/src/quantlib/ql/math/interpolations/bicubicsplineinterpolation.hpp

Source
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

/*
 Copyright (C) 2003 Ferdinando Ametrano
 Copyright (C) 2004 StatPro Italia srl

 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
 <https://www.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.
*/

/*! \file bicubicsplineinterpolation.hpp
    \brief bicubic spline interpolation between discrete points
*/

#ifndef quantlib_bicubic_spline_interpolation_hpp
#define quantlib_bicubic_spline_interpolation_hpp

#include <ql/math/interpolations/interpolation2d.hpp>
#include <ql/math/interpolations/cubicinterpolation.hpp>

namespace QuantLib {

    namespace detail {

        class BicubicSplineDerivatives {
          public:
            virtual ~BicubicSplineDerivatives() = default;
            virtual Real derivativeX(Real x, Real y) const = 0;
            virtual Real derivativeY(Real x, Real y) const = 0;
            virtual Real derivativeXY(Real x, Real y) const = 0;
            virtual Real secondDerivativeX(Real x, Real y) const = 0;
            virtual Real secondDerivativeY(Real x, Real y) const = 0;
        };
    
        template <class I1, class I2, class M>
        class BicubicSplineImpl
            : public Interpolation2D::templateImpl<I1,I2,M>,
              public BicubicSplineDerivatives {
          public:
            BicubicSplineImpl(const I1& xBegin, const I1& xEnd,
                              const I2& yBegin, const I2& yEnd,
                              const M& zData)
            : Interpolation2D::templateImpl<I1,I2,M>(xBegin,xEnd,
                                                     yBegin,yEnd,
                                                     zData) {
                BicubicSplineImpl::calculate();
            }
            void calculate() override {
                splines_.resize(this->zData_.rows());
                for (Size i=0; i<(this->zData_.rows()); ++i)
                    splines_[i] = CubicInterpolation(
                                this->xBegin_, this->xEnd_,
                                this->zData_.row_begin(i),
                                CubicInterpolation::Spline, false,
                                CubicInterpolation::SecondDerivative, 0.0,
                                CubicInterpolation::SecondDerivative, 0.0);
            }
            Real value(Real x, Real y) const override {
                std::vector<Real> section(splines_.size());
                for (Size i=0; i<splines_.size(); i++)
                    section[i]=splines_[i](x,true);

                CubicInterpolation spline(this->yBegin_, this->yEnd_,
                                          section.begin(),
                                          CubicInterpolation::Spline, false,
                                          CubicInterpolation::SecondDerivative, 0.0,
                                          CubicInterpolation::SecondDerivative, 0.0);
                return spline(y,true);
            }

            Real derivativeX(Real x, Real y) const override {
                std::vector<Real> section(this->zData_.columns());
                for (Size i=0; i < section.size(); ++i) {
                    section[i] = value(this->xBegin_[i], y);
                }
                
                return CubicInterpolation(
                    this->xBegin_, this->xEnd_,
                    section.begin(),
                    CubicInterpolation::Spline, false,
                    CubicInterpolation::SecondDerivative, 0.0,
                    CubicInterpolation::SecondDerivative, 0.0).derivative(x);
            }

            Real secondDerivativeX(Real x, Real y) const override {
                std::vector<Real> section(this->zData_.columns());
                for (Size i=0; i < section.size(); ++i) {
                    section[i] = value(this->xBegin_[i], y);
                }
                
                return CubicInterpolation(
                    this->xBegin_, this->xEnd_,
                    section.begin(),
                    CubicInterpolation::Spline, false,
                    CubicInterpolation::SecondDerivative, 0.0,
                    CubicInterpolation::SecondDerivative, 0.0)
                                                          .secondDerivative(x);
            }

            Real derivativeY(Real x, Real y) const override {
                std::vector<Real> section(splines_.size());
                for (Size i=0; i<splines_.size(); i++)
                    section[i]=splines_[i](x,true);

                return CubicInterpolation(
                    this->yBegin_, this->yEnd_,
                    section.begin(),
                    CubicInterpolation::Spline, false,
                    CubicInterpolation::SecondDerivative, 0.0,
                    CubicInterpolation::SecondDerivative, 0.0).derivative(y);
            }

            Real secondDerivativeY(Real x, Real y) const override {
                std::vector<Real> section(splines_.size());
                for (Size i=0; i<splines_.size(); i++)
                    section[i]=splines_[i](x,true);

                return CubicInterpolation(
                    this->yBegin_, this->yEnd_,
                    section.begin(),
                    CubicInterpolation::Spline, false,
                    CubicInterpolation::SecondDerivative, 0.0,
                    CubicInterpolation::SecondDerivative, 0.0)
                                                        .secondDerivative(y);
            }

            Real derivativeXY(Real x, Real y) const override {
                std::vector<Real> section(this->zData_.columns());
                for (Size i=0; i < section.size(); ++i) {
                    section[i] = derivativeY(this->xBegin_[i], y);
                }
                
                return CubicInterpolation(
                    this->xBegin_, this->xEnd_,
                    section.begin(),
                    CubicInterpolation::Spline, false,
                    CubicInterpolation::SecondDerivative, 0.0,
                    CubicInterpolation::SecondDerivative, 0.0).derivative(x);
            }

          private:
            std::vector<Interpolation> splines_;
        };

    }

    //! bicubic-spline interpolation between discrete points
    /*! \ingroup interpolations
        \todo revise end conditions
        \warning See the Interpolation class for information about the
                 required lifetime of the underlying data.
    */
    class BicubicSpline : public Interpolation2D {
      public:
        /*! \pre the \f$ x \f$ and \f$ y \f$ values must be sorted. */
        template <class I1, class I2, class M>
        BicubicSpline(const I1& xBegin, const I1& xEnd,
                      const I2& yBegin, const I2& yEnd,
                      const M& zData) {
            impl_ = ext::shared_ptr<Interpolation2D::Impl>(
                  new detail::BicubicSplineImpl<I1,I2,M>(xBegin, xEnd,
                                                         yBegin, yEnd, zData));
        }
        
        Real derivativeX(Real x, Real y) const {
            return ext::dynamic_pointer_cast<detail::BicubicSplineDerivatives>
                    (impl_)->derivativeX(x, y);
        }
        Real derivativeY(Real x, Real y) const {
            return ext::dynamic_pointer_cast<detail::BicubicSplineDerivatives>
                    (impl_)->derivativeY(x, y);
        }
        Real secondDerivativeX(Real x, Real y) const {
            return ext::dynamic_pointer_cast<detail::BicubicSplineDerivatives>
                    (impl_)->secondDerivativeX(x, y);
        }
        Real secondDerivativeY(Real x, Real y) const {
            return ext::dynamic_pointer_cast<detail::BicubicSplineDerivatives>
                    (impl_)->secondDerivativeY(x, y);
        }
        
        Real derivativeXY(Real x, Real y) const {
            return ext::dynamic_pointer_cast<detail::BicubicSplineDerivatives>
                    (impl_)->derivativeXY(x, y);            
        }
    };

    //! bicubic-spline-interpolation factory
    class Bicubic {
      public:
        template <class I1, class I2, class M>
        Interpolation2D interpolate(const I1& xBegin, const I1& xEnd,
                                    const I2& yBegin, const I2& yEnd,
                                    const M& z) const {
            return BicubicSpline(xBegin,xEnd,yBegin,yEnd,z);
        }
    };

}

#endif

Coverage Report

Created: 2025-11-04 06:12

Line	Count	Source
1		/* -- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -- */
2
3		/*
4		Copyright (C) 2003 Ferdinando Ametrano
5		Copyright (C) 2004 StatPro Italia srl
6
7		This file is part of QuantLib, a free-software/open-source library
8		for financial quantitative analysts and developers - http://quantlib.org/
9
10		QuantLib is free software: you can redistribute it and/or modify it
11		under the terms of the QuantLib license. You should have received a
12		copy of the license along with this program; if not, please email
13		<quantlib-dev@lists.sf.net>. The license is also available online at
14		<https://www.quantlib.org/license.shtml>.
15
16		This program is distributed in the hope that it will be useful, but WITHOUT
17		ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
18		FOR A PARTICULAR PURPOSE. See the license for more details.
19		*/
20
21		/*! \file bicubicsplineinterpolation.hpp
22		\brief bicubic spline interpolation between discrete points
23		*/
24
25		#ifndef quantlib_bicubic_spline_interpolation_hpp
26		#define quantlib_bicubic_spline_interpolation_hpp
27
28		#include <ql/math/interpolations/interpolation2d.hpp>
29		#include <ql/math/interpolations/cubicinterpolation.hpp>
30
31		namespace QuantLib {
32
33		namespace detail {
34
35		class BicubicSplineDerivatives {
36		public:
37	0	virtual ~BicubicSplineDerivatives() = default;
38		virtual Real derivativeX(Real x, Real y) const = 0;
39		virtual Real derivativeY(Real x, Real y) const = 0;
40		virtual Real derivativeXY(Real x, Real y) const = 0;
41		virtual Real secondDerivativeX(Real x, Real y) const = 0;
42		virtual Real secondDerivativeY(Real x, Real y) const = 0;
43		};
44
45		template <class I1, class I2, class M>
46		class BicubicSplineImpl
47		: public Interpolation2D::templateImpl<I1,I2,M>,
48		public BicubicSplineDerivatives {
49		public:
50		BicubicSplineImpl(const I1& xBegin, const I1& xEnd,
51		const I2& yBegin, const I2& yEnd,
52		const M& zData)
53	0	: Interpolation2D::templateImpl<I1,I2,M>(xBegin,xEnd,
54	0	yBegin,yEnd,
55	0	zData) {
56	0	BicubicSplineImpl::calculate();
57	0	} Unexecuted instantiation: QuantLib::detail::BicubicSplineImpl<std::__1::__wrap_iter<double>, std::__1::__wrap_iter<double>, QuantLib::Matrix>::BicubicSplineImpl(std::__1::__wrap_iter<double> const&, std::__1::__wrap_iter<double> const&, std::__1::__wrap_iter<double> const&, std::__1::__wrap_iter<double> const&, QuantLib::Matrix const&) Unexecuted instantiation: QuantLib::detail::BicubicSplineImpl<std::__1::__wrap_iter<double const>, std::__1::__wrap_iter<double const>, QuantLib::Matrix>::BicubicSplineImpl(std::__1::__wrap_iter<double const> const&, std::__1::__wrap_iter<double const> const&, std::__1::__wrap_iter<double const> const&, std::__1::__wrap_iter<double const> const&, QuantLib::Matrix const&)
58	0	void calculate() override {
59	0	splines_.resize(this->zData_.rows());
60	0	for (Size i=0; i<(this->zData_.rows()); ++i)
61	0	splines_[i] = CubicInterpolation(
62	0	this->xBegin_, this->xEnd_,
63	0	this->zData_.row_begin(i),
64	0	CubicInterpolation::Spline, false,
65	0	CubicInterpolation::SecondDerivative, 0.0,
66	0	CubicInterpolation::SecondDerivative, 0.0);
67	0	} Unexecuted instantiation: QuantLib::detail::BicubicSplineImpl<std::__1::__wrap_iter<double>, std::__1::__wrap_iter<double>, QuantLib::Matrix>::calculate() Unexecuted instantiation: QuantLib::detail::BicubicSplineImpl<std::__1::__wrap_iter<double const>, std::__1::__wrap_iter<double const>, QuantLib::Matrix>::calculate()
68	0	Real value(Real x, Real y) const override {
69	0	std::vector<Real> section(splines_.size());
70	0	for (Size i=0; i<splines_.size(); i++)
71	0	section[i]=splines_[i](x,true);
72
73	0	CubicInterpolation spline(this->yBegin_, this->yEnd_,
74	0	section.begin(),
75	0	CubicInterpolation::Spline, false,
76	0	CubicInterpolation::SecondDerivative, 0.0,
77	0	CubicInterpolation::SecondDerivative, 0.0);
78	0	return spline(y,true);
79	0	} Unexecuted instantiation: QuantLib::detail::BicubicSplineImpl<std::__1::__wrap_iter<double>, std::__1::__wrap_iter<double>, QuantLib::Matrix>::value(double, double) const Unexecuted instantiation: QuantLib::detail::BicubicSplineImpl<std::__1::__wrap_iter<double const>, std::__1::__wrap_iter<double const>, QuantLib::Matrix>::value(double, double) const
80
81	0	Real derivativeX(Real x, Real y) const override {
82	0	std::vector<Real> section(this->zData_.columns());
83	0	for (Size i=0; i < section.size(); ++i) {
84	0	section[i] = value(this->xBegin_[i], y);
85	0	}
86
87	0	return CubicInterpolation(
88	0	this->xBegin_, this->xEnd_,
89	0	section.begin(),
90	0	CubicInterpolation::Spline, false,
91	0	CubicInterpolation::SecondDerivative, 0.0,
92	0	CubicInterpolation::SecondDerivative, 0.0).derivative(x);
93	0	} Unexecuted instantiation: QuantLib::detail::BicubicSplineImpl<std::__1::__wrap_iter<double>, std::__1::__wrap_iter<double>, QuantLib::Matrix>::derivativeX(double, double) const Unexecuted instantiation: QuantLib::detail::BicubicSplineImpl<std::__1::__wrap_iter<double const>, std::__1::__wrap_iter<double const>, QuantLib::Matrix>::derivativeX(double, double) const
94
95	0	Real secondDerivativeX(Real x, Real y) const override {
96	0	std::vector<Real> section(this->zData_.columns());
97	0	for (Size i=0; i < section.size(); ++i) {
98	0	section[i] = value(this->xBegin_[i], y);
99	0	}
100
101	0	return CubicInterpolation(
102	0	this->xBegin_, this->xEnd_,
103	0	section.begin(),
104	0	CubicInterpolation::Spline, false,
105	0	CubicInterpolation::SecondDerivative, 0.0,
106	0	CubicInterpolation::SecondDerivative, 0.0)
107	0	.secondDerivative(x);
108	0	} Unexecuted instantiation: QuantLib::detail::BicubicSplineImpl<std::__1::__wrap_iter<double>, std::__1::__wrap_iter<double>, QuantLib::Matrix>::secondDerivativeX(double, double) const Unexecuted instantiation: QuantLib::detail::BicubicSplineImpl<std::__1::__wrap_iter<double const>, std::__1::__wrap_iter<double const>, QuantLib::Matrix>::secondDerivativeX(double, double) const
109
110	0	Real derivativeY(Real x, Real y) const override {
111	0	std::vector<Real> section(splines_.size());
112	0	for (Size i=0; i<splines_.size(); i++)
113	0	section[i]=splines_[i](x,true);
114
115	0	return CubicInterpolation(
116	0	this->yBegin_, this->yEnd_,
117	0	section.begin(),
118	0	CubicInterpolation::Spline, false,
119	0	CubicInterpolation::SecondDerivative, 0.0,
120	0	CubicInterpolation::SecondDerivative, 0.0).derivative(y);
121	0	} Unexecuted instantiation: QuantLib::detail::BicubicSplineImpl<std::__1::__wrap_iter<double>, std::__1::__wrap_iter<double>, QuantLib::Matrix>::derivativeY(double, double) const Unexecuted instantiation: QuantLib::detail::BicubicSplineImpl<std::__1::__wrap_iter<double const>, std::__1::__wrap_iter<double const>, QuantLib::Matrix>::derivativeY(double, double) const
122
123	0	Real secondDerivativeY(Real x, Real y) const override {
124	0	std::vector<Real> section(splines_.size());
125	0	for (Size i=0; i<splines_.size(); i++)
126	0	section[i]=splines_[i](x,true);
127
128	0	return CubicInterpolation(
129	0	this->yBegin_, this->yEnd_,
130	0	section.begin(),
131	0	CubicInterpolation::Spline, false,
132	0	CubicInterpolation::SecondDerivative, 0.0,
133	0	CubicInterpolation::SecondDerivative, 0.0)
134	0	.secondDerivative(y);
135	0	} Unexecuted instantiation: QuantLib::detail::BicubicSplineImpl<std::__1::__wrap_iter<double>, std::__1::__wrap_iter<double>, QuantLib::Matrix>::secondDerivativeY(double, double) const Unexecuted instantiation: QuantLib::detail::BicubicSplineImpl<std::__1::__wrap_iter<double const>, std::__1::__wrap_iter<double const>, QuantLib::Matrix>::secondDerivativeY(double, double) const
136
137	0	Real derivativeXY(Real x, Real y) const override {
138	0	std::vector<Real> section(this->zData_.columns());
139	0	for (Size i=0; i < section.size(); ++i) {
140	0	section[i] = derivativeY(this->xBegin_[i], y);
141	0	}
142
143	0	return CubicInterpolation(
144	0	this->xBegin_, this->xEnd_,
145	0	section.begin(),
146	0	CubicInterpolation::Spline, false,
147	0	CubicInterpolation::SecondDerivative, 0.0,
148	0	CubicInterpolation::SecondDerivative, 0.0).derivative(x);
149	0	} Unexecuted instantiation: QuantLib::detail::BicubicSplineImpl<std::__1::__wrap_iter<double>, std::__1::__wrap_iter<double>, QuantLib::Matrix>::derivativeXY(double, double) const Unexecuted instantiation: QuantLib::detail::BicubicSplineImpl<std::__1::__wrap_iter<double const>, std::__1::__wrap_iter<double const>, QuantLib::Matrix>::derivativeXY(double, double) const
150
151		private:
152		std::vector<Interpolation> splines_;
153		};
154
155		}
156
157		//! bicubic-spline interpolation between discrete points
158		/*! \ingroup interpolations
159		\todo revise end conditions
160		\warning See the Interpolation class for information about the
161		required lifetime of the underlying data.
162		*/
163		class BicubicSpline : public Interpolation2D {
164		public:
165		/! \pre the \f$ x \f$ and \f$ y \f$ values must be sorted. /
166		template <class I1, class I2, class M>
167		BicubicSpline(const I1& xBegin, const I1& xEnd,
168		const I2& yBegin, const I2& yEnd,
169	0	const M& zData) {
170	0	impl_ = ext::shared_ptr<Interpolation2D::Impl>(
171	0	new detail::BicubicSplineImpl<I1,I2,M>(xBegin, xEnd,
172	0	yBegin, yEnd, zData));
173	0	} Unexecuted instantiation: QuantLib::BicubicSpline::BicubicSpline<std::__1::__wrap_iter<double>, std::__1::__wrap_iter<double>, QuantLib::Matrix>(std::__1::__wrap_iter<double> const&, std::__1::__wrap_iter<double> const&, std::__1::__wrap_iter<double> const&, std::__1::__wrap_iter<double> const&, QuantLib::Matrix const&) Unexecuted instantiation: QuantLib::BicubicSpline::BicubicSpline<std::__1::__wrap_iter<double const>, std::__1::__wrap_iter<double const>, QuantLib::Matrix>(std::__1::__wrap_iter<double const> const&, std::__1::__wrap_iter<double const> const&, std::__1::__wrap_iter<double const> const&, std::__1::__wrap_iter<double const> const&, QuantLib::Matrix const&)
174
175	0	Real derivativeX(Real x, Real y) const {
176	0	return ext::dynamic_pointer_cast<detail::BicubicSplineDerivatives>
177	0	(impl_)->derivativeX(x, y);
178	0	}
179	0	Real derivativeY(Real x, Real y) const {
180	0	return ext::dynamic_pointer_cast<detail::BicubicSplineDerivatives>
181	0	(impl_)->derivativeY(x, y);
182	0	}
183	0	Real secondDerivativeX(Real x, Real y) const {
184	0	return ext::dynamic_pointer_cast<detail::BicubicSplineDerivatives>
185	0	(impl_)->secondDerivativeX(x, y);
186	0	}
187	0	Real secondDerivativeY(Real x, Real y) const {
188	0	return ext::dynamic_pointer_cast<detail::BicubicSplineDerivatives>
189	0	(impl_)->secondDerivativeY(x, y);
190	0	}
191
192	0	Real derivativeXY(Real x, Real y) const {
193	0	return ext::dynamic_pointer_cast<detail::BicubicSplineDerivatives>
194	0	(impl_)->derivativeXY(x, y);
195	0	}
196		};
197
198		//! bicubic-spline-interpolation factory
199		class Bicubic {
200		public:
201		template <class I1, class I2, class M>
202		Interpolation2D interpolate(const I1& xBegin, const I1& xEnd,
203		const I2& yBegin, const I2& yEnd,
204		const M& z) const {
205		return BicubicSpline(xBegin,xEnd,yBegin,yEnd,z);
206		}
207		};
208
209		}
210
211		#endif