Linear_algebra_tools_impl.h

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#ifndef Linear_algebra_tools_impl_H
#define Linear_algebra_tools_impl_H
#include <Linear_algebra_tools.h>
 
/*! @brief Computes the Linfini norm of the matrix. Property: denoting |x| as the Linfini norm of x (vector or matrix),
 *
 *   we have |m * x| <= |m| * |x|
 *  In practice: it is the max over j of the sum over i of std::fabs(m(i,j))
 *
 */
inline double Matrice33::norme_Linfini()
{
  double x = std::fabs(m[0][0]) + std::fabs(m[0][1]) + std::fabs(m[0][2]);
  double y = std::fabs(m[1][0]) + std::fabs(m[1][1]) + std::fabs(m[1][2]);
  double z = std::fabs(m[2][0]) + std::fabs(m[2][1]) + std::fabs(m[2][2]);
  double resu = ((x > y) ? x : y);
  resu = ((resu > z) ? resu : z);
  return resu;
}
 
/*! @brief Matrix-vector product with vector x.
 *
 */
inline void Matrice33::produit(const Matrice33& m, const Vecteur3& x, Vecteur3& y)
{
  y.init();
  for (int i=0; i<3; i++)
    for (int j=0; j<3; j++)
      y.v[i] += m.m[i][j] * x.v[j];
}
 
inline void Matrice33::produit_matriciel(const Matrice33& mat1, const Matrice33& mat2, Matrice33& res)
{
  res.init();
  for (int i=0; i<3; i++)
    for (int j=0; j<3; j++)
      for (int k=0; k<3; k++)
        res.m[i][j] += mat1.m[i][k] * mat2.m[k][j];
}
 
inline void Vecteur3::produit_vectoriel(const Vecteur3& x, const Vecteur3& y, Vecteur3& z)
{
  z.v[0] = x.v[1] * y.v[2] - x.v[2] * y.v[1];
  z.v[1] = x.v[2] * y.v[0] - x.v[0] * y.v[2];
  z.v[2] = x.v[0] * y.v[1] - x.v[1] * y.v[0];
}
 
inline double Vecteur3::produit_scalaire(const Vecteur3& x, const Vecteur3& y)
{
  double r = 0.;
  for (int i=0; i<3; i++)
    r += x.v[i] * y.v[i];
  return r;
}
 
/*! @brief L_infini norm, i.e. the max of abs(v[i])
 *
 */
inline double Vecteur3::norme_Linfini()
{
  double x = std::fabs(v[0]);
  double y = std::fabs(v[1]);
  double z = std::fabs(v[2]);
  double resu = ((x > y) ? x : y);
  resu = ((resu > z) ? resu : z);
  return resu;
}
 
/* ! @brief Computes the transpose
 *
 */
inline void Matrice33::transpose(const Matrice33& matrice, Matrice33& matrice_transpose)
{
  for (int i=0; i<3; i++)
    for (int j=0; j<3; j++)
      matrice_transpose.m[i][j] = matrice.m[j][i];
}
 
/*! @brief Computes the inverse.
 *
 * If the determinant of "matrice" is zero, exit() is called if exit_on_error (default value),
 *    otherwise matrice_inv is not filled and 0 is returned.
 *  Return value: determinant of "matrice" (not of the inverse!)
 *
 */
inline double Matrice33::inverse(const Matrice33& matrice, Matrice33& matrice_inv, int exit_on_error)
{
  const double a00 = matrice.m[0][0];
  const double a01 = matrice.m[0][1];
  const double a02 = matrice.m[0][2];
  const double a10 = matrice.m[1][0];
  const double a11 = matrice.m[1][1];
  const double a12 = matrice.m[1][2];
  const double a20 = matrice.m[2][0];
  const double a21 = matrice.m[2][1];
  const double a22 = matrice.m[2][2];
  // compute temporary values for optimization
  const double t4 = a00*a11;
  const double t6 = a00*a12;
  const double t8 = a01*a10;
  const double t10 = a02*a10;
  const double t12 = a01*a20;
  const double t14 = a02*a20;
  const double t = t4*a22-t6*a21-t8*a22+t10*a21+t12*a12-t14*a11;
  if (t==0.)
    {
      if (exit_on_error)
        {
          Cerr << "Error in Matrice33::inverse: determinant is null" << finl;
          Process::exit();
        }
      // To avoid the compiler to complain about "might be non initialized":
      for (int i = 0; i < 3; i++)
        for (int j = 0; j < 3; j++)
          matrice_inv.m[i][j] = 0.;
      return 0.;
    }
  const double t17 = 1/(t);
 
  //compute the inverse matrix
  matrice_inv.m[0][0] = (a11*a22-a12*a21)*t17;
  matrice_inv.m[0][1] = -(a01*a22-a02*a21)*t17;
  matrice_inv.m[0][2] = -(-a01*a12+a02*a11)*t17;
  matrice_inv.m[1][0] = (-a10*a22+a12*a20)*t17;
  matrice_inv.m[1][1] = (a00*a22-t14)*t17;
  matrice_inv.m[1][2] = -(t6-t10)*t17;
  matrice_inv.m[2][0] = -(-a10*a21+a11*a20)*t17;
  matrice_inv.m[2][1] = -(a00*a21-t12)*t17;
  matrice_inv.m[2][2] = (t4-t8)*t17;
  return t;
}
 
inline Vecteur3 operator-(const Vecteur3& x, const Vecteur3& y)
{
  Vecteur3 z;
  for (int i=0; i<3; i++)
    z.v[i] = x.v[i] - y.v[i];
  return z;
}
#endif