laplaceinterpolation.hpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2015, 2024 Peter Caspers
 
 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 laplaceinterpolation.hpp
    \brief Laplace interpolation of missing values
*/
 
#ifndef quantlib_laplace_interpolation
#define quantlib_laplace_interpolation
 
#include <ql/math/array.hpp>
#include <ql/math/matrix.hpp>
#include <ql/shared_ptr.hpp>
#include <ql/types.hpp>
 
#include <vector>
 
namespace QuantLib {
 
    class FdmLinearOpLayout;
 
    /*! Reconstruction of missing values using Laplace interpolation. We support an arbitrary number
       of dimensions n >= 1 and non-equidistant grids. For n = 1 the method is identical  to linear
       interpolation with flat extrapolation. Reference: Numerical Recipes, 3rd edition, ch. 3.8. */
 
    class LaplaceInterpolation {
      public:
        /*! Missing values y should be encoded as Null<Real>(). */
        LaplaceInterpolation(std::function<Real(const std::vector<Size>&)> y,
                             std::vector<std::vector<Real>> x,
                             Real relTol = 1E-6,
                             Size maxIterMultiplier = 10);
        Real operator()(const std::vector<Size>& coordinates) const;
 
      private:
        std::vector<Size> projectedCoordinates(const std::vector<Size>& coordinates) const;
        std::vector<Size> fullCoordinates(const std::vector<Size>& projectedCoordinates) const;
 
        std::function<Real(const std::vector<Size>&)> y_;
        std::vector<std::vector<Real>> x_;
        Real relTol_;
        Size maxIterMultiplier_;
 
        std::vector<bool> coordinateIncluded_;
        Size numberOfCoordinatesIncluded_;
 
        ext::shared_ptr<FdmLinearOpLayout> layout_;
        Array interpolatedValues_;
    };
 
    /*! Convenience function that Laplace-interpolates null values in a given matrix.
        If the x or y grid or both are not given, an equidistant grid is assumed. */
 
    void laplaceInterpolation(Matrix& A,
                              const std::vector<Real>& x = {},
                              const std::vector<Real>& y = {},
                              Real relTol = 1E-6,
                              Size maxIterMultiplier = 10);
}
 
#endif