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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(nx):
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
def fb(G):
return 0.5 * nx.sum(G ** 2)
ab, bb, Mb = nx.from_numpy(a, b, M)
reg = 1e-1
G, log = ot.optim.cg(a, b, M, reg, f, df, verbose=True, log=True)
Gb, log = ot.optim.cg(ab, bb, Mb, reg, fb, df, verbose=True, log=True)
Gb = nx.to_numpy(Gb)
np.testing.assert_allclose(Gb, G)
np.testing.assert_allclose(a, Gb.sum(1))
np.testing.assert_allclose(b, Gb.sum(0))
def test_conditional_gradient_itermax(nx):
n = 100 # 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
def fb(G):
return 0.5 * nx.sum(G ** 2)
ab, bb, Mb = nx.from_numpy(a, b, M)
reg = 1e-1
G, log = ot.optim.cg(a, b, M, reg, f, df, numItermaxEmd=10000,
verbose=True, log=True)
Gb, log = ot.optim.cg(ab, bb, Mb, reg, fb, df, numItermaxEmd=10000,
verbose=True, log=True)
Gb = nx.to_numpy(Gb)
np.testing.assert_allclose(Gb, G)
np.testing.assert_allclose(a, Gb.sum(1))
np.testing.assert_allclose(b, Gb.sum(0))
def test_generalized_conditional_gradient(nx):
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
def fb(G):
return 0.5 * nx.sum(G ** 2)
reg1 = 1e-3
reg2 = 1e-1
ab, bb, Mb = nx.from_numpy(a, b, M)
G, log = ot.optim.gcg(a, b, M, reg1, reg2, f, df, verbose=True, log=True)
Gb, log = ot.optim.gcg(ab, bb, Mb, reg1, reg2, fb, df, verbose=True, log=True)
Gb = nx.to_numpy(Gb)
np.testing.assert_allclose(Gb, G, atol=1e-12)
np.testing.assert_allclose(a, Gb.sum(1), atol=1e-05)
np.testing.assert_allclose(b, Gb.sum(0), atol=1e-05)
def test_solve_1d_linesearch_quad_funct():
np.testing.assert_allclose(ot.optim.solve_1d_linesearch_quad(1, -1), 0.5)
np.testing.assert_allclose(ot.optim.solve_1d_linesearch_quad(-1, 5), 0)
np.testing.assert_allclose(ot.optim.solve_1d_linesearch_quad(-1, 0.5), 1)
def test_line_search_armijo(nx):
xk = np.array([[0.25, 0.25], [0.25, 0.25]])
pk = np.array([[-0.25, 0.25], [0.25, -0.25]])
gfk = np.array([[23.04273441, 23.0449082], [23.04273441, 23.0449082]])
old_fval = -123.
xkb, pkb, gfkb = nx.from_numpy(xk, pk, gfk)
def f(x):
return 1.
# Should not throw an exception and return 0. for alpha
alpha, a, b = ot.optim.line_search_armijo(
f, xkb, pkb, gfkb, old_fval
)
alpha_np, anp, bnp = ot.optim.line_search_armijo(
f, xk, pk, gfk, old_fval
)
assert a == anp
assert b == bnp
assert alpha == 0.
# check line search armijo
def f(x):
return nx.sum((x - 5.0) ** 2)
def grad(x):
return 2 * (x - 5.0)
xk = nx.from_numpy(np.array([[[-5.0, -5.0]]]))
pk = nx.from_numpy(np.array([[[100.0, 100.0]]]))
gfk = grad(xk)
old_fval = f(xk)
# chech the case where the optimum is on the direction
alpha, _, _ = ot.optim.line_search_armijo(f, xk, pk, gfk, old_fval)
np.testing.assert_allclose(alpha, 0.1)
# check the case where the direction is not far enough
pk = nx.from_numpy(np.array([[[3.0, 3.0]]]))
alpha, _, _ = ot.optim.line_search_armijo(f, xk, pk, gfk, old_fval, alpha0=1.0)
np.testing.assert_allclose(alpha, 1.0)
# check the case where checking the wrong direction
alpha, _, _ = ot.optim.line_search_armijo(f, xk, -pk, gfk, old_fval)
assert alpha <= 0
# check the case where the point is not a vector
xk = nx.from_numpy(np.array(-5.0))
pk = nx.from_numpy(np.array(100.0))
gfk = grad(xk)
old_fval = f(xk)
alpha, _, _ = ot.optim.line_search_armijo(f, xk, pk, gfk, old_fval)
np.testing.assert_allclose(alpha, 0.1)
def test_line_search_armijo_dtype_device(nx):
for tp in nx.__type_list__:
def f(x):
return nx.sum((x - 5.0) ** 2)
def grad(x):
return 2 * (x - 5.0)
xk = np.array([[[-5.0, -5.0]]])
pk = np.array([[[100.0, 100.0]]])
xkb, pkb = nx.from_numpy(xk, pk, type_as=tp)
gfkb = grad(xkb)
old_fval = f(xkb)
# chech the case where the optimum is on the direction
alpha, _, fval = ot.optim.line_search_armijo(f, xkb, pkb, gfkb, old_fval)
alpha = nx.to_numpy(alpha)
np.testing.assert_allclose(alpha, 0.1)
nx.assert_same_dtype_device(old_fval, fval)
# check the case where the direction is not far enough
pk = np.array([[[3.0, 3.0]]])
pkb = nx.from_numpy(pk, type_as=tp)
alpha, _, fval = ot.optim.line_search_armijo(f, xkb, pkb, gfkb, old_fval, alpha0=1.0)
alpha = nx.to_numpy(alpha)
np.testing.assert_allclose(alpha, 1.0)
nx.assert_same_dtype_device(old_fval, fval)
# check the case where checking the wrong direction
alpha, _, fval = ot.optim.line_search_armijo(f, xkb, -pkb, gfkb, old_fval)
alpha = nx.to_numpy(alpha)
assert alpha <= 0
nx.assert_same_dtype_device(old_fval, fval)
# check the case where the point is not a vector
xkb = nx.from_numpy(np.array(-5.0), type_as=tp)
pkb = nx.from_numpy(np.array(100), type_as=tp)
gfkb = grad(xkb)
old_fval = f(xkb)
alpha, _, fval = ot.optim.line_search_armijo(f, xkb, pkb, gfkb, old_fval)
alpha = nx.to_numpy(alpha)
np.testing.assert_allclose(alpha, 0.1)
nx.assert_same_dtype_device(old_fval, fval)
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