jacobian()

_NonparametricOperator.jacobian(state, input_=None)

Construct the state Jacobian of the operator.

If \([\![\q]\!]_{i}\) denotes the entry \(i\) of a vector \(\q\), then the entries of the state Jacobian are given by

\[[\![\ddqhat\Ophat(\qhat,\u)]\!]_{i,j} = \frac{\partial}{\partial[\![\qhat]\!]_j} [\![\Ophat(\qhat,\u)]\!]_i.\]

If a child class does not implement this method, it is assumed that the Jacobian is zero (i.e., the operator does not act on the state).

Parameters

state(r,) ndarray

State vector.

input_(m,) ndarray or float or None

Input vector.

Returns

jac(r, r) ndarray

State Jacobian.