.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/backends/plot_dual_ot_pytorch.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_backends_plot_dual_ot_pytorch.py: ====================================================================== Dual OT solvers for entropic and quadratic regularized OT with Pytorch ====================================================================== .. note:: Example added in release: 0.8.2. .. GENERATED FROM PYTHON SOURCE LINES 11-24 .. code-block:: Python # Author: Remi Flamary # # License: MIT License # sphinx_gallery_thumbnail_number = 3 import numpy as np import matplotlib.pyplot as pl import torch import ot import ot.plot .. GENERATED FROM PYTHON SOURCE LINES 25-27 Data generation --------------- .. GENERATED FROM PYTHON SOURCE LINES 27-45 .. code-block:: Python torch.manual_seed(1) n_source_samples = 100 n_target_samples = 100 theta = 2 * np.pi / 20 noise_level = 0.1 Xs, ys = ot.datasets.make_data_classif("gaussrot", n_source_samples, nz=noise_level) Xt, yt = ot.datasets.make_data_classif( "gaussrot", n_target_samples, theta=theta, nz=noise_level ) # one of the target mode changes its variance (no linear mapping) Xt[yt == 2] *= 3 Xt = Xt + 4 .. GENERATED FROM PYTHON SOURCE LINES 46-48 Plot data --------- .. GENERATED FROM PYTHON SOURCE LINES 48-56 .. code-block:: Python pl.figure(1, (10, 5)) pl.clf() pl.scatter(Xs[:, 0], Xs[:, 1], marker="+", label="Source samples") pl.scatter(Xt[:, 0], Xt[:, 1], marker="o", label="Target samples") pl.legend(loc=0) pl.title("Source and target distributions") .. image-sg:: /auto_examples/backends/images/sphx_glr_plot_dual_ot_pytorch_001.png :alt: Source and target distributions :srcset: /auto_examples/backends/images/sphx_glr_plot_dual_ot_pytorch_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none Text(0.5, 1.0, 'Source and target distributions') .. GENERATED FROM PYTHON SOURCE LINES 57-59 Convert data to torch tensors ----------------------------- .. GENERATED FROM PYTHON SOURCE LINES 59-63 .. code-block:: Python xs = torch.tensor(Xs) xt = torch.tensor(Xt) .. GENERATED FROM PYTHON SOURCE LINES 64-66 Estimating dual variables for entropic OT ----------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 66-103 .. code-block:: Python u = torch.randn(n_source_samples, requires_grad=True) v = torch.randn(n_source_samples, requires_grad=True) reg = 0.5 optimizer = torch.optim.Adam([u, v], lr=1) # number of iteration n_iter = 200 losses = [] for i in range(n_iter): # generate noise samples # minus because we maximize the dual loss loss = -ot.stochastic.loss_dual_entropic(u, v, xs, xt, reg=reg) losses.append(float(loss.detach())) if i % 10 == 0: print("Iter: {:3d}, loss={}".format(i, losses[-1])) loss.backward() optimizer.step() optimizer.zero_grad() pl.figure(2) pl.plot(losses) pl.grid() pl.title("Dual objective (negative)") pl.xlabel("Iterations") Ge = ot.stochastic.plan_dual_entropic(u, v, xs, xt, reg=reg) .. image-sg:: /auto_examples/backends/images/sphx_glr_plot_dual_ot_pytorch_002.png :alt: Dual objective (negative) :srcset: /auto_examples/backends/images/sphx_glr_plot_dual_ot_pytorch_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none Iter: 0, loss=0.20204949002247385 Iter: 10, loss=-19.598840195117187 Iter: 20, loss=-31.45275877977004 Iter: 30, loss=-35.654959166703776 Iter: 40, loss=-38.55564856024449 Iter: 50, loss=-40.616177419309466 Iter: 60, loss=-41.31875285406105 Iter: 70, loss=-41.67965100682904 Iter: 80, loss=-41.869261766871475 Iter: 90, loss=-41.90013973873414 Iter: 100, loss=-41.932317369414754 Iter: 110, loss=-41.94220449340273 Iter: 120, loss=-41.950364300815394 Iter: 130, loss=-41.953795308746166 Iter: 140, loss=-41.95599677401932 Iter: 150, loss=-41.957543840951914 Iter: 160, loss=-41.95855874663437 Iter: 170, loss=-41.959284820103846 Iter: 180, loss=-41.959815373763206 Iter: 190, loss=-41.960213442186 .. GENERATED FROM PYTHON SOURCE LINES 104-106 Plot the estimated entropic OT plan ----------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 106-116 .. code-block:: Python pl.figure(3, (10, 5)) pl.clf() ot.plot.plot2D_samples_mat(Xs, Xt, Ge.detach().numpy(), alpha=0.1) pl.scatter(Xs[:, 0], Xs[:, 1], marker="+", label="Source samples", zorder=2) pl.scatter(Xt[:, 0], Xt[:, 1], marker="o", label="Target samples", zorder=2) pl.legend(loc=0) pl.title("Source and target distributions") .. image-sg:: /auto_examples/backends/images/sphx_glr_plot_dual_ot_pytorch_003.png :alt: Source and target distributions :srcset: /auto_examples/backends/images/sphx_glr_plot_dual_ot_pytorch_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none Text(0.5, 1.0, 'Source and target distributions') .. GENERATED FROM PYTHON SOURCE LINES 117-119 Estimating dual variables for quadratic OT ------------------------------------------ .. GENERATED FROM PYTHON SOURCE LINES 119-158 .. code-block:: Python u = torch.randn(n_source_samples, requires_grad=True) v = torch.randn(n_source_samples, requires_grad=True) reg = 0.01 optimizer = torch.optim.Adam([u, v], lr=1) # number of iteration n_iter = 200 losses = [] for i in range(n_iter): # generate noise samples # minus because we maximize the dual loss loss = -ot.stochastic.loss_dual_quadratic(u, v, xs, xt, reg=reg) losses.append(float(loss.detach())) if i % 10 == 0: print("Iter: {:3d}, loss={}".format(i, losses[-1])) loss.backward() optimizer.step() optimizer.zero_grad() pl.figure(4) pl.plot(losses) pl.grid() pl.title("Dual objective (negative)") pl.xlabel("Iterations") Gq = ot.stochastic.plan_dual_quadratic(u, v, xs, xt, reg=reg) .. image-sg:: /auto_examples/backends/images/sphx_glr_plot_dual_ot_pytorch_004.png :alt: Dual objective (negative) :srcset: /auto_examples/backends/images/sphx_glr_plot_dual_ot_pytorch_004.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none Iter: 0, loss=-0.0018442196020623663 Iter: 10, loss=-19.482693753355026 Iter: 20, loss=-31.031587667901338 Iter: 30, loss=-35.24412455339648 Iter: 40, loss=-38.34167509988665 Iter: 50, loss=-40.33264368175991 Iter: 60, loss=-41.05848772529333 Iter: 70, loss=-41.498203806732256 Iter: 80, loss=-41.701770668580316 Iter: 90, loss=-41.75788169087051 Iter: 100, loss=-41.78912743553177 Iter: 110, loss=-41.80275113616942 Iter: 120, loss=-41.81127971513494 Iter: 130, loss=-41.81620688759422 Iter: 140, loss=-41.81919900711129 Iter: 150, loss=-41.82131280293244 Iter: 160, loss=-41.82282129129657 Iter: 170, loss=-41.823959203849064 Iter: 180, loss=-41.82483864631298 Iter: 190, loss=-41.825524003745045 .. GENERATED FROM PYTHON SOURCE LINES 159-161 Plot the estimated quadratic OT plan ------------------------------------ .. GENERATED FROM PYTHON SOURCE LINES 161-169 .. code-block:: Python pl.figure(5, (10, 5)) pl.clf() ot.plot.plot2D_samples_mat(Xs, Xt, Gq.detach().numpy(), alpha=0.1) pl.scatter(Xs[:, 0], Xs[:, 1], marker="+", label="Source samples", zorder=2) pl.scatter(Xt[:, 0], Xt[:, 1], marker="o", label="Target samples", zorder=2) pl.legend(loc=0) pl.title("OT plan with quadratic regularization") .. image-sg:: /auto_examples/backends/images/sphx_glr_plot_dual_ot_pytorch_005.png :alt: OT plan with quadratic regularization :srcset: /auto_examples/backends/images/sphx_glr_plot_dual_ot_pytorch_005.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none Text(0.5, 1.0, 'OT plan with quadratic regularization') .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 14.855 seconds) .. _sphx_glr_download_auto_examples_backends_plot_dual_ot_pytorch.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_dual_ot_pytorch.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_dual_ot_pytorch.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_dual_ot_pytorch.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_