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+# -*- coding: utf-8 -*-
+"""
+==================================
+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.
+
+
+
+"""
+
+import numpy as np
+import matplotlib.pylab as pl
+import ot
+import ot.plot
+
+##############################################################################
+# Generate data
+# -------------
+
+#%% parameters
+
+n = 100  # nb bins
+
+# bin positions
+x = np.arange(n, dtype=np.float64)
+
+# Gaussian distributions
+a = ot.datasets.make_1D_gauss(n, m=20, s=5)  # m= mean, s= std
+b = ot.datasets.make_1D_gauss(n, m=60, s=10)
+
+# loss matrix
+M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
+M /= M.max()
+
+##############################################################################
+# Solve EMD
+# ---------
+
+#%% EMD
+
+G0 = ot.emd(a, b, M)
+
+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
+
+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')
+
+##############################################################################
+# 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
+
+Ge = ot.optim.cg(a, b, M, reg, f, df, verbose=True)
+
+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
+
+Gel2 = ot.optim.gcg(a, b, M, reg1, reg2, f, df, verbose=True)
+
+pl.figure(5, figsize=(5, 5))
+ot.plot.plot1D_mat(a, b, Gel2, 'OT entropic + matrix Frob. reg')
+pl.show()