jacobian()

InterpContinuousModel.jacobian(t, parameter, state, input_func=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 \(\ddqhat\fhat(\qhat(t), \u(t); \bfmu)\) where the model is given by \(\ddt\qhat(t; \bfmu) = \fhat(\qhat(t), \u(t); \bfmu)\).

Parameters:

tfloat

Time \(t\), a scalar.

parameter(p,) ndarray

Parameter value \(\bfmu\).

state(r,) ndarray

State vector \(\qhat(t)\) corresponding to time t.

input_funccallable(float) -> (m,), or None

Input function that maps time t to the input vector \(\u(t)\).

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(t, parameter, q, input_func)
...         for t, q in zip(times, states)]
# ...it is faster to do this.
>>> model_at_parameter = parametric_model.evaluate(parameter)
>>> jacs = [model_at_parameter.jacobian(t, parameter, q, input_func)
...         for t, q in zip(times, states)]