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/* -*- 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
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