.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/plot_OT_1D.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_OT_1D.py: ====================================== Optimal Transport for 1D distributions ====================================== This example illustrates the computation of EMD and Sinkhorn transport plans and their visualization. .. GENERATED FROM PYTHON SOURCE LINES 11-23 .. code-block:: Python # Author: Remi Flamary # # License: MIT License # sphinx_gallery_thumbnail_number = 3 import numpy as np import matplotlib.pylab as pl import ot import ot.plot from ot.datasets import make_1D_gauss as gauss .. GENERATED FROM PYTHON SOURCE LINES 24-26 Generate data ------------- .. GENERATED FROM PYTHON SOURCE LINES 29-44 .. code-block:: Python n = 100 # nb bins # bin positions x = np.arange(n, dtype=np.float64) # Gaussian distributions a = gauss(n, m=20, s=5) # m= mean, s= std b = gauss(n, m=60, s=10) # loss matrix M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1))) M /= M.max() .. GENERATED FROM PYTHON SOURCE LINES 45-47 Plot distributions and loss matrix ---------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 49-55 .. code-block:: Python pl.figure(1, figsize=(6.4, 3)) pl.plot(x, a, 'b', label='Source distribution') pl.plot(x, b, 'r', label='Target distribution') pl.legend() .. image-sg:: /auto_examples/images/sphx_glr_plot_OT_1D_001.png :alt: plot OT 1D :srcset: /auto_examples/images/sphx_glr_plot_OT_1D_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 56-60 .. code-block:: Python pl.figure(2, figsize=(5, 5)) ot.plot.plot1D_mat(a, b, M, 'Cost matrix M') .. image-sg:: /auto_examples/images/sphx_glr_plot_OT_1D_002.png :alt: Cost matrix M :srcset: /auto_examples/images/sphx_glr_plot_OT_1D_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 61-63 Solve EMD --------- .. GENERATED FROM PYTHON SOURCE LINES 66-76 .. code-block:: Python # use fast 1D solver G0 = ot.emd_1d(x, x, a, b) # Equivalent to # G0 = ot.emd(a, b, M) pl.figure(3, figsize=(5, 5)) ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0') .. image-sg:: /auto_examples/images/sphx_glr_plot_OT_1D_003.png :alt: OT matrix G0 :srcset: /auto_examples/images/sphx_glr_plot_OT_1D_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 77-79 Solve Sinkhorn -------------- .. GENERATED FROM PYTHON SOURCE LINES 82-90 .. code-block:: Python lambd = 1e-3 Gs = ot.sinkhorn(a, b, M, lambd, verbose=True) pl.figure(4, figsize=(5, 5)) ot.plot.plot1D_mat(a, b, Gs, 'OT matrix Sinkhorn') pl.show() .. image-sg:: /auto_examples/images/sphx_glr_plot_OT_1D_004.png :alt: OT matrix Sinkhorn :srcset: /auto_examples/images/sphx_glr_plot_OT_1D_004.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none It. |Err ------------------- 0|2.861463e-01| 10|1.860154e-01| 20|8.144529e-02| 30|3.130143e-02| 40|1.178815e-02| 50|4.426078e-03| 60|1.661047e-03| 70|6.233110e-04| 80|2.338932e-04| 90|8.776627e-05| 100|3.293340e-05| 110|1.235791e-05| 120|4.637176e-06| 130|1.740051e-06| 140|6.529356e-07| 150|2.450071e-07| 160|9.193632e-08| 170|3.449812e-08| 180|1.294505e-08| 190|4.857493e-09| It. |Err ------------------- 200|1.822723e-09| .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.628 seconds) .. _sphx_glr_download_auto_examples_plot_OT_1D.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_OT_1D.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_OT_1D.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_