add doc for gallery

1 files changed, 193 insertions, 0 deletions

diff --git a/docs/source/auto_examples/plot_barycenter_1D.rst b/docs/source/auto_examples/plot_barycenter_1D.rst
new file mode 100644
index 0000000..1b15c77
--- /dev/null
+++ b/docs/source/auto_examples/plot_barycenter_1D.rst
@@ -0,0 +1,193 @@
+
+
+.. _sphx_glr_auto_examples_plot_barycenter_1D.py:
+
+
+==============================
+1D Wasserstein barycenter demo
+==============================
+
+
+@author: rflamary
+
+
+
+
+.. rst-class:: sphx-glr-horizontal
+
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_001.png
+            :scale: 47
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_002.png
+            :scale: 47
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_003.png
+            :scale: 47
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_004.png
+            :scale: 47
+
+
+
+
+
+.. code-block:: python
+
+
+    import numpy as np
+    import matplotlib.pylab as pl
+    import ot
+    from mpl_toolkits.mplot3d import Axes3D #necessary for 3d plot even if not used
+    from matplotlib.collections import PolyCollection
+
+
+    #%% parameters
+
+    n=100 # nb bins
+
+    # bin positions
+    x=np.arange(n,dtype=np.float64)
+
+    # Gaussian distributions
+    a1=ot.datasets.get_1D_gauss(n,m=20,s=5) # m= mean, s= std
+    a2=ot.datasets.get_1D_gauss(n,m=60,s=8)
+
+    # creating matrix A containing all distributions
+    A=np.vstack((a1,a2)).T
+    nbd=A.shape[1]
+
+    # loss matrix + normalization
+    M=ot.utils.dist0(n)
+    M/=M.max()
+
+    #%% plot the distributions
+
+    pl.figure(1)
+    for i in range(nbd):
+        pl.plot(x,A[:,i])
+    pl.title('Distributions')
+
+    #%% barycenter computation
+
+    alpha=0.2 # 0<=alpha<=1
+    weights=np.array([1-alpha,alpha])
+
+    # l2bary
+    bary_l2=A.dot(weights)
+
+    # wasserstein
+    reg=1e-3
+    bary_wass=ot.bregman.barycenter(A,M,reg,weights)
+
+    pl.figure(2)
+    pl.clf()
+    pl.subplot(2,1,1)
+    for i in range(nbd):
+        pl.plot(x,A[:,i])
+    pl.title('Distributions')
+
+    pl.subplot(2,1,2)
+    pl.plot(x,bary_l2,'r',label='l2')
+    pl.plot(x,bary_wass,'g',label='Wasserstein')
+    pl.legend()
+    pl.title('Barycenters')
+
+
+    #%% barycenter interpolation
+
+    nbalpha=11
+    alphalist=np.linspace(0,1,nbalpha)
+
+
+    B_l2=np.zeros((n,nbalpha))
+
+    B_wass=np.copy(B_l2)
+
+    for i in range(0,nbalpha):
+        alpha=alphalist[i]
+        weights=np.array([1-alpha,alpha])
+        B_l2[:,i]=A.dot(weights)
+        B_wass[:,i]=ot.bregman.barycenter(A,M,reg,weights)
+
+    #%% plot interpolation
+
+    pl.figure(3,(10,5))
+
+    #pl.subplot(1,2,1)
+    cmap=pl.cm.get_cmap('viridis')
+    verts = []
+    zs = alphalist
+    for i,z in enumerate(zs):
+        ys = B_l2[:,i]
+        verts.append(list(zip(x, ys)))
+
+    ax = pl.gcf().gca(projection='3d')
+
+    poly = PolyCollection(verts,facecolors=[cmap(a) for a in alphalist])
+    poly.set_alpha(0.7)
+    ax.add_collection3d(poly, zs=zs, zdir='y')
+
+    ax.set_xlabel('x')
+    ax.set_xlim3d(0, n)
+    ax.set_ylabel('$\\alpha$')
+    ax.set_ylim3d(0,1)
+    ax.set_zlabel('')
+    ax.set_zlim3d(0, B_l2.max()*1.01)
+    pl.title('Barycenter interpolation with l2')
+
+    pl.show()
+
+    pl.figure(4,(10,5))
+
+    #pl.subplot(1,2,1)
+    cmap=pl.cm.get_cmap('viridis')
+    verts = []
+    zs = alphalist
+    for i,z in enumerate(zs):
+        ys = B_wass[:,i]
+        verts.append(list(zip(x, ys)))
+
+    ax = pl.gcf().gca(projection='3d')
+
+    poly = PolyCollection(verts,facecolors=[cmap(a) for a in alphalist])
+    poly.set_alpha(0.7)
+    ax.add_collection3d(poly, zs=zs, zdir='y')
+
+    ax.set_xlabel('x')
+    ax.set_xlim3d(0, n)
+    ax.set_ylabel('$\\alpha$')
+    ax.set_ylim3d(0,1)
+    ax.set_zlabel('')
+    ax.set_zlim3d(0, B_l2.max()*1.01)
+    pl.title('Barycenter interpolation with Wasserstein')
+
+    pl.show()
+**Total running time of the script:** ( 0 minutes  2.274 seconds)
+
+
+
+.. container:: sphx-glr-footer
+
+
+  .. container:: sphx-glr-download
+
+     :download:`Download Python source code: plot_barycenter_1D.py <plot_barycenter_1D.py>`
+
+
+
+  .. container:: sphx-glr-download
+
+     :download:`Download Jupyter notebook: plot_barycenter_1D.ipynb <plot_barycenter_1D.ipynb>`
+
+.. rst-class:: sphx-glr-signature
+
+    `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_