add test and example of UOT

Author: Hicham Janati

examples/plot_UOT_1D.py

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+# -*- coding: utf-8 -*-
+"""
+====================
+1D Unbalanced optimal transport
+====================
+
+This example illustrates the computation of Unbalanced Optimal transport
+using a Kullback-Leibler relaxation.
+"""
+
+# Author: Hicham Janati <hicham.janati@inria.fr>
+#
+# License: MIT License
+
+import numpy as np
+import matplotlib.pylab as pl
+import ot
+import ot.plot
+from ot.datasets import make_1D_gauss as gauss
+
+##############################################################################
+# Generate data
+# -------------
+
+
+#%% parameters
+
+n = 100  # nb bins
+
+# bin positions
+x = np.arange(n, dtype=np.float64)
+
+# Gaussian distributions
+a = gauss(n, m=20, s=5)  # m= mean, s= std
+b = gauss(n, m=60, s=10)
+
+# make distributions unbalanced
+b *= 5.
+
+# loss matrix
+M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
+M /= M.max()
+
+
+##############################################################################
+# Plot distributions and loss matrix
+# ----------------------------------
+
+#%% plot the distributions
+
+pl.figure(1, figsize=(6.4, 3))
+pl.plot(x, a, 'b', label='Source distribution')
+pl.plot(x, b, 'r', label='Target distribution')
+pl.legend()
+
+#%% plot distributions and loss matrix
+
+pl.figure(2, figsize=(5, 5))
+ot.plot.plot1D_mat(a, b, M, 'Cost matrix M')
+
+
+##############################################################################
+# Solve Unbalanced Sinkhorn
+# --------------
+
+
+#%% Sinkhorn
+
+lambd = 0.1
+alpha = 1.
+Gs = ot.unbalanced.sinkhorn_unbalanced(a, b, M, lambd, alpha, verbose=True)
+
+pl.figure(4, figsize=(5, 5))
+ot.plot.plot1D_mat(a, b, Gs, 'UOT matrix Sinkhorn')
+
+pl.show()

test/test_unbalanced.py

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+"""Tests for module Unbalanced OT with entropy regularization"""
+
+# Author: Hicham Janati <hicham.janati@inria.fr>
+#
+# License: MIT License
+
+import numpy as np
+import ot
+
+
+def test_unbalanced():
+    # test generalized sinkhorn for unbalanced OT
+    n = 100
+    rng = np.random.RandomState(42)
+
+    x = rng.randn(n, 2)
+    a = ot.utils.unif(n)
+    b = ot.utils.unif(n) * 1.5
+
+    M = ot.dist(x, x)
+    epsilon = 1.
+    alpha = 1.
+    K = np.exp(- M / epsilon)
+
+    G, log = ot.unbalanced.sinkhorn_unbalanced(a, b, M, reg=epsilon, alpha=alpha,
+                                               stopThr=1e-10, log=True)
+
+    # check fixed point equations
+    fi = alpha / (alpha + epsilon)
+    v_final = (b / K.T.dot(log["u"])) ** fi
+    u_final = (a / K.dot(log["v"])) ** fi
+
+    np.testing.assert_allclose(
+        u_final, log["u"], atol=1e-05)
+    np.testing.assert_allclose(
+        v_final, log["v"], atol=1e-05)