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"""
==========================
Stochastic test
==========================
This example is designed to test the stochatic optimization algorithms module
for descrete and semicontinous measures from the POT library.
"""
# Author: Kilian Fatras <kilian.fatras@gmail.com>
#
# License: MIT License
import numpy as np
import ot
#############################################################################
#
# TEST SAG algorithm
# ---------------------------------------------
# 2 identical discrete measures u defined on the same space with a
# regularization term, a learning rate and a number of iteration
def test_stochastic_sag():
# test sag
n = 15
reg = 1
numItermax = 300000
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
G = ot.stochastic.transportation_matrix_entropic(u, u, M, reg, "sag",
numItermax=numItermax)
# check constratints
np.testing.assert_allclose(
u, G.sum(1), atol=1e-04) # cf convergence sag
np.testing.assert_allclose(
u, G.sum(0), atol=1e-04) # cf convergence sag
#############################################################################
#
# TEST ASGD algorithm
# ---------------------------------------------
# 2 identical discrete measures u defined on the same space with a
# regularization term, a learning rate and a number of iteration
def test_stochastic_asgd():
# test asgd
n = 15
reg = 1
numItermax = 300000
lr = 1
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
G = ot.stochastic.transportation_matrix_entropic(u, u, M, reg, "asgd",
numItermax=numItermax,
lr=lr)
# check constratints
np.testing.assert_allclose(
u, G.sum(1), atol=1e-03) # cf convergence asgd
np.testing.assert_allclose(
u, G.sum(0), atol=1e-03) # cf convergence asgd
#############################################################################
#
# TEST Convergence SAG and ASGD toward Sinkhorn's solution
# --------------------------------------------------------
# 2 identical discrete measures u defined on the same space with a
# regularization term, a learning rate and a number of iteration
def test_sag_asgd_sinkhorn():
# test all algorithms
n = 15
reg = 1
nb_iter = 300000
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
zero = np.zeros(n)
M = ot.dist(x, x)
G_asgd = ot.stochastic.transportation_matrix_entropic(u, u, M, reg, "asgd",
numItermax=nb_iter,
lr=1)
G_sag = ot.stochastic.transportation_matrix_entropic(u, u, M, reg, "sag",
numItermax=nb_iter)
G_sinkhorn = ot.sinkhorn(u, u, M, reg)
# check constratints
np.testing.assert_allclose(
zero, (G_sag - G_sinkhorn).sum(1), atol=1e-03) # cf convergence sag
np.testing.assert_allclose(
zero, (G_sag - G_sinkhorn).sum(0), atol=1e-03) # cf convergence sag
np.testing.assert_allclose(
zero, (G_asgd - G_sinkhorn).sum(1), atol=1e-03) # cf convergence asgd
np.testing.assert_allclose(
zero, (G_asgd - G_sinkhorn).sum(0), atol=1e-03) # cf convergence asgd
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