numerical_function_spaces.orlicz_spaces.conjugate

Functions

right_side_derivative(Orlicz_function, u_max, du[, ...])

Calculates the right-side derivative of the Orlicz function for a given set of parameters.

conjugate_function(Orlicz_function, u_max, du[, ...])

Calculates the conjugate function Psi of the Orlicz function for a given set of parameters.

Module Contents

numerical_function_spaces.orlicz_spaces.conjugate.right_side_derivative(Orlicz_function, u_max: float, du: float, show_progress: bool = False)[source]

Calculates the right-side derivative of the Orlicz function for a given set of parameters.

Parameters:
  • Orlicz_function (function) – The Orlicz function to be used.

  • u_max (float) – The upper bound of the u domain.

  • du (float) – The step size for the u domain.

  • show_progress (bool, optional) – Whether to show a progress bar during computation, by default False.

Returns:

The right-side derivative of the Orlicz function evaluated at each point in the domain of Orlicz_function.

Return type:

np.ndarray

Examples

>>> def Orlicz_function(u):
...     return np.where(u <= 1, 0, u ** 2 - 1)
...
>>> right_side_derivative(Orlicz_function, u_max=5, du=0.5)
array([0. , 0. , 2.5, 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5])
numerical_function_spaces.orlicz_spaces.conjugate.conjugate_function(Orlicz_function, u_max, du: float, show_progress: bool = False)[source]

Calculates the conjugate function Psi of the Orlicz function for a given set of parameters.

Parameters:
  • Orlicz_function (function) – The Orlicz function to be used.

  • u_max (float) – The upper bound of the u domain.

  • du (float) – The step size for the u domain.

  • show_progress (bool, optional) – Whether to show a progress bar during computation, by default False.

Returns:

The conjugate function Psi of the Orlicz function evaluated at each point in the domain of Orlicz_function.

Return type:

np.ndarray

Examples

>>> def Orlicz_function(u):
...     return np.where(u <=1, 0, u**2)
...
>>> conjugate_function(Orlicz_function, u_max=5, du=0.5)
array([0. , 0.5, 1. , 1.5, 2. , 2.5, 3. , 3.5, 4. , 5. ])