orbithunter.EquilibriumOrbitKS.jacobian

EquilibriumOrbitKS.jacobian(**kwargs)

Jacobian matrix evaluated at the current state.

kwargs :

Unused, included to match signature in Orbit class.

Returns

jac_2-d ndarray

Jacobian matrix whose columns are derivatives with respect to all unconstrained state variables; including periods. Has dimensions dependent on number of spatiotemporal modes and free parameters, (self.shapes()[-1].size, self.shapes()[-1].size + n_params) Jacobian matrix of the KSe where n_params = 2 - sum(self.constraints)

Notes

Original implementation was pretty, but very inefficient. This now computes the Jacobian matrix, minimizing the amount of allocated memory by overwriting and performing matrix-free implementations of Fourier transform matrix operations. Computes the Jacobian \(J = D_t + D_xx + D_xxxx + F_t D_x F_x Diag(u) F_x^{-1} F_t^{-1}\) in the following steps: