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"""Tests for module optim fro OT optimization """
# Author: Remi Flamary <remi.flamary@unice.fr>
#
# License: MIT License
import numpy as np
import ot
def test_conditional_gradient():
n_bins = 100 # nb bins
np.random.seed(0)
# bin positions
x = np.arange(n_bins, dtype=np.float64)
# Gaussian distributions
a = ot.datasets.make_1D_gauss(n_bins, m=20, s=5) # m= mean, s= std
b = ot.datasets.make_1D_gauss(n_bins, m=60, s=10)
# loss matrix
M = ot.dist(x.reshape((n_bins, 1)), x.reshape((n_bins, 1)))
M /= M.max()
def f(G):
return 0.5 * np.sum(G**2)
def df(G):
return G
reg = 1e-1
G, log = ot.optim.cg(a, b, M, reg, f, df, verbose=True, log=True)
np.testing.assert_allclose(a, G.sum(1))
np.testing.assert_allclose(b, G.sum(0))
def test_conditional_gradient2():
n = 1000 # nb samples
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
mu_t = np.array([4, 4])
cov_t = np.array([[1, -.8], [-.8, 1]])
xs = ot.datasets.make_2D_samples_gauss(n, mu_s, cov_s)
xt = ot.datasets.make_2D_samples_gauss(n, mu_t, cov_t)
a, b = np.ones((n,)) / n, np.ones((n,)) / n
# loss matrix
M = ot.dist(xs, xt)
M /= M.max()
def f(G):
return 0.5 * np.sum(G**2)
def df(G):
return G
reg = 1e-1
G, log = ot.optim.cg(a, b, M, reg, f, df, numItermaxEmd=200000,
verbose=True, log=True)
np.testing.assert_allclose(a, G.sum(1))
np.testing.assert_allclose(b, G.sum(0))
def test_generalized_conditional_gradient():
n_bins = 100 # nb bins
np.random.seed(0)
# bin positions
x = np.arange(n_bins, dtype=np.float64)
# Gaussian distributions
a = ot.datasets.make_1D_gauss(n_bins, m=20, s=5) # m= mean, s= std
b = ot.datasets.make_1D_gauss(n_bins, m=60, s=10)
# loss matrix
M = ot.dist(x.reshape((n_bins, 1)), x.reshape((n_bins, 1)))
M /= M.max()
def f(G):
return 0.5 * np.sum(G**2)
def df(G):
return G
reg1 = 1e-3
reg2 = 1e-1
G, log = ot.optim.gcg(a, b, M, reg1, reg2, f, df, verbose=True, log=True)
np.testing.assert_allclose(a, G.sum(1), atol=1e-05)
np.testing.assert_allclose(b, G.sum(0), atol=1e-05)
def test_solve_1d_linesearch_quad_funct():
np.testing.assert_allclose(ot.optim.solve_1d_linesearch_quad(1, -1, 0), 0.5)
np.testing.assert_allclose(ot.optim.solve_1d_linesearch_quad(-1, 5, 0), 0)
np.testing.assert_allclose(ot.optim.solve_1d_linesearch_quad(-1, 0.5, 0), 1)
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