/*
Performs y <- S*^{-1} x
S*^{-1} = ( B' Bt' )^{-1} B' F' Bt' ( B' Bt' )^{-1}
where
F' = X1 F Y1
Bt' = X1 Bt Y2
B' = X2 B Y1
Thus, S*^{-1} = [ X2 B Y1 X1 Bt Y2 ]^{-1} . [ X2 B Y1 . X1 F Y1 . X1 Bt Y2 ] . [ X2 B Y1 X1 Bt Y2 ]^{-1}
= Y2^{-1} ksp_BBt X2^{-1} . [ B' F' Bt' ] . Y2^{-1} ksp_BBt X2^{-1}
= Y2^{-1} ksp_BBt . [ B Y1 . X1 F Y1 . X1 Bt ] . ksp_BBt X2^{-1}
*/
PetscErrorCode BSSCR_PCApply_ScGtKG( PC pc, Vec x, Vec y )
{
PC_SC_GtKG ctx = (PC_SC_GtKG)pc->data;
KSP ksp;
Mat F, Bt;
Vec s,t,X;
PetscLogDouble t0,t1;
ksp = ctx->ksp_BBt;
F = ctx->F;
Bt = ctx->Bt;
s = ctx->s;
t = ctx->t;
X = ctx->X;
/* Apply scaled Poisson operator */
/* scale x */
/* ========================================================
NOTE:
I THINK TO OMIT THESE AS WE WANT TO UNSCALE THE
PRECONDITIONER AS S IN THIS CASE IS NOT SCALED
======================================================== */
// VecPointwiseDivide( x, x, ctx->X2 ); /* x <- x/X2 */ /* NEED TO BE SURE */
if( ctx->BBt_has_cnst_nullspace == PETSC_TRUE ) {
BSSCR_VecRemoveConstNullspace( x, PETSC_NULL );
}
PetscGetTime(&t0);
KSPSolve( ksp, x, t ); /* t <- GtG_inv x */
PetscGetTime(&t1);
if (ctx->monitor_activated) {
BSSCR_PCScBFBTSubKSPMonitor(ksp,1,(t1-t0));
}
/* Apply Bt */
MatMult( Bt, t, s ); /* s <- G t */
VecPointwiseMult( s, s, ctx->X1 ); /* s <- s * X1 */
/* Apply F */
VecPointwiseMult( s, s, ctx->Y1 ); /* s <- s * Y1 */
MatMult( F, s, X ); /* X <- K s */
VecPointwiseMult( X, X, ctx->X1 ); /* X <- X * X1 */
/* Apply B */
VecPointwiseMult( X, X, ctx->Y1 ); /* X <- X * Y1 */
MatMultTranspose( Bt, X, t ); /* t <- Gt X */
if( ctx->BBt_has_cnst_nullspace == PETSC_TRUE ) {
BSSCR_VecRemoveConstNullspace( t, PETSC_NULL );
}
PetscGetTime(&t0);
KSPSolve( ksp, t, y ); /* y <- GtG_inv t */
PetscGetTime(&t1);
if (ctx->monitor_activated) {
BSSCR_PCScBFBTSubKSPMonitor(ksp,2,(t1-t0));
}
VecPointwiseMult( y, y, ctx->Y2 ); /* y <- y/Y2 */
/* undo modification made to x on entry */
// VecPointwiseMult( x, x, ctx->X2 ); /* x <- x/X2 */ /* NEED TO BE SURE */
PetscFunctionReturn(0);
}
void bsscr_summary(KSP_BSSCR * bsscrp_self, KSP ksp_S, KSP ksp_inner,
Mat K,Mat K2,Mat D,Mat G,Mat C,Vec u,Vec p,Vec f,Vec h,Vec t,
double penaltyNumber,PetscTruth KisJustK,double mgSetupTime,double scrSolveTime,double a11SingleSolveTime){
PetscTruth flg, found;
PetscInt uSize, pSize, lmax, lmin, iterations;
PetscReal rNorm, fNorm, uNorm, uNormInf, pNorm, pNormInf, p_sum, min, max;
Vec q, qq, t2, t3;
double solutionAnalysisTime;
PetscPrintf( PETSC_COMM_WORLD, "\n\nSCR Solver Summary:\n\n");
if(bsscrp_self->mg)
PetscPrintf( PETSC_COMM_WORLD, " Multigrid setup: = %.4g secs \n", mgSetupTime);
KSPGetIterationNumber( ksp_S, &iterations);
bsscrp_self->solver->stats.pressure_its = iterations;
PetscPrintf( PETSC_COMM_WORLD, " Pressure Solve: = %.4g secs / %d its\n", scrSolveTime, iterations);
KSPGetIterationNumber( ksp_inner, &iterations);
bsscrp_self->solver->stats.velocity_backsolve_its = iterations;
PetscPrintf( PETSC_COMM_WORLD, " Final V Solve: = %.4g secs / %d its\n\n", a11SingleSolveTime, iterations);
/***************************************************************************************************************/
flg = PETSC_TRUE; PetscOptionsGetTruth( PETSC_NULL, "-scr_ksp_solution_summary", &flg, &found );
if(flg) {
PetscScalar KuNorm;
solutionAnalysisTime = MPI_Wtime();
VecGetSize( u, &uSize );
VecGetSize( p, &pSize );
VecDuplicate( u, &t2 );
VecDuplicate( u, &t3 );
MatMult( K, u, t3); VecNorm( t3, NORM_2, &KuNorm );
double angle, kdot;
if(penaltyNumber > 1e-10){/* should change this to ifK2built maybe */
MatMult( K2, u, t2); VecNorm( t2, NORM_2, &rNorm );
VecDot(t2,t3,&kdot);
angle = (kdot/(rNorm*KuNorm));
PetscPrintf( PETSC_COMM_WORLD, " <K u, K2 u>/(|K u| |K2 u|) = %.6e\n", angle);
}
VecNorm( t, NORM_2, &rNorm ); /* t = f- G p should be the formal residual vector, calculated on line 267 in auglag-driver-DGTGD.c */
VecDot(t3,t,&kdot);
angle = (kdot/(rNorm*KuNorm));
PetscPrintf( PETSC_COMM_WORLD, " <K u, (f-G p)>/(|K u| |f- G p|) = %.6e\n\n", angle);
MatMult( K, u, t2); VecNorm(t2, NORM_2, &KuNorm);
VecAYPX( t2, -1.0, t ); /* t2 <- -t2 + t : t = f- G p should be the formal residual vector, calculated on line 267 in auglag-driver-DGTGD.c*/
VecNorm( t2, NORM_2, &rNorm );
VecNorm( f, NORM_2, &fNorm );
if(KisJustK){
PetscPrintf( PETSC_COMM_WORLD,"Velocity back-solve with original K matrix\n");
PetscPrintf( PETSC_COMM_WORLD,"Solved K u = G p -f\n");
PetscPrintf( PETSC_COMM_WORLD,"Residual with original K matrix\n");
PetscPrintf( PETSC_COMM_WORLD, " |f - K u - G p| = %.12e\n", rNorm);
PetscPrintf( PETSC_COMM_WORLD, " |f - K u - G p|/|f| = %.12e\n", rNorm/fNorm);
if(penaltyNumber > 1e-10){/* means the restore_K flag was used */
//if(K2 && f2){
MatAXPY(K,penaltyNumber,K2,DIFFERENT_NONZERO_PATTERN);/* Computes K = penaltyNumber*K2 + K */
//VecAXPY(f,penaltyNumber,f2); /* f = penaltyNumber*f2 + f */
KisJustK=PETSC_FALSE;
MatMult( K, u, t2);
MatMult( G, p, t);
VecAYPX( t, -1.0, f ); /* t <- -t + f */
VecAYPX( t2, -1.0, t ); /* t2 <- -t2 + t */
VecNorm( t2, NORM_2, &rNorm );
PetscPrintf( PETSC_COMM_WORLD,"Residual with K+K2 matrix and f rhs vector\n");
PetscPrintf( PETSC_COMM_WORLD, " |(f) - (K + K2) u - G p| = %.12e\n", rNorm);
//}
}
}
else{
PetscPrintf( PETSC_COMM_WORLD,"Velocity back-solve with K+K2 matrix\n");
PetscPrintf( PETSC_COMM_WORLD,"Solved (K + K2) u = G p - (f)\n");
PetscPrintf( PETSC_COMM_WORLD,"Residual with K+K2 matrix and f rhs vector\n");
PetscPrintf( PETSC_COMM_WORLD, " |(f) - (K + K2) u - G p| = %.12e\n", rNorm);
PetscReal KK2Norm,KK2Normf;
MatNorm(K,NORM_1,&KK2Norm);
MatNorm(K,NORM_FROBENIUS,&KK2Normf);
penaltyNumber = -penaltyNumber;
MatAXPY(K,penaltyNumber,K2,DIFFERENT_NONZERO_PATTERN);/* Computes K = penaltyNumber*K2 + K */
//VecAXPY(f,penaltyNumber,f2); /* f = penaltyNumber*f2 + f */
KisJustK=PETSC_FALSE;
MatMult( K, u, t2); /* t2 = K*u */
MatMult( G, p, t); /* t = G*p */
VecAYPX( t, -1.0, f ); /* t <- f - t ; t = f - G*p */
VecAYPX( t2, -1.0, t ); /* t2 <- t - t2; t2 = f - G*p - K*u */
VecNorm( t2, NORM_2, &rNorm );
PetscPrintf( PETSC_COMM_WORLD,"Residual with original K matrix\n");
PetscPrintf( PETSC_COMM_WORLD, " |f - K u - G p| = %.12e\n", rNorm);
PetscPrintf( PETSC_COMM_WORLD, " |f - K u - G p|/|f| = %.12e\n", rNorm/fNorm);
PetscReal KNorm, K2Norm;
MatNorm(K,NORM_1,&KNorm); MatNorm(K2,NORM_1,&K2Norm);
PetscPrintf( PETSC_COMM_WORLD,"K and K2 norm_1 %.12e %.12e ratio %.12e\n",KNorm,K2Norm,K2Norm/KNorm);
MatNorm(K,NORM_INFINITY,&KNorm); MatNorm(K2,NORM_INFINITY,&K2Norm);
PetscPrintf( PETSC_COMM_WORLD,"K and K2 norm_inf %.12e %.12e ratio %.12e\n",KNorm,K2Norm,K2Norm/KNorm);
MatNorm(K,NORM_FROBENIUS,&KNorm); MatNorm(K2,NORM_FROBENIUS,&K2Norm);
PetscPrintf( PETSC_COMM_WORLD,"K and K2 norm_frob %.12e %.12e ratio %.12e\n",KNorm,K2Norm,K2Norm/KNorm);
PetscPrintf( PETSC_COMM_WORLD,"K+r*K2 norm_1 %.12e\n",KK2Norm);
PetscPrintf( PETSC_COMM_WORLD,"K+r*K2 norm_frob %.12e\n",KK2Normf);
penaltyNumber = -penaltyNumber;
MatAXPY(K,penaltyNumber,K2,DIFFERENT_NONZERO_PATTERN);/* Computes K = penaltyNumber*K2 + K */
}
PetscPrintf( PETSC_COMM_WORLD,"\n");
PetscPrintf( PETSC_COMM_WORLD, " |K u| = %.12e\n", KuNorm);
if(penaltyNumber > 1e-10){
MatMult( K2, u, t2); VecNorm( t2, NORM_2, &rNorm );
PetscPrintf( PETSC_COMM_WORLD, " |K2 u| = %.12e\n", rNorm);
PetscPrintf( PETSC_COMM_WORLD,"\n");
}
VecDuplicate( p, &q );
MatMult( D, u, q ); /* q = G'*u = D*u */
VecNorm( u, NORM_2, &uNorm );
VecNorm( q, NORM_2, &rNorm );
PetscPrintf( PETSC_COMM_WORLD, " |G^T u|_2 = %.6e\n", rNorm );
PetscPrintf( PETSC_COMM_WORLD, " |G^T u|_2/|u|_2 = %.6e\n", sqrt( (double) uSize / (double) pSize ) * rNorm / uNorm);
VecDuplicate( p, &qq );
MatMultTranspose( G, u, qq );
VecNorm( qq, NORM_2, &rNorm );
PetscPrintf( PETSC_COMM_WORLD, " |G^T u|/|u| = %.8e\n", rNorm/uNorm ); /* to compare directly with Uzawa */
VecNorm( q, NORM_INFINITY, &rNorm );
PetscPrintf( PETSC_COMM_WORLD, " |G^T u|_infty/|u|_2 = %.6e\n", sqrt( (double) uSize ) * rNorm / uNorm);
/* create G'*u+C*p-h to check on this constraint */
/* already have q = D*u */
VecZeroEntries(qq);
if(C){
MatMult( C, p, qq );
}
VecAYPX( q, 1.0, qq ); /* q = q+qq; G'*u + C*p*/
VecAXPY( q, -1.0, h ); /* q = q-h; G'*u + C*p - h */
VecNorm( q, NORM_2, &rNorm );
PetscPrintf( PETSC_COMM_WORLD, " |G^T u + C p - h| = %.8e :constraint\n", rNorm );
VecNorm( u, NORM_INFINITY, &uNormInf );
VecNorm( u, NORM_2, &uNorm );
VecGetSize( u, &uSize );
VecNorm( p, NORM_INFINITY, &pNormInf );
VecNorm( p, NORM_2, &pNorm );
PetscPrintf( PETSC_COMM_WORLD, " |u|_{\\infty} = %.6e , u_rms = %.6e\n",
uNormInf, uNorm / sqrt( (double) uSize ) );
PetscPrintf( PETSC_COMM_WORLD, " |p|_{\\infty} = %.6e , p_rms = %.6e\n",
pNormInf, pNorm / sqrt( (double) pSize ) );
VecMax( u, &lmax, &max );
VecMin( u, &lmin, &min );
PetscPrintf( PETSC_COMM_WORLD, " min/max(u) = %.6e [%d] / %.6e [%d]\n",min,lmin,max,lmax);
bsscrp_self->solver->stats.vmin = min;
bsscrp_self->solver->stats.vmax = max;
VecMax( p, &lmax, &max );
VecMin( p, &lmin, &min );
PetscPrintf( PETSC_COMM_WORLD, " min/max(p) = %.6e [%d] / %.6e [%d]\n",min,lmin,max,lmax);
bsscrp_self->solver->stats.pmin = min;
bsscrp_self->solver->stats.pmax = max;
VecSum( p, &p_sum );
PetscPrintf( PETSC_COMM_WORLD, " \\sum_i p_i = %.6e \n", p_sum );
bsscrp_self->solver->stats.p_sum=p_sum;
solutionAnalysisTime = MPI_Wtime() - solutionAnalysisTime;
PetscPrintf( PETSC_COMM_WORLD, "\n Time for this analysis = %.4g secs\n\n",solutionAnalysisTime);
Stg_VecDestroy(&t2 );
Stg_VecDestroy(&t3 );
Stg_VecDestroy(&q );
Stg_VecDestroy(&qq );
}
}
PetscInt main(PetscInt argc,char **args)
{
PetscErrorCode ierr;
PetscMPIInt rank,size;
PetscInt N0=50,N1=20,N=N0*N1;
PetscRandom rdm;
PetscScalar a;
PetscReal enorm;
Vec x,y,z;
PetscBool view=PETSC_FALSE,use_interface=PETSC_TRUE;
ierr = PetscInitialize(&argc,&args,(char *)0,help);CHKERRQ(ierr);
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This example requires complex numbers");
#endif
ierr = PetscOptionsBegin(PETSC_COMM_WORLD, PETSC_NULL, "FFTW Options", "ex143");CHKERRQ(ierr);
ierr = PetscOptionsBool("-vec_view draw", "View the vectors", "ex143", view, &view, PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsBool("-use_FFTW_interface", "Use PETSc-FFTW interface", "ex143",use_interface, &use_interface, PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsEnd();CHKERRQ(ierr);
ierr = PetscOptionsGetBool(PETSC_NULL,"-use_FFTW_interface",&use_interface,PETSC_NULL);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &rank);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD, &rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
if (!use_interface){
/* Use mpi FFTW without PETSc-FFTW interface, 2D case only */
/*---------------------------------------------------------*/
fftw_plan fplan,bplan;
fftw_complex *data_in,*data_out,*data_out2;
ptrdiff_t alloc_local,local_n0,local_0_start;
if (!rank) printf("Use FFTW without PETSc-FFTW interface\n");
fftw_mpi_init();
N = N0*N1;
alloc_local = fftw_mpi_local_size_2d(N0,N1,PETSC_COMM_WORLD,&local_n0,&local_0_start);
data_in = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
data_out = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
data_out2 = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,1,(PetscInt)local_n0*N1,(PetscInt)N,(const PetscScalar*)data_in,&x);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) x, "Real Space vector");CHKERRQ(ierr);
ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,1,(PetscInt)local_n0*N1,(PetscInt)N,(const PetscScalar*)data_out,&y);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) y, "Frequency space vector");CHKERRQ(ierr);
ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,1,(PetscInt)local_n0*N1,(PetscInt)N,(const PetscScalar*)data_out2,&z);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) z, "Reconstructed vector");CHKERRQ(ierr);
fplan = fftw_mpi_plan_dft_2d(N0,N1,data_in,data_out,PETSC_COMM_WORLD,FFTW_FORWARD,FFTW_ESTIMATE);
bplan = fftw_mpi_plan_dft_2d(N0,N1,data_out,data_out2,PETSC_COMM_WORLD,FFTW_BACKWARD,FFTW_ESTIMATE);
ierr = VecSetRandom(x, rdm);CHKERRQ(ierr);
if (view){ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
fftw_execute(fplan);
if (view){ierr = VecView(y,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
fftw_execute(bplan);
/* Compare x and z. FFTW computes an unnormalized DFT, thus z = N*x */
a = 1.0/(PetscReal)N;
ierr = VecScale(z,a);CHKERRQ(ierr);
if (view){ierr = VecView(z, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
ierr = VecAXPY(z,-1.0,x);CHKERRQ(ierr);
ierr = VecNorm(z,NORM_1,&enorm);CHKERRQ(ierr);
if (enorm > 1.e-11){
ierr = PetscPrintf(PETSC_COMM_SELF," Error norm of |x - z| %G\n",enorm);CHKERRQ(ierr);
}
/* Free spaces */
fftw_destroy_plan(fplan);
fftw_destroy_plan(bplan);
fftw_free(data_in); ierr = VecDestroy(&x);CHKERRQ(ierr);
fftw_free(data_out); ierr = VecDestroy(&y);CHKERRQ(ierr);
fftw_free(data_out2);ierr = VecDestroy(&z);CHKERRQ(ierr);
} else {
/* Use PETSc-FFTW interface */
/*-------------------------------------------*/
PetscInt i,*dim,k,DIM;
Mat A;
N=1;
for (i=1; i<5; i++){
DIM = i;
ierr = PetscMalloc(i*sizeof(PetscInt),&dim);CHKERRQ(ierr);
for (k=0;k<i;k++){
dim[k]=30;
}
N *= dim[i-1];
/* Create FFTW object */
if (!rank) printf("Use PETSc-FFTW interface...%d-DIM:%d \n",DIM,N);
ierr = MatCreateFFT(PETSC_COMM_WORLD,DIM,dim,MATFFTW,&A);CHKERRQ(ierr);
/* Create vectors that are compatible with parallel layout of A - must call MatGetVecs()! */
ierr = MatGetVecsFFTW(A,&x,&y,&z);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) x, "Real space vector");CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) y, "Frequency space vector");CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) z, "Reconstructed vector");CHKERRQ(ierr);
/* Set values of space vector x */
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
if (view){ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
// Apply FFTW_FORWARD and FFTW_BACKWARD
ierr = MatMult(A,x,y);CHKERRQ(ierr);
if (view){ierr = VecView(y,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
ierr = MatMultTranspose(A,y,z);CHKERRQ(ierr);
// Compare x and z. FFTW computes an unnormalized DFT, thus z = N*x
a = 1.0/(PetscReal)N;
ierr = VecScale(z,a);CHKERRQ(ierr);
if (view){ierr = VecView(z,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
ierr = VecAXPY(z,-1.0,x);CHKERRQ(ierr);
ierr = VecNorm(z,NORM_1,&enorm);CHKERRQ(ierr);
if (enorm > 1.e-9 && !rank){
ierr = PetscPrintf(PETSC_COMM_SELF," Error norm of |x - z| %e\n",enorm);CHKERRQ(ierr);
}
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&z);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = PetscFree(dim);CHKERRQ(ierr);
}
}
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **argv)
{
Mat A,A11,A12,A21,A22;
Vec X,X1,X2,Y,Z,Z1,Z2;
PetscScalar *a,*b,*x,*y,*z,v,one=1;
PetscReal nrm;
PetscErrorCode ierr;
PetscInt size=8,size1=6,size2=2, i,j;
PetscInitialize(&argc,&argv,0,0);
/*
* Create matrix and three vectors: these are all normal
*/
ierr = PetscMalloc(size*size*sizeof(PetscScalar),&a);CHKERRQ(ierr);
ierr = PetscMalloc(size*size*sizeof(PetscScalar),&b);CHKERRQ(ierr);
for (i=0; i<size; i++) {
for (j=0; j<size; j++) {
a[i+j*size] = rand(); b[i+j*size] = a[i+j*size];
}
}
ierr = MatCreate(MPI_COMM_SELF,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,size,size,size,size);CHKERRQ(ierr);
ierr = MatSetType(A,MATSEQDENSE);CHKERRQ(ierr);
ierr = MatSeqDenseSetPreallocation(A,a);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = PetscMalloc(size*sizeof(PetscScalar),&x);CHKERRQ(ierr);
for (i=0; i<size; i++) {
x[i] = one;
}
ierr = VecCreateSeqWithArray(MPI_COMM_SELF,size,x,&X);CHKERRQ(ierr);
ierr = VecAssemblyBegin(X);CHKERRQ(ierr);
ierr = VecAssemblyEnd(X);CHKERRQ(ierr);
ierr = PetscMalloc(size*sizeof(PetscScalar),&y);CHKERRQ(ierr);
ierr = VecCreateSeqWithArray(MPI_COMM_SELF,size,y,&Y);CHKERRQ(ierr);
ierr = VecAssemblyBegin(Y);CHKERRQ(ierr);
ierr = VecAssemblyEnd(Y);CHKERRQ(ierr);
ierr = PetscMalloc(size*sizeof(PetscScalar),&z);CHKERRQ(ierr);
ierr = VecCreateSeqWithArray(MPI_COMM_SELF,size,z,&Z);CHKERRQ(ierr);
ierr = VecAssemblyBegin(Z);CHKERRQ(ierr);
ierr = VecAssemblyEnd(Z);CHKERRQ(ierr);
/*
* Now create submatrices and subvectors
*/
ierr = MatCreate(MPI_COMM_SELF,&A11);CHKERRQ(ierr);
ierr = MatSetSizes(A11,size1,size1,size1,size1);CHKERRQ(ierr);
ierr = MatSetType(A11,MATSEQDENSE);CHKERRQ(ierr);
ierr = MatSeqDenseSetPreallocation(A11,b);CHKERRQ(ierr);
ierr = MatSeqDenseSetLDA(A11,size);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A11,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A11,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatCreate(MPI_COMM_SELF,&A12);CHKERRQ(ierr);
ierr = MatSetSizes(A12,size1,size2,size1,size2);CHKERRQ(ierr);
ierr = MatSetType(A12,MATSEQDENSE);CHKERRQ(ierr);
ierr = MatSeqDenseSetPreallocation(A12,b+size1*size);CHKERRQ(ierr);
ierr = MatSeqDenseSetLDA(A12,size);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A12,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A12,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatCreate(MPI_COMM_SELF,&A21);CHKERRQ(ierr);
ierr = MatSetSizes(A21,size2,size1,size2,size1);CHKERRQ(ierr);
ierr = MatSetType(A21,MATSEQDENSE);CHKERRQ(ierr);
ierr = MatSeqDenseSetPreallocation(A21,b+size1);CHKERRQ(ierr);
ierr = MatSeqDenseSetLDA(A21,size);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A21,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A21,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatCreate(MPI_COMM_SELF,&A22);CHKERRQ(ierr);
ierr = MatSetSizes(A22,size2,size2,size2,size2);CHKERRQ(ierr);
ierr = MatSetType(A22,MATSEQDENSE);CHKERRQ(ierr);
ierr = MatSeqDenseSetPreallocation(A22,b+size1*size+size1);CHKERRQ(ierr);
ierr = MatSeqDenseSetLDA(A22,size);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A22,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A22,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = VecCreateSeqWithArray(MPI_COMM_SELF,size1,x,&X1);CHKERRQ(ierr);
ierr = VecCreateSeqWithArray(MPI_COMM_SELF,size2,x+size1,&X2);CHKERRQ(ierr);
ierr = VecCreateSeqWithArray(MPI_COMM_SELF,size1,z,&Z1);CHKERRQ(ierr);
ierr = VecCreateSeqWithArray(MPI_COMM_SELF,size2,z+size1,&Z2);CHKERRQ(ierr);
/*
* Now multiple matrix times input in two ways;
* compare the results
*/
ierr = MatMult(A,X,Y);CHKERRQ(ierr);
ierr = MatMult(A11,X1,Z1);CHKERRQ(ierr);
ierr = MatMultAdd(A12,X2,Z1,Z1);CHKERRQ(ierr);
ierr = MatMult(A22,X2,Z2);CHKERRQ(ierr);
ierr = MatMultAdd(A21,X1,Z2,Z2);CHKERRQ(ierr);
ierr = VecAXPY(Z,-1.0,Y);CHKERRQ(ierr);
ierr = VecNorm(Z,NORM_2,&nrm);
printf("Test1; error norm=%e\n",nrm);
/*
printf("MatMult the usual way:\n"); VecView(Y,0);
printf("MatMult by subblock:\n"); VecView(Z,0);
*/
/*
* Next test: change both matrices
*/
v = rand(); i=1; j=size-2;
ierr = MatSetValues(A,1,&i,1,&j,&v,INSERT_VALUES);CHKERRQ(ierr);
j -= size1;
ierr = MatSetValues(A12,1,&i,1,&j,&v,INSERT_VALUES);CHKERRQ(ierr);
v = rand(); i=j=size1+1;
ierr = MatSetValues(A,1,&i,1,&j,&v,INSERT_VALUES);CHKERRQ(ierr);
i=j=1;
ierr = MatSetValues(A22,1,&i,1,&j,&v,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A12,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A12,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A22,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A22,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatMult(A,X,Y);CHKERRQ(ierr);
ierr = MatMult(A11,X1,Z1);CHKERRQ(ierr);
ierr = MatMultAdd(A12,X2,Z1,Z1);CHKERRQ(ierr);
ierr = MatMult(A22,X2,Z2);CHKERRQ(ierr);
ierr = MatMultAdd(A21,X1,Z2,Z2);CHKERRQ(ierr);
ierr = VecAXPY(Z,-1.0,Y);CHKERRQ(ierr);
ierr = VecNorm(Z,NORM_2,&nrm);
printf("Test2; error norm=%e\n",nrm);
/*
* Transpose product
*/
ierr = MatMultTranspose(A,X,Y);CHKERRQ(ierr);
ierr = MatMultTranspose(A11,X1,Z1);CHKERRQ(ierr);
ierr = MatMultTransposeAdd(A21,X2,Z1,Z1);CHKERRQ(ierr);
ierr = MatMultTranspose(A22,X2,Z2);CHKERRQ(ierr);
ierr = MatMultTransposeAdd(A12,X1,Z2,Z2);CHKERRQ(ierr);
ierr = VecAXPY(Z,-1.0,Y);CHKERRQ(ierr);
ierr = VecNorm(Z,NORM_2,&nrm);
printf("Test3; error norm=%e\n",nrm);
ierr = PetscFree(a);CHKERRQ(ierr);
ierr = PetscFree(b);CHKERRQ(ierr);
ierr = PetscFree(x);CHKERRQ(ierr);
ierr = PetscFree(y);CHKERRQ(ierr);
ierr = PetscFree(z);CHKERRQ(ierr);
ierr = MatDestroy(A);CHKERRQ(ierr);
ierr = MatDestroy(A11);CHKERRQ(ierr);
ierr = MatDestroy(A12);CHKERRQ(ierr);
ierr = MatDestroy(A21);CHKERRQ(ierr);
ierr = MatDestroy(A22);CHKERRQ(ierr);
ierr = VecDestroy(X);CHKERRQ(ierr);
ierr = VecDestroy(Y);CHKERRQ(ierr);
ierr = VecDestroy(Z);CHKERRQ(ierr);
ierr = VecDestroy(X1);CHKERRQ(ierr);
ierr = VecDestroy(X2);CHKERRQ(ierr);
ierr = VecDestroy(Z1);CHKERRQ(ierr);
ierr = VecDestroy(Z2);CHKERRQ(ierr);
/*ierr = PetscLogPrintSummary(MPI_COMM_SELF,"ex2.log");CHKERRQ(ierr);*/
ierr = PetscFinalize();CHKERRQ(ierr);
return 0;
}
PetscInt main(PetscInt argc,char **args)
{
typedef enum {RANDOM, CONSTANT, TANH, NUM_FUNCS} FuncType;
const char *funcNames[NUM_FUNCS] = {"random", "constant", "tanh"};
Mat A, AA;
PetscMPIInt size;
PetscInt N,i, stencil=1,dof=1;
PetscInt dim[3] = {10,10,10}, ndim = 3;
Vec coords,x,y,z,xx,yy,zz;
PetscReal h[3];
PetscScalar s;
PetscRandom rdm;
PetscReal norm, enorm;
PetscInt func;
FuncType function = TANH;
DM da, coordsda;
PetscBool view_x = PETSC_FALSE, view_y = PETSC_FALSE, view_z = PETSC_FALSE;
PetscErrorCode ierr;
ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This is a uniprocessor example only!");
ierr = PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "USFFT Options", "ex27");CHKERRQ(ierr);
ierr = PetscOptionsEList("-function", "Function type", "ex27", funcNames, NUM_FUNCS, funcNames[function], &func, NULL);CHKERRQ(ierr);
function = (FuncType) func;
ierr = PetscOptionsEnd();CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-view_x",&view_x,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-view_y",&view_y,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-view_z",&view_z,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetIntArray(NULL,NULL,"-dim",dim,&ndim,NULL);CHKERRQ(ierr);
ierr = DMDACreate3d(PETSC_COMM_SELF,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,dim[0], dim[1], dim[2],
PETSC_DECIDE, PETSC_DECIDE, PETSC_DECIDE,dof, stencil,NULL, NULL, NULL,&da);CHKERRQ(ierr);
ierr = DMSetFromOptions(da);CHKERRQ(ierr);
ierr = DMSetUp(da);CHKERRQ(ierr);
/* Coordinates */
ierr = DMGetCoordinateDM(da, &coordsda);
ierr = DMGetGlobalVector(coordsda, &coords);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) coords, "Grid coordinates");CHKERRQ(ierr);
for (i = 0, N = 1; i < 3; i++) {
h[i] = 1.0/dim[i];
PetscScalar *a;
ierr = VecGetArray(coords, &a);CHKERRQ(ierr);
PetscInt j,k,n = 0;
for (i = 0; i < 3; ++i) {
for (j = 0; j < dim[i]; ++j) {
for (k = 0; k < 3; ++k) {
a[n] = j*h[i]; /* coordinate along the j-th point in the i-th dimension */
++n;
}
}
}
ierr = VecRestoreArray(coords, &a);CHKERRQ(ierr);
}
ierr = DMSetCoordinates(da, coords);CHKERRQ(ierr);
/* Work vectors */
ierr = DMGetGlobalVector(da, &x);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) x, "Real space vector");CHKERRQ(ierr);
ierr = DMGetGlobalVector(da, &xx);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) xx, "Real space vector");CHKERRQ(ierr);
ierr = DMGetGlobalVector(da, &y);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) y, "USFFT frequency space vector");CHKERRQ(ierr);
ierr = DMGetGlobalVector(da, &yy);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) yy, "FFTW frequency space vector");CHKERRQ(ierr);
ierr = DMGetGlobalVector(da, &z);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) z, "USFFT reconstructed vector");CHKERRQ(ierr);
ierr = DMGetGlobalVector(da, &zz);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) zz, "FFTW reconstructed vector");CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF, "%3-D: USFFT on vector of ");CHKERRQ(ierr);
for (i = 0, N = 1; i < 3; i++) {
ierr = PetscPrintf(PETSC_COMM_SELF, "dim[%d] = %d ",i,dim[i]);CHKERRQ(ierr);
N *= dim[i];
}
ierr = PetscPrintf(PETSC_COMM_SELF, "; total size %d \n",N);CHKERRQ(ierr);
if (function == RANDOM) {
ierr = PetscRandomCreate(PETSC_COMM_SELF, &rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
ierr = VecSetRandom(x, rdm);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
} else if (function == CONSTANT) {
ierr = VecSet(x, 1.0);CHKERRQ(ierr);
} else if (function == TANH) {
PetscScalar *a;
ierr = VecGetArray(x, &a);CHKERRQ(ierr);
PetscInt j,k = 0;
for (i = 0; i < 3; ++i) {
for (j = 0; j < dim[i]; ++j) {
a[k] = tanh((j - dim[i]/2.0)*(10.0/dim[i]));
++k;
}
}
ierr = VecRestoreArray(x, &a);CHKERRQ(ierr);
}
if (view_x) {
ierr = VecView(x, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = VecCopy(x,xx);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF, "|x|_2 = %g\n",norm);CHKERRQ(ierr);
/* create USFFT object */
ierr = MatCreateSeqUSFFT(coords,da,&A);CHKERRQ(ierr);
/* create FFTW object */
ierr = MatCreateSeqFFTW(PETSC_COMM_SELF,3,dim,&AA);CHKERRQ(ierr);
/* apply USFFT and FFTW FORWARD "preemptively", so the fftw_plans can be reused on different vectors */
ierr = MatMult(A,x,z);CHKERRQ(ierr);
ierr = MatMult(AA,xx,zz);CHKERRQ(ierr);
/* Now apply USFFT and FFTW forward several (3) times */
for (i=0; i<3; ++i) {
ierr = MatMult(A,x,y);CHKERRQ(ierr);
ierr = MatMult(AA,xx,yy);CHKERRQ(ierr);
ierr = MatMultTranspose(A,y,z);CHKERRQ(ierr);
ierr = MatMultTranspose(AA,yy,zz);CHKERRQ(ierr);
}
if (view_y) {
ierr = PetscPrintf(PETSC_COMM_WORLD, "y = \n");CHKERRQ(ierr);
ierr = VecView(y, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD, "yy = \n");CHKERRQ(ierr);
ierr = VecView(yy, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
if (view_z) {
ierr = PetscPrintf(PETSC_COMM_WORLD, "z = \n");CHKERRQ(ierr);
ierr = VecView(z, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD, "zz = \n");CHKERRQ(ierr);
ierr = VecView(zz, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
/* compare x and z. USFFT computes an unnormalized DFT, thus z = N*x */
s = 1.0/(PetscReal)N;
ierr = VecScale(z,s);CHKERRQ(ierr);
ierr = VecAXPY(x,-1.0,z);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_1,&enorm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF, "|x-z| = %g\n",enorm);CHKERRQ(ierr);
/* compare xx and zz. FFTW computes an unnormalized DFT, thus zz = N*x */
s = 1.0/(PetscReal)N;
ierr = VecScale(zz,s);CHKERRQ(ierr);
ierr = VecAXPY(xx,-1.0,zz);CHKERRQ(ierr);
ierr = VecNorm(xx,NORM_1,&enorm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF, "|xx-zz| = %g\n",enorm);CHKERRQ(ierr);
/* compare y and yy: USFFT and FFTW results*/
ierr = VecNorm(y,NORM_2,&norm);CHKERRQ(ierr);
ierr = VecAXPY(y,-1.0,yy);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_1,&enorm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF, "|y|_2 = %g\n",norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF, "|y-yy| = %g\n",enorm);CHKERRQ(ierr);
/* compare z and zz: USFFT and FFTW results*/
ierr = VecNorm(z,NORM_2,&norm);CHKERRQ(ierr);
ierr = VecAXPY(z,-1.0,zz);CHKERRQ(ierr);
ierr = VecNorm(z,NORM_1,&enorm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF, "|z|_2 = %g\n",norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF, "|z-zz| = %g\n",enorm);CHKERRQ(ierr);
/* free spaces */
ierr = DMRestoreGlobalVector(da,&x);CHKERRQ(ierr);
ierr = DMRestoreGlobalVector(da,&xx);CHKERRQ(ierr);
ierr = DMRestoreGlobalVector(da,&y);CHKERRQ(ierr);
ierr = DMRestoreGlobalVector(da,&yy);CHKERRQ(ierr);
ierr = DMRestoreGlobalVector(da,&z);CHKERRQ(ierr);
ierr = DMRestoreGlobalVector(da,&zz);CHKERRQ(ierr);
ierr = VecDestroy(&coords);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **args)
{
Mat A,C,Bdense,Cdense;
PetscErrorCode ierr;
PetscViewer fd; /* viewer */
char file[PETSC_MAX_PATH_LEN]; /* input file name */
PetscBool flg,viewmats=PETSC_FALSE;
PetscMPIInt rank,size;
PetscReal fill=1.0;
PetscInt m,n,i,j,BN=10,rstart,rend,*rows,*cols;
PetscScalar *Barray,*Carray,rval,*array;
Vec x,y;
PetscRandom rand;
PetscInitialize(&argc,&args,(char*)0,help);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
/* Determine file from which we read the matrix A */
ierr = PetscOptionsGetString(NULL,"-f",file,PETSC_MAX_PATH_LEN,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_WORLD,1,"Must indicate binary file with the -f option");
/* Load matrix A */
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,file,FILE_MODE_READ,&fd);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatLoad(A,fd);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&fd);CHKERRQ(ierr);
/* Print (for testing only) */
ierr = PetscOptionsHasName(NULL, "-view_mats", &viewmats);CHKERRQ(ierr);
if (viewmats) {
if (!rank) printf("A_aij:\n");
ierr = MatView(A,0);CHKERRQ(ierr);
}
/* Test MatTransposeMatMult_aij_aij() */
ierr = MatTransposeMatMult(A,A,MAT_INITIAL_MATRIX,fill,&C);CHKERRQ(ierr);
if (viewmats) {
if (!rank) printf("\nC = A_aij^T * A_aij:\n");
ierr = MatView(C,0);CHKERRQ(ierr);
}
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
/* create a dense matrix Bdense */
ierr = MatCreate(PETSC_COMM_WORLD,&Bdense);CHKERRQ(ierr);
ierr = MatSetSizes(Bdense,m,PETSC_DECIDE,PETSC_DECIDE,BN);CHKERRQ(ierr);
ierr = MatSetType(Bdense,MATDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(Bdense);CHKERRQ(ierr);
ierr = MatSetUp(Bdense);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(Bdense,&rstart,&rend);CHKERRQ(ierr);
//printf("[%d] rstart/end %d %d; local size %d %d\n",rank,rstart,rend,m,n);
ierr = PetscMalloc3(m,PetscInt,&rows,BN,PetscInt,&cols,m*BN,PetscScalar,&array);CHKERRQ(ierr);
for (i=0; i<m; i++) rows[i] = rstart + i;
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rand);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rand);CHKERRQ(ierr);
for (j=0; j<BN; j++) {
cols[j] = j;
for (i=0; i<m; i++) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
array[m*j+i] = rval;
}
}
ierr = MatSetValues(Bdense,m,rows,BN,cols,array,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(Bdense,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Bdense,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rand);CHKERRQ(ierr);
ierr = PetscFree3(rows,cols,array);CHKERRQ(ierr);
if (viewmats) {
if (!rank) printf("\nBdense:\n");
ierr = MatView(Bdense,0);CHKERRQ(ierr);
}
/* Test MatTransposeMatMult_aij_dense() */
ierr = MatTransposeMatMult(A,Bdense,MAT_INITIAL_MATRIX,fill,&C);CHKERRQ(ierr);
ierr = MatTransposeMatMult(A,Bdense,MAT_REUSE_MATRIX,fill,&C);CHKERRQ(ierr);
if (viewmats) {
if (!rank) printf("\nC=A^T*Bdense:\n");
ierr = MatView(C,0);CHKERRQ(ierr);
}
/* Check accuracy */
ierr = MatCreate(PETSC_COMM_WORLD,&Cdense);CHKERRQ(ierr);
ierr = MatSetSizes(Cdense,n,PETSC_DECIDE,PETSC_DECIDE,BN);CHKERRQ(ierr);
ierr = MatSetType(Cdense,MATDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(Cdense);CHKERRQ(ierr);
ierr = MatSetUp(Cdense);CHKERRQ(ierr);
ierr = MatAssemblyBegin(Cdense,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Cdense,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size == 1) {
ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,m,NULL,&x);CHKERRQ(ierr);
ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,n,NULL,&y);CHKERRQ(ierr);
} else {
ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,1,m,PETSC_DECIDE,NULL,&x);CHKERRQ(ierr);
ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&y);CHKERRQ(ierr);
}
/* Cdense[:,j] = A^T * Bdense[:,j] */
ierr = MatDenseGetArray(Bdense,&Barray);CHKERRQ(ierr);
ierr = MatDenseGetArray(Cdense,&Carray);CHKERRQ(ierr);
for (j=0; j<BN; j++) {
ierr = VecPlaceArray(x,Barray);CHKERRQ(ierr);
ierr = VecPlaceArray(y,Carray);CHKERRQ(ierr);
ierr = MatMultTranspose(A,x,y);CHKERRQ(ierr);
ierr = VecResetArray(x);CHKERRQ(ierr);
ierr = VecResetArray(y);CHKERRQ(ierr);
Barray += m;
Carray += n;
}
ierr = MatDenseRestoreArray(Bdense,&Barray);CHKERRQ(ierr);
ierr = MatDenseRestoreArray(Cdense,&Carray);CHKERRQ(ierr);
if (viewmats) {
if (!rank) printf("\nCdense:\n");
ierr = MatView(Cdense,0);CHKERRQ(ierr);
}
ierr = MatEqual(C,Cdense,&flg);CHKERRQ(ierr);
if (!flg) {
if (!rank) printf(" C != Cdense\n");
}
/* Free data structures */
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatDestroy(&Bdense);CHKERRQ(ierr);
ierr = MatDestroy(&Cdense);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
Mat C;
PetscErrorCode ierr;
PetscInt N = 2,rowidx,colidx;
Vec u,b,r;
KSP ksp;
PetscReal norm;
PetscMPIInt rank,size;
PetscScalar v;
ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
/* create stiffness matrix C = [1 2; 2 3] */
ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
if (!rank) {
rowidx = 0; colidx = 0; v = 1.0;
ierr = MatSetValues(C,1,&rowidx,1,&colidx,&v,INSERT_VALUES);CHKERRQ(ierr);
rowidx = 0; colidx = 1; v = 2.0;
ierr = MatSetValues(C,1,&rowidx,1,&colidx,&v,INSERT_VALUES);CHKERRQ(ierr);
rowidx = 1; colidx = 0; v = 2.0;
ierr = MatSetValues(C,1,&rowidx,1,&colidx,&v,INSERT_VALUES);CHKERRQ(ierr);
rowidx = 1; colidx = 1; v = 3.0;
ierr = MatSetValues(C,1,&rowidx,1,&colidx,&v,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* create right hand side and solution */
ierr = VecCreate(PETSC_COMM_WORLD,&u);CHKERRQ(ierr);
ierr = VecSetSizes(u,PETSC_DECIDE,N);CHKERRQ(ierr);
ierr = VecSetFromOptions(u);CHKERRQ(ierr);
ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
ierr = VecDuplicate(u,&r);CHKERRQ(ierr);
ierr = VecSet(u,0.0);CHKERRQ(ierr);
ierr = VecSet(b,1.0);CHKERRQ(ierr);
/* solve linear system C*u = b */
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,C,C);CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
ierr = KSPSolve(ksp,b,u);CHKERRQ(ierr);
/* check residual r = C*u - b */
ierr = MatMult(C,u,r);CHKERRQ(ierr);
ierr = VecAXPY(r,-1.0,b);CHKERRQ(ierr);
ierr = VecNorm(r,NORM_2,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"|| C*u - b|| = %g\n",(double)norm);CHKERRQ(ierr);
/* solve C^T*u = b twice */
ierr = KSPSolveTranspose(ksp,b,u);CHKERRQ(ierr);
/* check residual r = C^T*u - b */
ierr = MatMultTranspose(C,u,r);CHKERRQ(ierr);
ierr = VecAXPY(r,-1.0,b);CHKERRQ(ierr);
ierr = VecNorm(r,NORM_2,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"|| C^T*u - b|| = %g\n",(double)norm);CHKERRQ(ierr);
ierr = KSPSolveTranspose(ksp,b,u);CHKERRQ(ierr);
ierr = MatMultTranspose(C,u,r);CHKERRQ(ierr);
ierr = VecAXPY(r,-1.0,b);CHKERRQ(ierr);
ierr = VecNorm(r,NORM_2,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"|| C^T*u - b|| = %g\n",(double)norm);CHKERRQ(ierr);
/* solve C*u = b again */
ierr = KSPSolve(ksp,b,u);CHKERRQ(ierr);
ierr = MatMult(C,u,r);CHKERRQ(ierr);
ierr = VecAXPY(r,-1.0,b);CHKERRQ(ierr);
ierr = VecNorm(r,NORM_2,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"|| C*u - b|| = %g\n",(double)norm);CHKERRQ(ierr);
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&r);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **argv)
{
PetscInt M1 = 3,M2,dof = 1,s = 1,ratio = 2,dim = 1;
PetscErrorCode ierr;
DM da_c,da_f;
Vec v_c,v_f;
Mat Interp;
PetscScalar one = 1.0;
PetscBool pt;
DMDABoundaryType bx = DMDA_BOUNDARY_NONE,by = DMDA_BOUNDARY_NONE,bz = DMDA_BOUNDARY_NONE;
ierr = PetscInitialize(&argc,&argv,(char*)0,help);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-dim",&dim,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-M",&M1,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-stencil_width",&s,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-ratio",&ratio,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-dof",&dof,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,"-periodic",(PetscBool*)&pt,NULL);CHKERRQ(ierr);
if (pt) {
if (dim > 0) bx = DMDA_BOUNDARY_PERIODIC;
if (dim > 1) by = DMDA_BOUNDARY_PERIODIC;
if (dim > 2) bz = DMDA_BOUNDARY_PERIODIC;
}
if (bx == DMDA_BOUNDARY_NONE) {
M2 = ratio*(M1-1) + 1;
} else {
M2 = ratio*M1;
}
/* Set up the array */
if (dim == 1) {
ierr = DMDACreate1d(PETSC_COMM_WORLD,bx,M1,dof,s,NULL,&da_c);CHKERRQ(ierr);
ierr = DMDACreate1d(PETSC_COMM_WORLD,bx,M2,dof,s,NULL,&da_f);CHKERRQ(ierr);
} else if (dim == 2) {
ierr = DMDACreate2d(PETSC_COMM_WORLD,bx,by,DMDA_STENCIL_BOX,M1,M1,PETSC_DECIDE,PETSC_DECIDE,dof,s,NULL,NULL,&da_c);CHKERRQ(ierr);
ierr = DMDACreate2d(PETSC_COMM_WORLD,bx,by,DMDA_STENCIL_BOX,M2,M2,PETSC_DECIDE,PETSC_DECIDE,dof,s,NULL,NULL,&da_f);CHKERRQ(ierr);
} else if (dim == 3) {
ierr = DMDACreate3d(PETSC_COMM_WORLD,bx,by,bz,DMDA_STENCIL_BOX,M1,M1,M1,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,dof,s,NULL,NULL,NULL,&da_c);CHKERRQ(ierr);
ierr = DMDACreate3d(PETSC_COMM_WORLD,bx,by,bz,DMDA_STENCIL_BOX,M2,M2,M2,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,dof,s,NULL,NULL,NULL,&da_f);CHKERRQ(ierr);
} else SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"dim must be 1,2, or 3");
ierr = DMCreateGlobalVector(da_c,&v_c);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da_f,&v_f);CHKERRQ(ierr);
ierr = VecSet(v_c,one);CHKERRQ(ierr);
ierr = DMCreateInterpolation(da_c,da_f,&Interp,NULL);CHKERRQ(ierr);
ierr = MatMult(Interp,v_c,v_f);CHKERRQ(ierr);
ierr = VecView(v_f,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = MatMultTranspose(Interp,v_f,v_c);CHKERRQ(ierr);
ierr = VecView(v_c,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = MatDestroy(&Interp);CHKERRQ(ierr);
ierr = VecDestroy(&v_c);CHKERRQ(ierr);
ierr = DMDestroy(&da_c);CHKERRQ(ierr);
ierr = VecDestroy(&v_f);CHKERRQ(ierr);
ierr = DMDestroy(&da_f);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
Mat C;
Vec s,u,w,x,y,z;
PetscErrorCode ierr;
PetscInt i,j,m = 8,n,rstart,rend,vstart,vend;
PetscScalar one = 1.0,negone = -1.0,v,alpha=0.1;
PetscReal norm, tol = PETSC_SQRT_MACHINE_EPSILON;
PetscBool flg;
ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
ierr = PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_COMMON);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);CHKERRQ(ierr);
n = m;
ierr = PetscOptionsHasName(NULL,NULL,"-rectA",&flg);CHKERRQ(ierr);
if (flg) n += 2;
ierr = PetscOptionsHasName(NULL,NULL,"-rectB",&flg);CHKERRQ(ierr);
if (flg) n -= 2;
/* ---------- Assemble matrix and vectors ----------- */
ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,m,n);CHKERRQ(ierr);
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,PETSC_DECIDE,m);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&z);CHKERRQ(ierr);
ierr = VecDuplicate(x,&w);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&y);CHKERRQ(ierr);
ierr = VecSetSizes(y,PETSC_DECIDE,n);CHKERRQ(ierr);
ierr = VecSetFromOptions(y);CHKERRQ(ierr);
ierr = VecDuplicate(y,&u);CHKERRQ(ierr);
ierr = VecDuplicate(y,&s);CHKERRQ(ierr);
ierr = VecGetOwnershipRange(y,&vstart,&vend);CHKERRQ(ierr);
/* Assembly */
for (i=rstart; i<rend; i++) {
v = 100*(i+1);
ierr = VecSetValues(z,1,&i,&v,INSERT_VALUES);CHKERRQ(ierr);
for (j=0; j<n; j++) {
v = 10*(i+1)+j+1;
ierr = MatSetValues(C,1,&i,1,&j,&v,INSERT_VALUES);CHKERRQ(ierr);
}
}
/* Flush off proc Vec values and do more assembly */
ierr = VecAssemblyBegin(z);CHKERRQ(ierr);
for (i=vstart; i<vend; i++) {
v = one*((PetscReal)i);
ierr = VecSetValues(y,1,&i,&v,INSERT_VALUES);CHKERRQ(ierr);
v = 100.0*i;
ierr = VecSetValues(u,1,&i,&v,INSERT_VALUES);CHKERRQ(ierr);
}
/* Flush off proc Mat values and do more assembly */
ierr = MatAssemblyBegin(C,MAT_FLUSH_ASSEMBLY);CHKERRQ(ierr);
for (i=rstart; i<rend; i++) {
for (j=0; j<n; j++) {
v = 10*(i+1)+j+1;
ierr = MatSetValues(C,1,&i,1,&j,&v,INSERT_VALUES);CHKERRQ(ierr);
}
}
/* Try overlap Coomunication with the next stage XXXSetValues */
ierr = VecAssemblyEnd(z);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FLUSH_ASSEMBLY);CHKERRQ(ierr);
CHKMEMQ;
/* The Assembly for the second Stage */
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = VecAssemblyBegin(y);CHKERRQ(ierr);
ierr = VecAssemblyEnd(y);CHKERRQ(ierr);
ierr = MatScale(C,alpha);CHKERRQ(ierr);
ierr = VecAssemblyBegin(u);CHKERRQ(ierr);
ierr = VecAssemblyEnd(u);CHKERRQ(ierr);
/* ------------ Test MatMult(), MatMultAdd() ---------- */
ierr = PetscPrintf(PETSC_COMM_WORLD,"testing MatMult()\n");CHKERRQ(ierr);
CHKMEMQ;
ierr = MatMult(C,y,x);CHKERRQ(ierr);
CHKMEMQ;
ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"testing MatMultAdd()\n");CHKERRQ(ierr);
ierr = MatMultAdd(C,y,z,w);CHKERRQ(ierr);
ierr = VecAXPY(x,one,z);CHKERRQ(ierr);
ierr = VecAXPY(x,negone,w);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error difference = %g\n",(double)norm);CHKERRQ(ierr);
}
/* ------- Test MatMultTranspose(), MatMultTransposeAdd() ------- */
for (i=rstart; i<rend; i++) {
v = one*((PetscReal)i);
ierr = VecSetValues(x,1,&i,&v,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = VecAssemblyBegin(x);CHKERRQ(ierr);
ierr = VecAssemblyEnd(x);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"testing MatMultTranspose()\n");CHKERRQ(ierr);
ierr = MatMultTranspose(C,x,y);CHKERRQ(ierr);
ierr = VecView(y,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"testing MatMultTransposeAdd()\n");CHKERRQ(ierr);
ierr = MatMultTransposeAdd(C,x,u,s);CHKERRQ(ierr);
ierr = VecAXPY(y,one,u);CHKERRQ(ierr);
ierr = VecAXPY(y,negone,s);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error difference = %g\n",(double)norm);CHKERRQ(ierr);
}
/* -------------------- Test MatGetDiagonal() ------------------ */
ierr = PetscPrintf(PETSC_COMM_WORLD,"testing MatGetDiagonal(), MatDiagonalScale()\n");CHKERRQ(ierr);
ierr = MatView(C,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecSet(x,one);CHKERRQ(ierr);
ierr = MatGetDiagonal(C,x);CHKERRQ(ierr);
ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
for (i=vstart; i<vend; i++) {
v = one*((PetscReal)(i+1));
ierr = VecSetValues(y,1,&i,&v,INSERT_VALUES);CHKERRQ(ierr);
}
/* -------------------- Test () MatDiagonalScale ------------------ */
ierr = PetscOptionsHasName(NULL,NULL,"-test_diagonalscale",&flg);CHKERRQ(ierr);
if (flg) {
ierr = MatDiagonalScale(C,x,y);CHKERRQ(ierr);
ierr = MatView(C,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
/* Free data structures */
ierr = VecDestroy(&u);CHKERRQ(ierr); ierr = VecDestroy(&s);CHKERRQ(ierr);
ierr = VecDestroy(&w);CHKERRQ(ierr); ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr); ierr = VecDestroy(&z);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
PetscErrorCode KSPSolve_CGNE(KSP ksp)
{
PetscErrorCode ierr;
PetscInt i,stored_max_it,eigs;
PetscScalar dpi,a = 1.0,beta,betaold = 1.0,b = 0,*e = 0,*d = 0;
PetscReal dp = 0.0;
Vec X,B,Z,R,P,T;
KSP_CG *cg;
Mat Amat,Pmat;
PetscBool diagonalscale,transpose_pc;
PetscFunctionBegin;
ierr = PCGetDiagonalScale(ksp->pc,&diagonalscale);CHKERRQ(ierr);
if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);
ierr = PCApplyTransposeExists(ksp->pc,&transpose_pc);CHKERRQ(ierr);
cg = (KSP_CG*)ksp->data;
eigs = ksp->calc_sings;
stored_max_it = ksp->max_it;
X = ksp->vec_sol;
B = ksp->vec_rhs;
R = ksp->work[0];
Z = ksp->work[1];
P = ksp->work[2];
T = ksp->work[3];
#define VecXDot(x,y,a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x,y,a) : VecTDot(x,y,a))
if (eigs) {e = cg->e; d = cg->d; e[0] = 0.0; }
ierr = PCGetOperators(ksp->pc,&Amat,&Pmat);CHKERRQ(ierr);
ksp->its = 0;
ierr = MatMultTranspose(Amat,B,T);CHKERRQ(ierr);
if (!ksp->guess_zero) {
ierr = KSP_MatMult(ksp,Amat,X,P);CHKERRQ(ierr);
ierr = KSP_MatMultTranspose(ksp,Amat,P,R);CHKERRQ(ierr);
ierr = VecAYPX(R,-1.0,T);CHKERRQ(ierr);
} else {
ierr = VecCopy(T,R);CHKERRQ(ierr); /* r <- b (x is 0) */
}
ierr = KSP_PCApply(ksp,R,T);CHKERRQ(ierr);
if (transpose_pc) {
ierr = KSP_PCApplyTranspose(ksp,T,Z);CHKERRQ(ierr);
} else {
ierr = KSP_PCApply(ksp,T,Z);CHKERRQ(ierr);
}
if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
ierr = VecNorm(Z,NORM_2,&dp);CHKERRQ(ierr); /* dp <- z'*z */
} else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
ierr = VecNorm(R,NORM_2,&dp);CHKERRQ(ierr); /* dp <- r'*r */
} else if (ksp->normtype == KSP_NORM_NATURAL) {
ierr = VecXDot(Z,R,&beta);CHKERRQ(ierr);
dp = PetscSqrtReal(PetscAbsScalar(beta));
} else dp = 0.0;
ierr = KSPLogResidualHistory(ksp,dp);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,0,dp);CHKERRQ(ierr);
ksp->rnorm = dp;
ierr = (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP);CHKERRQ(ierr); /* test for convergence */
if (ksp->reason) PetscFunctionReturn(0);
i = 0;
do {
ksp->its = i+1;
ierr = VecXDot(Z,R,&beta);CHKERRQ(ierr); /* beta <- r'z */
if (beta == 0.0) {
ksp->reason = KSP_CONVERGED_ATOL;
ierr = PetscInfo(ksp,"converged due to beta = 0\n");CHKERRQ(ierr);
break;
#if !defined(PETSC_USE_COMPLEX)
} else if (beta < 0.0) {
ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
ierr = PetscInfo(ksp,"diverging due to indefinite preconditioner\n");CHKERRQ(ierr);
break;
#endif
}
if (!i) {
ierr = VecCopy(Z,P);CHKERRQ(ierr); /* p <- z */
b = 0.0;
} else {
b = beta/betaold;
if (eigs) {
if (ksp->max_it != stored_max_it) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
e[i] = PetscSqrtReal(PetscAbsScalar(b))/a;
}
ierr = VecAYPX(P,b,Z);CHKERRQ(ierr); /* p <- z + b* p */
}
betaold = beta;
ierr = MatMult(Amat,P,T);CHKERRQ(ierr);
ierr = MatMultTranspose(Amat,T,Z);CHKERRQ(ierr);
ierr = VecXDot(P,Z,&dpi);CHKERRQ(ierr); /* dpi <- z'p */
a = beta/dpi; /* a = beta/p'z */
if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b))*e[i] + 1.0/a;
ierr = VecAXPY(X,a,P);CHKERRQ(ierr); /* x <- x + ap */
ierr = VecAXPY(R,-a,Z);CHKERRQ(ierr); /* r <- r - az */
if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
ierr = KSP_PCApply(ksp,R,T);CHKERRQ(ierr);
if (transpose_pc) {
ierr = KSP_PCApplyTranspose(ksp,T,Z);CHKERRQ(ierr);
} else {
ierr = KSP_PCApply(ksp,T,Z);CHKERRQ(ierr);
}
ierr = VecNorm(Z,NORM_2,&dp);CHKERRQ(ierr); /* dp <- z'*z */
} else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
ierr = VecNorm(R,NORM_2,&dp);CHKERRQ(ierr);
} else if (ksp->normtype == KSP_NORM_NATURAL) {
dp = PetscSqrtReal(PetscAbsScalar(beta));
} else {
dp = 0.0;
}
ksp->rnorm = dp;
ierr = KSPLogResidualHistory(ksp,dp);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,i+1,dp);CHKERRQ(ierr);
ierr = (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
if (ksp->reason) break;
if (ksp->normtype != KSP_NORM_PRECONDITIONED) {
if (transpose_pc) {
ierr = KSP_PCApplyTranspose(ksp,T,Z);CHKERRQ(ierr);
} else {
ierr = KSP_PCApply(ksp,T,Z);CHKERRQ(ierr);
}
}
i++;
} while (i<ksp->max_it);
if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
PetscFunctionReturn(0);
}
