/usr/include/trilinos/Stokhos_LegendreBasis.hpp is in libtrilinos-stokhos-dev 12.10.1-3.
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#ifndef STOKHOS_LEGENDREBASIS_HPP
#define STOKHOS_LEGENDREBASIS_HPP
#include "Stokhos_RecurrenceBasis.hpp"
namespace Stokhos {
//! Legendre polynomial basis
/*!
* Legendre polynomials are defined by the recurrence relationship
* \f[
* \psi_{k+1}(x) = \frac{2k+1}{k+1}x\psi_{k}(x) - \frac{k}{k+1}\psi_{k-1}(x)
* \f]
* with \f$\psi_{-1}(x) = 0\f$ and \f$\psi_{0}(x) = 1\f$. The corresponding
* density function is
* \f[
* \rho(x) = \frac{1}{2}, \quad x\in[-1,1].
* \f]
*
* This class implements computeRecurrenceCoefficients() using the
* above formula.
*/
template <typename ordinal_type, typename value_type>
class LegendreBasis :
public RecurrenceBasis<ordinal_type, value_type> {
public:
//! Constructor
/*!
* \param p order of the basis
* \param normalize whether polynomials should be given unit norm
*/
LegendreBasis(ordinal_type p, bool normalize = false,
GrowthPolicy growth = SLOW_GROWTH);
//! Destructor
~LegendreBasis();
//! \name Implementation of Stokhos::OneDOrthogPolyBasis methods
//@{
/*!
* \brief Clone this object with the option of building a higher order
* basis.
*/
/*!
* This method is following the Prototype pattern (see Design Pattern's textbook).
* The slight variation is that it allows the order of the polynomial to be modified,
* otherwise an exact copy is formed. The use case for this is creating basis functions
* for column indices in a spatially varying adaptive refinement context.
*/
virtual Teuchos::RCP<OneDOrthogPolyBasis<ordinal_type,value_type> > cloneWithOrder(ordinal_type p) const;
//@}
protected:
//! \name Implementation of Stokhos::RecurrenceBasis methods
//@{
//! Compute recurrence coefficients
virtual bool
computeRecurrenceCoefficients(ordinal_type n,
Teuchos::Array<value_type>& alpha,
Teuchos::Array<value_type>& beta,
Teuchos::Array<value_type>& delta,
Teuchos::Array<value_type>& gamma) const;
//@}
//! Copy constructor with specified order
LegendreBasis(ordinal_type p, const LegendreBasis& basis);
private:
// Prohibit copying
LegendreBasis(const LegendreBasis&);
// Prohibit Assignment
LegendreBasis& operator=(const LegendreBasis& b);
}; // class LegendreBasis
} // Namespace Stokhos
// Include template definitions
#include "Stokhos_LegendreBasisImp.hpp"
#endif
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