.. _sphx_glr_auto_examples_plot_otda_linear_mapping.py:


============================
Linear OT mapping estimation
============================





.. code-block:: python


    # Author: Remi Flamary <remi.flamary@unice.fr>
    #
    # License: MIT License

    import numpy as np
    import pylab as pl
    import ot







Generate data
-------------



.. code-block:: python


    n = 1000
    d = 2
    sigma = .1

    # source samples
    angles = np.random.rand(n, 1) * 2 * np.pi
    xs = np.concatenate((np.sin(angles), np.cos(angles)),
                        axis=1) + sigma * np.random.randn(n, 2)
    xs[:n // 2, 1] += 2


    # target samples
    anglet = np.random.rand(n, 1) * 2 * np.pi
    xt = np.concatenate((np.sin(anglet), np.cos(anglet)),
                        axis=1) + sigma * np.random.randn(n, 2)
    xt[:n // 2, 1] += 2


    A = np.array([[1.5, .7], [.7, 1.5]])
    b = np.array([[4, 2]])
    xt = xt.dot(A) + b







Plot data
---------



.. code-block:: python


    pl.figure(1, (5, 5))
    pl.plot(xs[:, 0], xs[:, 1], '+')
    pl.plot(xt[:, 0], xt[:, 1], 'o')





.. image:: /auto_examples/images/sphx_glr_plot_otda_linear_mapping_001.png
    :align: center




Estimate linear mapping and transport
-------------------------------------



.. code-block:: python


    Ae, be = ot.da.OT_mapping_linear(xs, xt)

    xst = xs.dot(Ae) + be








Plot transported samples
------------------------



.. code-block:: python


    pl.figure(1, (5, 5))
    pl.clf()
    pl.plot(xs[:, 0], xs[:, 1], '+')
    pl.plot(xt[:, 0], xt[:, 1], 'o')
    pl.plot(xst[:, 0], xst[:, 1], '+')

    pl.show()




.. image:: /auto_examples/images/sphx_glr_plot_otda_linear_mapping_002.png
    :align: center




Load image data
---------------



.. code-block:: python



    def im2mat(I):
        """Converts and image to matrix (one pixel per line)"""
        return I.reshape((I.shape[0] * I.shape[1], I.shape[2]))


    def mat2im(X, shape):
        """Converts back a matrix to an image"""
        return X.reshape(shape)


    def minmax(I):
        return np.clip(I, 0, 1)


    # Loading images
    I1 = pl.imread('../data/ocean_day.jpg').astype(np.float64) / 256
    I2 = pl.imread('../data/ocean_sunset.jpg').astype(np.float64) / 256


    X1 = im2mat(I1)
    X2 = im2mat(I2)







Estimate mapping and adapt
----------------------------



.. code-block:: python


    mapping = ot.da.LinearTransport()

    mapping.fit(Xs=X1, Xt=X2)


    xst = mapping.transform(Xs=X1)
    xts = mapping.inverse_transform(Xt=X2)

    I1t = minmax(mat2im(xst, I1.shape))
    I2t = minmax(mat2im(xts, I2.shape))

    # %%








Plot transformed images
-----------------------



.. code-block:: python


    pl.figure(2, figsize=(10, 7))

    pl.subplot(2, 2, 1)
    pl.imshow(I1)
    pl.axis('off')
    pl.title('Im. 1')

    pl.subplot(2, 2, 2)
    pl.imshow(I2)
    pl.axis('off')
    pl.title('Im. 2')

    pl.subplot(2, 2, 3)
    pl.imshow(I1t)
    pl.axis('off')
    pl.title('Mapping Im. 1')

    pl.subplot(2, 2, 4)
    pl.imshow(I2t)
    pl.axis('off')
    pl.title('Inverse mapping Im. 2')



.. image:: /auto_examples/images/sphx_glr_plot_otda_linear_mapping_004.png
    :align: center




**Total running time of the script:** ( 0 minutes  0.635 seconds)



.. only :: html

 .. container:: sphx-glr-footer


  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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