gmm_opt.h

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/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================
 
 Copyright (C) 2003-2026 Yves Renard
 
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/**@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__
 
#include "gmm_dense_lu.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));
          lapack_ipvt 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));
      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;
        default : {
          if (N == 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;
            if (std::abs(det) > 1e-5) {
              *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;
            }
          }
          dense_matrix<T> B(mat_nrows(A), mat_ncols(A));
          lapack_ipvt 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);
          det = lu_det(B, ipvt);
          break;
        }
      }
    }
    return det;
  }
 
  
}
 
#endif //  GMM_OPT_H__