pymloc.solvers.dynamical_systems.sensitivities

Classes

SensInhomProjection(*args, **kwargs)

Subclass for case b) described in SensitivitiesSolver class

SensInhomProjectionNoSubset(*args, **kwargs)

Subclass for case c) described in SensitivitiesSolver class

SensInhomWithTimeDerivative(sensitivities, …)

Subclass for case a) described in SensitivitiesSolver class

SensitivitiesInhomogeneity(sensitivities, …)

Baseclass for the inhomogeneity used in both – forward and adjoint – sensitivity computations.

SensitivitiesSolver(bvp_param, *args, **kwargs)

Baseclass for both Sensitivity solvers.
class pymloc.solvers.dynamical_systems.sensitivities.SensInhomProjection(*args, **kwargs)

Bases: pymloc.solvers.dynamical_systems.sensitivities.SensitivitiesInhomogeneity

Subclass for case b) described in SensitivitiesSolver class

Parameters

  • sensitivities (SensitivitiesSolver object blabla) –

  • localized_bvp (localized BoundaryValueProblem object) –

  • solution –

  • parameter –

capital_f_theta(t)
temp2_f_a_theta(capital_f_theta, tau)
class pymloc.solvers.dynamical_systems.sensitivities.SensInhomProjectionNoSubset(*args, **kwargs)

Bases: pymloc.solvers.dynamical_systems.sensitivities.SensInhomProjection

Subclass for case c) described in SensitivitiesSolver class

Parameters

  • sensitivities (SensitivitiesSolver object blabla) –

  • localized_bvp (localized BoundaryValueProblem object) –

  • solution –

  • parameter –

capital_f_theta(t)
f_a_theta(tau)
projector_cal_theta(tau)
Parameters

tau (float) –

summand_2(tau)
class pymloc.solvers.dynamical_systems.sensitivities.SensInhomWithTimeDerivative(sensitivities, localized_bvp, solution, parameter)

Bases: pymloc.solvers.dynamical_systems.sensitivities.SensitivitiesInhomogeneity

Subclass for case a) described in SensitivitiesSolver class

Parameters

  • sensitivities (SensitivitiesSolver object blabla) –

  • localized_bvp (localized BoundaryValueProblem object) –

  • solution (pymloc.solvers.base_solver.TimeSolution) –

  • parameter (numpy.ndarray) –

capital_f_theta(t)
Parameters

t (float) –

capital_f_tilde(t)

Computes the quantity \(\tilde F^{(i)}\), where \(i\) depends on the chosen method.

Parameters

t (float) –

class pymloc.solvers.dynamical_systems.sensitivities.SensitivitiesInhomogeneity(sensitivities, localized_bvp, solution, parameter)

Bases: abc.ABC

Baseclass for the inhomogeneity used in both – forward and adjoint – sensitivity computations.

Concrete implementations depend on the chosen algorithm.

Parameters

  • sensitivities (SensitivitiesSolver object blabla) –

  • localized_bvp (localized BoundaryValueProblem object) –

  • solution (pymloc.solvers.base_solver.TimeSolution) –

  • parameter (numpy.ndarray) –

_set_eplus_e_derivatives(parameter)

Sets several derivative functions wrt. parameters.

Parameters

parameter (numpy.ndarray) –

a_dif(t)

Computes the derivative \(A_{\theta}(t)\).

Parameters

t (float) –

Return type

numpy.ndarray

abstract capital_f_theta(t)
Parameters

t (float) –

capital_f_tilde(t)

Computes the quantity \(\tilde F^{(i)}\), where \(i\) depends on the chosen method.

Parameters

t (float) –

Return type

numpy.ndarray

e_dif(t)

Computes the derivative \(E_{\theta}(t)\).

Parameters

t (float) –

Return type

numpy.ndarray

f_dif(t)

Computes the derivative \(f_{\theta}(t)\).

Parameters

t (float) –

Return type

numpy.ndarray

get_capital_fs()

Returns relevant functions for in the computation of the sensitivities

Return type

Sequence[Callable[[float], numpy.ndarray]]

property solution
x_d(t)

Computes the projected solution \(x_{\mathrm d}(t) = E^+E(t)\).

Parameters

t (float) –

Return type

numpy.ndarray

x_d_dot(t)

Computes the time derivative \(\dot{x}_{\mathrm d}(t)\).

Parameters

t (float) –

Return type

numpy.ndarray

x_dot(t)

Computes the time derivative \(\dot{x}(t)\).

Parameters

t (float) –

Return type

numpy.ndarray

class pymloc.solvers.dynamical_systems.sensitivities.SensitivitiesSolver(bvp_param, *args, **kwargs)

Bases: pymloc.solvers.base_solver.BaseSolver, abc.ABC

Baseclass for both Sensitivity solvers. The Forward and the Adjoint solver.

Parameters

bvp_param (pymloc.model.sensitivities.boundary_dae.BVPSensitivities) –

_capital_f_classes: Sequence[Type[pymloc.solvers.dynamical_systems.sensitivities.SensitivitiesInhomogeneity]] = (<class 'pymloc.solvers.dynamical_systems.sensitivities.SensInhomWithTimeDerivative'>, <class 'pymloc.solvers.dynamical_systems.sensitivities.SensInhomProjection'>, <class 'pymloc.solvers.dynamical_systems.sensitivities.SensInhomProjectionNoSubset'>)

Hard coded tuple of allowed subclasses

_get_capital_fs(*args, **kwargs)

Computes the capital_f_tilde quantity \(\tilde F^{(i)}\), that is used in the computation of both, forward and adjoint sensitivities. The concrete result depends on certain conditions.

  1. Compute forward or adjoint sensitivities?

  2. Regularity level

    1. Time derivative of the algebraic variables exist

    2. \((E^+E)_{\theta} E^+E = (E^+E)_{\theta}\)

      1. is not fulfilled

The forward approach can only be used in case a) and b). The adjoint approach can be used in all cases. However, in the most general case c) additional derivatives of the original data are necessary Approach a) has the additional disadvantage that the product \(E_{\theta} \dot{x}\) may not be available directly from most DAE solvers.

property bvp_param
property capital_f_class
capital_f_default_class: Type[pymloc.solvers.dynamical_systems.sensitivities.SensitivitiesInhomogeneity]

attribute that must be defined in subclasses to determine the appropriate subclass of SensitivitiesInhomogeneity for the computation of \(\tilde F^{(i)}\).

Available subclasses are listed in _capital_f_classes.

property dynamical_system