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 $\frac{\partial }{\partial \hat{\mathbf{q}}}\hat{\mathbf{f}}(\hat{\mathbf{q}},\mathbf{u};\mathit{\mu })$ where the model is given by $\hat{\mathbf{q}}(\mathit{\mu }{)}_{j+1}=\hat{\mathbf{f}}(\hat{\mathbf{q}}(\mathit{\mu }{)}_j,{\mathbf{u}}_j;\mathit{\mu })$.

Parameters:

parameter(p,) ndarray

Parameter value $\mathit{\mu }$.

state(r,) ndarray

State vector $\hat{\mathbf{q}}$.

input_(m,) ndarray or None

Input vector $\mathbf{u}$.

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]