tapcorrelations.hpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2007 François du Vignaud
 
 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.
*/
 
 
#ifndef quantlib_tap_correlations_hpp
#define quantlib_tap_correlations_hpp
 
#include <ql/functional.hpp>
#include <ql/math/matrix.hpp>
#include <ql/math/optimization/costfunction.hpp>
#include <ql/types.hpp>
#include <utility>
#include <vector>
 
namespace QuantLib {
 
    //! Returns the Triangular Angles Parametrized correlation matrix
    /*! The matrix \f$ m \f$ is filled with values corresponding to angles
        given in the \f$ angles \f$ vector. See equation (24) in
        "Parameterizing correlations: a geometric interpretation"
        by Francesco Rapisarda, Damiano Brigo, Fabio Mercurio
 
        \test
        - the correctness of the results is tested by reproducing
          known good data.
        - the correctness of the results is tested by checking
          returned values against numerical calculations.
    */
    Matrix triangularAnglesParametrization(const Array& angles,
                                           Size matrixSize,
                                           Size rank);
 
    Matrix lmmTriangularAnglesParametrization(const Array& angles,
                                              Size matrixSize,
                                              Size rank);
 
    // the same function using the angles parameterized by the following
    // transformation \f[ \teta_i = \frac{\Pi}{2} - arctan(x_i)\f]
    Matrix triangularAnglesParametrizationUnconstrained(const Array& x,
                                                        Size matrixSize,
                                                        Size rank);
 
    Matrix lmmTriangularAnglesParametrizationUnconstrained(const Array& x,
                                                           Size matrixSize,
                                                           Size rank);
 
 
    //! Returns the rank reduced Triangular Angles Parametrized correlation matrix
    /*! The matrix \f$ m \f$ is filled with values corresponding to angles
        corresponding  to the 3D spherical spiral parameterized by
        \f$ alpha \f$, \f$ t0 \f$, \f$ epsilon \f$ values. See equation (32) in
        "Parameterizing correlations: a geometric interpretation"
        by Francesco Rapisarda, Damiano Brigo, Fabio Mercurio
 
        \test
        - the correctness of the results is tested by reproducing
          known good data.
        - the correctness of the results is tested by checking
          returned values against numerical calculations.
    */
    Matrix triangularAnglesParametrizationRankThree(Real alpha,
                                                    Real t0,
                                                    Real epsilon,
                                                    Size nbRows);
 
    // the same function with parameters packed in an Array
    Matrix triangularAnglesParametrizationRankThreeVectorial(const Array& parameters,
                                                             Size nbRows);
 
    // Cost function associated with Frobenius norm.
    // <http://en.wikipedia.org/wiki/Matrix_norm>
    class FrobeniusCostFunction : public CostFunction{
      public:
        FrobeniusCostFunction(Matrix target,
                              ext::function<Matrix(const Array&, Size, Size)> f,
                              Size matrixSize,
                              Size rank)
        : target_(std::move(target)), f_(std::move(f)), matrixSize_(matrixSize), rank_(rank) {}
        Real value(const Array& x) const override;
        Array values(const Array& x) const override;
 
      private:
        Matrix target_;
        ext::function<Matrix(const Array&, Size, Size)> f_;
        Size matrixSize_;
        Size rank_;
    };
}
 
#endif