numerical_function_spaces.orlicz_spaces.conjugate
Functions
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Calculates the right-side derivative of the Orlicz function for a given set of parameters. |
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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. ])