1/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
2
3/*
4 Copyright (C) 2003, 2004 Ferdinando Ametrano
5
6 This file is part of QuantLib, a free-software/open-source library
7 for financial quantitative analysts and developers - http://quantlib.org/
8
9 QuantLib is free software: you can redistribute it and/or modify it
10 under the terms of the QuantLib license. You should have received a
11 copy of the license along with this program; if not, please email
12 <quantlib-dev@lists.sf.net>. The license is also available online at
13 <http://quantlib.org/license.shtml>.
14
15 This program is distributed in the hope that it will be useful, but WITHOUT
16 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
17 FOR A PARTICULAR PURPOSE. See the license for more details.
18*/
19
20/*! \file pseudosqrt.hpp
21 \brief pseudo square root of a real symmetric matrix
22*/
23
24#ifndef quantlib_pseudo_sqrt_hpp
25#define quantlib_pseudo_sqrt_hpp
26
27#include <ql/math/matrix.hpp>
28
29namespace QuantLib {
30
31 //! algorithm used for matricial pseudo square root
32 struct SalvagingAlgorithm {
33 enum Type { None, Spectral, Hypersphere, LowerDiagonal, Higham };
34 };
35
36 //! Returns the pseudo square root of a real symmetric matrix
37 /*! Given a matrix \f$ M \f$, the result \f$ S \f$ is defined
38 as the matrix such that \f$ S S^T = M. \f$
39 If the matrix is not positive semi definite, it can
40 return an approximation of the pseudo square root
41 using a (user selected) salvaging algorithm.
42
43 For more information see: R. Rebonato and P. Jäckel, The most
44 general methodology to create a valid correlation matrix for
45 risk management and option pricing purposes, The Journal of
46 Risk, 2(2), Winter 1999/2000.
47 http://www.rebonato.com/correlationmatrix.pdf
48
49 Revised and extended in "Monte Carlo Methods in Finance",
50 by Peter Jäckel, Chapter 6.
51
52 \pre the given matrix must be symmetric.
53
54 \relates Matrix
55
56 \warning Higham algorithm only works for correlation matrices.
57
58 \test
59 - the correctness of the results is tested by reproducing
60 known good data.
61 - the correctness of the results is tested by checking
62 returned values against numerical calculations.
63 */
64 Matrix pseudoSqrt(const Matrix&,
65 SalvagingAlgorithm::Type = SalvagingAlgorithm::None);
66
67 //! Returns the rank-reduced pseudo square root of a real symmetric matrix
68 /*! The result matrix has rank<=maxRank. If maxRank>=size, then the
69 specified percentage of eigenvalues out of the eigenvalues' sum is
70 retained.
71
72 If the input matrix is not positive semi definite, it can return an
73 approximation of the pseudo square root using a (user selected)
74 salvaging algorithm.
75
76 \pre the given matrix must be symmetric.
77
78 \relates Matrix
79 */
80 Matrix rankReducedSqrt(const Matrix&,
81 Size maxRank,
82 Real componentRetainedPercentage,
83 SalvagingAlgorithm::Type);
84}
85
86
87#endif
88

source code of quantlib/ql/math/matrixutilities/pseudosqrt.hpp