moorepenroseinverse.hpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2016 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 moorepenroseinverse.hpp
    \brief Moore Penrose inverse of a real matrix
*/
 
#ifndef quantlib_moore_penrose_inverse
#define quantlib_moore_penrose_inverse
 
#include <ql/math/matrixutilities/svd.hpp>
 
namespace QuantLib {
 
/*! Reference:
    http://de.mathworks.com/help/matlab/ref/pinv.html
    https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_pseudoinverse */
 
inline Matrix moorePenroseInverse(const Matrix &A,
                                  const Real tol = Null<Real>()) {
 
    Size m = A.rows();
    Size n = A.columns();
 
    SVD svd(A);
 
    Real tol0 = tol;
    if (tol0 == Null<Real>()) {
        tol0 = std::max(m, n) * QL_EPSILON * std::abs(svd.singularValues()[0]);
    }
 
    Matrix sp(n, n, 0.0);
    for (Size i = 0; i < n; ++i) {
        if (std::abs(svd.singularValues()[i]) > tol0) {
            sp(i, i) = 1.0 / svd.singularValues()[i];
        }
    }
 
    Matrix res = svd.V() * sp * transpose(svd.U());
    return res;
};
 
} // namespace QuantLib
 
#endif // include guard