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+
+
+.. _sphx_glr_auto_examples_plot_otda_linear_mapping.py:
+
+
+Created on Tue Mar 20 14:31:15 2018
+
+@author: rflamary
+
+
+
+.. code-block:: python
+
+
+    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  0.563 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
+
+    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_