""" ========================== 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 # # License: MIT License import numpy as np import ot ############################################################################# # COMPUTE TEST FOR SEMI-DUAL PROBLEM ############################################################################# ############################################################################# # # 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 = 30000 rng = np.random.RandomState(0) x = rng.randn(n, 2) u = ot.utils.unif(n) M = ot.dist(x, x) G = ot.stochastic.solve_semi_dual_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 = 100000 rng = np.random.RandomState(0) x = rng.randn(n, 2) u = ot.utils.unif(n) M = ot.dist(x, x) G, log = ot.stochastic.solve_semi_dual_entropic(u, u, M, reg, "asgd", numItermax=numItermax, log=True) # 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 = 100000 rng = np.random.RandomState(0) x = rng.randn(n, 2) u = ot.utils.unif(n) M = ot.dist(x, x) G_asgd = ot.stochastic.solve_semi_dual_entropic(u, u, M, reg, "asgd", numItermax=nb_iter) G_sag = ot.stochastic.solve_semi_dual_entropic(u, u, M, reg, "sag", numItermax=nb_iter) G_sinkhorn = ot.sinkhorn(u, u, M, reg) # check constratints np.testing.assert_allclose( G_sag.sum(1), G_sinkhorn.sum(1), atol=1e-03) np.testing.assert_allclose( G_sag.sum(0), G_sinkhorn.sum(0), atol=1e-03) np.testing.assert_allclose( G_asgd.sum(1), G_sinkhorn.sum(1), atol=1e-03) np.testing.assert_allclose( G_asgd.sum(0), G_sinkhorn.sum(0), atol=1e-03) np.testing.assert_allclose( G_sag, G_sinkhorn, atol=1e-03) # cf convergence sag np.testing.assert_allclose( G_asgd, G_sinkhorn, atol=1e-03) # cf convergence asgd ############################################################################# # COMPUTE TEST FOR DUAL PROBLEM ############################################################################# ############################################################################# # # TEST SGD algorithm # --------------------------------------------- # 2 identical discrete measures u defined on the same space with a # regularization term, a batch_size and a number of iteration def test_stochastic_dual_sgd(): # test sgd n = 10 reg = 1 numItermax = 15000 batch_size = 10 rng = np.random.RandomState(0) x = rng.randn(n, 2) u = ot.utils.unif(n) M = ot.dist(x, x) G, log = ot.stochastic.solve_dual_entropic(u, u, M, reg, batch_size, numItermax=numItermax, log=True) # check constratints np.testing.assert_allclose( u, G.sum(1), atol=1e-03) # cf convergence sgd np.testing.assert_allclose( u, G.sum(0), atol=1e-03) # cf convergence sgd ############################################################################# # # TEST Convergence SGD toward Sinkhorn's solution # -------------------------------------------------------- # 2 identical discrete measures u defined on the same space with a # regularization term, a batch_size and a number of iteration def test_dual_sgd_sinkhorn(): # test all dual algorithms n = 10 reg = 1 nb_iter = 15000 batch_size = 10 rng = np.random.RandomState(0) # Test uniform x = rng.randn(n, 2) u = ot.utils.unif(n) M = ot.dist(x, x) G_sgd = ot.stochastic.solve_dual_entropic(u, u, M, reg, batch_size, numItermax=nb_iter) G_sinkhorn = ot.sinkhorn(u, u, M, reg) # check constratints np.testing.assert_allclose( G_sgd.sum(1), G_sinkhorn.sum(1), atol=1e-03) np.testing.assert_allclose( G_sgd.sum(0), G_sinkhorn.sum(0), atol=1e-03) np.testing.assert_allclose( G_sgd, G_sinkhorn, atol=1e-03) # cf convergence sgd # Test gaussian n = 30 reg = 1 batch_size = 30 a = ot.datasets.make_1D_gauss(n, 15, 5) # m= mean, s= std b = ot.datasets.make_1D_gauss(n, 15, 5) X_source = np.arange(n, dtype=np.float64) Y_target = np.arange(n, dtype=np.float64) M = ot.dist(X_source.reshape((n, 1)), Y_target.reshape((n, 1))) M /= M.max() G_sgd = ot.stochastic.solve_dual_entropic(a, b, M, reg, batch_size, numItermax=nb_iter) G_sinkhorn = ot.sinkhorn(a, b, M, reg) # check constratints np.testing.assert_allclose( G_sgd.sum(1), G_sinkhorn.sum(1), atol=1e-03) np.testing.assert_allclose( G_sgd.sum(0), G_sinkhorn.sum(0), atol=1e-03) np.testing.assert_allclose( G_sgd, G_sinkhorn, atol=1e-03) # cf convergence sgd