PETSC_VERSION_MAJOR>3) )
MatSetUp(GTrans);
#endif
MatCopy( sle->dStiffMat->matrix, GTrans, DIFFERENT_NONZERO_PATTERN );
divMat = GTrans;
}
Stokes_SLE_PenaltySolver_MakePenalty( self, sle, &penalty );
/* Create CInv */
MatGetDiagonal( C_Mat, diagC );
VecReciprocal( diagC );
VecPointwiseMult( diagC, penalty, diagC );
{ /* Print the maximum and minimum penalties in my system. */
PetscInt idx;
PetscReal min, max;
VecMin( diagC, &idx, &min );
VecMax( diagC, &idx, &max );
if( rank == 0 ) {
printf( "PENALTY RANGE:\n" );
printf( " MIN: %e\n", min );
printf( " MAX: %e\n", max );
}
}
MatDiagonalSet( C_Mat, diagC, INSERT_VALUES );
C_InvMat = C_Mat; /* Use pointer CInv since C has been inverted */
/* Build RHS : rhs = f - GCInv h */
MatMult( C_InvMat, hVec, hTempVec ); /* hTempVec = C_InvMat * hVec */
VecScale( hTempVec, -1.0 );
MatMult( gradMat, hTempVec, fTempVec );
#if 0
VecPointwiseMult( fTempVec, penalty, fTempVec );
{ /* Print the maximum and minimum penalties in my system. */
PetscInt idx;
PetscReal min, max;
VecMin( fTempVec, &idx, &min );
VecMax( fTempVec, &idx, &max );
printf( "PENALTY RANGE:\n" );
printf( " MIN: %e\n", min );
printf( " MAX: %e\n", max );
}
#endif
VecAXPY( fTempVec, 1.0, fVec );
/*MatMultAdd( gradMat, hTempVec, fVec, fTempVec );*/
/* Build G CInv GTrans */
/* MatTranspose( gradMat, >rans ); */
/* since CInv is diagonal we can just scale mat entries by the diag vector */
MatDiagonalScale( divMat, diagC, PETSC_NULL ); /* Div = CInve Div */
MatMatMult( gradMat, divMat, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &kHat );
/*MatDiagonalScale( kHat, penalty, PETSC_NULL );*/
MatScale( kHat, -1.0 );
MatAXPY( kMatrix, 1.0, kHat, SAME_NONZERO_PATTERN );
/* Setup solver context and make sure that it uses a direct solver */
KSPCreate( sle->comm, &ksp_v );
Stg_KSPSetOperators( ksp_v, kMatrix, kMatrix, DIFFERENT_NONZERO_PATTERN );
KSPSetType( ksp_v, KSPPREONLY );
KSPGetPC( ksp_v, &pc );
PCSetType( pc, PCLU );
KSPSetFromOptions( ksp_v );
KSPSolve( ksp_v, fTempVec, uVec );
/* Recover p */
if( sle->dStiffMat == NULL ) {
/* since Div was modified when C is diagonal, re build the transpose */
if( GTrans != PETSC_NULL )
Stg_MatDestroy(>rans );
#if( PETSC_VERSION_MAJOR <= 2 )
MatTranspose( gradMat, >rans );
#else
MatTranspose( gradMat, MAT_INITIAL_MATRIX, >rans );
#endif
divMat = GTrans;
}
else {
/* never modified Div_null so set divMat to point back to it */
divMat = sle->dStiffMat->matrix;
}
MatMult( divMat, uVec, hTempVec ); /* hTemp = Div v */
VecAYPX( hTempVec, negOne, hVec ); /* hTemp = H - hTemp : hTemp = H - Div v */
MatMult( C_InvMat, hTempVec, pVec ); /* p = CInv hTemp : p = CInv ( H - Div v ) */
Stg_MatDestroy(&kHat );
if( fTempVec != PETSC_NULL ) Stg_VecDestroy(&fTempVec );
if( hTempVec != PETSC_NULL ) Stg_VecDestroy(&hTempVec );
if( diagC != PETSC_NULL ) Stg_VecDestroy(&diagC );
if( ksp_v != PETSC_NULL ) Stg_KSPDestroy(&ksp_v );
if( GTrans != PETSC_NULL ) Stg_MatDestroy(>rans );
}