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| -rw-r--r-- | include/2geom/symbolic/matrix.h | 265 |
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diff --git a/include/2geom/symbolic/matrix.h b/include/2geom/symbolic/matrix.h new file mode 100644 index 0000000..d9dc690 --- /dev/null +++ b/include/2geom/symbolic/matrix.h @@ -0,0 +1,265 @@ +/* + * Matrix<CoeffT> class template + * + * Authors: + * Marco Cecchetti <mrcekets at gmail.com> + * + * Copyright 2008 authors + * + * This library is free software; you can redistribute it and/or + * modify it either under the terms of the GNU Lesser General Public + * License version 2.1 as published by the Free Software Foundation + * (the "LGPL") or, at your option, under the terms of the Mozilla + * Public License Version 1.1 (the "MPL"). If you do not alter this + * notice, a recipient may use your version of this file under either + * the MPL or the LGPL. + * + * You should have received a copy of the LGPL along with this library + * in the file COPYING-LGPL-2.1; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + * You should have received a copy of the MPL along with this library + * in the file COPYING-MPL-1.1 + * + * The contents of this file are subject to the Mozilla Public License + * Version 1.1 (the "License"); you may not use this file except in + * compliance with the License. You may obtain a copy of the License at + * http://www.mozilla.org/MPL/ + * + * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY + * OF ANY KIND, either express or implied. See the LGPL or the MPL for + * the specific language governing rights and limitations. + * + */ + + +#ifndef _GEOM_SL_MATRIX_H_ +#define _GEOM_SL_MATRIX_H_ + + +#include <array> +#include <vector> +#include <map> + +#include <2geom/point.h> +#include <2geom/numeric/matrix.h> +#include <2geom/symbolic/multipoly.h> + + + + +namespace Geom { namespace SL { + +/* + * generic Matrix class template + * needed for building up a matrix with polynomial entries + */ +template< typename Coeff> +class Matrix +{ + public: + typedef Coeff coeff_type; + typedef std::vector<coeff_type> container_type; + + Matrix() + {} + + Matrix(size_t m, size_t n) + : m_data(m*n), m_rows(m), m_columns(n) + { + } + + void resize(size_t m, size_t n) + { + m_data.resize(m,n); + m_rows = m; + m_columns = n; + } + + size_t rows() const + { + return m_rows; + } + + size_t columns() const + { + return m_columns; + } + + coeff_type const& operator() (size_t i, size_t j) const + { + return m_data[i * columns() + j]; + } + + coeff_type & operator() (size_t i, size_t j) + { + return m_data[i * columns() + j]; + } + + + private: + container_type m_data; + size_t m_rows; + size_t m_columns; +}; + + +template< typename Coeff, typename charT > +inline +std::basic_ostream<charT> & +operator<< ( std::basic_ostream<charT> & os, + const Matrix<Coeff> & _matrix ) +{ + if (_matrix.rows() == 0 || _matrix.columns() == 0) return os; + + os << "{{" << _matrix(0,0); + for (size_t j = 1; j < _matrix.columns(); ++j) + { + os << ", " << _matrix(0,j); + } + os << "}"; + + for (size_t i = 1; i < _matrix.rows(); ++i) + { + os << ", {" << _matrix(i,0); + for (size_t j = 1; j < _matrix.columns(); ++j) + { + os << ", " << _matrix(i,j); + } + os << "}"; + } + os << "}"; + return os; +} + +template <size_t N, typename CoeffT, typename T> +void polynomial_matrix_evaluate (Matrix<T> & A, + Matrix< MultiPoly<N, CoeffT> > const& M, + std::array<T, N> const& X) +{ + A.resize(M.rows(), M.columns()); + for (size_t i = 0; i < M.rows(); ++i) + { + for (size_t j = 0; j < M.columns(); ++j) + { + A(i,j) = M(i,j)(X); + } + } +} + + +inline +void polynomial_matrix_evaluate (NL::Matrix & A, + Matrix< MultiPoly<2, double> > const& M, + Point const& P) +{ + for (size_t i = 0; i < M.rows(); ++i) + { + for (size_t j = 0; j < M.columns(); ++j) + { + A(i,j) = M(i,j)(P[X], P[Y]); + } + } +} + + +/* +template< typename Coeff> +class SymmetricSquareMatrix +{ + public: + typedef Coeff coeff_type; + typedef std::vector<coeff_type> container_type; + + SymmetricSquareMatrix(size_t n) + : m_data((n*n)/2 + n), m_size(n) + { + + } + + size_t rows() const + { + return m_size; + } + + size_t columns() const + { + return m_size; + } + + coeff_type const& operator() (size_t i, size_t j) const + { + return m_data[i * columns() + j]; + } + + coeff_type & operator() (size_t i, size_t j) + { + return m_data[i * columns() + j]; + } + + coeff_type det() + { + + } + + private: + container_type m_data; + size_t m_size; +}; +*/ + +/* + * This is an adaptation of the LU algorithm used in the numerical case. + * This algorithm is based on the article due to Bareiss: + * "Sylvester's identity and multistep integer-preserving Gaussian elimination" + */ + +/* +template< typename CoeffT > +CoeffT det(Matrix<CoeffT> const& M) +{ + assert(M.rows() == M.columns()); + + Matrix<CoeffT> A(M); + CoeffT n; + CoeffT d = one<CoeffT>()(); + for (size_t k = 1; k < A.rows(); ++k) + { + for (size_t i = k; i < A.rows(); ++i) + { + for (size_t j = k; j < A.columns(); ++j) + { + n = A(i,j) * A(k-1,k-1) - A(k-1,j) * A(i,k-1); +// std::cout << "k, i, j: " +// << k << ", " << i << ", " << j << std::endl; +// std::cout << "n = " << n << std::endl; +// std::cout << "d = " << d << std::endl; + A(i,j) = factor(n, d); + } + } + d = A(k-1,k-1); + } + return A(A.rows()-1, A.columns()-1); +} +*/ + + + +} /*end namespace Geom*/ } /*end namespace SL*/ + + +#include <2geom/symbolic/determinant-minor.h> + + +#endif // _GEOM_SL_MATRIX_H_ + + +/* + Local Variables: + mode:c++ + c-file-style:"stroustrup" + c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +)) + indent-tabs-mode:nil + fill-column:99 + End: +*/ +// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 : |