qrdecomposition.hpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2008 Klaus Spanderen
 
 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 qrdecomposition.hpp
    \brief QR decomposition
*/
 
#ifndef quantlib_qr_decomposition_hpp
#define quantlib_qr_decomposition_hpp
 
#include <ql/math/matrix.hpp>
 
namespace QuantLib {
 
    //! QR decompoisition
    /*! This implementation is based on MINPACK
        (<http://www.netlib.org/minpack>,
        <http://www.netlib.org/cephes/linalg.tgz>)
 
        This subroutine uses householder transformations with column
        pivoting (optional) to compute a qr factorization of the
        m by n matrix A. That is, qrfac determines an orthogonal
        matrix q, a permutation matrix p, and an upper trapezoidal
        matrix r with diagonal elements of nonincreasing magnitude,
        such that A*p = q*r.
 
        Return value ipvt is an integer array of length n, which
        defines the permutation matrix p such that A*p = q*r.
        Column j of p is column ipvt(j) of the identity matrix.
 
        See lmdiff.cpp for further details.
    */
    std::vector<Size> qrDecomposition(const Matrix& A,
                                      Matrix& q,
                                      Matrix& r,
                                      bool pivot = true);
 
    //! QR Solve
    /*! This implementation is based on MINPACK
        (<http://www.netlib.org/minpack>,
        <http://www.netlib.org/cephes/linalg.tgz>)
 
        Given an m by n matrix A, an n by n diagonal matrix d,
        and an m-vector b, the problem is to determine an x which
        solves the system
 
        A*x = b ,     d*x = 0 ,
 
        in the least squares sense.
 
        d is an input array of length n which must contain the
        diagonal elements of the matrix d.
 
        See lmdiff.cpp for further details.
    */
    Array qrSolve(const Matrix& a,
                  const Array& b,
                  bool pivot = true,
                  const Array& d = Array());
}
 
#endif