loginterpolation.hpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2002, 2003, 2008, 2009 Ferdinando Ametrano
 Copyright (C) 2004, 2007, 2008 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
 <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.
*/
 
/*! \file loginterpolation.hpp
    \brief log-linear and log-cubic interpolation between discrete points
*/
 
#ifndef quantlib_log_interpolation_hpp
#define quantlib_log_interpolation_hpp
 
#include <ql/math/interpolations/linearinterpolation.hpp>
#include <ql/math/interpolations/cubicinterpolation.hpp>
#include <ql/math/interpolations/mixedinterpolation.hpp>
#include <ql/utilities/dataformatters.hpp>
 
namespace QuantLib {
 
    namespace detail {
        template<class I1, class I2, class I> class LogInterpolationImpl;
        template<class I1, class I2, class IN1, class IN2> class LogMixedInterpolationImpl;
    }
 
    //! %log-linear interpolation between discrete points
    /*! \ingroup interpolations
        \warning See the Interpolation class for information about the
                 required lifetime of the underlying data.
    */
    class LogLinearInterpolation : public Interpolation {
      public:
        /*! \pre the \f$ x \f$ values must be sorted. */
        template <class I1, class I2>
        LogLinearInterpolation(const I1& xBegin, const I1& xEnd,
                               const I2& yBegin) {
            impl_ = ext::shared_ptr<Interpolation::Impl>(new
                detail::LogInterpolationImpl<I1, I2, Linear>(xBegin, xEnd,
                                                             yBegin));
            impl_->update();
        }
    };
 
    //! log-linear interpolation factory and traits
    /*! \ingroup interpolations */
    class LogLinear {
      public:
        template <class I1, class I2>
        Interpolation interpolate(const I1& xBegin, const I1& xEnd,
                                  const I2& yBegin) const {
            return LogLinearInterpolation(xBegin, xEnd, yBegin);
        }
        static const bool global = false;
        static const Size requiredPoints = 2;
    };
 
    //! %log-cubic interpolation between discrete points
    /*! \ingroup interpolations */
    class LogCubicInterpolation : public Interpolation {
      public:
        /*! \pre the \f$ x \f$ values must be sorted. */
        template <class I1, class I2>
        LogCubicInterpolation(const I1& xBegin, const I1& xEnd,
                              const I2& yBegin,
                              CubicInterpolation::DerivativeApprox da,
                              bool monotonic,
                              CubicInterpolation::BoundaryCondition leftC,
                              Real leftConditionValue,
                              CubicInterpolation::BoundaryCondition rightC,
                              Real rightConditionValue) {
            impl_ = ext::shared_ptr<Interpolation::Impl>(new
                detail::LogInterpolationImpl<I1, I2, Cubic>(
                    xBegin, xEnd, yBegin,
                    Cubic(da, monotonic,
                          leftC, leftConditionValue,
                          rightC, rightConditionValue)));
            impl_->update();
        }
    };
 
    //! log-cubic interpolation factory and traits
    /*! \ingroup interpolations */
    class LogCubic {
      public:
        LogCubic(CubicInterpolation::DerivativeApprox da,
                  bool monotonic = true,
                  CubicInterpolation::BoundaryCondition leftCondition
                      = CubicInterpolation::SecondDerivative,
                  Real leftConditionValue = 0.0,
                  CubicInterpolation::BoundaryCondition rightCondition
                      = CubicInterpolation::SecondDerivative,
                  Real rightConditionValue = 0.0)
        : 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 LogCubicInterpolation(xBegin, xEnd, yBegin,
                                         da_, monotonic_,
                                         leftType_, leftValue_,
                                         rightType_, rightValue_);
        }
        static const bool global = true;
        static const Size requiredPoints = 2;
      private:
        CubicInterpolation::DerivativeApprox da_;
        bool monotonic_;
        CubicInterpolation::BoundaryCondition leftType_, rightType_;
        Real leftValue_, rightValue_;
    };
 
    // convenience classes
 
    class DefaultLogCubic : public LogCubic {
      public:
        DefaultLogCubic()
        : LogCubic(CubicInterpolation::Kruger) {}
    };
 
    class MonotonicLogCubic : public LogCubic {
      public:
        MonotonicLogCubic()
        : LogCubic(CubicInterpolation::Spline, true,
                   CubicInterpolation::SecondDerivative, 0.0,
                   CubicInterpolation::SecondDerivative, 0.0) {}
    };
 
    class KrugerLog : public LogCubic {
      public:
        KrugerLog()
        : LogCubic(CubicInterpolation::Kruger, false,
                   CubicInterpolation::SecondDerivative, 0.0,
                   CubicInterpolation::SecondDerivative, 0.0) {}
    };
 
 
    class LogCubicNaturalSpline : public LogCubicInterpolation {
      public:
        /*! \pre the \f$ x \f$ values must be sorted. */
        template <class I1, class I2>
        LogCubicNaturalSpline(const I1& xBegin,
                              const I1& xEnd,
                              const I2& yBegin)
        : LogCubicInterpolation(xBegin, xEnd, yBegin,
                                CubicInterpolation::Spline, false,
                                CubicInterpolation::SecondDerivative, 0.0,
                                CubicInterpolation::SecondDerivative, 0.0) {}
    };
 
    class MonotonicLogCubicNaturalSpline : public LogCubicInterpolation {
      public:
        /*! \pre the \f$ x \f$ values must be sorted. */
        template <class I1, class I2>
        MonotonicLogCubicNaturalSpline(const I1& xBegin,
                                       const I1& xEnd,
                                       const I2& yBegin)
        : LogCubicInterpolation(xBegin, xEnd, yBegin,
                                CubicInterpolation::Spline, true,
                                CubicInterpolation::SecondDerivative, 0.0,
                                CubicInterpolation::SecondDerivative, 0.0) {}
    };
 
    class KrugerLogCubic : public LogCubicInterpolation {
      public:
        /*! \pre the \f$ x \f$ values must be sorted. */
        template <class I1, class I2>
        KrugerLogCubic(const I1& xBegin,
                       const I1& xEnd,
                       const I2& yBegin)
        : LogCubicInterpolation(xBegin, xEnd, yBegin,
                                CubicInterpolation::Kruger, false,
                                CubicInterpolation::SecondDerivative, 0.0,
                                CubicInterpolation::SecondDerivative, 0.0) {}
    };
 
    class HarmonicLogCubic : public LogCubicInterpolation {
      public:
        /*! \pre the \f$ x \f$ values must be sorted. */
        template <class I1, class I2>
        HarmonicLogCubic(const I1& xBegin,
                         const I1& xEnd,
                         const I2& yBegin)
        : LogCubicInterpolation(xBegin, xEnd, yBegin,
                                CubicInterpolation::Harmonic, false,
                                CubicInterpolation::SecondDerivative, 0.0,
                                CubicInterpolation::SecondDerivative, 0.0) {}
    };
 
    class FritschButlandLogCubic : public LogCubicInterpolation {
      public:
        /*! \pre the \f$ x \f$ values must be sorted. */
        template <class I1, class I2>
        FritschButlandLogCubic(const I1& xBegin,
                               const I1& xEnd,
                               const I2& yBegin)
        : LogCubicInterpolation(xBegin, xEnd, yBegin,
                                CubicInterpolation::FritschButland, false,
                                CubicInterpolation::SecondDerivative, 0.0,
                                CubicInterpolation::SecondDerivative, 0.0) {}
    };
 
    class LogParabolic : public LogCubicInterpolation {
      public:
        /*! \pre the \f$ x \f$ values must be sorted. */
        template <class I1, class I2>
        LogParabolic(const I1& xBegin,
                     const I1& xEnd,
                     const I2& yBegin)
        : LogCubicInterpolation(xBegin, xEnd, yBegin,
                                CubicInterpolation::Parabolic, false,
                                CubicInterpolation::SecondDerivative, 0.0,
                                CubicInterpolation::SecondDerivative, 0.0) {}
    };
 
    class MonotonicLogParabolic : public LogCubicInterpolation {
      public:
        /*! \pre the \f$ x \f$ values must be sorted. */
        template <class I1, class I2>
        MonotonicLogParabolic(const I1& xBegin,
                              const I1& xEnd,
                              const I2& yBegin)
        : LogCubicInterpolation(xBegin, xEnd, yBegin,
                                CubicInterpolation::Parabolic, true,
                                CubicInterpolation::SecondDerivative, 0.0,
                                CubicInterpolation::SecondDerivative, 0.0) {}
    };
 
    //! %log-mixedlinearcubic interpolation between discrete points
    /*! \ingroup interpolations */
    class LogMixedLinearCubicInterpolation : public Interpolation {
      public:
        /*! \pre the \f$ x \f$ values must be sorted. */
        template <class I1, class I2>
        LogMixedLinearCubicInterpolation(const I1& xBegin, const I1& xEnd,
                                         const I2& yBegin, const Size n,
                                         MixedInterpolation::Behavior behavior,
                                         CubicInterpolation::DerivativeApprox da,
                                         bool monotonic,
                                         CubicInterpolation::BoundaryCondition leftC,
                                         Real leftConditionValue,
                                         CubicInterpolation::BoundaryCondition rightC,
                                         Real rightConditionValue) {
            impl_ = ext::shared_ptr<Interpolation::Impl>(new
                detail::LogInterpolationImpl<I1, I2, MixedLinearCubic>(
                    xBegin, xEnd, yBegin,
                    MixedLinearCubic(n, behavior, da, monotonic,
                                     leftC, leftConditionValue,
                                     rightC, rightConditionValue)));
            impl_->update();
        }
    };
 
    //! log-cubic interpolation factory and traits
    /*! \ingroup interpolations */
    class LogMixedLinearCubic {
      public:
        LogMixedLinearCubic(const 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 LogMixedLinearCubicInterpolation(xBegin, xEnd, yBegin,
                                                    n_, behavior_,
                                                    da_, monotonic_,
                                                    leftType_, leftValue_,
                                                    rightType_, rightValue_);
        }
        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 DefaultLogMixedLinearCubic : public LogMixedLinearCubic {
      public:
        explicit DefaultLogMixedLinearCubic(const Size n,
                                            MixedInterpolation::Behavior behavior
                                            = MixedInterpolation::ShareRanges)
        : LogMixedLinearCubic(n, behavior,
                              CubicInterpolation::Kruger) {}
    };
 
    class MonotonicLogMixedLinearCubic : public LogMixedLinearCubic {
      public:
        explicit MonotonicLogMixedLinearCubic(const Size n,
                                              MixedInterpolation::Behavior behavior
                                              = MixedInterpolation::ShareRanges)
        : LogMixedLinearCubic(n, behavior,
                              CubicInterpolation::Spline, true,
                              CubicInterpolation::SecondDerivative, 0.0,
                              CubicInterpolation::SecondDerivative, 0.0) {}
    };
 
    class KrugerLogMixedLinearCubic: public LogMixedLinearCubic {
      public:
        explicit KrugerLogMixedLinearCubic(const Size n,
                                           MixedInterpolation::Behavior behavior
                                           = MixedInterpolation::ShareRanges)
        : LogMixedLinearCubic(n, behavior,
                              CubicInterpolation::Kruger, false,
                              CubicInterpolation::SecondDerivative, 0.0,
                              CubicInterpolation::SecondDerivative, 0.0) {}
    };
 
 
    class LogMixedLinearCubicNaturalSpline : public LogMixedLinearCubicInterpolation {
      public:
        /*! \pre the \f$ x \f$ values must be sorted. */
        template <class I1, class I2>
        LogMixedLinearCubicNaturalSpline(const I1& xBegin, const I1& xEnd,
                                         const I2& yBegin, const Size n,
                                         MixedInterpolation::Behavior behavior
                                             = MixedInterpolation::ShareRanges)
        : LogMixedLinearCubicInterpolation(xBegin, xEnd, yBegin, n, behavior,
                                           CubicInterpolation::Spline, false,
                                           CubicInterpolation::SecondDerivative, 0.0,
                                           CubicInterpolation::SecondDerivative, 0.0) {}
    };
 
 
    namespace detail {
 
        template <class I1, class I2, class Interpolator>
        class LogInterpolationImpl
            : public Interpolation::templateImpl<I1,I2> {
          public:
            LogInterpolationImpl(const I1& xBegin, const I1& xEnd,
                                 const I2& yBegin,
                                 const Interpolator& factory = Interpolator())
            : Interpolation::templateImpl<I1,I2>(xBegin, xEnd, yBegin,
                                                 Interpolator::requiredPoints),
              logY_(xEnd-xBegin) {
                interpolation_ = factory.interpolate(this->xBegin_,
                                                     this->xEnd_,
                                                     logY_.begin());
            }
            void update() override {
                for (Size i=0; i<logY_.size(); ++i) {
                    QL_REQUIRE(this->yBegin_[i]>0.0,
                               "invalid value (" << this->yBegin_[i]
                               << ") at index " << i);
                    logY_[i] = std::log(this->yBegin_[i]);
                }
                interpolation_.update();
            }
            Real value(Real x) const override { return std::exp(interpolation_(x, true)); }
            Real primitive(Real) const override {
                QL_FAIL("LogInterpolation primitive not implemented");
            }
            Real derivative(Real x) const override {
                return value(x)*interpolation_.derivative(x, true);
            }
            Real secondDerivative(Real x) const override {
                return derivative(x)*interpolation_.derivative(x, true) +
                            value(x)*interpolation_.secondDerivative(x, true);
            }
 
          private:
            std::vector<Real> logY_;
            Interpolation interpolation_;
        };
 
    }
 
}
 
#endif