path: root/test/test_ot.py

"""Tests for main module ot """

# Author: Remi Flamary <remi.flamary@unice.fr>
#
# License: MIT License

import warnings

import numpy as np
import pytest

import ot
from ot.datasets import make_1D_gauss as gauss
from ot.backend import torch, tf


def test_emd_dimension_and_mass_mismatch():
    # test emd and emd2 for dimension mismatch
    n_samples = 100
    n_features = 2
    rng = np.random.RandomState(0)

    x = rng.randn(n_samples, n_features)
    a = ot.utils.unif(n_samples + 1)

    M = ot.dist(x, x)

    np.testing.assert_raises(AssertionError, ot.emd, a, a, M)

    np.testing.assert_raises(AssertionError, ot.emd2, a, a, M)

    # test emd and emd2 for mass mismatch
    a = ot.utils.unif(n_samples)
    b = a.copy()
    a[0] = 100
    np.testing.assert_raises(AssertionError, ot.emd, a, b, M)
    np.testing.assert_raises(AssertionError, ot.emd2, a, b, M)


def test_emd_backends(nx):
    n_samples = 100
    n_features = 2
    rng = np.random.RandomState(0)

    x = rng.randn(n_samples, n_features)
    y = rng.randn(n_samples, n_features)
    a = ot.utils.unif(n_samples)

    M = ot.dist(x, y)

    G = ot.emd(a, a, M)

    ab, Mb = nx.from_numpy(a, M)

    Gb = ot.emd(ab, ab, Mb)

    np.allclose(G, nx.to_numpy(Gb))


def test_emd2_backends(nx):
    n_samples = 100
    n_features = 2
    rng = np.random.RandomState(0)

    x = rng.randn(n_samples, n_features)
    y = rng.randn(n_samples, n_features)
    a = ot.utils.unif(n_samples)

    M = ot.dist(x, y)

    val = ot.emd2(a, a, M)

    ab, Mb = nx.from_numpy(a, M)

    valb = ot.emd2(ab, ab, Mb)

    np.allclose(val, nx.to_numpy(valb))


def test_emd_emd2_types_devices(nx):
    n_samples = 100
    n_features = 2
    rng = np.random.RandomState(0)

    x = rng.randn(n_samples, n_features)
    y = rng.randn(n_samples, n_features)
    a = ot.utils.unif(n_samples)

    M = ot.dist(x, y)

    for tp in nx.__type_list__:
        print(nx.dtype_device(tp))

        ab, Mb = nx.from_numpy(a, M, type_as=tp)

        Gb = ot.emd(ab, ab, Mb)

        w = ot.emd2(ab, ab, Mb)

        nx.assert_same_dtype_device(Mb, Gb)
        nx.assert_same_dtype_device(Mb, w)


@pytest.mark.skipif(not tf, reason="tf not installed")
def test_emd_emd2_devices_tf():
    if not tf:
        return
    nx = ot.backend.TensorflowBackend()

    n_samples = 100
    n_features = 2
    rng = np.random.RandomState(0)
    x = rng.randn(n_samples, n_features)
    y = rng.randn(n_samples, n_features)
    a = ot.utils.unif(n_samples)
    M = ot.dist(x, y)

    # Check that everything stays on the CPU
    with tf.device("/CPU:0"):
        ab, Mb = nx.from_numpy(a, M)
        Gb = ot.emd(ab, ab, Mb)
        w = ot.emd2(ab, ab, Mb)
        nx.assert_same_dtype_device(Mb, Gb)
        nx.assert_same_dtype_device(Mb, w)

    if len(tf.config.list_physical_devices('GPU')) > 0:
        # Check that everything happens on the GPU
        ab, Mb = nx.from_numpy(a, M)
        Gb = ot.emd(ab, ab, Mb)
        w = ot.emd2(ab, ab, Mb)
        nx.assert_same_dtype_device(Mb, Gb)
        nx.assert_same_dtype_device(Mb, w)
        assert nx.dtype_device(Gb)[1].startswith("GPU")


def test_emd2_gradients():
    n_samples = 100
    n_features = 2
    rng = np.random.RandomState(0)

    x = rng.randn(n_samples, n_features)
    y = rng.randn(n_samples, n_features)
    a = ot.utils.unif(n_samples)

    M = ot.dist(x, y)

    if torch:

        a1 = torch.tensor(a, requires_grad=True)
        b1 = torch.tensor(a, requires_grad=True)
        M1 = torch.tensor(M, requires_grad=True)

        val, log = ot.emd2(a1, b1, M1, log=True)

        val.backward()

        assert a1.shape == a1.grad.shape
        assert b1.shape == b1.grad.shape
        assert M1.shape == M1.grad.shape

        assert np.allclose(a1.grad.cpu().detach().numpy(),
                           log['u'].cpu().detach().numpy() - log['u'].cpu().detach().numpy().mean())

        assert np.allclose(b1.grad.cpu().detach().numpy(),
                           log['v'].cpu().detach().numpy() - log['v'].cpu().detach().numpy().mean())

        # Testing for bug #309, checking for scaling of gradient
        a2 = torch.tensor(a, requires_grad=True)
        b2 = torch.tensor(a, requires_grad=True)
        M2 = torch.tensor(M, requires_grad=True)

        val = 10.0 * ot.emd2(a2, b2, M2)

        val.backward()

        assert np.allclose(10.0 * a1.grad.cpu().detach().numpy(),
                           a2.grad.cpu().detach().numpy())
        assert np.allclose(10.0 * b1.grad.cpu().detach().numpy(),
                           b2.grad.cpu().detach().numpy())
        assert np.allclose(10.0 * M1.grad.cpu().detach().numpy(),
                           M2.grad.cpu().detach().numpy())


def test_emd_emd2():
    # test emd and emd2 for simple identity
    n = 100
    rng = np.random.RandomState(0)

    x = rng.randn(n, 2)
    u = ot.utils.unif(n)

    M = ot.dist(x, x)

    G = ot.emd(u, u, M)

    # check G is identity
    np.testing.assert_allclose(G, np.eye(n) / n)
    # check constraints
    np.testing.assert_allclose(u, G.sum(1))  # cf convergence sinkhorn
    np.testing.assert_allclose(u, G.sum(0))  # cf convergence sinkhorn

    w = ot.emd2(u, u, M)
    # check loss=0
    np.testing.assert_allclose(w, 0)


def test_omp_emd2():
    # test emd2 and emd2 with openmp for simple identity
    n = 100
    rng = np.random.RandomState(0)

    x = rng.randn(n, 2)
    u = ot.utils.unif(n)

    M = ot.dist(x, x)

    w = ot.emd2(u, u, M)
    w2 = ot.emd2(u, u, M, numThreads=2)

    np.testing.assert_allclose(w, w2)


def test_emd_empty():
    # test emd and emd2 for simple identity
    n = 100
    rng = np.random.RandomState(0)

    x = rng.randn(n, 2)
    u = ot.utils.unif(n)

    M = ot.dist(x, x)

    G = ot.emd([], [], M)

    # check G is identity
    np.testing.assert_allclose(G, np.eye(n) / n)
    # check constraints
    np.testing.assert_allclose(u, G.sum(1))  # cf convergence sinkhorn
    np.testing.assert_allclose(u, G.sum(0))  # cf convergence sinkhorn

    w = ot.emd2([], [], M)
    # check loss=0
    np.testing.assert_allclose(w, 0)


def test_emd2_multi():
    n = 500  # nb bins

    # bin positions
    x = np.arange(n, dtype=np.float64)

    # Gaussian distributions
    a = gauss(n, m=20, s=5)  # m= mean, s= std

    ls = np.arange(20, 500, 100)
    nb = len(ls)
    b = np.zeros((n, nb))
    for i in range(nb):
        b[:, i] = gauss(n, m=ls[i], s=10)

    # loss matrix
    M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
    # M/=M.max()

    print('Computing {} EMD '.format(nb))

    # emd loss 1 proc
    ot.tic()
    emd1 = ot.emd2(a, b, M, 1)
    ot.toc('1 proc : {} s')

    # emd loss multipro proc
    ot.tic()
    emdn = ot.emd2(a, b, M)
    ot.toc('multi proc : {} s')

    np.testing.assert_allclose(emd1, emdn)

    # emd loss multipro proc with log
    ot.tic()
    emdn = ot.emd2(a, b, M, log=True, return_matrix=True)
    ot.toc('multi proc : {} s')

    for i in range(len(emdn)):
        emd = emdn[i]
        log = emd[1]
        cost = emd[0]
        check_duality_gap(a, b[:, i], M, log['G'], log['u'], log['v'], cost)
        emdn[i] = cost

    emdn = np.array(emdn)
    np.testing.assert_allclose(emd1, emdn)


def test_lp_barycenter():
    a1 = np.array([1.0, 0, 0])[:, None]
    a2 = np.array([0, 0, 1.0])[:, None]

    A = np.hstack((a1, a2))
    M = np.array([[0, 1.0, 4.0], [1.0, 0, 1.0], [4.0, 1.0, 0]])

    # obvious barycenter between two diracs
    bary0 = np.array([0, 1.0, 0])

    bary = ot.lp.barycenter(A, M, [.5, .5])

    np.testing.assert_allclose(bary, bary0, rtol=1e-5, atol=1e-7)
    np.testing.assert_allclose(bary.sum(), 1)


def test_free_support_barycenter():
    measures_locations = [np.array([-1.]).reshape((1, 1)), np.array([1.]).reshape((1, 1))]
    measures_weights = [np.array([1.]), np.array([1.])]

    X_init = np.array([-12.]).reshape((1, 1))

    # obvious barycenter location between two diracs
    bar_locations = np.array([0.]).reshape((1, 1))

    X = ot.lp.free_support_barycenter(measures_locations, measures_weights, X_init)

    np.testing.assert_allclose(X, bar_locations, rtol=1e-5, atol=1e-7)


def test_free_support_barycenter_backends(nx):

    measures_locations = [np.array([-1.]).reshape((1, 1)), np.array([1.]).reshape((1, 1))]
    measures_weights = [np.array([1.]), np.array([1.])]
    X_init = np.array([-12.]).reshape((1, 1))

    X = ot.lp.free_support_barycenter(measures_locations, measures_weights, X_init)

    measures_locations2 = nx.from_numpy(*measures_locations)
    measures_weights2 = nx.from_numpy(*measures_weights)
    X_init2 = nx.from_numpy(X_init)

    X2 = ot.lp.free_support_barycenter(measures_locations2, measures_weights2, X_init2)

    np.testing.assert_allclose(X, nx.to_numpy(X2))


def test_generalised_free_support_barycenter():
    np.random.seed(42)  # random inits
    X = [np.array([-1., -1.]).reshape((1, 2)), np.array([1., 1.]).reshape((1, 2))]  # two 2D points bar is obviously 0
    a = [np.array([1.]), np.array([1.])]

    P = [np.eye(2), np.eye(2)]

    Y_init = np.array([-12., 7.]).reshape((1, 2))

    # obvious barycenter location between two 2D diracs
    Y_true = np.array([0., .0]).reshape((1, 2))

    # test without log and no init
    Y = ot.lp.generalized_free_support_barycenter(X, a, P, 1)
    np.testing.assert_allclose(Y, Y_true, rtol=1e-5, atol=1e-7)

    # test with log and init
    Y, _ = ot.lp.generalized_free_support_barycenter(X, a, P, 1, Y_init=Y_init, b=np.array([1.]), log=True)
    np.testing.assert_allclose(Y, Y_true, rtol=1e-5, atol=1e-7)


def test_generalised_free_support_barycenter_backends(nx):
    np.random.seed(42)
    X = [np.array([-1.]).reshape((1, 1)), np.array([1.]).reshape((1, 1))]
    a = [np.array([1.]), np.array([1.])]
    P = [np.array([1.]).reshape((1, 1)), np.array([1.]).reshape((1, 1))]
    Y_init = np.array([-12.]).reshape((1, 1))

    Y = ot.lp.generalized_free_support_barycenter(X, a, P, 1, Y_init=Y_init)

    X2 = nx.from_numpy(*X)
    a2 = nx.from_numpy(*a)
    P2 = nx.from_numpy(*P)
    Y_init2 = nx.from_numpy(Y_init)

    Y2 = ot.lp.generalized_free_support_barycenter(X2, a2, P2, 1, Y_init=Y_init2)

    np.testing.assert_allclose(Y, nx.to_numpy(Y2))


@pytest.mark.skipif(not ot.lp.cvx.cvxopt, reason="No cvxopt available")
def test_lp_barycenter_cvxopt():
    a1 = np.array([1.0, 0, 0])[:, None]
    a2 = np.array([0, 0, 1.0])[:, None]

    A = np.hstack((a1, a2))
    M = np.array([[0, 1.0, 4.0], [1.0, 0, 1.0], [4.0, 1.0, 0]])

    # obvious barycenter between two diracs
    bary0 = np.array([0, 1.0, 0])

    bary = ot.lp.barycenter(A, M, [.5, .5], solver=None)

    np.testing.assert_allclose(bary, bary0, rtol=1e-5, atol=1e-7)
    np.testing.assert_allclose(bary.sum(), 1)


def test_warnings():
    n = 100  # nb bins
    m = 100  # nb bins

    mean1 = 30
    mean2 = 50

    # bin positions
    x = np.arange(n, dtype=np.float64)
    y = np.arange(m, dtype=np.float64)

    # Gaussian distributions
    a = gauss(n, m=mean1, s=5)  # m= mean, s= std

    b = gauss(m, m=mean2, s=10)

    # loss matrix
    M = ot.dist(x.reshape((-1, 1)), y.reshape((-1, 1))) ** (1. / 2)

    print('Computing {} EMD '.format(1))
    with warnings.catch_warnings(record=True) as w:
        warnings.simplefilter("always")
        print('Computing {} EMD '.format(1))
        ot.emd(a, b, M, numItermax=1)
        assert "numItermax" in str(w[-1].message)
        #assert len(w) == 1


def test_dual_variables():
    n = 500  # nb bins
    m = 600  # nb bins

    mean1 = 300
    mean2 = 400

    # bin positions
    x = np.arange(n, dtype=np.float64)
    y = np.arange(m, dtype=np.float64)

    # Gaussian distributions
    a = gauss(n, m=mean1, s=5)  # m= mean, s= std

    b = gauss(m, m=mean2, s=10)

    # loss matrix
    M = ot.dist(x.reshape((-1, 1)), y.reshape((-1, 1))) ** (1. / 2)

    print('Computing {} EMD '.format(1))

    # emd loss 1 proc
    ot.tic()
    G, log = ot.emd(a, b, M, log=True)
    ot.toc('1 proc : {} s')

    ot.tic()
    G2 = ot.emd(b, a, np.ascontiguousarray(M.T))
    ot.toc('1 proc : {} s')

    cost1 = (G * M).sum()
    # Check symmetry
    np.testing.assert_array_almost_equal(cost1, (M * G2.T).sum())
    # Check with closed-form solution for gaussians
    np.testing.assert_almost_equal(cost1, np.abs(mean1 - mean2))

    # Check that both cost computations are equivalent
    np.testing.assert_almost_equal(cost1, log['cost'])
    check_duality_gap(a, b, M, G, log['u'], log['v'], log['cost'])

    constraint_violation = log['u'][:, None] + log['v'][None, :] - M

    assert constraint_violation.max() < 1e-8


def check_duality_gap(a, b, M, G, u, v, cost):
    cost_dual = np.vdot(a, u) + np.vdot(b, v)
    # Check that dual and primal cost are equal
    np.testing.assert_almost_equal(cost_dual, cost)

    [ind1, ind2] = np.nonzero(G)

    # Check that reduced cost is zero on transport arcs
    np.testing.assert_array_almost_equal((M - u.reshape(-1, 1) - v.reshape(1, -1))[ind1, ind2],
                                         np.zeros(ind1.size))