.. only:: html

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

        Click :ref:`here <sphx_glr_download_gallery_scales_scales.py>`     to download the full example code
    .. rst-class:: sphx-glr-example-title

    .. _sphx_glr_gallery_scales_scales.py:


======
Scales
======

Illustrate the scale transformations applied to axes, e.g. log, symlog, logit.

The last two examples are examples of using the ``'function'`` scale by
supplying forward and inverse functions for the scale transformation.


.. code-block:: default


    import numpy as np
    import matplotlib.pyplot as plt
    from matplotlib.ticker import NullFormatter, FixedLocator

    # Fixing random state for reproducibility
    np.random.seed(19680801)

    # make up some data in the interval ]0, 1[
    y = np.random.normal(loc=0.5, scale=0.4, size=1000)
    y = y[(y > 0) & (y < 1)]
    y.sort()
    x = np.arange(len(y))

    # plot with various axes scales
    fig, axs = plt.subplots(3, 2, figsize=(6, 8),
                            constrained_layout=True)

    # linear
    ax = axs[0, 0]
    ax.plot(x, y)
    ax.set_yscale('linear')
    ax.set_title('linear')
    ax.grid(True)


    # log
    ax = axs[0, 1]
    ax.plot(x, y)
    ax.set_yscale('log')
    ax.set_title('log')
    ax.grid(True)


    # symmetric log
    ax = axs[1, 1]
    ax.plot(x, y - y.mean())
    ax.set_yscale('symlog', linthresh=0.02)
    ax.set_title('symlog')
    ax.grid(True)

    # logit
    ax = axs[1, 0]
    ax.plot(x, y)
    ax.set_yscale('logit')
    ax.set_title('logit')
    ax.grid(True)


    # Function x**(1/2)
    def forward(x):
        return x**(1/2)


    def inverse(x):
        return x**2


    ax = axs[2, 0]
    ax.plot(x, y)
    ax.set_yscale('function', functions=(forward, inverse))
    ax.set_title('function: $x^{1/2}$')
    ax.grid(True)
    ax.yaxis.set_major_locator(FixedLocator(np.arange(0, 1, 0.2)**2))
    ax.yaxis.set_major_locator(FixedLocator(np.arange(0, 1, 0.2)))


    # Function Mercator transform
    def forward(a):
        a = np.deg2rad(a)
        return np.rad2deg(np.log(np.abs(np.tan(a) + 1.0 / np.cos(a))))


    def inverse(a):
        a = np.deg2rad(a)
        return np.rad2deg(np.arctan(np.sinh(a)))

    ax = axs[2, 1]

    t = np.arange(0, 170.0, 0.1)
    s = t / 2.

    ax.plot(t, s, '-', lw=2)

    ax.set_yscale('function', functions=(forward, inverse))
    ax.set_title('function: Mercator')
    ax.grid(True)
    ax.set_xlim([0, 180])
    ax.yaxis.set_minor_formatter(NullFormatter())
    ax.yaxis.set_major_locator(FixedLocator(np.arange(0, 90, 10)))

    plt.show()




.. image:: /gallery/scales/images/sphx_glr_scales_001.png
    :alt: linear, log, logit, symlog, function: $x^{1/2}$, function: Mercator
    :class: sphx-glr-single-img





------------

References
""""""""""

The use of the following functions, methods, classes and modules is shown
in this example:


.. code-block:: default


    import matplotlib
    matplotlib.axes.Axes.set_yscale
    matplotlib.axes.Axes.set_xscale
    matplotlib.axis.Axis.set_major_locator
    matplotlib.scale.LogitScale
    matplotlib.scale.LogScale
    matplotlib.scale.LinearScale
    matplotlib.scale.SymmetricalLogScale
    matplotlib.scale.FuncScale








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

   **Total running time of the script:** ( 0 minutes  1.642 seconds)


.. _sphx_glr_download_gallery_scales_scales.py:


.. only :: html

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



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

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



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

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


.. only:: html

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

    Keywords: matplotlib code example, codex, python plot, pyplot
    `Gallery generated by Sphinx-Gallery
    <https://sphinx-gallery.readthedocs.io>`_