[MRG] Update examples in the doc (#359)

* add transparent color logo

* add transparent color logo

* move screenkhorn

* move stochastic and install ffmpeg on circleci

* try something

* add sudo

* install ffmpeg before python

* cleanup examples

* test svg scrapper

* add animation for reg path

* better example OT sivergence

* update ttles and add plots

* update free support

* proper figure indexes

* have less frame sin animation

* update readme and release file

* add tests for python 3.10

2 files changed, 102 insertions, 3 deletions

diff --git a/examples/unbalanced-partial/plot_UOT_1D.py b/examples/unbalanced-partial/plot_UOT_1D.py
index 183849c..06dd02d 100644
--- a/examples/unbalanced-partial/plot_UOT_1D.py
+++ b/examples/unbalanced-partial/plot_UOT_1D.py
@@ -12,6 +12,8 @@ using a Kullback-Leibler relaxation.
 #
 # License: MIT License
 
+# sphinx_gallery_thumbnail_number = 4
+
 import numpy as np
 import matplotlib.pylab as pl
 import ot
@@ -69,7 +71,20 @@ epsilon = 0.1  # entropy parameter
 alpha = 1.  # Unbalanced KL relaxation parameter
 Gs = ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha, verbose=True)
 
-pl.figure(4, figsize=(5, 5))
+pl.figure(3, figsize=(5, 5))
 ot.plot.plot1D_mat(a, b, Gs, 'UOT matrix Sinkhorn')
 
 pl.show()
+
+
+# %%
+# plot the transported mass
+# -------------------------
+
+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')
diff --git a/examples/unbalanced-partial/plot_regpath.py b/examples/unbalanced-partial/plot_regpath.py
index 4a51c2d..782e8c2 100644
--- a/examples/unbalanced-partial/plot_regpath.py
+++ b/examples/unbalanced-partial/plot_regpath.py
@@ -15,11 +15,12 @@ penalized linear regression.
 # Author: Haoran Wu <haoran.wu@univ-ubs.fr>
 # License: MIT License
 
+# sphinx_gallery_thumbnail_number = 2
 
 import numpy as np
 import matplotlib.pylab as pl
 import ot
-
+import matplotlib.animation as animation
 ##############################################################################
 # Generate data
 # -------------
@@ -72,6 +73,9 @@ t2, t_list2, g_list2 = ot.regpath.regularization_path(a, b, M, reg=final_gamma,
 ##############################################################################
 # Plot the regularization path
 # ----------------
+#
+# The OT plan is ploted as a function of $\gamma$ that is the inverse of the
+# weight on the marginal relaxations.
 
 #%% fully relaxed l2-penalized UOT
 
@@ -103,13 +107,53 @@ for p in range(4):
 pl.show()
 
 
+# %%
+# Animation of the regpath for UOT l2
+# ------------------------
+
+nv = 100
+g_list_v = np.logspace(-.5, -2.5, nv)
+
+pl.figure(3)
+
+
+def _update_plot(iv):
+    pl.clf()
+    tp = ot.regpath.compute_transport_plan(g_list_v[iv], g_list,
+                                           t_list)
+    P = tp.reshape((n, n))
+    if P.sum() > 0:
+        P = P / P.max()
+    for i in range(n):
+        for j in range(n):
+            if P[i, j] > 0:
+                pl.plot([xs[i, 0], xt[j, 0]], [xs[i, 1], xt[j, 1]], color='C2',
+                        alpha=P[i, j] * 0.5)
+    pl.scatter(xs[:, 0], xs[:, 1], c='C0', alpha=0.2)
+    pl.scatter(xt[:, 0], xt[:, 1], c='C1', alpha=0.2)
+    pl.scatter(xs[:, 0], xs[:, 1], c='C0', s=P.sum(1).ravel() * (1 + p) * 4,
+               label='Re-weighted source', alpha=1)
+    pl.scatter(xt[:, 0], xt[:, 1], c='C1', s=P.sum(0).ravel() * (1 + p) * 4,
+               label='Re-weighted target', alpha=1)
+    pl.plot([], [], color='C2', alpha=0.8, label='OT plan')
+    pl.title(r'$\ell_2$ UOT $\gamma$={:1.3f}'.format(g_list_v[iv]),
+             fontsize=11)
+    return 1
+
+
+i = 0
+_update_plot(i)
+
+ani = animation.FuncAnimation(pl.gcf(), _update_plot, nv, interval=50, repeat_delay=2000)
+
+
 ##############################################################################
 # Plot the semi-relaxed regularization path
 # -------------------
 
 #%% semi-relaxed l2-penalized UOT
 
-pl.figure(3)
+pl.figure(4)
 selected_gamma = [10, 1, 1e-1, 1e-2]
 for p in range(4):
     tp = ot.regpath.compute_transport_plan(selected_gamma[p], g_list2,
@@ -133,3 +177,43 @@ for p in range(4):
     if p < 2:
         pl.xticks(())
 pl.show()
+
+
+# %%
+# Animation of the regpath for semi-relaxed UOT l2
+# ------------------------
+
+nv = 100
+g_list_v = np.logspace(2.5, -2, nv)
+
+pl.figure(5)
+
+
+def _update_plot(iv):
+    pl.clf()
+    tp = ot.regpath.compute_transport_plan(g_list_v[iv], g_list2,
+                                           t_list2)
+    P = tp.reshape((n, n))
+    if P.sum() > 0:
+        P = P / P.max()
+    for i in range(n):
+        for j in range(n):
+            if P[i, j] > 0:
+                pl.plot([xs[i, 0], xt[j, 0]], [xs[i, 1], xt[j, 1]], color='C2',
+                        alpha=P[i, j] * 0.5)
+    pl.scatter(xs[:, 0], xs[:, 1], c='C0', alpha=0.2)
+    pl.scatter(xt[:, 0], xt[:, 1], c='C1', alpha=0.2)
+    pl.scatter(xs[:, 0], xs[:, 1], c='C0', s=P.sum(1).ravel() * (1 + p) * 4,
+               label='Re-weighted source', alpha=1)
+    pl.scatter(xt[:, 0], xt[:, 1], c='C1', s=P.sum(0).ravel() * (1 + p) * 4,
+               label='Re-weighted target', alpha=1)
+    pl.plot([], [], color='C2', alpha=0.8, label='OT plan')
+    pl.title(r'Semi-relaxed $\ell_2$ UOT $\gamma$={:1.3f}'.format(g_list_v[iv]),
+             fontsize=11)
+    return 1
+
+
+i = 0
+_update_plot(i)
+
+ani = animation.FuncAnimation(pl.gcf(), _update_plot, nv, interval=50, repeat_delay=2000)