Program Listing for File implicit_residual.m

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%> Compute the residual of system to be solved:
%>
%> \f[
%> \mathbf{F}_i\left(\mathbf{x}_k + \Delta t \displaystyle\sum_{j=1}^{s}
%>   a_{ij} \mathbf{K}_j, \, \mathbf{K}_i, \, t_k + c_i \Delta t
%> \right) = \mathbf{0}.
%> \f]
%>
%> \param x_k States value at \f$ k \f$-th time step \f$ \mathbf{x}(t_k) \f$.
%> \param K   Variable \f$ \mathbf{K} \f$ of the system to be solved.
%> \param t_k Time step \f$ t_k \f$.
%> \param d_t Advancing time step \f$ \Delta t\f$.
%>
%> \return The residual of system to be solved.
%
function out = implicit_residual( this, x_k, K_in, t_k, d_t )

  % Extract lengths
  nc = length(this.m_c);
  nx = length(x_k);
  K  = reshape(K_in, nx, nc);

  % Loop through each equation of the system
  res = zeros(nx, nc);
  for i = 1:nc
    t_i = t_k + this.m_c(i) * d_t;
    x_i = x_k + K * this.m_A(i,:).';
    v_i = this.m_sys.v(x_i, t_i);
    y_i = this.m_sys.y(x_i, v_i, t_i);
    res(:,i) = this.m_sys.F(x_i, K(:,i)./d_t, y_i, v_i, t_i);
  end
  out = reshape(res, nc*nx, 1);
end