//#####################################################################
// Function Fast_Singular_Value_Decomposition
//#####################################################################
template<class T> void Matrix<T,3,2>::
fast_singular_value_decomposition(Matrix<T,3,2>& U,DiagonalMatrix<T,2>& singular_values,Matrix<T,2>& V) const
{
if(!is_same<T,double>::value){
Matrix<double,3,2> U_double;DiagonalMatrix<double,2> singular_values_double;Matrix<double,2> V_double;
Matrix<double,3,2>(*this).fast_singular_value_decomposition(U_double,singular_values_double,V_double);
U=Matrix<T,3,2>(U_double);singular_values=DiagonalMatrix<T,2>(singular_values_double);V=Matrix<T,2>(V_double);return;}
// now T is double
DiagonalMatrix<T,2> lambda;normal_equations_matrix().solve_eigenproblem(lambda,V);
if(lambda.x11<0) lambda=lambda.clamp_min(0);
singular_values=lambda.sqrt();
U.set_column(0,(*this*V.column(0)).normalized());
Vector<T,3> other=cross(weighted_normal(),U.column(0));
T other_magnitude=other.magnitude();
U.set_column(1,other_magnitude?other/other_magnitude:U.column(0).unit_orthogonal_vector());
}
template<class T,int d> DiagonalMatrix<T,d> ConstitutiveModel<T,d>::clamp_f(const DiagonalMatrix<T,d>& F) const {
return F.clamp_min(failure_threshold);
}