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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>`_ |