CircleCI update of dev docs (2779).

Author: Circle CI

master/_downloads/0228827bdcc2a6735b1faf26c864145d/plot_OT_1D_smooth.zip

@@ -0,0 +1,115 @@
+{
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "\n# GMM Flow\n\nIllustration of the flow of a Gaussian Mixture with\nrespect to its GMM-OT distance with respect to a\nfixed GMM.\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "# Author: Eloi Tanguy <eloi.tanguy@u-paris>\n#         Remi Flamary <[email protected]>\n#         Julie Delon <[email protected]>\n#\n# License: MIT License\n\n# sphinx_gallery_thumbnail_number = 4\n\nimport numpy as np\nimport matplotlib.pylab as pl\nfrom matplotlib import colormaps as cm\nimport ot\nimport ot.plot\nfrom ot.utils import proj_SDP, proj_simplex\nfrom ot.gmm import gmm_ot_loss\nimport torch\nfrom torch.optim import Adam\nfrom matplotlib.patches import Ellipse"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "## Generate data and plot it\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "torch.manual_seed(3)\nks = 3\nkt = 2\nd = 2\neps = 0.1\nm_s = torch.randn(ks, d)\nm_s.requires_grad_()\nm_t = torch.randn(kt, d)\nC_s = torch.randn(ks, d, d)\nC_s = torch.matmul(C_s, torch.transpose(C_s, 2, 1))\nC_s += eps * torch.eye(d)[None, :, :] * torch.ones(ks, 1, 1)\nC_s.requires_grad_()\nC_t = torch.randn(kt, d, d)\nC_t = torch.matmul(C_t, torch.transpose(C_t, 2, 1))\nC_t += eps * torch.eye(d)[None, :, :] * torch.ones(kt, 1, 1)\nw_s = torch.randn(ks)\nw_s = proj_simplex(w_s)\nw_s.requires_grad_()\nw_t = torch.tensor(ot.unif(kt))\n\n\ndef draw_cov(mu, C, color=None, label=None, nstd=1, alpha=.5):\n\n    def eigsorted(cov):\n        vals, vecs = np.linalg.eigh(cov)\n        order = vals.argsort()[::-1]\n        return vals[order], vecs[:, order]\n\n    vals, vecs = eigsorted(C)\n    theta = np.degrees(np.arctan2(*vecs[:, 0][::-1]))\n    w, h = 2 * nstd * np.sqrt(vals)\n    ell = Ellipse(xy=(mu[0], mu[1]),\n                  width=w, height=h, alpha=alpha,\n                  angle=theta, facecolor=color, edgecolor=color, label=label, fill=True)\n    pl.gca().add_artist(ell)\n\n\ndef draw_gmm(ms, Cs, ws, color=None, nstd=.5, alpha=1):\n    for k in range(ms.shape[0]):\n        draw_cov(ms[k], Cs[k], color, None, nstd,\n                 alpha * ws[k])\n\n\naxis = [-3, 3, -3, 3]\npl.figure(1, (20, 10))\npl.clf()\n\npl.subplot(1, 2, 1)\npl.scatter(m_s[:, 0].detach(), m_s[:, 1].detach(), color='C0')\ndraw_gmm(m_s.detach(), C_s.detach(),\n         torch.softmax(w_s, 0).detach().numpy(),\n         color='C0')\npl.axis(axis)\npl.title('Source GMM')\n\npl.subplot(1, 2, 2)\npl.scatter(m_t[:, 0].detach(), m_t[:, 1].detach(), color='C1')\ndraw_gmm(m_t.detach(), C_t.detach(), w_t.numpy(), color='C1')\npl.axis(axis)\npl.title('Target GMM')"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "## Gradient descent loop\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "n_gd_its = 100\nlr = 3e-2\nopt = Adam([{'params': m_s, 'lr': 2 * lr},\n           {'params': C_s, 'lr': lr},\n           {'params': w_s, 'lr': lr}])\nm_list = [m_s.data.numpy().copy()]\nC_list = [C_s.data.numpy().copy()]\nw_list = [torch.softmax(w_s, 0).data.numpy().copy()]\nloss_list = []\n\nfor _ in range(n_gd_its):\n    opt.zero_grad()\n    loss = gmm_ot_loss(m_s, m_t, C_s, C_t,\n                       torch.softmax(w_s, 0), w_t)\n    loss.backward()\n    opt.step()\n    with torch.no_grad():\n        C_s.data = proj_SDP(C_s.data, vmin=1e-6)\n        m_list.append(m_s.data.numpy().copy())\n        C_list.append(C_s.data.numpy().copy())\n        w_list.append(torch.softmax(w_s, 0).data.numpy().copy())\n        loss_list.append(loss.item())\n\npl.figure(2)\npl.clf()\npl.plot(loss_list)\npl.title('Loss')\npl.xlabel('its')\npl.ylabel('loss')"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "## Last step visualisation\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "axis = [-3, 3, -3, 3]\npl.figure(3, (10, 10))\npl.clf()\npl.title('GMM flow, last step')\npl.scatter(m_list[0][:, 0], m_list[0][:, 1], color='C0', label='Source')\ndraw_gmm(m_list[0], C_list[0], w_list[0], color='C0')\npl.axis(axis)\n\npl.scatter(m_t[:, 0].detach(), m_t[:, 1].detach(), color='C1', label='Target')\ndraw_gmm(m_t.detach(), C_t.detach(), w_t.numpy(), color='C1')\npl.axis(axis)\n\nk = -1\npl.scatter(m_list[k][:, 0], m_list[k][:, 1], color='C2', alpha=1, label='Last step')\ndraw_gmm(m_list[k], C_list[k], w_list[0], color='C2', alpha=1)\n\npl.axis(axis)\npl.legend(fontsize=15)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "## Steps visualisation\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "def index_to_color(i):\n    return int(i**0.5)\n\n\nn_steps_visu = 100\npl.figure(3, (10, 10))\npl.clf()\npl.title('GMM flow, all steps')\n\nits_to_show = [int(x) for x in np.linspace(1, n_gd_its - 1, n_steps_visu)]\ncmp = cm['plasma'].resampled(index_to_color(n_steps_visu))\n\npl.scatter(m_list[0][:, 0], m_list[0][:, 1],\n           color=cmp(index_to_color(0)), label='Source')\ndraw_gmm(m_list[0], C_list[0], w_list[0],\n         color=cmp(index_to_color(0)))\n\npl.scatter(m_t[:, 0].detach(), m_t[:, 1].detach(),\n           color=cmp(index_to_color(n_steps_visu - 1)), label='Target')\ndraw_gmm(m_t.detach(), C_t.detach(), w_t.numpy(),\n         color=cmp(index_to_color(n_steps_visu - 1)))\n\n\nfor k in its_to_show:\n    pl.scatter(m_list[k][:, 0], m_list[k][:, 1],\n               color=cmp(index_to_color(k)), alpha=0.8)\n    draw_gmm(m_list[k], C_list[k], w_list[0],\n             color=cmp(index_to_color(k)), alpha=0.04)\n\npl.axis(axis)\npl.legend(fontsize=15)"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.10.14"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
+}

master/_downloads/06f3dd7c3258690ab730be0a658b5e36/plot_ssw_unif_torch.zip

@@ -1,3 +1,4 @@
+# %%
 # -*- coding: utf-8 -*-
 """
 ======================================

master/_downloads/07fcc19ba03226cd3d83d4e40ec44385/auto_examples_python.zip

@@ -0,0 +1,88 @@
+# %%
+# -*- coding: utf-8 -*-
+r"""
+====================================================
+GMM Plan 1D
+====================================================
+
+Illustration of the GMM plan for
+the Mixture Wasserstein between two GMM in 1D,
+as well as the two maps T_mean and T_rand.
+T_mean is the barycentric projection of the GMM coupling,
+and T_rand takes a random gaussian image between two components,
+according to the coupling and the GMMs.
+See [69] for details.
+.. [69] Delon, J., & Desolneux, A. (2020). A Wasserstein-type distance in the space of Gaussian mixture models. SIAM Journal on Imaging Sciences, 13(2), 936-970.
+
+"""
+
+# Author: Eloi Tanguy <eloi.tanguy@u-paris>
+#         Remi Flamary <[email protected]>
+#         Julie Delon <[email protected]>
+#
+# License: MIT License
+
+# sphinx_gallery_thumbnail_number = 1
+
+import numpy as np
+from ot.plot import plot1D_mat, rescale_for_imshow_plot
+from ot.gmm import gmm_ot_plan_density, gmm_pdf, gmm_ot_apply_map
+import matplotlib.pyplot as plt
+
+##############################################################################
+# Generate GMMOT plan plot it
+# ---------------------------
+ks = 2
+kt = 3
+d = 1
+eps = 0.1
+m_s = np.array([[1], [2]])
+m_t = np.array([[3], [4.2], [5]])
+C_s = np.array([[[.05]], [[.06]]])
+C_t = np.array([[[.03]], [[.07]], [[.04]]])
+w_s = np.array([.4, .6])
+w_t = np.array([.4, .2, .4])
+
+n = 500
+a_x, b_x = 0, 3
+x = np.linspace(a_x, b_x, n)
+a_y, b_y = 2, 6
+y = np.linspace(a_y, b_y, n)
+plan_density = gmm_ot_plan_density(x[:, None], y[:, None],
+                                   m_s, m_t, C_s, C_t, w_s, w_t,
+                                   plan=None, atol=2e-2)
+
+a = gmm_pdf(x[:, None], m_s, C_s, w_s)
+b = gmm_pdf(y[:, None], m_t, C_t, w_t)
+plt.figure(figsize=(8, 8))
+plot1D_mat(a, b, plan_density, title='GMM OT plan', plot_style='xy',
+           a_label='Source distribution', b_label='Target distribution')
+
+
+##############################################################################
+# Generate GMMOT maps and plot them over plan
+# -------------------------------------------
+plt.figure(figsize=(8, 8))
+ax_s, ax_t, ax_M = plot1D_mat(a, b, plan_density, plot_style='xy',
+                              title='GMM OT plan with T_mean and T_rand maps',
+                              a_label='Source distribution',
+                              b_label='Target distribution')
+T_mean = gmm_ot_apply_map(x[:, None], m_s, m_t, C_s, C_t,
+                          w_s, w_t, method='bary')[:, 0]
+x_rescaled, T_mean_rescaled = rescale_for_imshow_plot(x, T_mean, n,
+                                                      a_y=a_y, b_y=b_y)
+
+ax_M.plot(x_rescaled, T_mean_rescaled, label='T_mean', alpha=.5,
+          linewidth=5, color='aqua')
+
+T_rand = gmm_ot_apply_map(x[:, None], m_s, m_t, C_s, C_t,
+                          w_s, w_t, method='rand', seed=0)[:, 0]
+x_rescaled, T_rand_rescaled = rescale_for_imshow_plot(x, T_rand, n,
+                                                      a_y=a_y, b_y=b_y)
+
+ax_M.scatter(x_rescaled, T_rand_rescaled, label='T_rand', alpha=.5,
+             s=20, color='orange')
+
+ax_M.legend(loc='upper left', fontsize=13)
+
+# %%

master/_downloads/135d9df766cd2fdce616d2b7c6016c04/plot_otda_jcpot.zip

@@ -0,0 +1,79 @@
+{
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "\n# GMM Plan 1D\n\nIllustration of the GMM plan for\nthe Mixture Wasserstein between two GMM in 1D,\nas well as the two maps T_mean and T_rand.\nT_mean is the barycentric projection of the GMM coupling,\nand T_rand takes a random gaussian image between two components,\naccording to the coupling and the GMMs.\nSee [69] for details.\n.. [69] Delon, J., & Desolneux, A. (2020). A Wasserstein-type distance in the space of Gaussian mixture models. SIAM Journal on Imaging Sciences, 13(2), 936-970.\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "# Author: Eloi Tanguy <eloi.tanguy@u-paris>\n#         Remi Flamary <[email protected]>\n#         Julie Delon <[email protected]>\n#\n# License: MIT License\n\n# sphinx_gallery_thumbnail_number = 1\n\nimport numpy as np\nfrom ot.plot import plot1D_mat, rescale_for_imshow_plot\nfrom ot.gmm import gmm_ot_plan_density, gmm_pdf, gmm_ot_apply_map\nimport matplotlib.pyplot as plt"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "## Generate GMMOT plan plot it\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "ks = 2\nkt = 3\nd = 1\neps = 0.1\nm_s = np.array([[1], [2]])\nm_t = np.array([[3], [4.2], [5]])\nC_s = np.array([[[.05]], [[.06]]])\nC_t = np.array([[[.03]], [[.07]], [[.04]]])\nw_s = np.array([.4, .6])\nw_t = np.array([.4, .2, .4])\n\nn = 500\na_x, b_x = 0, 3\nx = np.linspace(a_x, b_x, n)\na_y, b_y = 2, 6\ny = np.linspace(a_y, b_y, n)\nplan_density = gmm_ot_plan_density(x[:, None], y[:, None],\n                                   m_s, m_t, C_s, C_t, w_s, w_t,\n                                   plan=None, atol=2e-2)\n\na = gmm_pdf(x[:, None], m_s, C_s, w_s)\nb = gmm_pdf(y[:, None], m_t, C_t, w_t)\nplt.figure(figsize=(8, 8))\nplot1D_mat(a, b, plan_density, title='GMM OT plan', plot_style='xy',\n           a_label='Source distribution', b_label='Target distribution')"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "## Generate GMMOT maps and plot them over plan\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "plt.figure(figsize=(8, 8))\nax_s, ax_t, ax_M = plot1D_mat(a, b, plan_density, plot_style='xy',\n                              title='GMM OT plan with T_mean and T_rand maps',\n                              a_label='Source distribution',\n                              b_label='Target distribution')\nT_mean = gmm_ot_apply_map(x[:, None], m_s, m_t, C_s, C_t,\n                          w_s, w_t, method='bary')[:, 0]\nx_rescaled, T_mean_rescaled = rescale_for_imshow_plot(x, T_mean, n,\n                                                      a_y=a_y, b_y=b_y)\n\nax_M.plot(x_rescaled, T_mean_rescaled, label='T_mean', alpha=.5,\n          linewidth=5, color='aqua')\n\nT_rand = gmm_ot_apply_map(x[:, None], m_s, m_t, C_s, C_t,\n                          w_s, w_t, method='rand', seed=0)[:, 0]\nx_rescaled, T_rand_rescaled = rescale_for_imshow_plot(x, T_rand, n,\n                                                      a_y=a_y, b_y=b_y)\n\nax_M.scatter(x_rescaled, T_rand_rescaled, label='T_rand', alpha=.5,\n             s=20, color='orange')\n\nax_M.legend(loc='upper left', fontsize=13)"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.10.14"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
+}