CircleCI update of dev docs (3297).

Author: Circle CI

master/_downloads/06f3dd7c3258690ab730be0a658b5e36/plot_ssw_unif_torch.zip

@@ -0,0 +1,146 @@
+# -*- coding: utf-8 -*-
+r"""
+=====================================
+Gaussian Mixture Model OT Barycenters
+=====================================
+
+This example illustrates the computation of a barycenter between Gaussian
+Mixtures in the sense of GMM-OT [69]. This computation is done using the
+fixed-point method for OT barycenters with generic costs [77], for which POT
+provides a general solver, and a specific GMM solver. Note that this is a
+'free-support' method, implying that the number of components of the barycenter
+GMM and their weights are fixed.
+
+The idea behind GMM-OT barycenters is to see the GMMs as discrete measures over
+the space of Gaussian distributions :math:`\mathcal{N}` (or equivalently the
+Bures-Wasserstein manifold), and to compute barycenters with respect to the
+2-Wasserstein distance between measures in :math:`\mathcal{P}(\mathcal{N})`: a
+gaussian mixture is a finite combination of Diracs on specific gaussians, and
+two mixtures are compared with the 2-Wasserstein distance on this space, where
+ground cost the squared Bures distance between gaussians.
+
+[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.
+
+[77] Tanguy, Eloi and Delon, Julie and Gozlan, Nathaël (2024). Computing
+Barycentres of Measures for Generic Transport Costs. arXiv preprint 2501.04016
+(2024)
+
+"""
+
+# Author: Eloi Tanguy <eloi.tanguy@math.cnrs.fr>
+#
+# License: MIT License
+
+# sphinx_gallery_thumbnail_number = 1
+
+# %%
+# Generate data
+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.patches import Ellipse
+import ot
+from ot.gmm import gmm_barycenter_fixed_point
+
+
+K = 3  # number of GMMs
+d = 2  # dimension
+n = 6  # number of components of the desired barycenter
+
+
+def get_random_gmm(K, d, seed=0, min_cov_eig=1, cov_scale=1e-2):
+    rng = np.random.RandomState(seed=seed)
+    means = rng.randn(K, d)
+    P = rng.randn(K, d, d) * cov_scale
+    # C[k] = P[k] @ P[k]^T + min_cov_eig * I
+    covariances = np.einsum("kab,kcb->kac", P, P)
+    covariances += min_cov_eig * np.array([np.eye(d) for _ in range(K)])
+    weights = rng.random(K)
+    weights /= np.sum(weights)
+    return means, covariances, weights
+
+
+m_list = [5, 6, 7]  # number of components in each GMM
+offsets = [np.array([-3, 0]), np.array([2, 0]), np.array([0, 4])]
+means_list = []  # list of means for each GMM
+covs_list = []  # list of covariances for each GMM
+w_list = []  # list of weights for each GMM
+
+# generate GMMs
+for k in range(K):
+    means, covs, b = get_random_gmm(
+        m_list[k], d, seed=k, min_cov_eig=0.25, cov_scale=0.5
+    )
+    means = means / 2 + offsets[k][None, :]
+    means_list.append(means)
+    covs_list.append(covs)
+    w_list.append(b)
+
+# %%
+# Compute the barycenter using the fixed-point method
+init_means, init_covs, _ = get_random_gmm(n, d, seed=0)
+weights = ot.unif(K)  # barycenter coefficients
+means_bar, covs_bar, log = gmm_barycenter_fixed_point(
+    means_list,
+    covs_list,
+    w_list,
+    init_means,
+    init_covs,
+    weights,
+    iterations=3,
+    log=True,
+)
+
+
+# %%
+# Define plotting functions
+
+
+# draw a covariance ellipse
+def draw_cov(mu, C, color=None, label=None, nstd=1, alpha=0.5, ax=None):
+    def eigsorted(cov):
+        vals, vecs = np.linalg.eigh(cov)
+        order = vals.argsort()[::-1].copy()
+        return vals[order], vecs[:, order]
+
+    vals, vecs = eigsorted(C)
+    theta = np.degrees(np.arctan2(*vecs[:, 0][::-1]))
+    w, h = 2 * nstd * np.sqrt(vals)
+    ell = Ellipse(
+        xy=(mu[0], mu[1]),
+        width=w,
+        height=h,
+        alpha=alpha,
+        angle=theta,
+        facecolor=color,
+        edgecolor=color,
+        label=label,
+        fill=True,
+    )
+    if ax is None:
+        ax = plt.gca()
+    ax.add_artist(ell)
+
+
+# draw a gmm as a set of ellipses with weights shown in alpha value
+def draw_gmm(ms, Cs, ws, color=None, nstd=0.5, alpha=1, label=None, ax=None):
+    for k in range(ms.shape[0]):
+        draw_cov(
+            ms[k], Cs[k], color, label if k == 0 else None, nstd, alpha * ws[k], ax=ax
+        )
+
+
+# %%
+# Plot the results
+c_list = ["#7ED321", "#4A90E2", "#9013FE", "#F5A623"]
+c_bar = "#D0021B"
+fig, ax = plt.subplots(figsize=(6, 6))
+axis = [-4, 4, -2, 6]
+ax.set_title("Fixed Point Barycenter (3 Iterations)", fontsize=16)
+for k in range(K):
+    draw_gmm(means_list[k], covs_list[k], w_list[k], color=c_list[k], ax=ax)
+draw_gmm(means_bar, covs_bar, ot.unif(n), color=c_bar, ax=ax)
+ax.axis(axis)
+ax.axis("off")
+
+# %%

master/_downloads/0d375ec8926c2b3582030c452de6f5b5/plot_gmm_barycenter.py

@@ -15,7 +15,7 @@
       },
       "outputs": [],
       "source": [
-        "# Author: Eloi Tanguy <eloi.tanguy@u-paris>\n#         Remi Flamary <remi.flamary@polytehnique.edu>\n#         Julie Delon <julie.delon@math.cnrs.fr>\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"
+        "# Author: Eloi Tanguy <eloi.tanguy@math.cnrs.fr>\n#         Remi Flamary <remi.flamary@polytehnique.edu>\n#         Julie Delon <julie.delon@math.cnrs.fr>\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"
       ]
     },
     {

master/_downloads/0dbd57c6090215001a0a712021c577e5/plot_GMMOT_plan.ipynb

@@ -41,7 +41,7 @@
         2017.
 """
 
-# Author: Eloi Tanguy <eloi.tanguy@u-paris.fr>
+# Author: Eloi Tanguy <eloi.tanguy@math.cnrs.fr>
 # License: MIT License
 
 # sphinx_gallery_thumbnail_number = 3

master/_downloads/0fe57e4a52ca493c3f53f92371df1dca/plot_lowrank_GW.zip

@@ -15,7 +15,7 @@
       },
       "outputs": [],
       "source": [
-        "# Author: Eloi Tanguy <eloi.tanguy@polytechnique.edu>\n#\n# License: MIT License\n\n# sphinx_gallery_thumbnail_number = 2\n\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport matplotlib.pylab as pl\nimport ot\nimport matplotlib.animation as animation"
+        "# Author: Eloi Tanguy <eloi.tanguy@math.cnrs.fr>\n#\n# License: MIT License\n\n# sphinx_gallery_thumbnail_number = 2\n\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport matplotlib.pylab as pl\nimport ot\nimport matplotlib.animation as animation"
       ]
     },
     {