text: /* -*- 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 */
      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_ = std::make_shared<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_ = std::make_shared<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 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_ = std::make_shared<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 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() {
                  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 {
                  return std::exp(interpolation_(x, true));
              }
              Real primitive(Real) const {
                  QL_FAIL("LogInterpolation primitive not implemented");
              }
              Real derivative(Real x) const {
                  return value(x)*interpolation_.derivative(x, true);
              }
              Real secondDerivative(Real x) const {
                  return derivative(x)*interpolation_.derivative(x, true) +
                              value(x)*interpolation_.secondDerivative(x, true);
              }
            private:
              std::vector<Real> logY_;
              Interpolation interpolation_;
          };
  
      }
  
  }
  
  #endif
  