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Joris Gillis edited this page Apr 4, 2023 · 2 revisions

Standard documentation for collocation_interpolators:

 [INTERNAL] 

::

 collocation_interpolators([float] tau) -> ([[float]] OUTPUT, [float] OUTPUT)

Obtain collocation interpolating matrices.

A collocation method poses a polynomial Pi that interpolates exactly

through an initial state (0,X_0) and helper states at collocation points (tau_j,X:collPoint(j)).

This function computes the linear mapping between dPi/dt and coefficients Z=[X_0 X:collPoints].

Parameters:

tau: location of collocation points, as obtained from collocation_points

C: interpolating coefficients to obtain derivatives. Length: order+1,

order+1

::

dPi/dt @Z_j = (1/h) Sum_i C[j][i]*Z_i,

with h the length of the integration interval.

Parameters:

D: interpolating coefficients to obtain end state. Length: order+1

::

Pi @X_f = Sum_i D[i]*Z_i

Extra doc: https://github.com/casadi/casadi/wiki/L_1sp

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.hpp#L189

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.cpp#L189-L231

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