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‎master/.github/CODE_OF_CONDUCT.html‎

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‎master/.github/CONTRIBUTING.html‎

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<a href="../index.html" class="icon icon-home">
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POT Python Optimal Transport
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<img src="../_static/logo_dark.svg" class="logo" alt="Logo"/>
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<div class="version">
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0.8.3dev
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‎master/_downloads/07fcc19ba03226cd3d83d4e40ec44385/auto_examples_python.zip‎

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‎master/_downloads/182cd2b5746acd3aca9f610eab3f97ef/plot_ssw_unif_torch.py‎

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# -*- coding: utf-8 -*-
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r"""
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================================================
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Spherical Sliced-Wasserstein Embedding on Sphere
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================================================
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Here, we aim at transforming samples into a uniform
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distribution on the sphere by minimizing SSW:
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.. math::
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\min_{x} SSW_2(\nu, \frac{1}{n}\sum_{i=1}^n \delta_{x_i})
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where :math:`\nu=\mathrm{Unif}(S^1)`.
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"""
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# Author: Clément Bonet <clement.bonet@univ-ubs.fr>
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#
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# License: MIT License
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# sphinx_gallery_thumbnail_number = 3
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import numpy as np
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import matplotlib.pyplot as pl
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import matplotlib.animation as animation
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import torch
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import torch.nn.functional as F
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import ot
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# %%
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# Data generation
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# ---------------
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torch.manual_seed(1)
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N = 1000
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x0 = torch.rand(N, 3)
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x0 = F.normalize(x0, dim=-1)
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# %%
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# Plot data
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# ---------
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def plot_sphere(ax):
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xlist = np.linspace(-1.0, 1.0, 50)
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ylist = np.linspace(-1.0, 1.0, 50)
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r = np.linspace(1.0, 1.0, 50)
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X, Y = np.meshgrid(xlist, ylist)
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Z = np.sqrt(r**2 - X**2 - Y**2)
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ax.plot_wireframe(X, Y, Z, color="gray", alpha=.3)
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ax.plot_wireframe(X, Y, -Z, color="gray", alpha=.3) # Now plot the bottom half
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# plot the distributions
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pl.figure(1)
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ax = pl.axes(projection='3d')
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plot_sphere(ax)
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ax.scatter(x0[:, 0], x0[:, 1], x0[:, 2], label='Data samples', alpha=0.5)
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ax.set_title('Data distribution')
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ax.legend()
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# %%
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# Gradient descent
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# ----------------
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x = x0.clone()
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x.requires_grad_(True)
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n_iter = 500
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lr = 100
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losses = []
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xvisu = torch.zeros(n_iter, N, 3)
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for i in range(n_iter):
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sw = ot.sliced_wasserstein_sphere_unif(x, n_projections=500)
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grad_x = torch.autograd.grad(sw, x)[0]
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x = x - lr * grad_x
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x = F.normalize(x, p=2, dim=1)
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losses.append(sw.item())
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xvisu[i, :, :] = x.detach().clone()
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if i % 100 == 0:
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print("Iter: {:3d}, loss={}".format(i, losses[-1]))
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pl.figure(1)
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pl.semilogy(losses)
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pl.grid()
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pl.title('SSW')
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pl.xlabel("Iterations")
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# %%
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# Plot trajectories of generated samples along iterations
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# -------------------------------------------------------
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ivisu = [0, 25, 50, 75, 100, 150, 200, 350, 499]
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fig = pl.figure(3, (10, 10))
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for i in range(9):
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# pl.subplot(3, 3, i + 1)
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# ax = pl.axes(projection='3d')
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ax = fig.add_subplot(3, 3, i + 1, projection='3d')
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plot_sphere(ax)
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ax.scatter(xvisu[ivisu[i], :, 0], xvisu[ivisu[i], :, 1], xvisu[ivisu[i], :, 2], label='Data samples', alpha=0.5)
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ax.set_title('Iter. {}'.format(ivisu[i]))
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#ax.axis("off")
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if i == 0:
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ax.legend()
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# %%
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# Animate trajectories of generated samples along iteration
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# -------------------------------------------------------
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pl.figure(4, (8, 8))
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def _update_plot(i):
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i = 3 * i
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pl.clf()
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ax = pl.axes(projection='3d')
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plot_sphere(ax)
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ax.scatter(xvisu[i, :, 0], xvisu[i, :, 1], xvisu[i, :, 2], label='Data samples$', alpha=0.5)
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ax.axis("off")
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ax.set_xlim((-1.5, 1.5))
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ax.set_ylim((-1.5, 1.5))
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ax.set_title('Iter. {}'.format(i))
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return 1
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print(xvisu.shape)
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i = 0
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ax = pl.axes(projection='3d')
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plot_sphere(ax)
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ax.scatter(xvisu[i, :, 0], xvisu[i, :, 1], xvisu[i, :, 2], label='Data samples from $G\#\mu_n$', alpha=0.5)
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ax.axis("off")
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ax.set_xlim((-1.5, 1.5))
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ax.set_ylim((-1.5, 1.5))
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ax.set_title('Iter. {}'.format(ivisu[i]))
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ani = animation.FuncAnimation(pl.gcf(), _update_plot, n_iter // 5, interval=100, repeat_delay=2000)
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# %%

‎master/_downloads/61dc96aac601dfe57940dfd3ab23ab76/plot_compute_wasserstein_circle.ipynb‎

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"%matplotlib inline"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\n# OT distance on the Circle\n\nShows how to compute the Wasserstein distance on the circle\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"# Author: Cl\u00e9ment Bonet <clement.bonet@univ-ubs.fr>\n#\n# License: MIT License\n\n# sphinx_gallery_thumbnail_number = 2\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\n\nfrom scipy.special import iv"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Plot data\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"def pdf_von_Mises(theta, mu, kappa):\n pdf = np.exp(kappa * np.cos(theta - mu)) / (2.0 * np.pi * iv(0, kappa))\n return pdf\n\n\nt = np.linspace(0, 2 * np.pi, 1000, endpoint=False)\n\nmu1 = 1\nkappa1 = 20\n\nmu_targets = np.linspace(mu1, mu1 + 2 * np.pi, 10)\n\n\npdf1 = pdf_von_Mises(t, mu1, kappa1)\n\n\npl.figure(1)\nfor k, mu in enumerate(mu_targets):\n pdf_t = pdf_von_Mises(t, mu, kappa1)\n if k == 0:\n label = \"Source distributions\"\n else:\n label = None\n pl.plot(t / (2 * np.pi), pdf_t, c='b', label=label)\n\npl.plot(t / (2 * np.pi), pdf1, c=\"r\", label=\"Target distribution\")\npl.legend()\n\nmu2 = 0\nkappa2 = kappa1\n\nx1 = np.random.vonmises(mu1, kappa1, size=(10,)) + np.pi\nx2 = np.random.vonmises(mu2, kappa2, size=(10,)) + np.pi\n\nangles = np.linspace(0, 2 * np.pi, 150)\n\npl.figure(2)\npl.plot(np.cos(angles), np.sin(angles), c=\"k\")\npl.xlim(-1.25, 1.25)\npl.ylim(-1.25, 1.25)\npl.scatter(np.cos(x1), np.sin(x1), c=\"b\")\npl.scatter(np.cos(x2), np.sin(x2), c=\"r\")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Compare the Euclidean Wasserstein distance with the Wasserstein distance on the circle\nThis examples illustrates the periodicity of the Wasserstein distance on the circle.\nWe choose as target distribution a von Mises distribution with mean $\\mu_{\\mathrm{target}}$\nand $\\kappa=20$. Then, we compare the distances with samples obtained from a von Mises distribution\nwith parameters $\\mu_{\\mathrm{source}}$ and $\\kappa=20$.\nThe Wasserstein distance on the circle takes into account the periodicity\nand attains its maximum in $\\mu_{\\mathrm{target}}+1$ (the antipodal point) contrary to the\nEuclidean version.\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"mu_targets = np.linspace(0, 2 * np.pi, 200)\nxs = np.random.vonmises(mu1 - np.pi, kappa1, size=(500,)) + np.pi\n\nn_try = 5\n\nxts = np.zeros((n_try, 200, 500))\nfor i in range(n_try):\n for k, mu in enumerate(mu_targets):\n # np.random.vonmises deals with data on [-pi, pi[\n xt = np.random.vonmises(mu - np.pi, kappa2, size=(500,)) + np.pi\n xts[i, k] = xt\n\n# Put data on S^1=[0,1[\nxts2 = xts / (2 * np.pi)\nxs2 = np.concatenate([xs[None] for k in range(200)], axis=0) / (2 * np.pi)\n\nL_w2_circle = np.zeros((n_try, 200))\nL_w2 = np.zeros((n_try, 200))\n\nfor i in range(n_try):\n w2_circle = ot.wasserstein_circle(xs2.T, xts2[i].T, p=2)\n w2 = ot.wasserstein_1d(xs2.T, xts2[i].T, p=2)\n\n L_w2_circle[i] = w2_circle\n L_w2[i] = w2\n\nm_w2_circle = np.mean(L_w2_circle, axis=0)\nstd_w2_circle = np.std(L_w2_circle, axis=0)\n\nm_w2 = np.mean(L_w2, axis=0)\nstd_w2 = np.std(L_w2, axis=0)\n\npl.figure(1)\npl.plot(mu_targets / (2 * np.pi), m_w2_circle, label=\"Wasserstein circle\")\npl.fill_between(mu_targets / (2 * np.pi), m_w2_circle - 2 * std_w2_circle, m_w2_circle + 2 * std_w2_circle, alpha=0.5)\npl.plot(mu_targets / (2 * np.pi), m_w2, label=\"Euclidean Wasserstein\")\npl.fill_between(mu_targets / (2 * np.pi), m_w2 - 2 * std_w2, m_w2 + 2 * std_w2, alpha=0.5)\npl.vlines(x=[mu1 / (2 * np.pi)], ymin=0, ymax=np.max(w2), linestyle=\"--\", color=\"k\", label=r\"$\\mu_{\\mathrm{target}}$\")\npl.legend()\npl.xlabel(r\"$\\mu_{\\mathrm{source}}$\")\npl.show()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Wasserstein distance between von Mises and uniform for different kappa\nWhen $\\kappa=0$, the von Mises distribution is the uniform distribution on $S^1$.\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"kappas = np.logspace(-5, 2, 100)\nn_try = 20\n\nxts = np.zeros((n_try, 100, 500))\nfor i in range(n_try):\n for k, kappa in enumerate(kappas):\n # np.random.vonmises deals with data on [-pi, pi[\n xt = np.random.vonmises(0, kappa, size=(500,)) + np.pi\n xts[i, k] = xt / (2 * np.pi)\n\nL_w2 = np.zeros((n_try, 100))\nfor i in range(n_try):\n L_w2[i] = ot.semidiscrete_wasserstein2_unif_circle(xts[i].T)\n\nm_w2 = np.mean(L_w2, axis=0)\nstd_w2 = np.std(L_w2, axis=0)\n\npl.figure(1)\npl.plot(kappas, m_w2)\npl.fill_between(kappas, m_w2 - std_w2, m_w2 + std_w2, alpha=0.5)\npl.title(r\"Evolution of $W_2^2(vM(0,\\kappa), Unif(S^1))$\")\npl.xlabel(r\"$\\kappa$\")\npl.show()"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.9.16"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}

‎master/_downloads/6f1e7a639e0699d6164445b55e6c116d/auto_examples_jupyter.zip‎

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