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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
<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.
*/
#ifndef quantlib_tap_correlations_hpp
#define quantlib_tap_correlations_hpp
#include <ql/math/matrix.hpp>
#include <ql/math/optimization/costfunction.hpp>
#include <ql/types.hpp>
#include <functional>
#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,
std::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_;
std::function<Matrix(const Array&, Size, Size)> f_;
Size matrixSize_;
Size rank_;
};
}
#endif
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