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"""Tests for module gaussian"""
# Author: Eloi Tanguy <eloi.tanguy@u-paris>
# Remi Flamary <remi.flamary@polytehnique.edu>
# Julie Delon <julie.delon@math.cnrs.fr>
#
# License: MIT License
import numpy as np
import pytest
from ot.utils import proj_simplex
from ot.gmm import (
gaussian_pdf,
gmm_pdf,
dist_bures_squared,
gmm_ot_loss,
gmm_ot_plan,
gmm_ot_apply_map,
gmm_ot_plan_density,
)
try:
import torch
except ImportError:
torch = False
def get_gmms(nx=None):
rng = np.random.RandomState(seed=42)
ks = 3
kt = 5
d = 3
m_s = rng.randn(ks, d)
m_t = rng.randn(kt, d)
C_s = rng.randn(ks, d, d)
C_s = np.matmul(C_s, np.transpose(C_s, (0, 2, 1)))
C_t = rng.randn(kt, d, d)
C_t = np.matmul(C_t, np.transpose(C_t, (0, 2, 1)))
w_s = proj_simplex(rng.rand(ks))
w_t = proj_simplex(rng.rand(kt))
if nx is not None:
m_s = nx.from_numpy(m_s)
m_t = nx.from_numpy(m_t)
C_s = nx.from_numpy(C_s)
C_t = nx.from_numpy(C_t)
w_s = nx.from_numpy(w_s)
w_t = nx.from_numpy(w_t)
return m_s, m_t, C_s, C_t, w_s, w_t
def test_gaussian_pdf(nx):
rng = np.random.RandomState(seed=42)
n = 7
d = 3
x = nx.from_numpy(rng.randn(n, d))
m, _, C, _, _, _ = get_gmms(nx)
pdf = gaussian_pdf(x, m[0], C[0])
assert pdf.shape == (n,)
x = nx.from_numpy(rng.randn(n, n, d))
pdf = gaussian_pdf(x, m[0], C[0])
assert pdf.shape == (
n,
n,
)
with pytest.raises(AssertionError):
gaussian_pdf(x, m[0, :-1], C[0])
def test_gmm_pdf(nx):
rng = np.random.RandomState(seed=42)
n = 7
d = 3
x = nx.from_numpy(rng.randn(n, d))
m, _, C, _, w, _ = get_gmms(nx)
pdf = gmm_pdf(x, m, C, w)
assert pdf.shape == (n,)
x = nx.from_numpy(rng.randn(n, n, d))
pdf = gmm_pdf(x, m, C, w)
assert pdf.shape == (
n,
n,
)
with pytest.raises(AssertionError):
gmm_pdf(x, m[:-1], C, w)
@pytest.skip_backend("tf") # skips because of array assignment
@pytest.skip_backend("jax")
def test_dist_bures_squared(nx):
m_s, m_t, C_s, C_t, _, _ = get_gmms(nx)
dist_bures_squared(m_s, m_t, C_s, C_t)
D0 = dist_bures_squared(m_s, m_s, C_s, C_s)
assert np.allclose(np.diag(D0), 0, atol=1e-6)
with pytest.raises(AssertionError):
dist_bures_squared(m_s[:, 1:], m_t, C_s, C_t)
with pytest.raises(AssertionError):
dist_bures_squared(m_s[1:], m_t, C_s, C_t)
with pytest.raises(AssertionError):
dist_bures_squared(m_s, m_t[1:], C_s, C_t)
@pytest.skip_backend("tf") # skips because of array assignment
@pytest.skip_backend("jax")
def test_gmm_ot_loss(nx):
m_s, m_t, C_s, C_t, w_s, w_t = get_gmms(nx)
loss = gmm_ot_loss(m_s, m_t, C_s, C_t, w_s, w_t)
assert loss > 0
loss = gmm_ot_loss(m_s, m_s, C_s, C_s, w_s, w_s)
assert np.allclose(loss, 0, atol=1e-6)
with pytest.raises(AssertionError):
gmm_ot_loss(m_s, m_t, C_s, C_t, w_s[1:], w_t)
with pytest.raises(AssertionError):
gmm_ot_loss(m_s, m_t, C_s, C_t, w_s, w_t[1:])
@pytest.skip_backend("tf") # skips because of array assignment
@pytest.skip_backend("jax")
def test_gmm_ot_plan(nx):
m_s, m_t, C_s, C_t, w_s, w_t = get_gmms(nx)
plan = gmm_ot_plan(m_s, m_t, C_s, C_t, w_s, w_t)
assert np.allclose(plan.sum(0), w_t, atol=1e-6)
assert np.allclose(plan.sum(1), w_s, atol=1e-6)
plan = gmm_ot_plan(m_s, m_s + 1, C_s, C_s, w_s, w_s)
assert np.allclose(plan, np.diag(w_s), atol=1e-6)
with pytest.raises(AssertionError):
gmm_ot_loss(m_s, m_t, C_s, C_t, w_s[1:], w_t)
with pytest.raises(AssertionError):
gmm_ot_loss(m_s, m_t, C_s, C_t, w_s, w_t[1:])
def test_gmm_apply_map():
m_s, m_t, C_s, C_t, w_s, w_t = get_gmms()
rng = np.random.RandomState(seed=42)
x = rng.randn(7, 3)
for method in ["bary", "rand"]:
gmm_ot_apply_map(x, m_s, m_t, C_s, C_t, w_s, w_t, method=method)
plan = gmm_ot_plan(m_s, m_t, C_s, C_t, w_s, w_t)
gmm_ot_apply_map(x, m_s, m_t, C_s, C_t, w_s, w_t, plan=plan)
@pytest.mark.skipif(not torch, reason="No torch available")
def test_gradient_gmm_ot_loss_pytorch():
m_s, m_t, C_s, C_t, w_s, w_t = get_gmms()
m_s = torch.tensor(m_s, requires_grad=True)
m_t = torch.tensor(m_t, requires_grad=True)
C_s = torch.tensor(C_s, requires_grad=True)
C_t = torch.tensor(C_t, requires_grad=True)
w_s = torch.tensor(w_s, requires_grad=True)
w_t = torch.tensor(w_t, requires_grad=True)
loss = gmm_ot_loss(m_s, m_t, C_s, C_t, w_s, w_t)
loss.backward()
grad_m_s = m_s.grad
grad_C_s = C_s.grad
grad_w_s = w_s.grad
assert (grad_m_s**2).sum().item() > 0
assert (grad_C_s**2).sum().item() > 0
assert (grad_w_s**2).sum().item() > 0
def test_gmm_ot_plan_density(nx):
m_s, m_t, C_s, C_t, w_s, w_t = get_gmms(nx)
rng = np.random.RandomState(seed=42)
n = 7
x = nx.from_numpy(rng.randn(n, 3))
y = nx.from_numpy(rng.randn(n + 1, 3))
density = gmm_ot_plan_density(x, y, m_s, m_t, C_s, C_t, w_s, w_t)
assert density.shape == (n, n + 1)
plan = gmm_ot_plan(m_s, m_t, C_s, C_t, w_s, w_t)
gmm_ot_plan_density(x, x, m_s, m_t, C_s, C_t, w_s, w_t, plan=plan)
with pytest.raises(AssertionError):
gmm_ot_plan_density(x[:, 1:], y, m_s, m_t, C_s, C_t, w_s, w_t)
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