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79 lines
1.9 KiB
79 lines
1.9 KiB
// (C) Copyright John Maddock 2006. |
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// Use, modification and distribution are subject to the |
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// Boost Software License, Version 1.0. (See accompanying file |
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) |
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#ifndef BOOST_MATH_TOOLS_SOLVE_HPP |
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#define BOOST_MATH_TOOLS_SOLVE_HPP |
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#ifdef _MSC_VER |
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#pragma once |
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#endif |
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#include <boost/config.hpp> |
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#include <boost/assert.hpp> |
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#ifdef BOOST_MSVC |
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#pragma warning(push) |
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#pragma warning(disable:4996 4267 4244) |
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#endif |
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#include <boost/numeric/ublas/lu.hpp> |
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#include <boost/numeric/ublas/matrix.hpp> |
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#include <boost/numeric/ublas/vector.hpp> |
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#ifdef BOOST_MSVC |
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#pragma warning(pop) |
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#endif |
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namespace boost{ namespace math{ namespace tools{ |
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// |
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// Find x such that Ax = b |
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// |
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// Caution: this uses undocumented, and untested ublas code, |
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// however short of writing our own LU-decompostion code |
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// it's the only game in town. |
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// |
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template <class T> |
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boost::numeric::ublas::vector<T> solve( |
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const boost::numeric::ublas::matrix<T>& A_, |
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const boost::numeric::ublas::vector<T>& b_) |
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{ |
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//BOOST_ASSERT(A_.size() == b_.size()); |
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boost::numeric::ublas::matrix<T> A(A_); |
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boost::numeric::ublas::vector<T> b(b_); |
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boost::numeric::ublas::permutation_matrix<> piv(b.size()); |
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lu_factorize(A, piv); |
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lu_substitute(A, piv, b); |
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// |
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// iterate to reduce error: |
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// |
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boost::numeric::ublas::vector<T> delta(b.size()); |
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for(unsigned i = 0; i < 1; ++i) |
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{ |
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noalias(delta) = prod(A_, b); |
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delta -= b_; |
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lu_substitute(A, piv, delta); |
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b -= delta; |
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T max_error = 0; |
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for(unsigned i = 0; i < delta.size(); ++i) |
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{ |
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T err = fabs(delta[i] / b[i]); |
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if(err > max_error) |
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max_error = err; |
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} |
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//std::cout << "Max change in LU error correction: " << max_error << std::endl; |
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} |
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return b; |
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} |
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}}} // namespaces |
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#endif // BOOST_MATH_TOOLS_SOLVE_HPP |
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