.. 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 16-21

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 22-23

Version of Biogeme.

.. GENERATED FROM PYTHON SOURCE LINES 23-25

.. code-block:: default

    print(getText())





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

 .. code-block:: none

    biogeme 3.2.13 [2023-12-23]
    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 26-27

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

.. GENERATED FROM PYTHON SOURCE LINES 27-29

.. code-block:: default

    np.random.seed(90267)








.. GENERATED FROM PYTHON SOURCE LINES 30-32

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

.. GENERATED FROM PYTHON SOURCE LINES 34-35

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

.. GENERATED FROM PYTHON SOURCE LINES 35-38

.. code-block:: default

    draws = dr.getUniform(sample_size=3, number_of_draws=10, symmetric=False)
    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 {
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          <th>2</th>
          <th>3</th>
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          <th>5</th>
          <th>6</th>
          <th>7</th>
          <th>8</th>
          <th>9</th>
        </tr>
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      <tbody>
        <tr>
          <th>0</th>
          <td>0.406996</td>
          <td>0.952091</td>
          <td>0.393300</td>
          <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 39-42

.. code-block:: default

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






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
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          <th>6</th>
          <th>7</th>
          <th>8</th>
          <th>9</th>
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      <tbody>
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          <th>0</th>
          <td>0.541595</td>
          <td>-0.613439</td>
          <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 43-46

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 48-51

.. code-block:: default

    latin_hypercube = dr.getLatinHypercubeDraws(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>
        .dataframe tbody tr th:only-of-type {
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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>0.325211</td>
          <td>0.630001</td>
          <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 52-53

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

.. GENERATED FROM PYTHON SOURCE LINES 55-60

.. code-block:: default

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






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
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          <td>-0.997732</td>
          <td>0.685466</td>
          <td>-0.929016</td>
          <td>0.815377</td>
          <td>0.060902</td>
          <td>-0.703703</td>
          <td>-0.660290</td>
        </tr>
        <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>
        </tr>
        <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 61-62

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

.. GENERATED FROM PYTHON SOURCE LINES 62-65

.. code-block:: default

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






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
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        <tr>
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          <td>0.201607</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.779832</td>
        </tr>
        <tr>
          <th>3</th>
          <td>0.602527</td>
        </tr>
        <tr>
          <th>4</th>
          <td>0.696678</td>
        </tr>
        <tr>
          <th>5</th>
          <td>0.764274</td>
        </tr>
        <tr>
          <th>6</th>
          <td>0.568655</td>
        </tr>
        <tr>
          <th>7</th>
          <td>0.371194</td>
        </tr>
        <tr>
          <th>8</th>
          <td>0.233237</td>
        </tr>
        <tr>
          <th>9</th>
          <td>0.023673</td>
        </tr>
        <tr>
          <th>10</th>
          <td>0.339896</td>
        </tr>
        <tr>
          <th>11</th>
          <td>0.060995</td>
        </tr>
        <tr>
          <th>12</th>
          <td>0.221347</td>
        </tr>
        <tr>
          <th>13</th>
          <td>0.476015</td>
        </tr>
        <tr>
          <th>14</th>
          <td>0.866055</td>
        </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 66-71

.. code-block:: default

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






.. raw:: html

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    <div>
    <style scoped>
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          <th>7</th>
          <th>8</th>
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          <td>0.407378</td>
          <td>0.274441</td>
          <td>0.628585</td>
          <td>0.901100</td>
          <td>0.596822</td>
          <td>0.300789</td>
          <td>0.245706</td>
          <td>0.218955</td>
        </tr>
        <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 72-73

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

.. GENERATED FROM PYTHON SOURCE LINES 73-76

.. code-block:: default

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






.. raw:: html

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          <th>5</th>
          <th>6</th>
          <th>7</th>
          <th>8</th>
          <th>9</th>
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      <tbody>
        <tr>
          <th>0</th>
          <td>0.429347</td>
          <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 77-82

.. code-block:: default

    latin_hypercube = dr.getLatinHypercubeDraws(
        sample_size=3, number_of_draws=10, uniformNumbers=my_unif
    )
    pd.DataFrame(latin_hypercube)






.. raw:: html

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          <th>8</th>
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          <td>0.493108</td>
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          <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 83-85

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

.. GENERATED FROM PYTHON SOURCE LINES 87-88

One Halton sequence.

.. GENERATED FROM PYTHON SOURCE LINES 88-91

.. code-block:: default

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






.. raw:: html

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    <div>
    <style scoped>
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    <table border="1" class="dataframe">
      <thead>
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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 92-93

Several Halton sequences.

.. GENERATED FROM PYTHON SOURCE LINES 93-96

.. code-block:: default

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






.. raw:: html

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    <div>
    <style scoped>
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        }

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    </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>0.50000</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 97-98

Shuffled Halton sequences.

.. GENERATED FROM PYTHON SOURCE LINES 98-101

.. code-block:: default

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






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    <div>
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          <th></th>
          <th>0</th>
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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>0.25000</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 102-104

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 104-107

.. code-block:: default

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






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          <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>0.37037</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 108-110

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 110-113

.. code-block:: default

    halton = dr.getHaltonDraws(sample_size=1, number_of_draws=10, base=3, skip=10)
    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>0.703704</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 114-116

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

.. GENERATED FROM PYTHON SOURCE LINES 118-119

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

.. GENERATED FROM PYTHON SOURCE LINES 119-122

.. code-block:: default

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






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          <th></th>
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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>0.422126</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 123-124

Antithetic MLHS

.. GENERATED FROM PYTHON SOURCE LINES 124-127

.. code-block:: default

    draws = dr.getAntithetic(dr.getLatinHypercubeDraws, 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>0.078073</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 128-129

Antithetic Halton.

.. GENERATED FROM PYTHON SOURCE LINES 129-133

.. code-block:: default

    draws = dr.getAntithetic(dr.getHaltonDraws, 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 134-136

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

.. GENERATED FROM PYTHON SOURCE LINES 136-141

.. code-block:: default

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









.. GENERATED FROM PYTHON SOURCE LINES 142-145

.. code-block:: default

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






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          <th></th>
          <th>0</th>
          <th>1</th>
          <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 146-148

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

.. GENERATED FROM PYTHON SOURCE LINES 150-153

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 153-156

.. code-block:: default

    draws = dr.getNormalWichuraDraws(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 157-159

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

.. GENERATED FROM PYTHON SOURCE LINES 159-162

.. code-block:: default

    draws = dr.getNormalWichuraDraws(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 163-167

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 167-170

.. code-block:: default

    my_unif = dr.getLatinHypercubeDraws(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 171-176

.. code-block:: default

    draws = dr.getNormalWichuraDraws(
        sample_size=3, number_of_draws=10, uniformNumbers=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 177-178

The same with Halton draws.

.. GENERATED FROM PYTHON SOURCE LINES 178-181

.. code-block:: default

    my_unif = dr.getHaltonDraws(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 182-186

.. code-block:: default

    draws = dr.getNormalWichuraDraws(
        number_of_draws=10, sample_size=2, uniformNumbers=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;
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    </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>0.535083</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 0.020 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-python

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

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

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


.. only:: html

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

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