void
Stokhos::StieltjesPCEBasis<ordinal_type, value_type>::
setup()
{
// Evaluate PCE at quad points
const Teuchos::Array< Teuchos::Array<value_type> >& quad_points =
quad->getQuadPoints();
ordinal_type nqp = pce_weights.size();
pce_vals.resize(nqp);
phi_vals.resize(nqp);
for (ordinal_type i=0; i<nqp; i++) {
pce_vals[i] = pce->evaluate(quad_points[i], basis_values[i]);
phi_vals[i].resize(this->p+1);
}
if (project_integrals)
phi_pce_coeffs.resize(basis->size());
RecurrenceBasis<ordinal_type,value_type>::setup();
ordinal_type sz = pce->size();
fromStieltjesMat.putScalar(0.0);
for (ordinal_type i=0; i<=this->p; i++) {
for (ordinal_type j=0; j<sz; j++) {
for (ordinal_type k=0; k<nqp; k++)
fromStieltjesMat(i,j) +=
pce_weights[k]*phi_vals[k][i]*basis_values[k][j];
fromStieltjesMat(i,j) /= basis->norm_squared(j);
}
}
}
void
Stokhos::LanczosPCEBasis<ordinal_type, value_type>::
setup()
{
RecurrenceBasis<ordinal_type,value_type>::setup();
// Compute transformation matrix back to original basis
ordinal_type sz = pce->size();
fromStieltjesMat.shape(sz, this->p+1);
fromStieltjesMat.putScalar(0.0);
const Teuchos::Array< Teuchos::Array<value_type> >& basis_values =
quad->getBasisAtQuadPoints();
for (ordinal_type i=0; i<sz; i++) {
for (ordinal_type j=0; j<=this->p; j++) {
for (ordinal_type k=0; k<nqp; k++)
fromStieltjesMat(i,j) +=
pce_weights[k]*lanczos_vecs(k,j)*basis_values[k][i];
fromStieltjesMat(i,j) /= pce->basis()->norm_squared(i);
}
}
// Project original PCE into the new basis
new_pce.resize(this->p+1);
vector_type u(sz);
for (ordinal_type i=0; i<sz; i++)
u[i] = (*pce)[i]*pce->basis()->norm_squared(i);
new_pce.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, 1.0, fromStieltjesMat, u,
0.0);
for (ordinal_type i=0; i<=this->p; i++)
new_pce[i] /= this->norms[i];
}
Stokhos::StieltjesPCEBasis<ordinal_type, value_type>::
StieltjesPCEBasis(
ordinal_type p,
const Teuchos::RCP<const Stokhos::OrthogPolyApprox<ordinal_type, value_type> >& pce_,
const Teuchos::RCP<const Stokhos::Quadrature<ordinal_type, value_type> >& quad_,
bool use_pce_quad_points_,
bool normalize,
bool project_integrals_,
const Teuchos::RCP<const Stokhos::Sparse3Tensor<ordinal_type, value_type> >& Cijk_) :
RecurrenceBasis<ordinal_type, value_type>("Stieltjes PCE", p, normalize),
pce(pce_),
quad(quad_),
pce_weights(quad->getQuadWeights()),
basis_values(quad->getBasisAtQuadPoints()),
pce_vals(),
phi_vals(),
use_pce_quad_points(use_pce_quad_points_),
fromStieltjesMat(p+1,pce->size()),
project_integrals(project_integrals_),
basis(pce->basis()),
Cijk(Cijk_),
phi_pce_coeffs()
{
// Evaluate PCE at quad points
const Teuchos::Array< Teuchos::Array<value_type> >& quad_points =
quad->getQuadPoints();
ordinal_type nqp = pce_weights.size();
pce_vals.resize(nqp);
phi_vals.resize(nqp);
for (ordinal_type i=0; i<nqp; i++) {
pce_vals[i] = pce->evaluate(quad_points[i], basis_values[i]);
phi_vals[i].resize(p+1);
}
if (project_integrals)
phi_pce_coeffs.resize(basis->size());
// Compute coefficients via Stieltjes
stieltjes(0, p+1, pce_weights, pce_vals, this->alpha, this->beta, this->norms,
phi_vals);
for (ordinal_type i=0; i<=p; i++)
this->delta[i] = value_type(1.0);
ordinal_type sz = pce->size();
fromStieltjesMat.putScalar(0.0);
for (ordinal_type i=0; i<=p; i++) {
for (ordinal_type j=0; j<sz; j++) {
for (ordinal_type k=0; k<nqp; k++)
fromStieltjesMat(i,j) +=
pce_weights[k]*phi_vals[k][i]*basis_values[k][j];
fromStieltjesMat(i,j) /= basis->norm_squared(j);
}
}
// Setup rest of recurrence basis
//this->setup();
this->gamma[0] = value_type(1);
for (ordinal_type k=1; k<=p; k++) {
this->gamma[k] = value_type(1);
}
//If you want normalized polynomials, set gamma and reset the norms to 1.
if( normalize ) {
for (ordinal_type k=0; k<=p; k++) {
this->gamma[k] = value_type(1)/std::sqrt(this->norms[k]);
this->norms[k] = value_type(1);
}
}
}
