/*
BVOrthogonalizeCGS1 - Compute |v'| (estimated), |v| and one step of CGS with
only one global synchronization
*/
PetscErrorCode BVOrthogonalizeCGS1(BV bv,PetscInt j,Vec v,PetscScalar *H,PetscReal *onorm,PetscReal *norm)
{
PetscErrorCode ierr;
PetscInt i;
PetscReal sum,nrm,beta;
Vec w=v;
PetscFunctionBegin;
/* h = W^* v ; alpha = (v, v) */
bv->k = j;
if (onorm || norm) {
if (!v) {
bv->k++;
ierr = BVGetColumn(bv,j,&w);CHKERRQ(ierr);
}
ierr = BVDotVec(bv,w,H);CHKERRQ(ierr);
if (!v) {
ierr = BVRestoreColumn(bv,j,&w);CHKERRQ(ierr);
bv->k--;
beta = PetscSqrtReal(PetscRealPart(H[bv->nc+j]));
} else {
ierr = BVNormVec(bv,w,NORM_2,&beta);CHKERRQ(ierr);
}
} else {
if (!v) { ierr = BVDotColumn(bv,j,H);CHKERRQ(ierr); }
else { ierr = BVDotVec(bv,w,H);CHKERRQ(ierr); }
}
/* q = v - V h */
if (bv->indef) {
for (i=0;i<bv->nc+j;i++) H[i] /= bv->omega[i]; /* apply inverse of signature */
}
if (!v) { ierr = BVMultColumn(bv,-1.0,1.0,j,H);CHKERRQ(ierr); }
else { ierr = BVMultVec(bv,-1.0,1.0,w,H);CHKERRQ(ierr); }
if (bv->indef) {
for (i=0;i<bv->nc+j;i++) H[i] *= bv->omega[i]; /* revert signature */
}
/* compute |v| */
if (onorm) *onorm = beta;
if (bv->indef) {
if (!v) { ierr = BVNormColumn(bv,j,NORM_2,&nrm);CHKERRQ(ierr); }
else { ierr = BVNormVec(bv,w,NORM_2,&nrm);CHKERRQ(ierr); }
if (norm) *norm = nrm;
bv->omega[bv->nc+j] = (nrm<0.0)? -1.0: 1.0;
} else if (norm) {
/* estimate |v'| from |v| */
sum = 0.0;
for (i=0;i<bv->nc+j;i++) sum += PetscRealPart(H[i]*PetscConj(H[i]));
*norm = beta*beta-sum;
if (*norm <= 0.0) {
if (!v) { ierr = BVNormColumn(bv,j,NORM_2,norm);CHKERRQ(ierr); }
else { ierr = BVNormVec(bv,w,NORM_2,norm);CHKERRQ(ierr); }
} else *norm = PetscSqrtReal(*norm);
}
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
PetscErrorCode ierr;
Vec t,v;
Mat Q,M;
BV X,Y;
PetscInt i,j,n=10,kx=6,lx=3,ky=5,ly=2;
PetscScalar *q,*z;
PetscReal nrm;
PetscViewer view;
PetscBool verbose,trans;
SlepcInitialize(&argc,&argv,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-kx",&kx,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-lx",&lx,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-ky",&ky,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-ly",&ly,NULL);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,"-verbose",&verbose);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"First BV with %D active columns (%D leading columns) of dimension %D.\n",kx,lx,n);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Second BV with %D active columns (%D leading columns) of dimension %D.\n",ky,ly,n);CHKERRQ(ierr);
/* Create template vector */
ierr = VecCreate(PETSC_COMM_WORLD,&t);CHKERRQ(ierr);
ierr = VecSetSizes(t,PETSC_DECIDE,n);CHKERRQ(ierr);
ierr = VecSetFromOptions(t);CHKERRQ(ierr);
/* Create BV object X */
ierr = BVCreate(PETSC_COMM_WORLD,&X);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)X,"X");CHKERRQ(ierr);
ierr = BVSetSizesFromVec(X,t,kx+2);CHKERRQ(ierr); /* two extra columns to test active columns */
ierr = BVSetFromOptions(X);CHKERRQ(ierr);
ierr = BVSetActiveColumns(X,lx,kx);CHKERRQ(ierr);
/* Set up viewer */
ierr = PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&view);CHKERRQ(ierr);
if (verbose) {
ierr = PetscViewerPushFormat(view,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
}
/* Fill X entries */
for (j=0;j<kx+2;j++) {
ierr = BVGetColumn(X,j,&v);CHKERRQ(ierr);
ierr = VecZeroEntries(v);CHKERRQ(ierr);
for (i=0;i<4;i++) {
if (i+j<n) {
ierr = VecSetValue(v,i+j,(PetscScalar)(3*i+j-2),INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = VecAssemblyBegin(v);CHKERRQ(ierr);
ierr = VecAssemblyEnd(v);CHKERRQ(ierr);
ierr = BVRestoreColumn(X,j,&v);CHKERRQ(ierr);
}
if (verbose) {
ierr = BVView(X,view);CHKERRQ(ierr);
}
/* Create BV object Y */
ierr = BVCreate(PETSC_COMM_WORLD,&Y);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)Y,"Y");CHKERRQ(ierr);
ierr = BVSetSizesFromVec(Y,t,ky+1);CHKERRQ(ierr);
ierr = BVSetFromOptions(Y);CHKERRQ(ierr);
ierr = BVSetActiveColumns(Y,ly,ky);CHKERRQ(ierr);
/* Fill Y entries */
for (j=0;j<ky+1;j++) {
ierr = BVGetColumn(Y,j,&v);CHKERRQ(ierr);
ierr = VecSet(v,(PetscScalar)(j+1)/4.0);CHKERRQ(ierr);
ierr = BVRestoreColumn(Y,j,&v);CHKERRQ(ierr);
}
if (verbose) {
ierr = BVView(Y,view);CHKERRQ(ierr);
}
/* Create Mat */
ierr = MatCreateSeqDense(PETSC_COMM_SELF,kx,ky,NULL,&Q);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)Q,"Q");CHKERRQ(ierr);
ierr = MatDenseGetArray(Q,&q);CHKERRQ(ierr);
for (i=0;i<kx;i++)
for (j=0;j<ky;j++)
q[i+j*kx] = (i<j)? 2.0: -0.5;
ierr = MatDenseRestoreArray(Q,&q);CHKERRQ(ierr);
if (verbose) {
ierr = MatView(Q,NULL);CHKERRQ(ierr);
}
/* Test BVMult */
ierr = BVMult(Y,2.0,1.0,X,Q);CHKERRQ(ierr);
if (verbose) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"After BVMult - - - - - - - - -\n");CHKERRQ(ierr);
ierr = BVView(Y,view);CHKERRQ(ierr);
}
/* Test BVMultVec */
ierr = BVGetColumn(Y,0,&v);CHKERRQ(ierr);
ierr = PetscMalloc1(kx-lx,&z);CHKERRQ(ierr);
z[0] = 2.0;
for (i=1;i<kx-lx;i++) z[i] = -0.5*z[i-1];
ierr = BVMultVec(X,-1.0,1.0,v,z);CHKERRQ(ierr);
ierr = PetscFree(z);CHKERRQ(ierr);
ierr = BVRestoreColumn(Y,0,&v);CHKERRQ(ierr);
if (verbose) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"After BVMultVec - - - - - - -\n");CHKERRQ(ierr);
ierr = BVView(Y,view);CHKERRQ(ierr);
}
/* Test BVDot */
ierr = MatCreateSeqDense(PETSC_COMM_SELF,ky,kx,NULL,&M);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)M,"M");CHKERRQ(ierr);
ierr = BVDot(X,Y,M);CHKERRQ(ierr);
if (verbose) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"After BVDot - - - - - - - - -\n");CHKERRQ(ierr);
ierr = MatView(M,NULL);CHKERRQ(ierr);
}
/* Test BVDotVec */
ierr = BVGetColumn(Y,0,&v);CHKERRQ(ierr);
ierr = PetscMalloc1(kx-lx,&z);CHKERRQ(ierr);
ierr = BVDotVec(X,v,z);CHKERRQ(ierr);
ierr = BVRestoreColumn(Y,0,&v);CHKERRQ(ierr);
if (verbose) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"After BVDotVec - - - - - - -\n");CHKERRQ(ierr);
ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,kx-lx,z,&v);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)v,"z");CHKERRQ(ierr);
ierr = VecView(v,view);CHKERRQ(ierr);
ierr = VecDestroy(&v);CHKERRQ(ierr);
}
ierr = PetscFree(z);CHKERRQ(ierr);
/* Test BVMultInPlace and BVScale */
ierr = PetscOptionsHasName(NULL,"-trans",&trans);CHKERRQ(ierr);
if (trans) {
Mat Qt;
ierr = MatTranspose(Q,MAT_INITIAL_MATRIX,&Qt);CHKERRQ(ierr);
ierr = BVMultInPlaceTranspose(X,Qt,lx+1,ky);CHKERRQ(ierr);
ierr = MatDestroy(&Qt);CHKERRQ(ierr);
} else {
ierr = BVMultInPlace(X,Q,lx+1,ky);CHKERRQ(ierr);
}
ierr = BVScale(X,2.0);CHKERRQ(ierr);
if (verbose) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"After BVMultInPlace - - - - -\n");CHKERRQ(ierr);
ierr = BVView(X,view);CHKERRQ(ierr);
}
/* Test BVNorm */
ierr = BVNormColumn(X,lx,NORM_2,&nrm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"2-Norm or X[%D] = %g\n",lx,(double)nrm);CHKERRQ(ierr);
ierr = BVNorm(X,NORM_FROBENIUS,&nrm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Frobenius Norm or X = %g\n",(double)nrm);CHKERRQ(ierr);
ierr = BVDestroy(&X);CHKERRQ(ierr);
ierr = BVDestroy(&Y);CHKERRQ(ierr);
ierr = MatDestroy(&Q);CHKERRQ(ierr);
ierr = MatDestroy(&M);CHKERRQ(ierr);
ierr = VecDestroy(&t);CHKERRQ(ierr);
ierr = SlepcFinalize();
return 0;
}
static PetscErrorCode SVDOneSideTRLanczosCGS(SVD svd,PetscReal *alpha,PetscReal *beta,BV V,BV U,PetscInt nconv,PetscInt l,PetscInt n,PetscScalar* work)
{
PetscErrorCode ierr;
PetscReal a,b,eta;
PetscScalar gamma;
PetscInt i,j,k=nconv+l;
Vec ui,ui1,vi;
BVOrthogRefineType refine;
PetscFunctionBegin;
ierr = BVGetColumn(V,k,&vi);CHKERRQ(ierr);
ierr = BVGetColumn(U,k,&ui);CHKERRQ(ierr);
ierr = SVDMatMult(svd,PETSC_FALSE,vi,ui);CHKERRQ(ierr);
ierr = BVRestoreColumn(V,k,&vi);CHKERRQ(ierr);
ierr = BVRestoreColumn(U,k,&ui);CHKERRQ(ierr);
if (l>0) {
ierr = BVMultColumn(U,-1.0,1.0,k,&gamma);CHKERRQ(ierr);
beta[nconv] = PetscRealPart(gamma);
}
ierr = BVGetOrthogonalization(V,NULL,&refine,&eta);CHKERRQ(ierr);
for (i=k+1;i<n;i++) {
ierr = BVGetColumn(V,i,&vi);CHKERRQ(ierr);
ierr = BVGetColumn(U,i-1,&ui1);CHKERRQ(ierr);
ierr = SVDMatMult(svd,PETSC_TRUE,ui1,vi);CHKERRQ(ierr);
ierr = BVRestoreColumn(V,i,&vi);CHKERRQ(ierr);
ierr = BVRestoreColumn(U,i-1,&ui1);CHKERRQ(ierr);
ierr = BVNormColumn(U,i-1,NORM_2,&a);CHKERRQ(ierr);
if (refine == BV_ORTHOG_REFINE_IFNEEDED) {
ierr = BVSetActiveColumns(V,0,i+1);CHKERRQ(ierr);
ierr = BVGetColumn(V,i,&vi);CHKERRQ(ierr);
ierr = BVDotVec(V,vi,work);CHKERRQ(ierr);
ierr = BVRestoreColumn(V,i,&vi);CHKERRQ(ierr);
ierr = BVSetActiveColumns(V,0,i);CHKERRQ(ierr);
} else {
ierr = BVSetActiveColumns(V,0,i);CHKERRQ(ierr);
ierr = BVDotColumn(V,i,work);CHKERRQ(ierr);
}
ierr = BVScaleColumn(U,i-1,1.0/a);CHKERRQ(ierr);
for (j=0;j<i;j++) work[j] = work[j] / a;
ierr = BVMultColumn(V,-1.0,1.0/a,i,work);CHKERRQ(ierr);
ierr = SVDOrthogonalizeCGS(V,i,work,a,refine,eta,&b);CHKERRQ(ierr);
ierr = BVScaleColumn(V,i,1.0/b);CHKERRQ(ierr);
ierr = BVGetColumn(V,i,&vi);CHKERRQ(ierr);
ierr = BVGetColumn(U,i,&ui);CHKERRQ(ierr);
ierr = BVGetColumn(U,i-1,&ui1);CHKERRQ(ierr);
ierr = SVDMatMult(svd,PETSC_FALSE,vi,ui);CHKERRQ(ierr);
ierr = VecAXPY(ui,-b,ui1);CHKERRQ(ierr);
ierr = BVRestoreColumn(V,i,&vi);CHKERRQ(ierr);
ierr = BVRestoreColumn(U,i,&ui);CHKERRQ(ierr);
ierr = BVRestoreColumn(U,i-1,&ui1);CHKERRQ(ierr);
alpha[i-1] = a;
beta[i-1] = b;
}
ierr = BVGetColumn(V,n,&vi);CHKERRQ(ierr);
ierr = BVGetColumn(U,n-1,&ui1);CHKERRQ(ierr);
ierr = SVDMatMult(svd,PETSC_TRUE,ui1,vi);CHKERRQ(ierr);
ierr = BVRestoreColumn(V,n,&vi);CHKERRQ(ierr);
ierr = BVRestoreColumn(U,n-1,&ui1);CHKERRQ(ierr);
ierr = BVNormColumn(svd->U,n-1,NORM_2,&a);CHKERRQ(ierr);
if (refine == BV_ORTHOG_REFINE_IFNEEDED) {
ierr = BVSetActiveColumns(V,0,n+1);CHKERRQ(ierr);
ierr = BVGetColumn(V,n,&vi);CHKERRQ(ierr);
ierr = BVDotVec(V,vi,work);CHKERRQ(ierr);
ierr = BVRestoreColumn(V,n,&vi);CHKERRQ(ierr);
} else {
ierr = BVSetActiveColumns(V,0,n);CHKERRQ(ierr);
ierr = BVDotColumn(V,n,work);CHKERRQ(ierr);
}
ierr = BVScaleColumn(U,n-1,1.0/a);CHKERRQ(ierr);
for (j=0;j<n;j++) work[j] = work[j] / a;
ierr = BVMultColumn(V,-1.0,1.0/a,n,work);CHKERRQ(ierr);
ierr = SVDOrthogonalizeCGS(V,n,work,a,refine,eta,&b);CHKERRQ(ierr);
ierr = BVSetActiveColumns(V,nconv,n);CHKERRQ(ierr);
alpha[n-1] = a;
beta[n-1] = b;
PetscFunctionReturn(0);
}
