/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 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
    /*! \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) {
            impl_ = ext::make_shared<detail::MixedInterpolationImpl<I1, I2>>(
                xBegin, xEnd, yBegin, n, behavior,
                Linear(),
                Cubic(da, monotonic,
                      leftC, leftConditionValue,
                      rightC, rightConditionValue));
            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) const {
            return MixedLinearCubicInterpolation(xBegin, xEnd,
                                                 yBegin, n_, behavior_,
                                                 da_, monotonic_,
                                                 leftType_, leftValue_,
                                                 rightType_, rightValue_);
        }
        // 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 MixedInterpolationImpl
            : 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)
            : Interpolation::templateImpl<I1, I2>(xBegin, xEnd, yBegin, 1) {
                Size maxN = static_cast<Size>(xEnd - xBegin);
                // SplitRanges needs xBegin2_+1 to be valid
                if (behavior == MixedInterpolation::SplitRanges) {
                    --maxN;
                }
                // 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_ = factory1.interpolate(this->xBegin_,
                                                           this->xEnd_,
                                                           this->yBegin_);
                    interpolation2_ = factory2.interpolate(this->xBegin_,
                                                           this->xEnd_,
                                                           this->yBegin_);
                    break;
                  case MixedInterpolation::SplitRanges:
                    interpolation1_ = factory1.interpolate(this->xBegin_,
                                                           this->xBegin2_ + 1,
                                                           this->yBegin_);
                    interpolation2_ = factory2.interpolate(this->xBegin2_,
                                                           this->xEnd_,
                                                           this->yBegin_ + n);
                    break;
                  default:
                    QL_FAIL("unknown mixed-interpolation behavior: " << behavior);
                }
            }

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

    }

}

#endif

Coverage Report

Created: 2025-12-08 06:13

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
35		template <class I1, class I2>
36		class MixedInterpolationImpl;
37
38		}
39
40
41		struct MixedInterpolation {
42		enum Behavior {
43		ShareRanges, /*!< Define both interpolations over the
44		whole range defined by the passed
45		iterators. This is the default
46		behavior. */
47		SplitRanges /*!< Define the first interpolation over the
48		first part of the range, and the second
49		interpolation over the second part. */
50		};
51		};
52
53		//! mixed linear/cubic interpolation between discrete points
54		/*! \ingroup interpolations
55		\warning See the Interpolation class for information about the
56		required lifetime of the underlying data.
57		*/
58		class MixedLinearCubicInterpolation : public Interpolation {
59		public:
60		/! \pre the \f$ x \f$ values must be sorted. /
61		template <class I1, class I2>
62		MixedLinearCubicInterpolation(const I1& xBegin, const I1& xEnd,
63		const I2& yBegin, Size n,
64		MixedInterpolation::Behavior behavior,
65		CubicInterpolation::DerivativeApprox da,
66		bool monotonic,
67		CubicInterpolation::BoundaryCondition leftC,
68		Real leftConditionValue,
69		CubicInterpolation::BoundaryCondition rightC,
70		Real rightConditionValue) {
71		impl_ = ext::make_shared<detail::MixedInterpolationImpl<I1, I2>>(
72		xBegin, xEnd, yBegin, n, behavior,
73		Linear(),
74		Cubic(da, monotonic,
75		leftC, leftConditionValue,
76		rightC, rightConditionValue));
77		impl_->update();
78		}
79		};
80
81		//! mixed linear/cubic interpolation factory and traits
82		/! \ingroup interpolations /
83		class MixedLinearCubic {
84		public:
85		MixedLinearCubic(Size n,
86		MixedInterpolation::Behavior behavior,
87		CubicInterpolation::DerivativeApprox da,
88		bool monotonic = true,
89		CubicInterpolation::BoundaryCondition leftCondition
90		= CubicInterpolation::SecondDerivative,
91		Real leftConditionValue = 0.0,
92		CubicInterpolation::BoundaryCondition rightCondition
93		= CubicInterpolation::SecondDerivative,
94		Real rightConditionValue = 0.0)
95		: n_(n), behavior_(behavior), da_(da), monotonic_(monotonic),
96		leftType_(leftCondition), rightType_(rightCondition),
97	0	leftValue_(leftConditionValue), rightValue_(rightConditionValue) {}
98		template <class I1, class I2>
99		Interpolation interpolate(const I1& xBegin, const I1& xEnd,
100		const I2& yBegin) const {
101		return MixedLinearCubicInterpolation(xBegin, xEnd,
102		yBegin, n_, behavior_,
103		da_, monotonic_,
104		leftType_, leftValue_,
105		rightType_, rightValue_);
106		}
107		// fix below
108		static const bool global = true;
109		static const Size requiredPoints = 3;
110		private:
111		Size n_;
112		MixedInterpolation::Behavior behavior_;
113		CubicInterpolation::DerivativeApprox da_;
114		bool monotonic_;
115		CubicInterpolation::BoundaryCondition leftType_, rightType_;
116		Real leftValue_, rightValue_;
117		};
118
119		// convenience classes
120
121		class MixedLinearCubicNaturalSpline : public MixedLinearCubicInterpolation {
122		public:
123		/! \pre the \f$ x \f$ values must be sorted. /
124		template <class I1, class I2>
125		MixedLinearCubicNaturalSpline(const I1& xBegin, const I1& xEnd,
126		const I2& yBegin, Size n,
127		MixedInterpolation::Behavior behavior
128		= MixedInterpolation::ShareRanges)
129		: MixedLinearCubicInterpolation(xBegin, xEnd, yBegin, n, behavior,
130		CubicInterpolation::Spline, false,
131		CubicInterpolation::SecondDerivative, 0.0,
132		CubicInterpolation::SecondDerivative, 0.0) {}
133		};
134
135		class MixedLinearMonotonicCubicNaturalSpline : public MixedLinearCubicInterpolation {
136		public:
137		/! \pre the \f$ x \f$ values must be sorted. /
138		template <class I1, class I2>
139		MixedLinearMonotonicCubicNaturalSpline(const I1& xBegin, const I1& xEnd,
140		const I2& yBegin, Size n,
141		MixedInterpolation::Behavior behavior
142		= MixedInterpolation::ShareRanges)
143		: MixedLinearCubicInterpolation(xBegin, xEnd, yBegin, n, behavior,
144		CubicInterpolation::Spline, true,
145		CubicInterpolation::SecondDerivative, 0.0,
146		CubicInterpolation::SecondDerivative, 0.0) {}
147		};
148
149		class MixedLinearKrugerCubic : public MixedLinearCubicInterpolation {
150		public:
151		/! \pre the \f$ x \f$ values must be sorted. /
152		template <class I1, class I2>
153		MixedLinearKrugerCubic(const I1& xBegin, const I1& xEnd,
154		const I2& yBegin, Size n,
155		MixedInterpolation::Behavior behavior
156		= MixedInterpolation::ShareRanges)
157		: MixedLinearCubicInterpolation(xBegin, xEnd, yBegin, n, behavior,
158		CubicInterpolation::Kruger, false,
159		CubicInterpolation::SecondDerivative, 0.0,
160		CubicInterpolation::SecondDerivative, 0.0) {}
161		};
162
163		class MixedLinearFritschButlandCubic : public MixedLinearCubicInterpolation {
164		public:
165		/! \pre the \f$ x \f$ values must be sorted. /
166		template <class I1, class I2>
167		MixedLinearFritschButlandCubic(const I1& xBegin, const I1& xEnd,
168		const I2& yBegin, Size n,
169		MixedInterpolation::Behavior behavior
170		= MixedInterpolation::ShareRanges)
171		: MixedLinearCubicInterpolation(xBegin, xEnd, yBegin, n, behavior,
172		CubicInterpolation::FritschButland, false,
173		CubicInterpolation::SecondDerivative, 0.0,
174		CubicInterpolation::SecondDerivative, 0.0) {}
175		};
176
177		class MixedLinearParabolic : public MixedLinearCubicInterpolation {
178		public:
179		/! \pre the \f$ x \f$ values must be sorted. /
180		template <class I1, class I2>
181		MixedLinearParabolic(const I1& xBegin, const I1& xEnd,
182		const I2& yBegin, Size n,
183		MixedInterpolation::Behavior behavior
184		= MixedInterpolation::ShareRanges)
185		: MixedLinearCubicInterpolation(xBegin, xEnd, yBegin, n, behavior,
186		CubicInterpolation::Parabolic, false,
187		CubicInterpolation::SecondDerivative, 0.0,
188		CubicInterpolation::SecondDerivative, 0.0) {}
189		};
190
191		class MixedLinearMonotonicParabolic : public MixedLinearCubicInterpolation {
192		public:
193		/! \pre the \f$ x \f$ values must be sorted. /
194		template <class I1, class I2>
195		MixedLinearMonotonicParabolic(const I1& xBegin, const I1& xEnd,
196		const I2& yBegin, Size n,
197		MixedInterpolation::Behavior behavior
198		= MixedInterpolation::ShareRanges)
199		: MixedLinearCubicInterpolation(xBegin, xEnd, yBegin, n, behavior,
200		CubicInterpolation::Parabolic, true,
201		CubicInterpolation::SecondDerivative, 0.0,
202		CubicInterpolation::SecondDerivative, 0.0) {}
203		};
204
205		namespace detail {
206
207		template <class I1, class I2>
208		class MixedInterpolationImpl
209		: public Interpolation::templateImpl<I1, I2> {
210		public:
211		template <class Interpolator1, class Interpolator2>
212		MixedInterpolationImpl(const I1& xBegin, const I1& xEnd,
213		const I2& yBegin, Size n,
214		MixedInterpolation::Behavior behavior,
215		const Interpolator1& factory1,
216		const Interpolator2& factory2)
217		: Interpolation::templateImpl<I1, I2>(xBegin, xEnd, yBegin, 1) {
218		Size maxN = static_cast<Size>(xEnd - xBegin);
219		// SplitRanges needs xBegin2_+1 to be valid
220		if (behavior == MixedInterpolation::SplitRanges) {
221		--maxN;
222		}
223		// This only checks that we pass valid iterators into interpolate()
224		// calls below. The calls themselves check requiredPoints for each
225		// of the segments.
226		QL_REQUIRE(n <= maxN, "n is too large (" << n << " > " << maxN << ")");
227
228		xBegin2_ = this->xBegin_ + n;
229
230		switch (behavior) {
231		case MixedInterpolation::ShareRanges:
232		interpolation1_ = factory1.interpolate(this->xBegin_,
233		this->xEnd_,
234		this->yBegin_);
235		interpolation2_ = factory2.interpolate(this->xBegin_,
236		this->xEnd_,
237		this->yBegin_);
238		break;
239		case MixedInterpolation::SplitRanges:
240		interpolation1_ = factory1.interpolate(this->xBegin_,
241		this->xBegin2_ + 1,
242		this->yBegin_);
243		interpolation2_ = factory2.interpolate(this->xBegin2_,
244		this->xEnd_,
245		this->yBegin_ + n);
246		break;
247		default:
248		QL_FAIL("unknown mixed-interpolation behavior: " << behavior);
249		}
250		}
251
252		void update() {
253		interpolation1_.update();
254		interpolation2_.update();
255		}
256		Real value(Real x) const {
257		if (x<*xBegin2_)
258		return interpolation1_(x, true);
259		return interpolation2_(x, true);
260		}
261		Real primitive(Real x) const {
262		if (x<*xBegin2_)
263		return interpolation1_.primitive(x, true);
264		return interpolation2_.primitive(x, true) -
265		interpolation2_.primitive(*xBegin2_, true) +
266		interpolation1_.primitive(*xBegin2_, true);
267		}
268		Real derivative(Real x) const {
269		if (x<*xBegin2_)
270		return interpolation1_.derivative(x, true);
271		return interpolation2_.derivative(x, true);
272		}
273		Real secondDerivative(Real x) const {
274		if (x<*xBegin2_)
275		return interpolation1_.secondDerivative(x, true);
276		return interpolation2_.secondDerivative(x, true);
277		}
278		private:
279		I1 xBegin2_;
280		Interpolation interpolation1_, interpolation2_;
281		};
282
283		}
284
285		}
286
287		#endif