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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_graphs_plot_graphs_loglikelihood_contour.py>`
        to download the full example code.

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

.. _sphx_glr_auto_graphs_plot_graphs_loglikelihood_contour.py:


Plot the log-likelihood contours of a distribution
==================================================

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In this example, we show how to plot the bidimensionnal log-likelihood contours of function given a sample.

.. GENERATED FROM PYTHON SOURCE LINES 10-18

.. code-block:: Python

    from matplotlib import pylab as plt
    import openturns.viewer as viewer
    import openturns as ot

    ot.RandomGenerator.SetSeed(0)
    ot.Log.Show(ot.Log.NONE)
    ot.ResourceMap.SetAsString("Contour-DefaultColorMap", "viridis")








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Generate a sample
-----------------

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We create a `TruncatedNormal` and generate a small sample.

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.. code-block:: Python

    a = -1
    b = 2.5
    mu = 2.0
    sigma = 3.0
    distribution = ot.TruncatedNormal(mu, sigma, a, b)
    sample = distribution.getSample(11)








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In order to see the distribution and the sample, we draw the PDF of the distribution and generate a clouds which X coordinates are the sample values.

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.. code-block:: Python

    graph = distribution.drawPDF()
    graph.setLegends(["TruncatedNormal"])
    graph.setColors(["red"])
    zeros = ot.Sample(sample.getSize(), 1)
    cloud = ot.Cloud(sample, zeros)
    cloud.setLegend("Sample")
    graph.add(cloud)
    graph.setLegendPosition("upper left")
    view = viewer.View(graph)





.. image-sg:: /auto_graphs/images/sphx_glr_plot_graphs_loglikelihood_contour_001.png
   :alt: plot graphs loglikelihood contour
   :srcset: /auto_graphs/images/sphx_glr_plot_graphs_loglikelihood_contour_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 49-52

The following function computes the log-likelihood of a `TruncatedNormal`
which mean and standard deviations are given as input arguments.
The lower and upper bounds of the distribution are computed as minimum and maximum of the sample.

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Define the log-likelihood function
----------------------------------

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The following function evaluates the log-likelihood function given a point :math:`X=(\mu,\sigma`).
In order to evaluate the likelihood on the sample, we use a trick: we evaluate
the `computeMean` method on the log-PDF sample, then multiply by the sample size.
This is much faster than using a `for` loop.

.. GENERATED FROM PYTHON SOURCE LINES 65-83

.. code-block:: Python

    def logLikelihood(X):
        """
        Evaluate the log-likelihood of a TruncatedNormal on a sample.
        """
        samplesize = sample.getSize()
        mu = X[0]
        sigma = X[1]
        a = sample.getMin()[0]
        b = sample.getMax()[0]
        delta = (b - a) / samplesize
        a -= delta
        b += delta
        distribution = ot.TruncatedNormal(mu, sigma, a, b)
        samplelogpdf = distribution.computeLogPDF(sample)
        loglikelihood = samplelogpdf.computeMean() * samplesize
        return loglikelihood









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With the draw method
--------------------

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In this section, we use the `draw` method which is available for any `Function` which has 1 or 2 input arguments.
In our case, the log-likelihood function has two inputs: :math:`x_0=\mu` and :math:`x_1=\sigma`.

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Draw the log-likelihood function with the `draw` method: this is much faster than using a `for` loop.
In order to print LaTeX X and Y labels, we use the `"r"` character in front of the string containing the LaTeX command.

.. GENERATED FROM PYTHON SOURCE LINES 96-102

.. code-block:: Python

    logLikelihoodFunction = ot.PythonFunction(2, 1, logLikelihood)
    graphBasic = logLikelihoodFunction.draw([-3.0, 0.1], [5.0, 7.0], [50] * 2)
    graphBasic.setXTitle(r"$\mu$")
    graphBasic.setYTitle(r"$\sigma$")
    view = viewer.View(graphBasic)




.. image-sg:: /auto_graphs/images/sphx_glr_plot_graphs_loglikelihood_contour_002.png
   :alt: y0 as a function of (x0,x1)
   :srcset: /auto_graphs/images/sphx_glr_plot_graphs_loglikelihood_contour_002.png
   :class: sphx-glr-single-img





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Customizing the number of levels
--------------------------------

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The level values are computed from the quantiles of the data, so that the contours are equally spaced.
We can configure the number of levels by setting the `Contour-DefaultLevelsNumber` key in the `ResourceMap`.

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.. code-block:: Python

    ot.ResourceMap.SetAsUnsignedInteger("Contour-DefaultLevelsNumber", 5)
    logLikelihoodFunction = ot.PythonFunction(2, 1, logLikelihood)
    graphBasic = logLikelihoodFunction.draw([-3.0, 0.1], [5.0, 7.0], [50] * 2)
    graphBasic.setXTitle(r"$\mu$")
    graphBasic.setYTitle(r"$\sigma$")
    view = viewer.View(graphBasic)




.. image-sg:: /auto_graphs/images/sphx_glr_plot_graphs_loglikelihood_contour_003.png
   :alt: y0 as a function of (x0,x1)
   :srcset: /auto_graphs/images/sphx_glr_plot_graphs_loglikelihood_contour_003.png
   :class: sphx-glr-single-img





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We get the underlying `Contour` object as a `Drawable`.

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.. code-block:: Python


    contour = graphBasic.getDrawable(0)








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To be able to use specific `Contour` methods like `buildDefaultLevels`, we need to use `getImplementation`.

.. GENERATED FROM PYTHON SOURCE LINES 125-133

.. code-block:: Python


    contour = contour.getImplementation()
    contour.buildDefaultLevels(50)

    manyLevelGraph = ot.Graph()
    manyLevelGraph.add(contour)
    view = viewer.View(manyLevelGraph)




.. image-sg:: /auto_graphs/images/sphx_glr_plot_graphs_loglikelihood_contour_004.png
   :alt: plot graphs loglikelihood contour
   :srcset: /auto_graphs/images/sphx_glr_plot_graphs_loglikelihood_contour_004.png
   :class: sphx-glr-single-img





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Using a rank-based normalization of the colors
----------------------------------------------
%%
In the previous plots, there was little color variation for isolines corresponding to high log-likelihood values.
This is due to a steep cliff visible for low values of :math:`\sigma`.
To make the color variation clearer around -13, we use a normalization based on the rank of the level curve and not on its value.

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.. code-block:: Python

    contour.setColorMapNorm("rank")
    rankGraph = ot.Graph()
    rankGraph.add(contour)
    view = viewer.View(rankGraph)




.. image-sg:: /auto_graphs/images/sphx_glr_plot_graphs_loglikelihood_contour_005.png
   :alt: plot graphs loglikelihood contour
   :srcset: /auto_graphs/images/sphx_glr_plot_graphs_loglikelihood_contour_005.png
   :class: sphx-glr-single-img





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Fill the contour graph
----------------------

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Areas between contour lines can be colored by requesting a filled outline.

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.. code-block:: Python


    # sphinx_gallery_thumbnail_number = 6
    contour.setIsFilled(True)
    filledGraph = ot.Graph()
    filledGraph.add(contour)
    view = viewer.View(filledGraph)




.. image-sg:: /auto_graphs/images/sphx_glr_plot_graphs_loglikelihood_contour_006.png
   :alt: plot graphs loglikelihood contour
   :srcset: /auto_graphs/images/sphx_glr_plot_graphs_loglikelihood_contour_006.png
   :class: sphx-glr-single-img





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Getting the level values
------------------------

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The level values can be retrieved with the `getLevels` method.

.. GENERATED FROM PYTHON SOURCE LINES 166-170

.. code-block:: Python

    drawables = graphBasic.getDrawables()
    levels = drawables[0].getLevels()
    levels






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    class=Point name=Unnamed dimension=5 values=[-37.5422,-13.7386,-13.1559,-13.0795,-13.0552]
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 171-173

Monochrome contour plot
-----------------------

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We first configure the contour plot.
We use the `getDrawable` method to take the first contour as the only one with multiple levels.
Then we use the `setLevels` method: we could have changed the levels.
We use the `setColor` method to get a monochrome contour.
In order to inline the level values labels, we use the `setDrawLabels` method.

.. GENERATED FROM PYTHON SOURCE LINES 182-187

.. code-block:: Python

    contour = graphBasic.getDrawable(0)
    contour.setLevels(levels)
    contour.setDrawLabels(True)
    contour.setColor("red")








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Hide the color bar.
The method to do this is not available to generic Drawables,
so we need to get the actual `Contour` object.

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.. code-block:: Python


    contour = contour.getImplementation()
    contour.setColorBarPosition("")








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Then we create a new graph. Finally, we use `setDrawables` to define this `Contour` object as the single Drawable.

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.. code-block:: Python


    graphFineTune = ot.Graph("Log-Likelihood", r"$\mu$", r"$\sigma$", True, "")
    graphFineTune.setDrawables([contour])
    view = viewer.View(graphFineTune)




.. image-sg:: /auto_graphs/images/sphx_glr_plot_graphs_loglikelihood_contour_007.png
   :alt: Log-Likelihood
   :srcset: /auto_graphs/images/sphx_glr_plot_graphs_loglikelihood_contour_007.png
   :class: sphx-glr-single-img





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Set multiple colors manually
----------------------------

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The `Contour` class does not allow us to manually set multiple colors.
Here we show how to assign explicit colors to the different contour lines by passing keyword
arguments to the `viewer.View` class.

.. GENERATED FROM PYTHON SOURCE LINES 210-217

.. code-block:: Python


    # Build a range of colors corresponding to the Tableau palette
    palette = ot.Drawable.BuildTableauPalette(len(levels))
    view = viewer.View(graphFineTune, contour_kw={"colors": palette, "cmap": None})

    plt.show()




.. image-sg:: /auto_graphs/images/sphx_glr_plot_graphs_loglikelihood_contour_008.png
   :alt: Log-Likelihood
   :srcset: /auto_graphs/images/sphx_glr_plot_graphs_loglikelihood_contour_008.png
   :class: sphx-glr-single-img





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Reset default settings

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.. code-block:: Python

    ot.ResourceMap.Reload()








.. _sphx_glr_download_auto_graphs_plot_graphs_loglikelihood_contour.py:

.. only:: html

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

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

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

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

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