/* -*- 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;

    }

}