1 files changed, 83 insertions, 28 deletions
diff --git a/docs/source/auto_examples/plot_optim_OTreg.py b/docs/source/auto_examples/plot_optim_OTreg.py
index 8abb426..e1a737e 100644
--- a/docs/source/auto_examples/plot_optim_OTreg.py
+++ b/docs/source/auto_examples/plot_optim_OTreg.py
@@ -4,6 +4,24 @@
 Regularized OT with generic solver
 ==================================
 
+Illustrates the use of the generic solver for regularized OT with
+user-designed regularization term. It uses Conditional gradient as in [6] and
+generalized Conditional Gradient as proposed in [5][7].
+
+
+[5] N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy, Optimal Transport for
+Domain Adaptation, in IEEE Transactions on Pattern Analysis and Machine
+Intelligence , vol.PP, no.99, pp.1-1.
+
+[6] Ferradans, S., Papadakis, N., Peyré, G., & Aujol, J. F. (2014).
+Regularized discrete optimal transport. SIAM Journal on Imaging Sciences,
+7(3), 1853-1882.
+
+[7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). Generalized
+conditional gradient: analysis of convergence and applications.
+arXiv preprint arXiv:1510.06567.
+
+
 
 """
 
@@ -12,63 +30,100 @@ import matplotlib.pylab as pl
 import ot
 
 
+##############################################################################
+# Generate data
+# -------------
 
 #%% parameters
 
-n=100 # nb bins
+n = 100  # nb bins
 
 # bin positions
-x=np.arange(n,dtype=np.float64)
+x = np.arange(n, dtype=np.float64)
 
 # Gaussian distributions
-a=ot.datasets.get_1D_gauss(n,m=20,s=5) # m= mean, s= std
-b=ot.datasets.get_1D_gauss(n,m=60,s=10)
+a = ot.datasets.get_1D_gauss(n, m=20, s=5)  # m= mean, s= std
+b = ot.datasets.get_1D_gauss(n, m=60, s=10)
 
 # loss matrix
-M=ot.dist(x.reshape((n,1)),x.reshape((n,1)))
-M/=M.max()
+M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
+M /= M.max()
+
+##############################################################################
+# Solve EMD
+# ---------
 
 #%% EMD
 
-G0=ot.emd(a,b,M)
+G0 = ot.emd(a, b, M)
 
-pl.figure(3)
-ot.plot.plot1D_mat(a,b,G0,'OT matrix G0')
+pl.figure(3, figsize=(5, 5))
+ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0')
+
+##############################################################################
+# Solve EMD with Frobenius norm regularization
+# --------------------------------------------
 
 #%% Example with Frobenius norm regularization
 
-def f(G): return 0.5*np.sum(G**2)
-def df(G): return G
 
-reg=1e-1
+def f(G):
+    return 0.5 * np.sum(G**2)
+
+
+def df(G):
+    return G
+
 
-Gl2=ot.optim.cg(a,b,M,reg,f,df,verbose=True)
+reg = 1e-1
+
+Gl2 = ot.optim.cg(a, b, M, reg, f, df, verbose=True)
 
 pl.figure(3)
-ot.plot.plot1D_mat(a,b,Gl2,'OT matrix Frob. reg')
+ot.plot.plot1D_mat(a, b, Gl2, 'OT matrix Frob. reg')
+
+##############################################################################
+# Solve EMD with entropic regularization
+# --------------------------------------
 
 #%% Example with entropic regularization
 
-def f(G): return np.sum(G*np.log(G))
-def df(G): return np.log(G)+1
 
-reg=1e-3
+def f(G):
+    return np.sum(G * np.log(G))
+
+
+def df(G):
+    return np.log(G) + 1.
+
+
+reg = 1e-3
 
-Ge=ot.optim.cg(a,b,M,reg,f,df,verbose=True)
+Ge = ot.optim.cg(a, b, M, reg, f, df, verbose=True)
 
-pl.figure(4)
-ot.plot.plot1D_mat(a,b,Ge,'OT matrix Entrop. reg')
+pl.figure(4, figsize=(5, 5))
+ot.plot.plot1D_mat(a, b, Ge, 'OT matrix Entrop. reg')
+
+##############################################################################
+# Solve EMD with Frobenius norm + entropic regularization
+# -------------------------------------------------------
 
 #%% Example with Frobenius norm + entropic regularization with gcg
 
-def f(G): return 0.5*np.sum(G**2)
-def df(G): return G
 
-reg1=1e-3
-reg2=1e-1
+def f(G):
+    return 0.5 * np.sum(G**2)
+
+
+def df(G):
+    return G
+
+
+reg1 = 1e-3
+reg2 = 1e-1
 
-Gel2=ot.optim.gcg(a,b,M,reg1,reg2,f,df,verbose=True)
+Gel2 = ot.optim.gcg(a, b, M, reg1, reg2, f, df, verbose=True)
 
-pl.figure(5)
-ot.plot.plot1D_mat(a,b,Gel2,'OT entropic + matrix Frob. reg')
-pl.show()
-\ No newline at end of file
+pl.figure(5, figsize=(5, 5))
+ot.plot.plot1D_mat(a, b, Gel2, 'OT entropic + matrix Frob. reg')
+pl.show()