gaussianorthogonalpolynomial.hpp

/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2005, 2006 Klaus Spanderen
 
 This file is part of QuantLib, a free-software/open-source library
 for financial quantitative analysts and developers - http://quantlib.org/
 
 QuantLib is free software: you can redistribute it and/or modify it
 under the terms of the QuantLib license.  You should have received a
 copy of the license along with this program; if not, please email
 <quantlib-dev@lists.sf.net>. The license is also available online at
 <http://quantlib.org/license.shtml>.
 
 This program is distributed in the hope that it will be useful, but WITHOUT
 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
 FOR A PARTICULAR PURPOSE.  See the license for more details.
*/
 
#ifndef quantlib_gaussian_orthogonal_polynomial_hpp
#define quantlib_gaussian_orthogonal_polynomial_hpp
 
#include <ql/types.hpp>
 
namespace QuantLib {
 
 
    class GaussianOrthogonalPolynomial {
      public:
        virtual ~GaussianOrthogonalPolynomial() = default;
        virtual Real mu_0()        const = 0;
        virtual Real alpha(Size i) const = 0;
        virtual Real beta(Size i)  const = 0;
        virtual Real w(Real x)     const = 0;
 
        Real value(Size i, Real x) const;
        Real weightedValue(Size i, Real x) const;
    };
 
    class GaussLaguerrePolynomial : public GaussianOrthogonalPolynomial {
      public:
        explicit GaussLaguerrePolynomial(Real s = 0.0);
 
        Real mu_0() const override;
        Real alpha(Size i) const override;
        Real beta(Size i) const override;
        Real w(Real x) const override;
 
      private:
        const Real s_;
    };
 
    class GaussHermitePolynomial : public GaussianOrthogonalPolynomial {
      public:
        explicit GaussHermitePolynomial(Real mu = 0.0);
 
        Real mu_0() const override;
        Real alpha(Size i) const override;
        Real beta(Size i) const override;
        Real w(Real x) const override;
 
      private:
        const Real mu_;
    };
 
    class GaussJacobiPolynomial : public GaussianOrthogonalPolynomial {
      public:
        explicit GaussJacobiPolynomial(Real alpha, Real beta);
 
        Real mu_0() const override;
        Real alpha(Size i) const override;
        Real beta(Size i) const override;
        Real w(Real x) const override;
 
      private:
        const Real alpha_;
        const Real beta_;
    };
 
    class GaussLegendrePolynomial : public GaussJacobiPolynomial {
      public:
        GaussLegendrePolynomial();
    };
 
    class GaussChebyshevPolynomial : public GaussJacobiPolynomial {
      public:
        GaussChebyshevPolynomial();
    };
 
    class GaussChebyshev2ndPolynomial : public GaussJacobiPolynomial {
      public:
        GaussChebyshev2ndPolynomial();
    };
 
    class GaussGegenbauerPolynomial : public GaussJacobiPolynomial {
      public:
        explicit GaussGegenbauerPolynomial(Real lambda);
    };
 
    class GaussHyperbolicPolynomial : public GaussianOrthogonalPolynomial {
      public:
        Real mu_0() const override;
        Real alpha(Size i) const override;
        Real beta(Size i) const override;
        Real w(Real x) const override;
    };
 
}
 
#endif