.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/unbalanced-partial/plot_UOT_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_unbalanced-partial_plot_UOT_1D.py: =============================== 1D Unbalanced optimal transport =============================== This example illustrates the computation of Unbalanced Optimal transport using a Kullback-Leibler relaxation. .. GENERATED FROM PYTHON SOURCE LINES 10-25 .. code-block:: Python # Author: Hicham Janati # Clément Bonet # # License: MIT License # sphinx_gallery_thumbnail_number = 4 import numpy as np import matplotlib.pylab as pl import ot import ot.plot from ot.datasets import make_1D_gauss as gauss import torch .. GENERATED FROM PYTHON SOURCE LINES 26-28 Generate data ------------- .. GENERATED FROM PYTHON SOURCE LINES 31-48 .. 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) # make distributions unbalanced b *= 5.0 # loss matrix M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1))) .. GENERATED FROM PYTHON SOURCE LINES 49-51 Plot distributions and loss matrix ---------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 53-65 .. 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() # plot distributions and loss matrix pl.figure(2, figsize=(5, 5)) ot.plot.plot1D_mat(a, b, M, "Cost matrix M") .. rst-class:: sphx-glr-horizontal * .. image-sg:: /auto_examples/unbalanced-partial/images/sphx_glr_plot_UOT_1D_001.png :alt: plot UOT 1D :srcset: /auto_examples/unbalanced-partial/images/sphx_glr_plot_UOT_1D_001.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/unbalanced-partial/images/sphx_glr_plot_UOT_1D_002.png :alt: plot UOT 1D :srcset: /auto_examples/unbalanced-partial/images/sphx_glr_plot_UOT_1D_002.png :class: sphx-glr-multi-img .. rst-class:: sphx-glr-script-out .. code-block:: none (, , ) .. GENERATED FROM PYTHON SOURCE LINES 66-68 Solve Unbalanced OT with MM Unbalanced ----------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 70-92 .. code-block:: Python alpha = 1.0 # Unbalanced KL relaxation parameter Gs, log = ot.unbalanced.mm_unbalanced(a, b, M / M.max(), alpha, verbose=False, log=True) pl.figure(3, figsize=(5, 5)) ot.plot.plot1D_mat(a, b, Gs, "UOT plan") pl.show() pl.figure(4, figsize=(6.4, 3)) pl.plot(x, a, "b", label="Source distribution") pl.plot(x, b, "r", label="Target distribution") pl.fill(x, Gs.sum(1), "b", alpha=0.5, label="Transported source") pl.fill(x, Gs.sum(0), "r", alpha=0.5, label="Transported target") pl.legend(loc="upper right") pl.title("Distributions and transported mass for UOT") pl.show() print("Mass of reweighted marginals:", Gs.sum()) print("Unbalanced OT loss:", log["total_cost"] * M.max()) .. rst-class:: sphx-glr-horizontal * .. image-sg:: /auto_examples/unbalanced-partial/images/sphx_glr_plot_UOT_1D_003.png :alt: plot UOT 1D :srcset: /auto_examples/unbalanced-partial/images/sphx_glr_plot_UOT_1D_003.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/unbalanced-partial/images/sphx_glr_plot_UOT_1D_004.png :alt: Distributions and transported mass for UOT :srcset: /auto_examples/unbalanced-partial/images/sphx_glr_plot_UOT_1D_004.png :class: sphx-glr-multi-img .. rst-class:: sphx-glr-script-out .. code-block:: none Mass of reweighted marginals: 2.061425461509171 Unbalanced OT loss: 18397.928984107042 .. GENERATED FROM PYTHON SOURCE LINES 93-95 Solve 1D UOT with Frank-Wolfe ----------------------------- .. GENERATED FROM PYTHON SOURCE LINES 98-125 .. code-block:: Python alpha = M.max() # Unbalanced KL relaxation parameter a_reweighted, b_reweighted, loss = ot.unbalanced.uot_1d( torch.tensor(x, dtype=torch.float64), torch.tensor(x, dtype=torch.float64), alpha, u_weights=torch.tensor(a, dtype=torch.float64), v_weights=torch.tensor(b, dtype=torch.float64), p=2, returnCost="total", ) pl.figure(4, figsize=(6.4, 3)) pl.plot(x, a, "b", label="Source distribution") pl.plot(x, b, "r", label="Target distribution") pl.fill(x, a_reweighted, "b", alpha=0.5, label="Transported source") pl.fill(x, b_reweighted, "r", alpha=0.5, label="Transported target") pl.legend(loc="upper right") pl.title("Distributions and transported mass for UOT") pl.show() print("Mass of reweighted marginals:", a_reweighted.sum().item()) print("Unbalanced OT loss:", loss.item()) .. image-sg:: /auto_examples/unbalanced-partial/images/sphx_glr_plot_UOT_1D_005.png :alt: Distributions and transported mass for UOT :srcset: /auto_examples/unbalanced-partial/images/sphx_glr_plot_UOT_1D_005.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none Mass of reweighted marginals: 2.062383712135279 Unbalanced OT loss: 18379.180712239286 .. GENERATED FROM PYTHON SOURCE LINES 126-128 Solve Unbalanced Sinkhorn ------------------------- .. GENERATED FROM PYTHON SOURCE LINES 130-151 .. code-block:: Python # Sinkhorn epsilon = 0.1 # entropy parameter alpha = 1.0 # Unbalanced KL relaxation parameter Gs = ot.unbalanced.sinkhorn_unbalanced(a, b, M / M.max(), epsilon, alpha, verbose=True) pl.figure(3, figsize=(5, 5)) ot.plot.plot1D_mat(a, b, Gs, "Entropic UOT plan") pl.show() pl.figure(4, figsize=(6.4, 3)) pl.plot(x, a, "b", label="Source distribution") pl.plot(x, b, "r", label="Target distribution") pl.fill(x, Gs.sum(1), "b", alpha=0.5, label="Transported source") pl.fill(x, Gs.sum(0), "r", alpha=0.5, label="Transported target") pl.legend(loc="upper right") pl.title("Distributions and transported mass for UOT") pl.show() print("Mass of reweighted marginals:", Gs.sum()) .. rst-class:: sphx-glr-horizontal * .. image-sg:: /auto_examples/unbalanced-partial/images/sphx_glr_plot_UOT_1D_006.png :alt: plot UOT 1D :srcset: /auto_examples/unbalanced-partial/images/sphx_glr_plot_UOT_1D_006.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/unbalanced-partial/images/sphx_glr_plot_UOT_1D_007.png :alt: Distributions and transported mass for UOT :srcset: /auto_examples/unbalanced-partial/images/sphx_glr_plot_UOT_1D_007.png :class: sphx-glr-multi-img .. rst-class:: sphx-glr-script-out .. code-block:: none Mass of reweighted marginals: 2.1410336580797993 .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.607 seconds) .. _sphx_glr_download_auto_examples_unbalanced-partial_plot_UOT_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_UOT_1D.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_UOT_1D.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_UOT_1D.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_