jacobian()

ParametricDiscreteModel.jacobian(parameter, state, input_=None)

Sum the state Jacobian of each model operator.

This the derivative of the right-hand side of the model with respect to the state, i.e., the function \(\ddqhat\fhat(\qhat, \u; \bfmu)\) where the model is given by \(\qhat(\bfmu)_{j+1} = \fhat(\qhat(\bfmu)_{j}, \u_{j}; \bfmu)\).

Parameters:

parameter(p,) ndarray

Parameter value \(\bfmu\).

state(r,) ndarray

State vector \(\qhat\).

input_(m,) ndarray or None

Input vector \(\u\).

Returns:

jac(r, r) ndarray

State Jacobian of the right-hand side of the model.

Notes

For repeated jacobian() calls with the same parameter value, use evaluate() to first get the nonparametric model corresponding to the parameter value.

# Instead of this...
>>> jacs = [parametric_model.jacobian(parameter, q, input_)
...         for q in list_of_states]
# ...it is faster to do this.
>>> model_at_parameter = parametric_model.evaluate(parameter)
>>> jacs = [model_at_parameter.jacobian(q, input_)
...         for q in list_of_states]