.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/programmers/plot_draws.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_programmers_plot_draws.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_programmers_plot_draws.py:


biogeme.draws
=============

Examples of use of several functions.

This is designed for programmers who need examples of use of the
functions of the module. The examples are designed to illustrate the
syntax. They do not correspond to any meaningful model.

:author: Michel Bierlaire
:date: Tue Nov 21 18:36:59 2023

.. GENERATED FROM PYTHON SOURCE LINES 17-22

.. code-block:: Python

    import numpy as np
    import pandas as pd
    from biogeme.version import get_text
    import biogeme.draws as dr








.. GENERATED FROM PYTHON SOURCE LINES 23-24

Version of Biogeme.

.. GENERATED FROM PYTHON SOURCE LINES 24-26

.. code-block:: Python

    print(get_text())





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    biogeme 3.2.14 [2024-08-05]
    Home page: http://biogeme.epfl.ch
    Submit questions to https://groups.google.com/d/forum/biogeme
    Michel Bierlaire, Transport and Mobility Laboratory, Ecole Polytechnique Fédérale de Lausanne (EPFL)





.. GENERATED FROM PYTHON SOURCE LINES 27-28

We set the seed so that the outcome of random operations is always the same.

.. GENERATED FROM PYTHON SOURCE LINES 28-30

.. code-block:: Python

    np.random.seed(90267)








.. GENERATED FROM PYTHON SOURCE LINES 31-33

Uniform draws
-------------

.. GENERATED FROM PYTHON SOURCE LINES 35-36

Uniform [0,1]. The output is transformed into a data frame just for the display.

.. GENERATED FROM PYTHON SOURCE LINES 36-39

.. code-block:: Python

    draws = dr.get_uniform(sample_size=3, number_of_draws=10, symmetric=False)
    pd.DataFrame(draws)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
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          <th>8</th>
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          <td>0.422424</td>
          <td>0.392314</td>
          <td>0.656022</td>
          <td>0.071824</td>
          <td>0.282152</td>
          <td>0.294621</td>
          <td>0.294378</td>
        </tr>
        <tr>
          <th>1</th>
          <td>0.719719</td>
          <td>0.976471</td>
          <td>0.860015</td>
          <td>0.637804</td>
          <td>0.097748</td>
          <td>0.215859</td>
          <td>0.901997</td>
          <td>0.259457</td>
          <td>0.246732</td>
          <td>0.608131</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.914063</td>
          <td>0.253449</td>
          <td>0.299638</td>
          <td>0.023243</td>
          <td>0.008511</td>
          <td>0.309165</td>
          <td>0.172084</td>
          <td>0.848053</td>
          <td>0.775280</td>
          <td>0.234141</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 40-43

.. code-block:: Python

    draws = dr.get_uniform(sample_size=3, number_of_draws=10, symmetric=True)
    pd.DataFrame(draws)






.. raw:: html

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          <td>0.410899</td>
          <td>0.656565</td>
          <td>-0.377678</td>
          <td>0.978805</td>
          <td>-0.199249</td>
          <td>-0.499704</td>
          <td>-0.941578</td>
          <td>0.433283</td>
        </tr>
        <tr>
          <th>1</th>
          <td>-0.395955</td>
          <td>0.442475</td>
          <td>0.265263</td>
          <td>0.511135</td>
          <td>-0.507459</td>
          <td>0.738372</td>
          <td>-0.868453</td>
          <td>-0.620988</td>
          <td>0.553554</td>
          <td>-0.213905</td>
        </tr>
        <tr>
          <th>2</th>
          <td>-0.797249</td>
          <td>0.439322</td>
          <td>0.127049</td>
          <td>0.979762</td>
          <td>0.609904</td>
          <td>-0.430471</td>
          <td>0.380190</td>
          <td>0.536699</td>
          <td>0.022698</td>
          <td>-0.761527</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 44-47

LatinHypercube: the Modified Latin Hypercube Sampling (MLHS, Hess et al, 2006)
provides U[0,1] draws from a perturbed grid, designed for
Monte-Carlo integration.

.. GENERATED FROM PYTHON SOURCE LINES 49-52

.. code-block:: Python

    latin_hypercube = dr.get_latin_hypercube_draws(sample_size=3, number_of_draws=10)
    pd.DataFrame(latin_hypercube)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
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          <td>0.177462</td>
          <td>0.530946</td>
          <td>0.417055</td>
          <td>0.825831</td>
          <td>0.782322</td>
          <td>0.088749</td>
          <td>0.155039</td>
          <td>0.539467</td>
        </tr>
        <tr>
          <th>1</th>
          <td>0.986429</td>
          <td>0.028337</td>
          <td>0.585812</td>
          <td>0.846593</td>
          <td>0.661135</td>
          <td>0.925723</td>
          <td>0.397986</td>
          <td>0.350411</td>
          <td>0.955311</td>
          <td>0.702116</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.744942</td>
          <td>0.884753</td>
          <td>0.046556</td>
          <td>0.131465</td>
          <td>0.463126</td>
          <td>0.289113</td>
          <td>0.685699</td>
          <td>0.251115</td>
          <td>0.204371</td>
          <td>0.481789</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 53-54

The same method can be used to generate draws from U[-1,1]

.. GENERATED FROM PYTHON SOURCE LINES 56-61

.. code-block:: Python

    latin_hypercube = dr.get_latin_hypercube_draws(
        sample_size=5, number_of_draws=10, symmetric=True
    )
    pd.DataFrame(latin_hypercube)






.. raw:: html

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          <td>-0.929016</td>
          <td>0.815377</td>
          <td>0.060902</td>
          <td>-0.703703</td>
          <td>-0.660290</td>
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        <tr>
          <th>1</th>
          <td>-0.119771</td>
          <td>0.903854</td>
          <td>0.518566</td>
          <td>-0.175317</td>
          <td>-0.593672</td>
          <td>-0.476686</td>
          <td>-0.249879</td>
          <td>0.014049</td>
          <td>0.592416</td>
          <td>0.333544</td>
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        <tr>
          <th>2</th>
          <td>-0.536467</td>
          <td>-0.602720</td>
          <td>0.421731</td>
          <td>0.258026</td>
          <td>-0.369102</td>
          <td>-0.215673</td>
          <td>0.960123</td>
          <td>-0.406895</td>
          <td>0.652804</td>
          <td>0.186110</td>
        </tr>
        <tr>
          <th>3</th>
          <td>0.149259</td>
          <td>-0.053414</td>
          <td>-0.356505</td>
          <td>0.636484</td>
          <td>0.521282</td>
          <td>-0.866888</td>
          <td>-0.784501</td>
          <td>0.312416</td>
          <td>-0.747227</td>
          <td>0.112625</td>
        </tr>
        <tr>
          <th>4</th>
          <td>-0.914200</td>
          <td>0.238546</td>
          <td>0.738524</td>
          <td>-0.027154</td>
          <td>0.798928</td>
          <td>-0.134140</td>
          <td>-0.800939</td>
          <td>0.460820</td>
          <td>0.362292</td>
          <td>0.852471</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 62-63

The user can provide her own series of U[0,1] draws.

.. GENERATED FROM PYTHON SOURCE LINES 63-66

.. code-block:: Python

    my_unif = np.random.uniform(size=30)
    pd.DataFrame(my_unif)






.. raw:: html

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    <div>
    <style scoped>
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        <tr>
          <th>8</th>
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        <tr>
          <th>9</th>
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          <th>10</th>
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        <tr>
          <th>11</th>
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        <tr>
          <th>12</th>
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        <tr>
          <th>13</th>
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        </tr>
        <tr>
          <th>14</th>
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        </tr>
        <tr>
          <th>15</th>
          <td>0.350926</td>
        </tr>
        <tr>
          <th>16</th>
          <td>0.644284</td>
        </tr>
        <tr>
          <th>17</th>
          <td>0.904649</td>
        </tr>
        <tr>
          <th>18</th>
          <td>0.857553</td>
        </tr>
        <tr>
          <th>19</th>
          <td>0.132332</td>
        </tr>
        <tr>
          <th>20</th>
          <td>0.408866</td>
        </tr>
        <tr>
          <th>21</th>
          <td>0.415191</td>
        </tr>
        <tr>
          <th>22</th>
          <td>0.502339</td>
        </tr>
        <tr>
          <th>23</th>
          <td>0.498379</td>
        </tr>
        <tr>
          <th>24</th>
          <td>0.612381</td>
        </tr>
        <tr>
          <th>25</th>
          <td>0.675059</td>
        </tr>
        <tr>
          <th>26</th>
          <td>0.349810</td>
        </tr>
        <tr>
          <th>27</th>
          <td>0.033002</td>
        </tr>
        <tr>
          <th>28</th>
          <td>0.145176</td>
        </tr>
        <tr>
          <th>29</th>
          <td>0.237861</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 67-72

.. code-block:: Python

    latin_hypercube = dr.get_latin_hypercube_draws(
        sample_size=3, number_of_draws=10, symmetric=False, uniform_numbers=my_unif
    )
    pd.DataFrame(latin_hypercube)






.. raw:: html

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          <td>0.628585</td>
          <td>0.901100</td>
          <td>0.596822</td>
          <td>0.300789</td>
          <td>0.245706</td>
          <td>0.218955</td>
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        <tr>
          <th>1</th>
          <td>0.002059</td>
          <td>0.750078</td>
          <td>0.554809</td>
          <td>0.156556</td>
          <td>0.974595</td>
          <td>0.192142</td>
          <td>0.820413</td>
          <td>0.040054</td>
          <td>0.680296</td>
          <td>0.938173</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.511698</td>
          <td>0.449200</td>
          <td>0.637744</td>
          <td>0.120084</td>
          <td>0.855835</td>
          <td>0.878327</td>
          <td>0.368700</td>
          <td>0.713840</td>
          <td>0.344663</td>
          <td>0.495535</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 73-74

The uniform draws can also be arranged in a two-dimension array

.. GENERATED FROM PYTHON SOURCE LINES 74-77

.. code-block:: Python

    my_unif = dr.get_uniform(sample_size=3, number_of_draws=10)
    pd.DataFrame(my_unif)






.. raw:: html

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          <th>8</th>
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          <td>0.603875</td>
          <td>0.896565</td>
          <td>0.754603</td>
          <td>0.769762</td>
          <td>0.451352</td>
          <td>0.832002</td>
          <td>0.224726</td>
          <td>0.904498</td>
          <td>0.097305</td>
        </tr>
        <tr>
          <th>1</th>
          <td>0.091637</td>
          <td>0.288086</td>
          <td>0.133953</td>
          <td>0.360001</td>
          <td>0.793237</td>
          <td>0.569249</td>
          <td>0.338901</td>
          <td>0.982264</td>
          <td>0.660052</td>
          <td>0.075265</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.336336</td>
          <td>0.374114</td>
          <td>0.464009</td>
          <td>0.227873</td>
          <td>0.008158</td>
          <td>0.286625</td>
          <td>0.934171</td>
          <td>0.109902</td>
          <td>0.945957</td>
          <td>0.756240</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 78-83

.. code-block:: Python

    latin_hypercube = dr.get_latin_hypercube_draws(
        sample_size=3, number_of_draws=10, uniform_numbers=my_unif
    )
    pd.DataFrame(latin_hypercube)






.. raw:: html

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          <td>0.493108</td>
          <td>0.518975</td>
          <td>0.774262</td>
          <td>0.544630</td>
          <td>0.599409</td>
          <td>0.125153</td>
        </tr>
        <tr>
          <th>1</th>
          <td>0.677878</td>
          <td>0.991875</td>
          <td>0.748800</td>
          <td>0.336388</td>
          <td>0.445333</td>
          <td>0.404465</td>
          <td>0.712470</td>
          <td>0.158992</td>
          <td>0.014312</td>
          <td>0.635842</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.096552</td>
          <td>0.296817</td>
          <td>0.053463</td>
          <td>0.240824</td>
          <td>0.303244</td>
          <td>0.842887</td>
          <td>0.227733</td>
          <td>0.376270</td>
          <td>0.964865</td>
          <td>0.622002</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 84-86

Halton draws
------------

.. GENERATED FROM PYTHON SOURCE LINES 88-89

One Halton sequence.

.. GENERATED FROM PYTHON SOURCE LINES 89-92

.. code-block:: Python

    halton = dr.get_halton_draws(sample_size=2, number_of_draws=10, base=3)
    pd.DataFrame(halton)






.. raw:: html

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    <div>
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          <th></th>
          <th>0</th>
          <th>1</th>
          <th>2</th>
          <th>3</th>
          <th>4</th>
          <th>5</th>
          <th>6</th>
          <th>7</th>
          <th>8</th>
          <th>9</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.333333</td>
          <td>0.666667</td>
          <td>0.111111</td>
          <td>0.444444</td>
          <td>0.777778</td>
          <td>0.222222</td>
          <td>0.555556</td>
          <td>0.888889</td>
          <td>0.037037</td>
          <td>0.370370</td>
        </tr>
        <tr>
          <th>1</th>
          <td>0.703704</td>
          <td>0.148148</td>
          <td>0.481481</td>
          <td>0.814815</td>
          <td>0.259259</td>
          <td>0.592593</td>
          <td>0.925926</td>
          <td>0.074074</td>
          <td>0.407407</td>
          <td>0.740741</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 93-94

Several Halton sequences.

.. GENERATED FROM PYTHON SOURCE LINES 94-97

.. code-block:: Python

    halton = dr.get_halton_draws(sample_size=3, number_of_draws=10)
    pd.DataFrame(halton)






.. raw:: html

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    <div>
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    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>0</th>
          <th>1</th>
          <th>2</th>
          <th>3</th>
          <th>4</th>
          <th>5</th>
          <th>6</th>
          <th>7</th>
          <th>8</th>
          <th>9</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.50000</td>
          <td>0.25000</td>
          <td>0.75000</td>
          <td>0.12500</td>
          <td>0.62500</td>
          <td>0.37500</td>
          <td>0.87500</td>
          <td>0.06250</td>
          <td>0.56250</td>
          <td>0.31250</td>
        </tr>
        <tr>
          <th>1</th>
          <td>0.81250</td>
          <td>0.18750</td>
          <td>0.68750</td>
          <td>0.43750</td>
          <td>0.93750</td>
          <td>0.03125</td>
          <td>0.53125</td>
          <td>0.28125</td>
          <td>0.78125</td>
          <td>0.15625</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.65625</td>
          <td>0.40625</td>
          <td>0.90625</td>
          <td>0.09375</td>
          <td>0.59375</td>
          <td>0.34375</td>
          <td>0.84375</td>
          <td>0.21875</td>
          <td>0.71875</td>
          <td>0.46875</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 98-99

Shuffled Halton sequences.

.. GENERATED FROM PYTHON SOURCE LINES 99-102

.. code-block:: Python

    halton = dr.get_halton_draws(sample_size=3, number_of_draws=10, shuffled=True)
    pd.DataFrame(halton)






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          <th>3</th>
          <th>4</th>
          <th>5</th>
          <th>6</th>
          <th>7</th>
          <th>8</th>
          <th>9</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.25000</td>
          <td>0.12500</td>
          <td>0.28125</td>
          <td>0.46875</td>
          <td>0.53125</td>
          <td>0.59375</td>
          <td>0.09375</td>
          <td>0.31250</td>
          <td>0.81250</td>
          <td>0.21875</td>
        </tr>
        <tr>
          <th>1</th>
          <td>0.71875</td>
          <td>0.78125</td>
          <td>0.50000</td>
          <td>0.37500</td>
          <td>0.93750</td>
          <td>0.62500</td>
          <td>0.87500</td>
          <td>0.90625</td>
          <td>0.40625</td>
          <td>0.65625</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.84375</td>
          <td>0.18750</td>
          <td>0.43750</td>
          <td>0.56250</td>
          <td>0.34375</td>
          <td>0.03125</td>
          <td>0.68750</td>
          <td>0.15625</td>
          <td>0.06250</td>
          <td>0.75000</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 103-105

The above sequences were generated using the default base: 2. It is
possible to generate sequences using different prime numbers.

.. GENERATED FROM PYTHON SOURCE LINES 105-108

.. code-block:: Python

    halton = dr.get_halton_draws(sample_size=1, number_of_draws=10, base=3)
    pd.DataFrame(halton)






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          <th>5</th>
          <th>6</th>
          <th>7</th>
          <th>8</th>
          <th>9</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.333333</td>
          <td>0.666667</td>
          <td>0.111111</td>
          <td>0.444444</td>
          <td>0.777778</td>
          <td>0.222222</td>
          <td>0.555556</td>
          <td>0.888889</td>
          <td>0.037037</td>
          <td>0.37037</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 109-111

It is also possible to skip the first items of the sequence. This is
desirable in the context of Monte-Carlo integration.

.. GENERATED FROM PYTHON SOURCE LINES 111-114

.. code-block:: Python

    halton = dr.get_halton_draws(sample_size=1, number_of_draws=10, base=3, skip=10)
    pd.DataFrame(halton)






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          <th>2</th>
          <th>3</th>
          <th>4</th>
          <th>5</th>
          <th>6</th>
          <th>7</th>
          <th>8</th>
          <th>9</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.703704</td>
          <td>0.148148</td>
          <td>0.481481</td>
          <td>0.814815</td>
          <td>0.259259</td>
          <td>0.592593</td>
          <td>0.925926</td>
          <td>0.074074</td>
          <td>0.407407</td>
          <td>0.740741</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 115-117

Antithetic draws
----------------

.. GENERATED FROM PYTHON SOURCE LINES 119-120

Antithetic draws can be generated from any function generating uniform draws.

.. GENERATED FROM PYTHON SOURCE LINES 120-123

.. code-block:: Python

    draws = dr.get_antithetic(dr.get_uniform, sample_size=3, number_of_draws=10)
    pd.DataFrame(draws)






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          <th>0</th>
          <th>1</th>
          <th>2</th>
          <th>3</th>
          <th>4</th>
          <th>5</th>
          <th>6</th>
          <th>7</th>
          <th>8</th>
          <th>9</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.422126</td>
          <td>0.471794</td>
          <td>0.148715</td>
          <td>0.738601</td>
          <td>0.041052</td>
          <td>0.577874</td>
          <td>0.528206</td>
          <td>0.851285</td>
          <td>0.261399</td>
          <td>0.958948</td>
        </tr>
        <tr>
          <th>1</th>
          <td>0.512323</td>
          <td>0.765719</td>
          <td>0.501317</td>
          <td>0.146468</td>
          <td>0.558539</td>
          <td>0.487677</td>
          <td>0.234281</td>
          <td>0.498683</td>
          <td>0.853532</td>
          <td>0.441461</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.417705</td>
          <td>0.778921</td>
          <td>0.752020</td>
          <td>0.043203</td>
          <td>0.255528</td>
          <td>0.582295</td>
          <td>0.221079</td>
          <td>0.247980</td>
          <td>0.956797</td>
          <td>0.744472</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 124-125

Antithetic MLHS

.. GENERATED FROM PYTHON SOURCE LINES 125-130

.. code-block:: Python

    draws = dr.get_antithetic(
        dr.get_latin_hypercube_draws, sample_size=3, number_of_draws=10
    )
    pd.DataFrame(draws)






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          <th>3</th>
          <th>4</th>
          <th>5</th>
          <th>6</th>
          <th>7</th>
          <th>8</th>
          <th>9</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.078073</td>
          <td>0.313795</td>
          <td>0.158663</td>
          <td>0.015185</td>
          <td>0.421812</td>
          <td>0.921927</td>
          <td>0.686205</td>
          <td>0.841337</td>
          <td>0.984815</td>
          <td>0.578188</td>
        </tr>
        <tr>
          <th>1</th>
          <td>0.478287</td>
          <td>0.769973</td>
          <td>0.244302</td>
          <td>0.612203</td>
          <td>0.906746</td>
          <td>0.521713</td>
          <td>0.230027</td>
          <td>0.755698</td>
          <td>0.387797</td>
          <td>0.093254</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.949357</td>
          <td>0.561688</td>
          <td>0.722550</td>
          <td>0.350440</td>
          <td>0.807525</td>
          <td>0.050643</td>
          <td>0.438312</td>
          <td>0.277450</td>
          <td>0.649560</td>
          <td>0.192475</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 131-132

Antithetic Halton.

.. GENERATED FROM PYTHON SOURCE LINES 132-136

.. code-block:: Python

    draws = dr.get_antithetic(dr.get_halton_draws, sample_size=1, number_of_draws=10)
    pd.DataFrame(draws)







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          <th>2</th>
          <th>3</th>
          <th>4</th>
          <th>5</th>
          <th>6</th>
          <th>7</th>
          <th>8</th>
          <th>9</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.5</td>
          <td>0.25</td>
          <td>0.75</td>
          <td>0.125</td>
          <td>0.625</td>
          <td>0.5</td>
          <td>0.75</td>
          <td>0.25</td>
          <td>0.875</td>
          <td>0.375</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 137-139

As antithetic Halton draws may be correlated, it is a good idea to
skip the first draws.

.. GENERATED FROM PYTHON SOURCE LINES 139-144

.. code-block:: Python

    def uniform_halton(sample_size: int, number_of_draws: int) -> np.ndarray:
        """Function generating uniform draws for the antithetic draws"""
        return dr.get_halton_draws(number_of_draws, sample_size, skip=100)









.. GENERATED FROM PYTHON SOURCE LINES 145-148

.. code-block:: Python

    draws = dr.get_antithetic(uniform_halton, sample_size=3, number_of_draws=10)
    pd.DataFrame(draws)






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          <th>2</th>
          <th>3</th>
          <th>4</th>
          <th>5</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.648438</td>
          <td>0.398438</td>
          <td>0.898438</td>
          <td>0.351562</td>
          <td>0.601562</td>
          <td>0.101562</td>
        </tr>
        <tr>
          <th>1</th>
          <td>0.085938</td>
          <td>0.585938</td>
          <td>0.335938</td>
          <td>0.914062</td>
          <td>0.414062</td>
          <td>0.664062</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.835938</td>
          <td>0.210938</td>
          <td>0.710938</td>
          <td>0.164062</td>
          <td>0.789062</td>
          <td>0.289062</td>
        </tr>
        <tr>
          <th>3</th>
          <td>0.460938</td>
          <td>0.960938</td>
          <td>0.054688</td>
          <td>0.539062</td>
          <td>0.039062</td>
          <td>0.945312</td>
        </tr>
        <tr>
          <th>4</th>
          <td>0.554688</td>
          <td>0.304688</td>
          <td>0.804688</td>
          <td>0.445312</td>
          <td>0.695312</td>
          <td>0.195312</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 149-151

Normal draws
------------

.. GENERATED FROM PYTHON SOURCE LINES 153-156

Generate pseudo-random numbers from a normal distribution N(0,1)
using the Algorithm AS241 Appl. Statist. (1988) Vol. 37, No. 3 by
Wichura

.. GENERATED FROM PYTHON SOURCE LINES 156-159

.. code-block:: Python

    draws = dr.get_normal_wichura_draws(sample_size=3, number_of_draws=10)
    pd.DataFrame(draws)






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          <th>2</th>
          <th>3</th>
          <th>4</th>
          <th>5</th>
          <th>6</th>
          <th>7</th>
          <th>8</th>
          <th>9</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.468384</td>
          <td>0.309445</td>
          <td>-0.727051</td>
          <td>1.477318</td>
          <td>2.324986</td>
          <td>-0.385240</td>
          <td>2.417537</td>
          <td>-0.898517</td>
          <td>1.043511</td>
          <td>-0.527998</td>
        </tr>
        <tr>
          <th>1</th>
          <td>1.928242</td>
          <td>0.392652</td>
          <td>-1.698057</td>
          <td>0.722431</td>
          <td>0.231537</td>
          <td>1.291789</td>
          <td>-0.390652</td>
          <td>0.757420</td>
          <td>-0.111766</td>
          <td>-0.253738</td>
        </tr>
        <tr>
          <th>2</th>
          <td>-1.628487</td>
          <td>0.809681</td>
          <td>-0.477319</td>
          <td>-0.605592</td>
          <td>-1.042455</td>
          <td>2.172230</td>
          <td>-1.201602</td>
          <td>1.831441</td>
          <td>-1.492897</td>
          <td>0.730499</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 160-162

The antithetic version actually generates half of the draws and
complete them with their antithetic version

.. GENERATED FROM PYTHON SOURCE LINES 162-165

.. code-block:: Python

    draws = dr.get_normal_wichura_draws(sample_size=3, number_of_draws=10, antithetic=True)
    pd.DataFrame(draws)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>0</th>
          <th>1</th>
          <th>2</th>
          <th>3</th>
          <th>4</th>
          <th>5</th>
          <th>6</th>
          <th>7</th>
          <th>8</th>
          <th>9</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>-0.397450</td>
          <td>-0.397369</td>
          <td>1.096720</td>
          <td>-0.516517</td>
          <td>0.252910</td>
          <td>0.397450</td>
          <td>0.397369</td>
          <td>-1.096720</td>
          <td>0.516517</td>
          <td>-0.252910</td>
        </tr>
        <tr>
          <th>1</th>
          <td>-0.318315</td>
          <td>0.481563</td>
          <td>0.992685</td>
          <td>0.364958</td>
          <td>0.601621</td>
          <td>0.318315</td>
          <td>-0.481563</td>
          <td>-0.992685</td>
          <td>-0.364958</td>
          <td>-0.601621</td>
        </tr>
        <tr>
          <th>2</th>
          <td>-0.086190</td>
          <td>0.780599</td>
          <td>-0.178448</td>
          <td>0.164590</td>
          <td>-0.035292</td>
          <td>0.086190</td>
          <td>-0.780599</td>
          <td>0.178448</td>
          <td>-0.164590</td>
          <td>0.035292</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 166-170

The user can provide her own series of U[0,1] draws. In this
example, we use the MLHS procedure to generate these draws. Note
that, if the antithetic version is used, only half of the requested
draws must be provided.

.. GENERATED FROM PYTHON SOURCE LINES 170-173

.. code-block:: Python

    my_unif = dr.get_latin_hypercube_draws(sample_size=3, number_of_draws=5)
    pd.DataFrame(my_unif)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>0</th>
          <th>1</th>
          <th>2</th>
          <th>3</th>
          <th>4</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.730781</td>
          <td>0.974142</td>
          <td>0.544797</td>
          <td>0.090617</td>
          <td>0.654064</td>
        </tr>
        <tr>
          <th>1</th>
          <td>0.528956</td>
          <td>0.221999</td>
          <td>0.009099</td>
          <td>0.420511</td>
          <td>0.877654</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.154954</td>
          <td>0.848118</td>
          <td>0.760657</td>
          <td>0.335545</td>
          <td>0.326175</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 174-179

.. code-block:: Python

    draws = dr.get_normal_wichura_draws(
        sample_size=3, number_of_draws=10, uniform_numbers=my_unif, antithetic=True
    )
    pd.DataFrame(draws)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>0</th>
          <th>1</th>
          <th>2</th>
          <th>3</th>
          <th>4</th>
          <th>5</th>
          <th>6</th>
          <th>7</th>
          <th>8</th>
          <th>9</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.615176</td>
          <td>1.945487</td>
          <td>0.112528</td>
          <td>-1.336963</td>
          <td>0.396315</td>
          <td>-0.615176</td>
          <td>-1.945487</td>
          <td>-0.112528</td>
          <td>1.336963</td>
          <td>-0.396315</td>
        </tr>
        <tr>
          <th>1</th>
          <td>0.072645</td>
          <td>-0.765461</td>
          <td>-2.361127</td>
          <td>-0.200585</td>
          <td>1.163339</td>
          <td>-0.072645</td>
          <td>0.765461</td>
          <td>2.361127</td>
          <td>0.200585</td>
          <td>-1.163339</td>
        </tr>
        <tr>
          <th>2</th>
          <td>-1.015414</td>
          <td>1.028396</td>
          <td>0.708416</td>
          <td>-0.424651</td>
          <td>-0.450501</td>
          <td>1.015414</td>
          <td>-1.028396</td>
          <td>-0.708416</td>
          <td>0.424651</td>
          <td>0.450501</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 180-181

The same with Halton draws.

.. GENERATED FROM PYTHON SOURCE LINES 181-184

.. code-block:: Python

    my_unif = dr.get_halton_draws(sample_size=2, number_of_draws=5, base=3, skip=10)
    pd.DataFrame(my_unif)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>0</th>
          <th>1</th>
          <th>2</th>
          <th>3</th>
          <th>4</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.703704</td>
          <td>0.148148</td>
          <td>0.481481</td>
          <td>0.814815</td>
          <td>0.259259</td>
        </tr>
        <tr>
          <th>1</th>
          <td>0.592593</td>
          <td>0.925926</td>
          <td>0.074074</td>
          <td>0.407407</td>
          <td>0.740741</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 185-189

.. code-block:: Python

    draws = dr.get_normal_wichura_draws(
        number_of_draws=10, sample_size=2, uniform_numbers=my_unif, antithetic=True
    )
    pd.DataFrame(draws)





.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
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          <th>1</th>
          <th>2</th>
          <th>3</th>
          <th>4</th>
          <th>5</th>
          <th>6</th>
          <th>7</th>
          <th>8</th>
          <th>9</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.535083</td>
          <td>-1.044409</td>
          <td>-0.046436</td>
          <td>0.895780</td>
          <td>-0.645631</td>
          <td>-0.535083</td>
          <td>1.044409</td>
          <td>0.046436</td>
          <td>-0.895780</td>
          <td>0.645631</td>
        </tr>
        <tr>
          <th>1</th>
          <td>0.234219</td>
          <td>1.446104</td>
          <td>-1.446104</td>
          <td>-0.234219</td>
          <td>0.645631</td>
          <td>-0.234219</td>
          <td>-1.446104</td>
          <td>1.446104</td>
          <td>0.234219</td>
          <td>-0.645631</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />


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

   **Total running time of the script:** (0 minutes 0.017 seconds)


.. _sphx_glr_download_auto_examples_programmers_plot_draws.py:

.. only:: html

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

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_draws.zip <plot_draws.zip>`


.. only:: html

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

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