numerical_function_spaces.orlicz_spaces.conjugate
=================================================

.. py:module:: numerical_function_spaces.orlicz_spaces.conjugate


Functions
---------

.. autoapisummary::

   numerical_function_spaces.orlicz_spaces.conjugate.right_side_derivative
   numerical_function_spaces.orlicz_spaces.conjugate.conjugate_function


Module Contents
---------------

.. py:function:: right_side_derivative(Orlicz_function, u_max: float, du: float, show_progress: bool = False)

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

   :param Orlicz_function: The Orlicz function to be used.
   :type Orlicz_function: function
   :param u_max: The upper bound of the u domain.
   :type u_max: float
   :param du: The step size for the u domain.
   :type du: float
   :param show_progress: Whether to show a progress bar during computation, by default False.
   :type show_progress: bool, optional

   :returns: The right-side derivative of the Orlicz function evaluated at each point in the domain of Orlicz_function.
   :rtype: np.ndarray

   .. rubric:: 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])


.. py:function:: conjugate_function(Orlicz_function, u_max, du: float, show_progress: bool = False)

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

   :param Orlicz_function: The Orlicz function to be used.
   :type Orlicz_function: function
   :param u_max: The upper bound of the u domain.
   :type u_max: float
   :param du: The step size for the u domain.
   :type du: float
   :param show_progress: Whether to show a progress bar during computation, by default False.
   :type show_progress: bool, optional

   :returns: The conjugate function Psi of the Orlicz function evaluated at each point in the domain of Orlicz_function.
   :rtype: np.ndarray

   .. rubric:: 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. ])