.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/stochastic_processes/translation/translation.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_stochastic_processes_translation_translation.py>`
        to download the full example code or to run this example in your browser via Binder

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_stochastic_processes_translation_translation.py:


Translation
=================================================================

In this example, a Gaussian stochastic processes is translated into a stochastic processes of a number of distributions.
This example illustrates how to use the :class:`.Correlate` class to translate from Gaussian to other probability
distributions and compare how the statistics of the translated stochastic processes change along with distributions.

.. GENERATED FROM PYTHON SOURCE LINES 13-15

Import the necessary libraries. Here we import standard libraries such as numpy and matplotlib, but also need to
import the class:`.Correlate` class from the :py:mod:`stochastic_processes` module of UQpy.

.. GENERATED FROM PYTHON SOURCE LINES 18-25

.. code-block:: default


    from UQpy.stochastic_process import Translation, SpectralRepresentation
    import numpy as np
    import matplotlib.pyplot as plt

    plt.style.use('seaborn')


.. GENERATED FROM PYTHON SOURCE LINES 26-27

Firstly we generate Gaussian Stochastic Processes using the Spectral Representation Method.

.. GENERATED FROM PYTHON SOURCE LINES 30-61

.. code-block:: default


    n_sim = 10000  # Num of samples
    T = 100  # Time(1 / T = dw)
    nt = 256  # Num.of Discretized Time
    F = 1 / T * nt / 2  # Frequency.(Hz)
    nw = 128  # Num of Discretized Freq.
    dt = T / nt
    t = np.linspace(0, T - dt, nt)
    dw = F / nw
    w = np.linspace(0, F - dw, nw)
    S = 125 * w ** 2 * np.exp(-2 * w)

    SRM_object = SpectralRepresentation(n_sim, S, dt, dw, nt, nw, random_state=128)
    samples = SRM_object.samples


    def S_to_R(S, w, t):
        dw = w[1] - w[0]
        fac = np.ones(len(w))
        fac[1: len(w) - 1: 2] = 4
        fac[2: len(w) - 2: 2] = 2
        fac = fac * dw / 3
        R = np.zeros(len(t))
        for i in range(len(t)):
            R[i] = 2 * np.dot(fac, S * np.cos(w * t[i]))
        return R


    R_g = S_to_R(S, w, t)
    r_g = R_g / R_g[0]


.. GENERATED FROM PYTHON SOURCE LINES 62-63

We translate the samples to be Uniform samples from :math:`1` to :math:`2`

.. GENERATED FROM PYTHON SOURCE LINES 66-80

.. code-block:: default


    from UQpy.distributions import Lognormal

    distribution = Lognormal(0.5)
    samples = samples.flatten()[:, np.newaxis]

    Translate_object = Translation(distributions=distribution, time_interval=dt, frequency_interval=dw,
                                   n_time_intervals=nt, n_frequency_intervals=nw,
                                   correlation_function_gaussian=R_g, samples_gaussian=samples)
    samples_ng = Translate_object.samples_non_gaussian

    R_ng = Translate_object.scaled_correlation_function_non_gaussian
    r_ng = Translate_object.correlation_function_non_gaussian


.. GENERATED FROM PYTHON SOURCE LINES 81-82

Plotting the actual and translated autocorrelation functions

.. GENERATED FROM PYTHON SOURCE LINES 85-92

.. code-block:: default


    fig1 = plt.figure()
    plt.plot(r_g, label='Gaussian')
    plt.plot(r_ng, label='non-Gaussian')
    plt.title('Correlation Function (r)')
    plt.legend()
    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  0.000 seconds)


.. _sphx_glr_download_auto_examples_stochastic_processes_translation_translation.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example


    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/SURGroup/UQpy/master?urlpath=lab/tree/notebooks/auto_examples/stochastic_processes/translation/translation.ipynb
        :alt: Launch binder
        :width: 150 px



    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: translation.py <translation.py>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: translation.ipynb <translation.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_