void
Stokhos::StieltjesPCEBasis<ordinal_type, value_type>::
integrateBasisSquaredProj(
ordinal_type k,
const Teuchos::Array<value_type>& a,
const Teuchos::Array<value_type>& b,
const Teuchos::Array<value_type>& weights,
const Teuchos::Array<value_type>& points,
Teuchos::Array< Teuchos::Array<value_type> >& phi_vals,
value_type& val1, value_type& val2) const
{
ordinal_type nqp = weights.size();
ordinal_type npc = basis->size();
const Teuchos::Array<value_type>& norms = basis->norm_squared();
// Compute PC expansion of phi_k in original basis
evaluateRecurrence(k, a, b, points, phi_vals);
for (ordinal_type j=0; j<npc; j++) {
value_type c = value_type(0);
for (ordinal_type i=0; i<nqp; i++)
c += weights[i]*phi_vals[i][k]*basis_values[i][j];
c /= norms[j];
phi_pce_coeffs[j] = c;
}
// Compute \int phi_k^2(\eta) d\eta
val1 = value_type(0);
for (ordinal_type j=0; j<npc; j++)
val1 += phi_pce_coeffs[j]*phi_pce_coeffs[j]*norms[j];
// Compute \int \eta phi_k^2(\eta) d\eta
val2 = value_type(0);
for (typename Cijk_type::k_iterator k_it = Cijk->k_begin();
k_it != Cijk->k_end(); ++k_it) {
ordinal_type l = index(k_it);
for (typename Cijk_type::kj_iterator j_it = Cijk->j_begin(k_it);
j_it != Cijk->j_end(k_it); ++j_it) {
ordinal_type j = index(j_it);
for (typename Cijk_type::kji_iterator i_it = Cijk->i_begin(j_it);
i_it != Cijk->i_end(j_it); ++i_it) {
ordinal_type i = index(i_it);
value_type c = value(i_it);
val2 += phi_pce_coeffs[i]*phi_pce_coeffs[j]*(*pce)[l]*c;
}
}
}
}
void
Stokhos::StieltjesPCEBasis<ordinal_type, value_type>::
integrateBasisSquaredProj(
ordinal_type k,
const Teuchos::Array<value_type>& a,
const Teuchos::Array<value_type>& b,
const Teuchos::Array<value_type>& weights,
const Teuchos::Array<value_type>& points,
Teuchos::Array< Teuchos::Array<value_type> >& phi_vals,
value_type& val1, value_type& val2) const
{
ordinal_type nqp = weights.size();
ordinal_type npc = basis->size();
const Teuchos::Array<value_type>& norms = basis->norm_squared();
// Compute PC expansion of phi_k in original basis
evaluateRecurrence(k, a, b, points, phi_vals);
for (ordinal_type j=0; j<npc; j++) {
value_type c = value_type(0);
for (ordinal_type i=0; i<nqp; i++)
c += weights[i]*phi_vals[i][k]*basis_values[i][j];
c /= norms[j];
phi_pce_coeffs[j] = c;
}
// Compute \int phi_k^2(\eta) d\eta
val1 = value_type(0);
for (ordinal_type j=0; j<npc; j++)
val1 += phi_pce_coeffs[j]*phi_pce_coeffs[j]*norms[j];
// Compute \int \eta phi_k^2(\eta) d\eta
val2 = value_type(0);
for (ordinal_type l=0; l<npc; l++) {
int nj = Cijk->num_j(l);
const Teuchos::Array<ordinal_type>& j_indices = Cijk->Jindices(l);
for (ordinal_type jj=0; jj<nj; jj++) {
ordinal_type j = j_indices[jj];
const Teuchos::Array<ordinal_type>& i_indices = Cijk->Iindices(l,jj);
const Teuchos::Array<value_type>& c_values = Cijk->values(l,jj);
ordinal_type ni = i_indices.size();
for (ordinal_type ii=0; ii<ni; ii++) {
ordinal_type i = i_indices[ii];
val2 += phi_pce_coeffs[l]*phi_pce_coeffs[i]*(*pce)[j]*c_values[ii];
}
}
}
}
value_type
Stokhos::DiscretizedStieltjesBasis<ordinal_type,value_type>::
expectedValue_J_nsquared(const ordinal_type& order,
const Teuchos::Array<value_type>& alpha,
const Teuchos::Array<value_type>& beta) const
{
//Impliments a gaussian quadrature routineroutine to evaluate the integral,
// \int_-c^c J_n(x)^2w(x)dx. This is needed to compute the recurrance coefficients.
value_type integral = 0;
for(ordinal_type quadIdx = 0;
quadIdx < static_cast<ordinal_type>(quad_points.size()); quadIdx++){
value_type x = (rightEndPt_ - leftEndPt_)*.5*quad_points[quadIdx] +
(rightEndPt_ + leftEndPt_)*.5;
value_type val = evaluateRecurrence(x,order,alpha,beta);
integral += val*val*evaluateWeight(x)*quad_weights[quadIdx];
}
return integral*(rightEndPt_ - leftEndPt_);
}
void
Stokhos::StieltjesPCEBasis<ordinal_type, value_type>::
integrateBasisSquared(ordinal_type k,
const Teuchos::Array<value_type>& a,
const Teuchos::Array<value_type>& b,
const Teuchos::Array<value_type>& weights,
const Teuchos::Array<value_type>& points,
Teuchos::Array< Teuchos::Array<value_type> >& phi_vals,
value_type& val1, value_type& val2) const
{
evaluateRecurrence(k, a, b, points, phi_vals);
ordinal_type nqp = weights.size();
val1 = value_type(0);
val2 = value_type(0);
for (ordinal_type i=0; i<nqp; i++) {
val1 += weights[i]*phi_vals[i][k]*phi_vals[i][k];
val2 += weights[i]*phi_vals[i][k]*phi_vals[i][k]*points[i];
}
}
