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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
<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.
*/
#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;
}
}
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