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added Laguerre sine and cosine quadrature
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184 changes: 51 additions & 133 deletions
184
ql/experimental/math/gaussiannoncentralchisquaredpolynomial.cpp
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| /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */ | ||
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| /* | ||
| Copyright (C) 2020 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. | ||
| */ | ||
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| /*! \file gausslaguerrecosinepolynomial.hpp | ||
| \brief Laguerre-Cosine Gaussian quadrature | ||
| */ | ||
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| #ifndef quantlib_gauss_laguerre_cosine_polynomial_hpp | ||
| #define quantlib_gauss_laguerre_cosine_polynomial_hpp | ||
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| #include <ql/math/functional.hpp> | ||
| #include <ql/math/integrals/momentbasedgaussianpolynomial.hpp> | ||
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| namespace QuantLib { | ||
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| template <class mp_real> | ||
| class GaussLaguerreTrigonometricBase | ||
| : public MomentBasedGaussianPolynomial<mp_real> { | ||
| public: | ||
| explicit GaussLaguerreTrigonometricBase(Real u) | ||
| : u_(u) { } | ||
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| protected: | ||
| virtual mp_real m0() const = 0; | ||
| virtual mp_real m1() const = 0; | ||
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| mp_real moment_(Size n) const { | ||
| if (m_.size() <= n) | ||
| m_.resize(n+1, std::numeric_limits<mp_real>::quiet_NaN()); | ||
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| if (boost::math::isnan(m_[n])) { | ||
| if (n == 0) | ||
| m_[0] = m0(); | ||
| else if (n == 1) | ||
| m_[1] = m1(); | ||
| else | ||
| m_[n] = (2*n*moment_(n-1) | ||
| - n*(n-1)*moment_(n-2))/(1+u_*u_); | ||
| } | ||
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| return m_[n]; | ||
| } | ||
| mp_real fact(Size n) const { | ||
| if (f_.size() <= n) | ||
| f_.resize(n+1, std::numeric_limits<mp_real>::quiet_NaN()); | ||
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| if (boost::math::isnan(f_[n])) { | ||
| if (n == 0) | ||
| f_[0] = 1.0; | ||
| else | ||
| f_[n] = n*fact(n-1); | ||
| } | ||
| return f_[n]; | ||
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| } | ||
| const Real u_; | ||
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| private: | ||
| mutable std::vector<mp_real> m_, f_; | ||
| }; | ||
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| //! Gauss-Laguerre Cosine integration | ||
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| /*! This class performs a 1-dimensional Gauss-Laguerre-Cosine integration. | ||
| \f[ | ||
| \int_{0}^{\inf} f(x) \mathrm{d}x | ||
| \f] | ||
| The weighting function is | ||
| \f[ | ||
| w(x;u)=e^{-x}*\cos{u*x} | ||
| \f] | ||
| */ | ||
| template <class mp_real> | ||
| class GaussLaguerreCosinePolynomial | ||
| : public GaussLaguerreTrigonometricBase<mp_real> { | ||
| public: | ||
| explicit GaussLaguerreCosinePolynomial(Real u) | ||
| : GaussLaguerreTrigonometricBase<mp_real>(u), | ||
| m0_(1.0+1.0/(1.0+u*u)) { } | ||
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| mp_real moment(Size n) const { | ||
| return (this->moment_(n) + this->fact(n))/m0_; | ||
| } | ||
| Real w(Real x) const { | ||
| return std::exp(-x)*(1 + std::cos(this->u_*x))/m0_; | ||
| } | ||
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| protected: | ||
| mp_real m0() const { | ||
| return 1/(1 + this->u_*this->u_); | ||
| } | ||
| mp_real m1() const { | ||
| return (1 - this->u_*this->u_) | ||
| /square<mp_real>()(1 + this->u_*this->u_); | ||
| } | ||
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| private: | ||
| const Real m0_; | ||
| }; | ||
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| //! Gauss-Laguerre Sine integration | ||
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| /*! This class performs a 1-dimensional Gauss-Laguerre-Cosine integration. | ||
| \f[ | ||
| \int_{0}^{\inf} f(x) \mathrm{d}x | ||
| \f] | ||
| The weighting function is | ||
| \f[ | ||
| w(x;u)=e^{-x}*\sin{u*x} | ||
| \f] | ||
| */ | ||
| template <class mp_real> | ||
| class GaussLaguerreSinePolynomial | ||
| : public GaussLaguerreTrigonometricBase<mp_real> { | ||
| public: | ||
| explicit GaussLaguerreSinePolynomial(Real u) | ||
| : GaussLaguerreTrigonometricBase<mp_real>(u), | ||
| m0_(1.0+u/(1.0+u*u)) { } | ||
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| mp_real moment(Size n) const { | ||
| return (this->moment_(n) + this->fact(n))/m0_; | ||
| } | ||
| Real w(Real x) const { | ||
| return std::exp(-x)*(1 + std::sin(this->u_*x))/m0_; | ||
| } | ||
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| protected: | ||
| mp_real m0() const { | ||
| return this->u_/(1 + this->u_*this->u_); | ||
| } | ||
| mp_real m1() const { | ||
| return 2*this->u_/square<mp_real>()(1 + this->u_*this->u_); | ||
| } | ||
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| private: | ||
| const Real m0_; | ||
| }; | ||
| } | ||
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| #endif |
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