.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/plot_compute_emd.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_plot_compute_emd.py: ================== OT distances in 1D ================== Shows how to compute multiple Wasserstein and Sinkhorn with two different ground metrics and plot their values for different distributions. .. GENERATED FROM PYTHON SOURCE LINES 12-25 .. code-block:: Python # Author: Remi Flamary # # License: MIT License # sphinx_gallery_thumbnail_number = 2 import numpy as np import matplotlib.pylab as pl import ot from ot.datasets import make_1D_gauss as gauss .. GENERATED FROM PYTHON SOURCE LINES 26-28 Generate data ------------- .. GENERATED FROM PYTHON SOURCE LINES 30-54 .. code-block:: Python n = 100 # nb bins n_target = 20 # nb target distributions # bin positions x = np.arange(n, dtype=np.float64) lst_m = np.linspace(20, 90, n_target) # Gaussian distributions a = gauss(n, m=20, s=5) # m= mean, s= std B = np.zeros((n, n_target)) for i, m in enumerate(lst_m): B[:, i] = gauss(n, m=m, s=5) # loss matrix and normalization M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), 'euclidean') M /= M.max() * 0.1 M2 = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), 'sqeuclidean') M2 /= M2.max() * 0.1 .. GENERATED FROM PYTHON SOURCE LINES 55-57 Plot data --------- .. GENERATED FROM PYTHON SOURCE LINES 59-72 .. code-block:: Python pl.figure(1) pl.subplot(2, 1, 1) pl.plot(x, a, 'r', label='Source distribution') pl.title('Source distribution') pl.subplot(2, 1, 2) for i in range(n_target): pl.plot(x, B[:, i], 'b', alpha=i / n_target) pl.plot(x, B[:, -1], 'b', label='Target distributions') pl.title('Target distributions') pl.tight_layout() .. image-sg:: /auto_examples/images/sphx_glr_plot_compute_emd_001.png :alt: Source distribution, Target distributions :srcset: /auto_examples/images/sphx_glr_plot_compute_emd_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 73-75 Compute EMD for the different losses ------------------------------------ .. GENERATED FROM PYTHON SOURCE LINES 77-101 .. code-block:: Python d_emd = ot.emd2(a, B, M) # direct computation of OT loss d_emd2 = ot.emd2(a, B, M2) # direct computation of OT loss with metric M2 d_tv = [np.sum(abs(a - B[:, i])) for i in range(n_target)] pl.figure(2) pl.subplot(2, 1, 1) pl.plot(x, a, 'r', label='Source distribution') pl.title('Distributions') for i in range(n_target): pl.plot(x, B[:, i], 'b', alpha=i / n_target) pl.plot(x, B[:, -1], 'b', label='Target distributions') pl.ylim((-.01, 0.13)) pl.xticks(()) pl.legend() pl.subplot(2, 1, 2) pl.plot(d_emd, label='Euclidean OT') pl.plot(d_emd2, label='Squared Euclidean OT') pl.plot(d_tv, label='Total Variation (TV)') #pl.xlim((-7,23)) pl.xlabel('Displacement') pl.title('Divergences') pl.legend() .. image-sg:: /auto_examples/images/sphx_glr_plot_compute_emd_002.png :alt: Distributions, Divergences :srcset: /auto_examples/images/sphx_glr_plot_compute_emd_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 102-104 Compute Sinkhorn for the different losses ----------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 106-133 .. code-block:: Python reg = 1e-1 d_sinkhorn = ot.sinkhorn2(a, B, M, reg) d_sinkhorn2 = ot.sinkhorn2(a, B, M2, reg) pl.figure(3) pl.clf() pl.subplot(2, 1, 1) pl.plot(x, a, 'r', label='Source distribution') pl.title('Distributions') for i in range(n_target): pl.plot(x, B[:, i], 'b', alpha=i / n_target) pl.plot(x, B[:, -1], 'b', label='Target distributions') pl.ylim((-.01, 0.13)) pl.xticks(()) pl.legend() pl.subplot(2, 1, 2) pl.plot(d_emd, label='Euclidean OT') pl.plot(d_emd2, label='Squared Euclidean OT') pl.plot(d_sinkhorn, '+', label='Euclidean Sinkhorn') pl.plot(d_sinkhorn2, '+', label='Squared Euclidean Sinkhorn') pl.plot(d_tv, label='Total Variation (TV)') #pl.xlim((-7,23)) pl.xlabel('Displacement') pl.title('Divergences') pl.legend() pl.show() .. image-sg:: /auto_examples/images/sphx_glr_plot_compute_emd_003.png :alt: Distributions, Divergences :srcset: /auto_examples/images/sphx_glr_plot_compute_emd_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.601 seconds) .. _sphx_glr_download_auto_examples_plot_compute_emd.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_compute_emd.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_compute_emd.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_