void Residual<_Type>::jacobian( const DenseVector<_Type>& state, DenseMatrix<_Type>& jac ) const
{
DenseVector<_Type> new_state( state );
// evaluation of the function
DenseVector<_Type> f_at_new_state( ORDER_OF_SYSTEM, 0.0 );
// default is to FD the Jacobian
for ( std::size_t i = 0; i < NUMBER_OF_VARS; ++i )
{
new_state[ i ] += DELTA;
residual_fn( new_state, f_at_new_state );
new_state[ i ] -= DELTA;
jac.set_col( i, ( f_at_new_state - FN_AT_LAST_STATE ) / DELTA );
}
}
void Tresidual<T>::jacobian( Tmatrix<T>& J, const Tvector<T>& x_k ) const
{
Tvector<T> new_state( ORDER, 0.0 ); // New state vector
Tvector<T> f_eval( ORDER, 0.0 ); // Function evaluation
Tvector<T> f_at_new_state( ORDER, 0.0); // Function evaluation at the new state
for ( std::size_t alpha = 0; alpha < ORDER; ++alpha ) // Row index
{
for ( std::size_t beta = 0; beta < ORDER; ++beta ) // Column index
{
Tvector<T> delta(ORDER,0.0); // Perturbation vector
delta[ beta ] += DELTA;
new_state = x_k + delta; // Perturb the known value
// Perurbed function evaluation
residual_function( f_at_new_state, new_state );
residual_function( f_eval, x_k );
// Approximate the entry in the Jacobian
J(alpha,beta) = ( f_at_new_state[ alpha ] - f_eval[ alpha ] ) / DELTA;
}
}
}
