/usr/include/trilinos/Stokhos_LegendreBasisImp.hpp is in libtrilinos-stokhos-dev 12.4.2-2.
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// $Source$
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// Stokhos Package
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template <typename ordinal_type, typename value_type>
Stokhos::LegendreBasis<ordinal_type, value_type>::
LegendreBasis(ordinal_type p, bool normalize, Stokhos::GrowthPolicy growth) :
RecurrenceBasis<ordinal_type, value_type>("Legendre", p, normalize, growth)
{
this->setup();
#ifdef HAVE_STOKHOS_DAKOTA
this->setSparseGridGrowthRule(webbur::level_to_order_linear_wn);
#endif
}
template <typename ordinal_type, typename value_type>
Stokhos::LegendreBasis<ordinal_type, value_type>::
LegendreBasis(ordinal_type p, const LegendreBasis& basis) :
RecurrenceBasis<ordinal_type, value_type>(p, basis)
{
// Compute coefficients in 3-term recurrsion
computeRecurrenceCoefficients(p+1, this->alpha, this->beta, this->delta,
this->gamma);
// Setup rest of recurrence basis
this->setup();
}
template <typename ordinal_type, typename value_type>
Stokhos::LegendreBasis<ordinal_type, value_type>::
~LegendreBasis()
{
}
template <typename ordinal_type, typename value_type>
bool
Stokhos::LegendreBasis<ordinal_type, value_type>::
computeRecurrenceCoefficients(ordinal_type n,
Teuchos::Array<value_type>& theAlpha,
Teuchos::Array<value_type>& theBeta,
Teuchos::Array<value_type>& theDelta,
Teuchos::Array<value_type>& theGamma) const
{
// Legendre 3 term recurrence:
// P_0(x) = 1
// P_1(x) = x
// P_i(x) = (2*i-1)/i*x*P_{i-1}(x) - (i-1)/i*P_{i-2}(x), i=2,3,...
theAlpha[0] = 0.0;
theBeta[0] = 1.0;
theDelta[0] = 1.0;
theGamma[0] = 1.0;
for (ordinal_type i=1; i<n; i++) {
theAlpha[i] = 0.0;
//theBeta[i] = value_type(i*i) / value_type((2*i-1)*(2*i+1));
theBeta[i] = value_type(i) / value_type(i+1);
theDelta[i] = value_type(2*i+1) / value_type(i+1);
theGamma[i] = 1.0;
}
return false;
}
template <typename ordinal_type, typename value_type>
Teuchos::RCP<Stokhos::OneDOrthogPolyBasis<ordinal_type,value_type> >
Stokhos::LegendreBasis<ordinal_type,value_type>::
cloneWithOrder(ordinal_type pp) const
{
return
Teuchos::rcp(new Stokhos::LegendreBasis<ordinal_type,value_type>(pp,*this));
}
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