jacobian()

InputOperator.jacobian(state, input_=None) → ndarray

Construct the state Jacobian of the operator.

If \([\![\q]\!]_{i}\) denotes the \(i\)-th entry of a vector \(\q\), then the \((i,j)\)-th entry of the state Jacobian is 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.