blockmatrixinverse.hpp

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/*
 Copyright (C) 2016 Quaternion Risk Management Ltd
 All rights reserved.
 
 This file is part of ORE, a free-software/open-source library
 for transparent pricing and risk analysis - http://opensourcerisk.org
 
 ORE is free software: you can redistribute it and/or modify it
 under the terms of the Modified BSD License.  You should have received a
 copy of the license along with this program.
 The license is also available online at <http://opensourcerisk.org>
 
 This program is distributed on the basis that it will form a useful
 contribution to risk analytics and model standardisation, but WITHOUT
 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 FITNESS FOR A PARTICULAR PURPOSE. See the license for more details.
*/
 
/*! \file qle/math/blockmatrixinverse.hpp
    \brief inverse of a matrix using a block formula
    \ingroup math
*/
 
#ifndef quantext_blockmatrixinverse_hpp
#define quantext_blockmatrixinverse_hpp
 
#include <ql/math/matrix.hpp>
#include <ql/math/matrixutilities/sparsematrix.hpp>
 
namespace QuantExt {
 
/* inverse of a sparse matrix per LU decomposition */
QuantLib::SparseMatrix inverse(QuantLib::SparseMatrix m);
 
/* Reference: https://en.wikipedia.org/wiki/Invertible_matrix#Blockwise_inversion */
QuantLib::Matrix blockMatrixInverse(const QuantLib::Matrix& A, const std::vector<QuantLib::Size>& blockIndices);
QuantLib::SparseMatrix blockMatrixInverse(const QuantLib::SparseMatrix& A, const std::vector<QuantLib::Size>& blockIndices);
 
/*! modified max norm of a sparse matrix, i.e. std::sqrt(row * columns) * max_i,j abs(a_i,j) */
QuantLib::Real modifiedMaxNorm(const QuantLib::SparseMatrix& A);
 
} // namespace QuantExt
 
#endif