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

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

/*
 Copyright (C) 2010 Ferdinando Ametrano

 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 mixedinterpolation.hpp
    \brief mixed interpolation between discrete points
*/

#ifndef quantlib_mixed_interpolation_hpp
#define quantlib_mixed_interpolation_hpp

#include <ql/math/interpolations/linearinterpolation.hpp>
#include <ql/math/interpolations/cubicinterpolation.hpp>
#include <ql/utilities/dataformatters.hpp>

namespace QuantLib {

    namespace detail {
        template <class I1, class I2, class SwitchFn>
        class MixedInterpolationImpl;
    }

    struct MixedInterpolation {
        enum Behavior {
            ShareRanges,  /*!< Define both interpolations over the
                               whole range defined by the passed
                               iterators. This is the default
                               behavior. */
            SplitRanges   /*!< Define the first interpolation over the
                               first part of the range, and the second
                               interpolation over the second part. */
        };
    };

    //! mixed linear/cubic interpolation between discrete points
    //
    // When using SplitRanges one can set leftC to FirstDerivative and
    // leftConditionValue to Null to match the first derivatives at the
    // switch point.
    /*! \ingroup interpolations
        \warning See the Interpolation class for information about the
                 required lifetime of the underlying data.
    */
    class MixedLinearCubicInterpolation : public Interpolation {
      public:
        /*! \pre the \f$ x \f$ values must be sorted. */
        template <class I1, class I2>
        MixedLinearCubicInterpolation(const I1& xBegin, const I1& xEnd,
                                      const I2& yBegin, Size n,
                                      MixedInterpolation::Behavior behavior,
                                      CubicInterpolation::DerivativeApprox da,
                                      bool monotonic,
                                      CubicInterpolation::BoundaryCondition leftC,
                                      Real leftConditionValue,
                                      CubicInterpolation::BoundaryCondition rightC,
                                      Real rightConditionValue,
                                      bool update = true) {
            bool matchDerivatives = leftC == CubicInterpolation::FirstDerivative &&
                                    leftConditionValue == Null<Real>();
            QL_REQUIRE(!matchDerivatives || behavior == MixedInterpolation::SplitRanges,
                       "matching derivatives is only supported with SplitRanges");

            auto switchFn = [=](Interpolation& left, Interpolation& right, Real x) {
                if (!matchDerivatives) return;
                // NOLINTNEXTLINE(cppcoreguidelines-pro-type-static-cast-downcast)
                auto& cubicImpl = static_cast<detail::CubicInterpolationBaseImpl&>(*right.impl_);
                cubicImpl.leftValue_ = left.derivative(x, true);
            };
            impl_ = ext::make_shared<detail::MixedInterpolationImpl<I1, I2, decltype(switchFn)>>(
                xBegin, xEnd, yBegin, n, behavior,
                Linear(),
                Cubic(da, monotonic,
                      leftC, leftConditionValue,
                      rightC, rightConditionValue),
                std::move(switchFn));
            if (update)
                impl_->update();
        }
    };

    //! mixed linear/cubic interpolation factory and traits
    /*! \ingroup interpolations */
    class MixedLinearCubic {
      public:
        MixedLinearCubic(Size n,
                         MixedInterpolation::Behavior behavior,
                         CubicInterpolation::DerivativeApprox da,
                         bool monotonic = true,
                         CubicInterpolation::BoundaryCondition leftCondition
                             = CubicInterpolation::SecondDerivative,
                         Real leftConditionValue = 0.0,
                         CubicInterpolation::BoundaryCondition rightCondition
                             = CubicInterpolation::SecondDerivative,
                         Real rightConditionValue = 0.0)
        : n_(n), behavior_(behavior), da_(da), monotonic_(monotonic),
          leftType_(leftCondition), rightType_(rightCondition),
          leftValue_(leftConditionValue), rightValue_(rightConditionValue) {}
        template <class I1, class I2>
        Interpolation interpolate(const I1& xBegin, const I1& xEnd,
                                  const I2& yBegin, bool update = true) const {
            return MixedLinearCubicInterpolation(xBegin, xEnd,
                                                 yBegin, n_, behavior_,
                                                 da_, monotonic_,
                                                 leftType_, leftValue_,
                                                 rightType_, rightValue_,
                                                 update);
        }
        // fix below
        static const bool global = true;
        static const Size requiredPoints = 3;
      private:
        Size n_;
        MixedInterpolation::Behavior behavior_;
        CubicInterpolation::DerivativeApprox da_;
        bool monotonic_;
        CubicInterpolation::BoundaryCondition leftType_, rightType_;
        Real leftValue_, rightValue_;
    };

    // convenience classes

    class MixedLinearCubicNaturalSpline : public MixedLinearCubicInterpolation {
      public:
        /*! \pre the \f$ x \f$ values must be sorted. */
        template <class I1, class I2>
        MixedLinearCubicNaturalSpline(const I1& xBegin, const I1& xEnd,
                                      const I2& yBegin, Size n,
                                      MixedInterpolation::Behavior behavior
                                            = MixedInterpolation::ShareRanges)
        : MixedLinearCubicInterpolation(xBegin, xEnd, yBegin, n, behavior,
                                        CubicInterpolation::Spline, false,
                                        CubicInterpolation::SecondDerivative, 0.0,
                                        CubicInterpolation::SecondDerivative, 0.0) {}
    };

    class MixedLinearMonotonicCubicNaturalSpline : public MixedLinearCubicInterpolation {
      public:
        /*! \pre the \f$ x \f$ values must be sorted. */
        template <class I1, class I2>
        MixedLinearMonotonicCubicNaturalSpline(const I1& xBegin, const I1& xEnd,
                                               const I2& yBegin, Size n,
                                               MixedInterpolation::Behavior behavior
                                                   = MixedInterpolation::ShareRanges)
        : MixedLinearCubicInterpolation(xBegin, xEnd, yBegin, n, behavior,
                                        CubicInterpolation::Spline, true,
                                        CubicInterpolation::SecondDerivative, 0.0,
                                        CubicInterpolation::SecondDerivative, 0.0) {}
    };

    class MixedLinearKrugerCubic : public MixedLinearCubicInterpolation {
      public:
        /*! \pre the \f$ x \f$ values must be sorted. */
        template <class I1, class I2>
        MixedLinearKrugerCubic(const I1& xBegin, const I1& xEnd,
                               const I2& yBegin, Size n,
                               MixedInterpolation::Behavior behavior
                                            = MixedInterpolation::ShareRanges)
        : MixedLinearCubicInterpolation(xBegin, xEnd, yBegin, n, behavior,
                                        CubicInterpolation::Kruger, false,
                                        CubicInterpolation::SecondDerivative, 0.0,
                                        CubicInterpolation::SecondDerivative, 0.0) {}
    };

    class MixedLinearFritschButlandCubic : public MixedLinearCubicInterpolation {
      public:
        /*! \pre the \f$ x \f$ values must be sorted. */
        template <class I1, class I2>
        MixedLinearFritschButlandCubic(const I1& xBegin, const I1& xEnd,
                                       const I2& yBegin, Size n,
                                       MixedInterpolation::Behavior behavior
                                            = MixedInterpolation::ShareRanges)
        : MixedLinearCubicInterpolation(xBegin, xEnd, yBegin, n, behavior,
                                        CubicInterpolation::FritschButland, false,
                                        CubicInterpolation::SecondDerivative, 0.0,
                                        CubicInterpolation::SecondDerivative, 0.0) {}
    };

    class MixedLinearParabolic : public MixedLinearCubicInterpolation {
      public:
        /*! \pre the \f$ x \f$ values must be sorted. */
        template <class I1, class I2>
        MixedLinearParabolic(const I1& xBegin, const I1& xEnd,
                             const I2& yBegin, Size n,
                             MixedInterpolation::Behavior behavior
                                            = MixedInterpolation::ShareRanges)
        : MixedLinearCubicInterpolation(xBegin, xEnd, yBegin, n, behavior,
                                        CubicInterpolation::Parabolic, false,
                                        CubicInterpolation::SecondDerivative, 0.0,
                                        CubicInterpolation::SecondDerivative, 0.0) {}
    };

    class MixedLinearMonotonicParabolic : public MixedLinearCubicInterpolation {
      public:
        /*! \pre the \f$ x \f$ values must be sorted. */
        template <class I1, class I2>
        MixedLinearMonotonicParabolic(const I1& xBegin, const I1& xEnd,
                                      const I2& yBegin, Size n,
                                      MixedInterpolation::Behavior behavior
                                            = MixedInterpolation::ShareRanges)
        : MixedLinearCubicInterpolation(xBegin, xEnd, yBegin, n, behavior,
                                        CubicInterpolation::Parabolic, true,
                                        CubicInterpolation::SecondDerivative, 0.0,
                                        CubicInterpolation::SecondDerivative, 0.0) {}
    };

    namespace detail {

        template <class I1, class I2, class SwitchFn>
        class MixedInterpolationImpl final
            : public Interpolation::templateImpl<I1, I2> {
          public:
            template <class Interpolator1, class Interpolator2>
            MixedInterpolationImpl(const I1& xBegin, const I1& xEnd,
                                   const I2& yBegin, Size n,
                                   MixedInterpolation::Behavior behavior,
                                   const Interpolator1& factory1,
                                   const Interpolator2& factory2,
                                   SwitchFn switchFn)
            : Interpolation::templateImpl<I1, I2>(xBegin, xEnd, yBegin, 1),
              switchFn_(std::move(switchFn)) {
                // the switch point xBegin_ + n is dereferenced in update() and
                // value(), so it must be a valid element; for SplitRanges the
                // first segment additionally reads xBegin_ + n + 1
                Size maxN = static_cast<Size>(xEnd - xBegin) - 1;
                // This only checks that we pass valid iterators into interpolate()
                // calls below. The calls themselves check requiredPoints for each
                // of the segments.
                QL_REQUIRE(n <= maxN, "n is too large (" << n << " > " << maxN << ")");

                xBegin2_ = this->xBegin_ + n;

                switch (behavior) {
                  case MixedInterpolation::ShareRanges:
                    interpolation1_ = detail::interpolateWithoutUpdate(
                        factory1, this->xBegin_, this->xEnd_, this->yBegin_);
                    interpolation2_ = detail::interpolateWithoutUpdate(
                        factory2, this->xBegin_, this->xEnd_, this->yBegin_);
                    break;
                  case MixedInterpolation::SplitRanges:
                    interpolation1_ = detail::interpolateWithoutUpdate(
                        factory1, this->xBegin_, this->xBegin2_ + 1, this->yBegin_);
                    interpolation2_ = detail::interpolateWithoutUpdate(
                        factory2, this->xBegin2_, this->xEnd_, this->yBegin_ + n);
                    break;
                  default:
                    QL_FAIL("unknown mixed-interpolation behavior: " << behavior);
                }
            }

            void update() override {
                interpolation1_.update();
                switchFn_(interpolation1_, interpolation2_, *xBegin2_);
                interpolation2_.update();
            }
            Real value(Real x) const override {
                if (x<*xBegin2_)
                    return interpolation1_(x, true);
                return interpolation2_(x, true);
            }
            Real primitive(Real x) const override {
                if (x<*xBegin2_)
                    return interpolation1_.primitive(x, true);
                return interpolation2_.primitive(x, true) -
                    interpolation2_.primitive(*xBegin2_, true) +
                    interpolation1_.primitive(*xBegin2_, true);
            }
            Real derivative(Real x) const override {
                if (x<*xBegin2_)
                    return interpolation1_.derivative(x, true);
                return interpolation2_.derivative(x, true);
            }
            Real secondDerivative(Real x) const override {
                if (x<*xBegin2_)
                    return interpolation1_.secondDerivative(x, true);
                return interpolation2_.secondDerivative(x, true);
            }
          private:
            I1 xBegin2_;
            Interpolation interpolation1_, interpolation2_;
            SwitchFn switchFn_;
        };

    }

}

#endif

Coverage Report

Created: 2026-06-23 06:40

Line	Count	Source
1		/* -- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -- */
2
3		/*
4		Copyright (C) 2010 Ferdinando Ametrano
5
6		This file is part of QuantLib, a free-software/open-source library
7		for financial quantitative analysts and developers - http://quantlib.org/
8
9		QuantLib is free software: you can redistribute it and/or modify it
10		under the terms of the QuantLib license. You should have received a
11		copy of the license along with this program; if not, please email
12		<quantlib-dev@lists.sf.net>. The license is also available online at
13		<https://www.quantlib.org/license.shtml>.
14
15		This program is distributed in the hope that it will be useful, but WITHOUT
16		ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
17		FOR A PARTICULAR PURPOSE. See the license for more details.
18		*/
19
20		/*! \file mixedinterpolation.hpp
21		\brief mixed interpolation between discrete points
22		*/
23
24		#ifndef quantlib_mixed_interpolation_hpp
25		#define quantlib_mixed_interpolation_hpp
26
27		#include <ql/math/interpolations/linearinterpolation.hpp>
28		#include <ql/math/interpolations/cubicinterpolation.hpp>
29		#include <ql/utilities/dataformatters.hpp>
30
31		namespace QuantLib {
32
33		namespace detail {
34		template <class I1, class I2, class SwitchFn>
35		class MixedInterpolationImpl;
36		}
37
38		struct MixedInterpolation {
39		enum Behavior {
40		ShareRanges, /*!< Define both interpolations over the
41		whole range defined by the passed
42		iterators. This is the default
43		behavior. */
44		SplitRanges /*!< Define the first interpolation over the
45		first part of the range, and the second
46		interpolation over the second part. */
47		};
48		};
49
50		//! mixed linear/cubic interpolation between discrete points
51		//
52		// When using SplitRanges one can set leftC to FirstDerivative and
53		// leftConditionValue to Null to match the first derivatives at the
54		// switch point.
55		/*! \ingroup interpolations
56		\warning See the Interpolation class for information about the
57		required lifetime of the underlying data.
58		*/
59		class MixedLinearCubicInterpolation : public Interpolation {
60		public:
61		/! \pre the \f$ x \f$ values must be sorted. /
62		template <class I1, class I2>
63		MixedLinearCubicInterpolation(const I1& xBegin, const I1& xEnd,
64		const I2& yBegin, Size n,
65		MixedInterpolation::Behavior behavior,
66		CubicInterpolation::DerivativeApprox da,
67		bool monotonic,
68		CubicInterpolation::BoundaryCondition leftC,
69		Real leftConditionValue,
70		CubicInterpolation::BoundaryCondition rightC,
71		Real rightConditionValue,
72		bool update = true) {
73		bool matchDerivatives = leftC == CubicInterpolation::FirstDerivative &&
74		leftConditionValue == Null<Real>();
75		QL_REQUIRE(!matchDerivatives \|\| behavior == MixedInterpolation::SplitRanges,
76		"matching derivatives is only supported with SplitRanges");
77
78		auto switchFn = [=](Interpolation& left, Interpolation& right, Real x) {
79		if (!matchDerivatives) return;
80		// NOLINTNEXTLINE(cppcoreguidelines-pro-type-static-cast-downcast)
81		auto& cubicImpl = static_cast<detail::CubicInterpolationBaseImpl&>(*right.impl_);
82		cubicImpl.leftValue_ = left.derivative(x, true);
83		};
84		impl_ = ext::make_shared<detail::MixedInterpolationImpl<I1, I2, decltype(switchFn)>>(
85		xBegin, xEnd, yBegin, n, behavior,
86		Linear(),
87		Cubic(da, monotonic,
88		leftC, leftConditionValue,
89		rightC, rightConditionValue),
90		std::move(switchFn));
91		if (update)
92		impl_->update();
93		}
94		};
95
96		//! mixed linear/cubic interpolation factory and traits
97		/! \ingroup interpolations /
98		class MixedLinearCubic {
99		public:
100		MixedLinearCubic(Size n,
101		MixedInterpolation::Behavior behavior,
102		CubicInterpolation::DerivativeApprox da,
103		bool monotonic = true,
104		CubicInterpolation::BoundaryCondition leftCondition
105		= CubicInterpolation::SecondDerivative,
106		Real leftConditionValue = 0.0,
107		CubicInterpolation::BoundaryCondition rightCondition
108		= CubicInterpolation::SecondDerivative,
109		Real rightConditionValue = 0.0)
110		: n_(n), behavior_(behavior), da_(da), monotonic_(monotonic),
111		leftType_(leftCondition), rightType_(rightCondition),
112	0	leftValue_(leftConditionValue), rightValue_(rightConditionValue) {}
113		template <class I1, class I2>
114		Interpolation interpolate(const I1& xBegin, const I1& xEnd,
115		const I2& yBegin, bool update = true) const {
116		return MixedLinearCubicInterpolation(xBegin, xEnd,
117		yBegin, n_, behavior_,
118		da_, monotonic_,
119		leftType_, leftValue_,
120		rightType_, rightValue_,
121		update);
122		}
123		// fix below
124		static const bool global = true;
125		static const Size requiredPoints = 3;
126		private:
127		Size n_;
128		MixedInterpolation::Behavior behavior_;
129		CubicInterpolation::DerivativeApprox da_;
130		bool monotonic_;
131		CubicInterpolation::BoundaryCondition leftType_, rightType_;
132		Real leftValue_, rightValue_;
133		};
134
135		// convenience classes
136
137		class MixedLinearCubicNaturalSpline : public MixedLinearCubicInterpolation {
138		public:
139		/! \pre the \f$ x \f$ values must be sorted. /
140		template <class I1, class I2>
141		MixedLinearCubicNaturalSpline(const I1& xBegin, const I1& xEnd,
142		const I2& yBegin, Size n,
143		MixedInterpolation::Behavior behavior
144		= MixedInterpolation::ShareRanges)
145		: MixedLinearCubicInterpolation(xBegin, xEnd, yBegin, n, behavior,
146		CubicInterpolation::Spline, false,
147		CubicInterpolation::SecondDerivative, 0.0,
148		CubicInterpolation::SecondDerivative, 0.0) {}
149		};
150
151		class MixedLinearMonotonicCubicNaturalSpline : public MixedLinearCubicInterpolation {
152		public:
153		/! \pre the \f$ x \f$ values must be sorted. /
154		template <class I1, class I2>
155		MixedLinearMonotonicCubicNaturalSpline(const I1& xBegin, const I1& xEnd,
156		const I2& yBegin, Size n,
157		MixedInterpolation::Behavior behavior
158		= MixedInterpolation::ShareRanges)
159		: MixedLinearCubicInterpolation(xBegin, xEnd, yBegin, n, behavior,
160		CubicInterpolation::Spline, true,
161		CubicInterpolation::SecondDerivative, 0.0,
162		CubicInterpolation::SecondDerivative, 0.0) {}
163		};
164
165		class MixedLinearKrugerCubic : public MixedLinearCubicInterpolation {
166		public:
167		/! \pre the \f$ x \f$ values must be sorted. /
168		template <class I1, class I2>
169		MixedLinearKrugerCubic(const I1& xBegin, const I1& xEnd,
170		const I2& yBegin, Size n,
171		MixedInterpolation::Behavior behavior
172		= MixedInterpolation::ShareRanges)
173		: MixedLinearCubicInterpolation(xBegin, xEnd, yBegin, n, behavior,
174		CubicInterpolation::Kruger, false,
175		CubicInterpolation::SecondDerivative, 0.0,
176		CubicInterpolation::SecondDerivative, 0.0) {}
177		};
178
179		class MixedLinearFritschButlandCubic : public MixedLinearCubicInterpolation {
180		public:
181		/! \pre the \f$ x \f$ values must be sorted. /
182		template <class I1, class I2>
183		MixedLinearFritschButlandCubic(const I1& xBegin, const I1& xEnd,
184		const I2& yBegin, Size n,
185		MixedInterpolation::Behavior behavior
186		= MixedInterpolation::ShareRanges)
187		: MixedLinearCubicInterpolation(xBegin, xEnd, yBegin, n, behavior,
188		CubicInterpolation::FritschButland, false,
189		CubicInterpolation::SecondDerivative, 0.0,
190		CubicInterpolation::SecondDerivative, 0.0) {}
191		};
192
193		class MixedLinearParabolic : public MixedLinearCubicInterpolation {
194		public:
195		/! \pre the \f$ x \f$ values must be sorted. /
196		template <class I1, class I2>
197		MixedLinearParabolic(const I1& xBegin, const I1& xEnd,
198		const I2& yBegin, Size n,
199		MixedInterpolation::Behavior behavior
200		= MixedInterpolation::ShareRanges)
201		: MixedLinearCubicInterpolation(xBegin, xEnd, yBegin, n, behavior,
202		CubicInterpolation::Parabolic, false,
203		CubicInterpolation::SecondDerivative, 0.0,
204		CubicInterpolation::SecondDerivative, 0.0) {}
205		};
206
207		class MixedLinearMonotonicParabolic : public MixedLinearCubicInterpolation {
208		public:
209		/! \pre the \f$ x \f$ values must be sorted. /
210		template <class I1, class I2>
211		MixedLinearMonotonicParabolic(const I1& xBegin, const I1& xEnd,
212		const I2& yBegin, Size n,
213		MixedInterpolation::Behavior behavior
214		= MixedInterpolation::ShareRanges)
215		: MixedLinearCubicInterpolation(xBegin, xEnd, yBegin, n, behavior,
216		CubicInterpolation::Parabolic, true,
217		CubicInterpolation::SecondDerivative, 0.0,
218		CubicInterpolation::SecondDerivative, 0.0) {}
219		};
220
221		namespace detail {
222
223		template <class I1, class I2, class SwitchFn>
224		class MixedInterpolationImpl final
225		: public Interpolation::templateImpl<I1, I2> {
226		public:
227		template <class Interpolator1, class Interpolator2>
228		MixedInterpolationImpl(const I1& xBegin, const I1& xEnd,
229		const I2& yBegin, Size n,
230		MixedInterpolation::Behavior behavior,
231		const Interpolator1& factory1,
232		const Interpolator2& factory2,
233		SwitchFn switchFn)
234		: Interpolation::templateImpl<I1, I2>(xBegin, xEnd, yBegin, 1),
235		switchFn_(std::move(switchFn)) {
236		// the switch point xBegin_ + n is dereferenced in update() and
237		// value(), so it must be a valid element; for SplitRanges the
238		// first segment additionally reads xBegin_ + n + 1
239		Size maxN = static_cast<Size>(xEnd - xBegin) - 1;
240		// This only checks that we pass valid iterators into interpolate()
241		// calls below. The calls themselves check requiredPoints for each
242		// of the segments.
243		QL_REQUIRE(n <= maxN, "n is too large (" << n << " > " << maxN << ")");
244
245		xBegin2_ = this->xBegin_ + n;
246
247		switch (behavior) {
248		case MixedInterpolation::ShareRanges:
249		interpolation1_ = detail::interpolateWithoutUpdate(
250		factory1, this->xBegin_, this->xEnd_, this->yBegin_);
251		interpolation2_ = detail::interpolateWithoutUpdate(
252		factory2, this->xBegin_, this->xEnd_, this->yBegin_);
253		break;
254		case MixedInterpolation::SplitRanges:
255		interpolation1_ = detail::interpolateWithoutUpdate(
256		factory1, this->xBegin_, this->xBegin2_ + 1, this->yBegin_);
257		interpolation2_ = detail::interpolateWithoutUpdate(
258		factory2, this->xBegin2_, this->xEnd_, this->yBegin_ + n);
259		break;
260		default:
261		QL_FAIL("unknown mixed-interpolation behavior: " << behavior);
262		}
263		}
264
265		void update() override {
266		interpolation1_.update();
267		switchFn_(interpolation1_, interpolation2_, *xBegin2_);
268		interpolation2_.update();
269		}
270		Real value(Real x) const override {
271		if (x<*xBegin2_)
272		return interpolation1_(x, true);
273		return interpolation2_(x, true);
274		}
275		Real primitive(Real x) const override {
276		if (x<*xBegin2_)
277		return interpolation1_.primitive(x, true);
278		return interpolation2_.primitive(x, true) -
279		interpolation2_.primitive(*xBegin2_, true) +
280		interpolation1_.primitive(*xBegin2_, true);
281		}
282		Real derivative(Real x) const override {
283		if (x<*xBegin2_)
284		return interpolation1_.derivative(x, true);
285		return interpolation2_.derivative(x, true);
286		}
287		Real secondDerivative(Real x) const override {
288		if (x<*xBegin2_)
289		return interpolation1_.secondDerivative(x, true);
290		return interpolation2_.secondDerivative(x, true);
291		}
292		private:
293		I1 xBegin2_;
294		Interpolation interpolation1_, interpolation2_;
295		SwitchFn switchFn_;
296		};
297
298		}
299
300		}
301
302		#endif