+++ /dev/null
-/* -*- C++ -*- ------------------------------------------------------------
-
-Copyright (c) 2007 Jesse Anders and Demian Nave http://cmldev.net/
-
-The Configurable Math Library (CML) is distributed under the terms of the
-Boost Software License, v1.0 (see cml/LICENSE for details).
-
- *-----------------------------------------------------------------------*/
-/** @file
- * @brief Compute the inverse of a matrix by LU factorization.
- */
-
-#ifndef matrix_inverse_h
-#define matrix_inverse_h
-
-#include <vector>
-#include <cml/matrix/lu.h>
-
-namespace cml {
-namespace detail {
-
-/* Need to use a functional, since template functions cannot be
- * specialized. _tag is used to specialize based upon dimension:
- */
-template<typename MatT, int _tag> struct inverse_f;
-
-/* @todo: Reciprocal optimization for division by determinant.
- */
-
-/* 2x2 inverse. Despite being marked for fixed_size matrices, this can
- * be used for dynamic-sized ones also:
- */
-template<typename MatT>
-struct inverse_f<MatT,2>
-{
- typename MatT::temporary_type operator()(const MatT& M) const
- {
- typedef typename MatT::temporary_type temporary_type;
- typedef typename temporary_type::value_type value_type;
-
- /* Matrix containing the inverse: */
- temporary_type Z;
- cml::et::detail::Resize(Z,2,2);
-
- /* Compute determinant and inverse: */
- value_type D = value_type(1) / (M(0,0)*M(1,1) - M(0,1)*M(1,0));
- Z(0,0) = M(1,1)*D; Z(0,1) = - M(0,1)*D;
- Z(1,0) = - M(1,0)*D; Z(1,1) = M(0,0)*D;
-
- return Z;
- }
-};
-
-/* 3x3 inverse. Despite being marked for fixed_size matrices, this can
- * be used for dynamic-sized ones also:
- */
-template<typename MatT>
-struct inverse_f<MatT,3>
-{
- /* [00 01 02]
- * M = [10 11 12]
- * [20 21 22]
- */
- typename MatT::temporary_type operator()(const MatT& M) const
- {
- /* Shorthand. */
- typedef typename MatT::value_type value_type;
-
- /* Compute cofactors for each entry: */
- value_type m_00 = M(1,1)*M(2,2) - M(1,2)*M(2,1);
- value_type m_01 = M(1,2)*M(2,0) - M(1,0)*M(2,2);
- value_type m_02 = M(1,0)*M(2,1) - M(1,1)*M(2,0);
-
- value_type m_10 = M(0,2)*M(2,1) - M(0,1)*M(2,2);
- value_type m_11 = M(0,0)*M(2,2) - M(0,2)*M(2,0);
- value_type m_12 = M(0,1)*M(2,0) - M(0,0)*M(2,1);
-
- value_type m_20 = M(0,1)*M(1,2) - M(0,2)*M(1,1);
- value_type m_21 = M(0,2)*M(1,0) - M(0,0)*M(1,2);
- value_type m_22 = M(0,0)*M(1,1) - M(0,1)*M(1,0);
-
- /* Compute determinant from the minors: */
- value_type D =
- value_type(1) / (M(0,0)*m_00 + M(0,1)*m_01 + M(0,2)*m_02);
-
- /* Matrix containing the inverse: */
- typename MatT::temporary_type Z;
- cml::et::detail::Resize(Z,3,3);
-
- /* Assign the inverse as (1/D) * (cofactor matrix)^T: */
- Z(0,0) = m_00*D; Z(0,1) = m_10*D; Z(0,2) = m_20*D;
- Z(1,0) = m_01*D; Z(1,1) = m_11*D; Z(1,2) = m_21*D;
- Z(2,0) = m_02*D; Z(2,1) = m_12*D; Z(2,2) = m_22*D;
-
- return Z;
- }
-};
-
-/* 4x4 inverse. Despite being marked for fixed_size matrices, this can
- * be used for dynamic-sized ones also:
- */
-template<typename MatT>
-struct inverse_f<MatT,4>
-{
- /* [00 01 02 03]
- * M = [10 11 12 13]
- * [20 21 22 23]
- * [30 31 32 33]
- *
- * |11 12 13| |10 12 13|
- * C00 = |21 22 23| C01 = |20 22 23|
- * |31 32 33| |30 32 33|
- *
- * |10 11 13| |10 11 12|
- * C02 = |20 21 23| C03 = |20 21 22|
- * |30 31 33| |30 31 32|
- */
- typename MatT::temporary_type operator()(const MatT& M) const
- {
- /* Shorthand. */
- typedef typename MatT::value_type value_type;
-
- /* Common cofactors, rows 0,1: */
- value_type m_22_33_23_32 = M(2,2)*M(3,3) - M(2,3)*M(3,2);
- value_type m_23_30_20_33 = M(2,3)*M(3,0) - M(2,0)*M(3,3);
- value_type m_20_31_21_30 = M(2,0)*M(3,1) - M(2,1)*M(3,0);
- value_type m_21_32_22_31 = M(2,1)*M(3,2) - M(2,2)*M(3,1);
- value_type m_23_31_21_33 = M(2,3)*M(3,1) - M(2,1)*M(3,3);
- value_type m_20_32_22_30 = M(2,0)*M(3,2) - M(2,2)*M(3,0);
-
- /* Compute minors: */
- value_type d00
- = M(1,1)*m_22_33_23_32+M(1,2)*m_23_31_21_33+M(1,3)*m_21_32_22_31;
-
- value_type d01
- = M(1,0)*m_22_33_23_32+M(1,2)*m_23_30_20_33+M(1,3)*m_20_32_22_30;
-
- value_type d02
- = M(1,0)*-m_23_31_21_33+M(1,1)*m_23_30_20_33+M(1,3)*m_20_31_21_30;
-
- value_type d03
- = M(1,0)*m_21_32_22_31+M(1,1)*-m_20_32_22_30+M(1,2)*m_20_31_21_30;
-
- /* Compute minors: */
- value_type d10
- = M(0,1)*m_22_33_23_32+M(0,2)*m_23_31_21_33+M(0,3)*m_21_32_22_31;
-
- value_type d11
- = M(0,0)*m_22_33_23_32+M(0,2)*m_23_30_20_33+M(0,3)*m_20_32_22_30;
-
- value_type d12
- = M(0,0)*-m_23_31_21_33+M(0,1)*m_23_30_20_33+M(0,3)*m_20_31_21_30;
-
- value_type d13
- = M(0,0)*m_21_32_22_31+M(0,1)*-m_20_32_22_30+M(0,2)*m_20_31_21_30;
-
- /* Common cofactors, rows 2,3: */
- value_type m_02_13_03_12 = M(0,2)*M(1,3) - M(0,3)*M(1,2);
- value_type m_03_10_00_13 = M(0,3)*M(1,0) - M(0,0)*M(1,3);
- value_type m_00_11_01_10 = M(0,0)*M(1,1) - M(0,1)*M(1,0);
- value_type m_01_12_02_11 = M(0,1)*M(1,2) - M(0,2)*M(1,1);
- value_type m_03_11_01_13 = M(0,3)*M(1,1) - M(0,1)*M(1,3);
- value_type m_00_12_02_10 = M(0,0)*M(1,2) - M(0,2)*M(1,0);
-
- /* Compute minors (uses row 3 as the multipliers instead of row 0,
- * which uses the same signs as row 0):
- */
- value_type d20
- = M(3,1)*m_02_13_03_12+M(3,2)*m_03_11_01_13+M(3,3)*m_01_12_02_11;
-
- value_type d21
- = M(3,0)*m_02_13_03_12+M(3,2)*m_03_10_00_13+M(3,3)*m_00_12_02_10;
-
- value_type d22
- = M(3,0)*-m_03_11_01_13+M(3,1)*m_03_10_00_13+M(3,3)*m_00_11_01_10;
-
- value_type d23
- = M(3,0)*m_01_12_02_11+M(3,1)*-m_00_12_02_10+M(3,2)*m_00_11_01_10;
-
- /* Compute minors: */
- value_type d30
- = M(2,1)*m_02_13_03_12+M(2,2)*m_03_11_01_13+M(2,3)*m_01_12_02_11;
-
- value_type d31
- = M(2,0)*m_02_13_03_12+M(2,2)*m_03_10_00_13+M(2,3)*m_00_12_02_10;
-
- value_type d32
- = M(2,0)*-m_03_11_01_13+M(2,1)*m_03_10_00_13+M(2,3)*m_00_11_01_10;
-
- value_type d33
- = M(2,0)*m_01_12_02_11+M(2,1)*-m_00_12_02_10+M(2,2)*m_00_11_01_10;
-
- /* Finally, compute determinant from the minors, and assign the
- * inverse as (1/D) * (cofactor matrix)^T:
- */
- typename MatT::temporary_type Z;
- cml::et::detail::Resize(Z,4,4);
-
- value_type D = value_type(1) /
- (M(0,0)*d00 - M(0,1)*d01 + M(0,2)*d02 - M(0,3)*d03);
- Z(0,0) = +d00*D; Z(0,1) = -d10*D; Z(0,2) = +d20*D; Z(0,3) = -d30*D;
- Z(1,0) = -d01*D; Z(1,1) = +d11*D; Z(1,2) = -d21*D; Z(1,3) = +d31*D;
- Z(2,0) = +d02*D; Z(2,1) = -d12*D; Z(2,2) = +d22*D; Z(2,3) = -d32*D;
- Z(3,0) = -d03*D; Z(3,1) = +d13*D; Z(3,2) = -d23*D; Z(3,3) = +d33*D;
-
- return Z;
- }
-};
-
-/* If more extensive general linear algebra functionality is offered in
- * future versions it may be useful to make the elementary row and column
- * operations separate functions. For now they're simply performed in place,
- * but the commented-out lines of code show where the calls to these functions
- * should go if and when they become available.
- */
-
-/* @todo: In-place version, and address memory allocation for pivot vector.
- */
-
-/* General NxN inverse by Gauss-Jordan elimination with full pivoting: */
-template<typename MatT, int _tag>
-struct inverse_f
-{
- typename MatT::temporary_type operator()(const MatT& M) const
- {
- /* Shorthand. */
- typedef typename MatT::value_type value_type;
-
- /* Size of matrix */
- size_t N = M.rows();
-
- /* Matrix containing the inverse: */
- typename MatT::temporary_type Z;
- cml::et::detail::Resize(Z,N,N);
- Z = M;
-
- /* For tracking pivots */
- std::vector<size_t> row_index(N);
- std::vector<size_t> col_index(N);
- std::vector<size_t> pivoted(N,0);
-
- /* For each column */
- for (size_t i = 0; i < N; ++i) {
-
- /* Find the pivot */
- size_t row = 0, col = 0;
- value_type max = value_type(0);
- for (size_t j = 0; j < N; ++j) {
- if (!pivoted[j]) {
- for (size_t k = 0; k < N; ++k) {
- if (!pivoted[k]) {
- value_type mag = std::fabs(Z(j,k));
- if (mag > max) {
- max = mag;
- row = j;
- col = k;
- }
- }
- }
- }
- }
-
- /* TODO: Check max against epsilon here to catch singularity */
-
- row_index[i] = row;
- col_index[i] = col;
-
- /* Swap rows if necessary */
- if (row != col) {
- /*Z.row_op_swap(row,col);*/
- for (size_t j = 0; j < Z.cols(); ++j) {
- std::swap(Z(row,j),Z(col,j));
- }
- }
-
- /* Process pivot row */
- pivoted[col] = true;
- value_type pivot = Z(col,col);
- Z(col,col) = value_type(1);
- /*Z.row_op_mult(col,value_type(1)/pivot);*/
- value_type k = value_type(1)/pivot;
- for (size_t j = 0; j < Z.cols(); ++j) {
- Z(col,j) *= k;
- }
-
- /* Process other rows */
- for (size_t j = 0; j < N; ++j) {
- if (j != col) {
- value_type mult = -Z(j,col);
- Z(j,col) = value_type(0);
- /*Z.row_op_add_mult(col,j,mult);*/
- for (size_t k = 0; k < Z.cols(); ++k) {
- Z(j,k) += mult * Z(col,k);
- }
- }
- }
- }
-
- /* Swap columns if necessary */
- for (int i = N-1; i >= 0; --i) {
- if (row_index[i] != col_index[i]) {
- /*Z.col_op_swap(row_index[i],col_index[i]);*/
- for (size_t j = 0; j < Z.rows(); ++j) {
- std::swap(Z(j,row_index[i]),Z(j,col_index[i]));
- }
- }
- }
-
- /* Return result */
- return Z;
- }
-};
-
-/* Inversion by LU factorization is turned off for now due to lack of
- * pivoting in the implementation, but we may switch back to it at some future
- * time.
- */
-
-#if 0
-
-/* General NxN inverse by LU factorization: */
-template<typename MatT, int _tag>
-struct inverse_f
-{
- typename MatT::temporary_type operator()(const MatT& M) const
- {
- /* Shorthand. */
- typedef typename MatT::value_type value_type;
-
- /* Compute LU factorization: */
- size_t N = M.rows();
- typename MatT::temporary_type LU;
- cml::et::detail::Resize(LU,N,N);
- LU = lu(M);
-
- /* Matrix containing the inverse: */
- typename MatT::temporary_type Z;
- cml::et::detail::Resize(Z,N,N);
-
- typename MatT::col_vector_type v, x;
- cml::et::detail::Resize(v,N);
- cml::et::detail::Resize(x,N);
- for(size_t i = 0; i < N; ++i)
- v[i] = value_type(0);
- /* XXX Need a fill() function here. */
-
- /* Use lu_solve to solve M*x = v for x, where v = [0 ... 1 ... 0]^T: */
- for(size_t i = 0; i < N; ++i) {
- v[i] = 1.;
- x = lu_solve(LU,v);
-
- /* x is column i of the inverse of LU: */
- for(size_t k = 0; k < N; ++ k) {
- Z(k,i) = x[k];
- }
- v[i] = 0.;
- }
-
- return Z;
- }
-
-};
-
-#endif
-
-/* Note: force_NxN is for checking general NxN inversion against the special-
- * case 2x2, 3x3 and 4x4 code. I'm leaving it in for now since we may need to
- * test the NxN code further if the implementation changes. At some future
- * time when the implementation is stable, everything related to force_NxN can
- * be taken out.
- */
-
-/* Note: Commenting the force_NxN stuff out, but leaving the code here in
- * case we need to do more testing in the future.
- */
-
-/* Generator for the inverse functional for fixed-size matrices: */
-template<typename MatT> typename MatT::temporary_type
-inverse(const MatT& M, fixed_size_tag/*, bool force_NxN*/)
-{
- /* Require a square matrix: */
- cml::et::CheckedSquare(M, fixed_size_tag());
-
- /*
- if (force_NxN) {
- return inverse_f<MatT,0>()(M);
- } else {
- */
- return inverse_f<MatT,MatT::array_rows>()(M);
- /*
- }
- */
-}
-
-/* Generator for the inverse functional for dynamic-size matrices: */
-template<typename MatT> typename MatT::temporary_type
-inverse(const MatT& M, dynamic_size_tag/*, bool force_NxN*/)
-{
- /* Require a square matrix: */
- cml::et::CheckedSquare(M, dynamic_size_tag());
-
- /*
- if (force_NxN) {
- return inverse_f<MatT,0>()(M);
- } else {
- */
- /* Dispatch based upon the matrix dimension: */
- switch(M.rows()) {
- case 2: return inverse_f<MatT,2>()(M); // 2x2
- case 3: return inverse_f<MatT,3>()(M); // 3x3
- case 4: return inverse_f<MatT,4>()(M); // 4x4
- default: return inverse_f<MatT,0>()(M); // > 4x4 (or 1x1)
- }
- /*
- }
- */
-}
-
-} // namespace detail
-
-/** Inverse of a matrix. */
-template<typename E, class AT, typename BO, typename L> inline
-typename matrix<E,AT,BO,L>::temporary_type
-inverse(const matrix<E,AT,BO,L>& M/*, bool force_NxN = false*/)
-{
- typedef typename matrix<E,AT,BO,L>::size_tag size_tag;
- return detail::inverse(M,size_tag()/*,force_NxN*/);
-}
-
-/** Inverse of a matrix expression. */
-template<typename XprT> inline
-typename et::MatrixXpr<XprT>::temporary_type
-inverse(const et::MatrixXpr<XprT>& e/*, bool force_NxN = false*/)
-{
- typedef typename et::MatrixXpr<XprT>::size_tag size_tag;
- return detail::inverse(e,size_tag()/*,force_NxN*/);
-}
-
-} // namespace cml
-
-#endif
-
-// -------------------------------------------------------------------------
-// vim:ft=cpp
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