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126 lines
4.7 KiB
126 lines
4.7 KiB
/* -*- c++ -*- (enables emacs c++ mode) */
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/*===========================================================================
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Copyright (C) 2003-2012 Yves Renard
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This file is a part of GETFEM++
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Getfem++ is free software; you can redistribute it and/or modify it
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under the terms of the GNU Lesser General Public License as published
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by the Free Software Foundation; either version 3 of the License, or
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(at your option) any later version along with the GCC Runtime Library
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Exception either version 3.1 or (at your option) any later version.
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This program is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License and GCC Runtime Library Exception for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with this program; if not, write to the Free Software Foundation,
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Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.
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As a special exception, you may use this file as it is a part of a free
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software library without restriction. Specifically, if other files
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instantiate templates or use macros or inline functions from this file,
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or you compile this file and link it with other files to produce an
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executable, this file does not by itself cause the resulting executable
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to be covered by the GNU Lesser General Public License. This exception
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does not however invalidate any other reasons why the executable file
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might be covered by the GNU Lesser General Public License.
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===========================================================================*/
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/**@file gmm_opt.h
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@author Yves Renard <Yves.Renard@insa-lyon.fr>
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@date July 9, 2003.
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@brief Optimization for some small cases (inversion of 2x2 matrices etc.)
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*/
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#ifndef GMM_OPT_H__
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#define GMM_OPT_H__
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namespace gmm {
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/* ********************************************************************* */
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/* Optimized determinant and inverse for small matrices (2x2 and 3x3) */
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/* with dense_matrix<T>. */
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/* ********************************************************************* */
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template <typename T> T lu_det(const dense_matrix<T> &A) {
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size_type n(mat_nrows(A));
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if (n) {
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const T *p = &(A(0,0));
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switch (n) {
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case 1 : return (*p);
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case 2 : return (*p) * (*(p+3)) - (*(p+1)) * (*(p+2));
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// Not stable for nearly singular matrices
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// case 3 : return (*p) * ((*(p+4)) * (*(p+8)) - (*(p+5)) * (*(p+7)))
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// - (*(p+1)) * ((*(p+3)) * (*(p+8)) - (*(p+5)) * (*(p+6)))
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// + (*(p+2)) * ((*(p+3)) * (*(p+7)) - (*(p+4)) * (*(p+6)));
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default :
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{
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dense_matrix<T> B(mat_nrows(A), mat_ncols(A));
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std::vector<size_type> ipvt(mat_nrows(A));
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gmm::copy(A, B);
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lu_factor(B, ipvt);
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return lu_det(B, ipvt);
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}
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}
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}
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return T(1);
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}
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template <typename T> T lu_inverse(const dense_matrix<T> &A_) {
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dense_matrix<T>& A = const_cast<dense_matrix<T> &>(A_);
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size_type N = mat_nrows(A);
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T det(1);
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if (N) {
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T *p = &(A(0,0));
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if (N <= 2) {
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switch (N) {
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case 1 : {
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det = *p;
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GMM_ASSERT1(det!=T(0), "non invertible matrix");
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*p = T(1) / det;
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} break;
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case 2 : {
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det = (*p) * (*(p+3)) - (*(p+1)) * (*(p+2));
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GMM_ASSERT1(det!=T(0), "non invertible matrix");
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std::swap(*p, *(p+3));
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*p++ /= det; *p++ /= -det; *p++ /= -det; *p++ /= det;
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} break;
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// case 3 : { // not stable for nearly singular matrices
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// T a, b, c, d, e, f, g, h, i;
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// a = (*(p+4)) * (*(p+8)) - (*(p+5)) * (*(p+7));
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// b = - (*(p+1)) * (*(p+8)) + (*(p+2)) * (*(p+7));
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// c = (*(p+1)) * (*(p+5)) - (*(p+2)) * (*(p+4));
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// d = - (*(p+3)) * (*(p+8)) + (*(p+5)) * (*(p+6));
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// e = (*(p+0)) * (*(p+8)) - (*(p+2)) * (*(p+6));
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// f = - (*(p+0)) * (*(p+5)) + (*(p+2)) * (*(p+3));
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// g = (*(p+3)) * (*(p+7)) - (*(p+4)) * (*(p+6));
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// h = - (*(p+0)) * (*(p+7)) + (*(p+1)) * (*(p+6));
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// i = (*(p+0)) * (*(p+4)) - (*(p+1)) * (*(p+3));
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// det = (*p) * a + (*(p+1)) * d + (*(p+2)) * g;
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// GMM_ASSERT1(det!=T(0), "non invertible matrix");
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// *p++ = a / det; *p++ = b / det; *p++ = c / det;
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// *p++ = d / det; *p++ = e / det; *p++ = f / det;
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// *p++ = g / det; *p++ = h / det; *p++ = i / det;
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// } break;
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}
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}
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else {
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dense_matrix<T> B(mat_nrows(A), mat_ncols(A));
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std::vector<int> ipvt(mat_nrows(A));
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gmm::copy(A, B);
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size_type info = lu_factor(B, ipvt);
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GMM_ASSERT1(!info, "non invertible matrix");
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lu_inverse(B, ipvt, A);
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return lu_det(B, ipvt);
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}
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}
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return det;
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}
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}
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#endif // GMM_OPT_H__
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