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/* -*- c++ -*- (enables emacs c++ mode) *//*===========================================================================
Copyright (C) 2003-2017 Yves Renard
This file is a part of GetFEM++
GetFEM++ is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version along with the GCC Runtime Library Exception either version 3.1 or (at your option) any later version. 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 GNU Lesser General Public License and GCC Runtime Library Exception for more details. You should have received a copy of the GNU Lesser General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.
As a special exception, you may use this file as it is a part of a free software library without restriction. Specifically, if other files instantiate templates or use macros or inline functions from this file, or you compile this file and link it with other files to produce an executable, this file does not by itself cause the resulting executable to be covered by the GNU Lesser General Public License. This exception does not however invalidate any other reasons why the executable file might be covered by the GNU Lesser General Public License.
===========================================================================*/
/**@file gmm_opt.h
@author Yves Renard <Yves.Renard@insa-lyon.fr> @date July 9, 2003. @brief Optimization for some small cases (inversion of 2x2 matrices etc.)*/#ifndef GMM_OPT_H__
#define GMM_OPT_H__
namespace gmm {
/* ********************************************************************* */ /* Optimized determinant and inverse for small matrices (2x2 and 3x3) */ /* with dense_matrix<T>. */ /* ********************************************************************* */
template <typename T> T lu_det(const dense_matrix<T> &A) { size_type n(mat_nrows(A)); if (n) { const T *p = &(A(0,0)); switch (n) { case 1 : return (*p); case 2 : return (*p) * (*(p+3)) - (*(p+1)) * (*(p+2));// Not stable for nearly singular matrices
// case 3 : return (*p) * ((*(p+4)) * (*(p+8)) - (*(p+5)) * (*(p+7)))
// - (*(p+1)) * ((*(p+3)) * (*(p+8)) - (*(p+5)) * (*(p+6)))
// + (*(p+2)) * ((*(p+3)) * (*(p+7)) - (*(p+4)) * (*(p+6)));
default : { dense_matrix<T> B(mat_nrows(A), mat_ncols(A)); std::vector<size_type> ipvt(mat_nrows(A)); gmm::copy(A, B); lu_factor(B, ipvt); return lu_det(B, ipvt); } } } return T(1); }
template <typename T> T lu_inverse(const dense_matrix<T> &A_, bool doassert = true) { dense_matrix<T>& A = const_cast<dense_matrix<T> &>(A_); size_type N = mat_nrows(A); T det(1); if (N) { T *p = &(A(0,0)); if (N <= 2) { switch (N) { case 1 : { det = *p; if (doassert) GMM_ASSERT1(det!=T(0), "non invertible matrix"); if (det == T(0)) break; *p = T(1) / det; } break; case 2 : { det = (*p) * (*(p+3)) - (*(p+1)) * (*(p+2)); if (doassert) GMM_ASSERT1(det!=T(0), "non invertible matrix"); if (det == T(0)) break; std::swap(*p, *(p+3)); *p++ /= det; *p++ /= -det; *p++ /= -det; *p++ /= det; } break;// case 3 : { // not stable for nearly singular matrices
// T a, b, c, d, e, f, g, h, i;
// a = (*(p+4)) * (*(p+8)) - (*(p+5)) * (*(p+7));
// b = - (*(p+1)) * (*(p+8)) + (*(p+2)) * (*(p+7));
// c = (*(p+1)) * (*(p+5)) - (*(p+2)) * (*(p+4));
// d = - (*(p+3)) * (*(p+8)) + (*(p+5)) * (*(p+6));
// e = (*(p+0)) * (*(p+8)) - (*(p+2)) * (*(p+6));
// f = - (*(p+0)) * (*(p+5)) + (*(p+2)) * (*(p+3));
// g = (*(p+3)) * (*(p+7)) - (*(p+4)) * (*(p+6));
// h = - (*(p+0)) * (*(p+7)) + (*(p+1)) * (*(p+6));
// i = (*(p+0)) * (*(p+4)) - (*(p+1)) * (*(p+3));
// det = (*p) * a + (*(p+1)) * d + (*(p+2)) * g;
// GMM_ASSERT1(det!=T(0), "non invertible matrix");
// *p++ = a / det; *p++ = b / det; *p++ = c / det;
// *p++ = d / det; *p++ = e / det; *p++ = f / det;
// *p++ = g / det; *p++ = h / det; *p++ = i / det;
// } break;
} } else { dense_matrix<T> B(mat_nrows(A), mat_ncols(A)); std::vector<int> ipvt(mat_nrows(A)); gmm::copy(A, B); size_type info = lu_factor(B, ipvt); GMM_ASSERT1(!info, "non invertible matrix"); lu_inverse(B, ipvt, A); return lu_det(B, ipvt); } } return det; }
}
#endif // GMM_OPT_H__
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