choleskydecomposition.cpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2003, 2004 Ferdinando Ametrano
 Copyright (C) 2016 Peter Caspers
 Copyright (C) 2024 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.
*/
 
#include <ql/math/matrixutilities/choleskydecomposition.hpp>
#include <ql/math/comparison.hpp>
 
namespace QuantLib {
 
    Matrix CholeskyDecomposition(const Matrix& S, bool flexible) {
        Size i, j, size = S.rows();
 
        QL_REQUIRE(size == S.columns(),
                   "input matrix is not a square matrix");
        #if defined(QL_EXTRA_SAFETY_CHECKS)
        for (i=0; i<S.rows(); i++)
            for (j=0; j<i; j++)
                QL_REQUIRE(S[i][j] == S[j][i],
                           "input matrix is not symmetric");
        #endif
 
        Matrix result(size, size, 0.0);
        Real sum;
        for (i=0; i<size; i++) {
            for (j=i; j<size; j++) {
                sum = S[i][j];
                for (Integer k=0; k<=Integer(i)-1; k++) {
                    sum -= result[i][k]*result[j][k];
                }
                if (i == j) {
                    QL_REQUIRE(flexible || sum > 0.0,
                               "input matrix is not positive definite");
                    // To handle positive semi-definite matrices take the
                    // square root of sum if positive, else zero.
                    result[i][i] = std::sqrt(std::max<Real>(sum, 0.0));
                } else {
                    // With positive semi-definite matrices is possible
                    // to have result[i][i]==0.0
                    // In this case sum happens to be zero as well
                    result[j][i] = close_enough(result[i][i], 0.0)
                                       ? 0.0
                                       : Real(sum / result[i][i]);
                }
            }
        }
        return result;
    }
 
    Array CholeskySolveFor(const Matrix& L, const Array& b) {
        const Size n = b.size();
 
        QL_REQUIRE(L.columns() == n && L.rows() == n,
            "Size of input matrix and vector does not match.");
 
        Array x(n);
        for (Size i=0; i < n; ++i) {
            x[i] = -std::inner_product(L.row_begin(i), L.row_begin(i)+i, x.begin(), Real(-b[i]));
            x[i] /= L[i][i];
        }
 
        for (Integer i=n-1; i >=0; --i) {
            x[i] = -std::inner_product(
                        L.column_begin(i)+i+1, L.column_end(i), x.begin()+i+1, Real(-x[i]));
            x[i] /= L[i][i];
        }
 
        return x;
    }
}