# Copyright 2018 the GPflow authors.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

import numpy as np
import pytest
import tensorflow as tf
from numpy.testing import assert_allclose

import gpflow.quadrature as quadrature


@pytest.mark.parametrize('mu', [np.array([1.0, 1.3])])
@pytest.mark.parametrize('var', [np.array([3.0, 3.5])])
def test_diagquad_1d(mu, var):
    num_gauss_hermite_points = 25
    quad = quadrature.ndiagquad([lambda *X: tf.exp(X[0])],
                                num_gauss_hermite_points, [mu], [var])
    expected = np.exp(mu + var / 2)
    assert_allclose(quad[0], expected)


@pytest.mark.parametrize('mu1', [np.array([1.0, 1.3])])
@pytest.mark.parametrize('var1', [np.array([3.0, 3.5])])
@pytest.mark.parametrize('mu2', [np.array([-2.0, 0.3])])
@pytest.mark.parametrize('var2', [np.array([4.0, 4.2])])
def test_diagquad_2d(mu1, var1, mu2, var2):
    alpha = 2.5
    # using logspace=True we can reduce this, see test_diagquad_logspace
    num_gauss_hermite_points = 35
    quad = quadrature.ndiagquad(lambda *X: tf.exp(X[0] + alpha * X[1]),
                                num_gauss_hermite_points, [mu1, mu2],
                                [var1, var2])
    expected = np.exp(mu1 + var1 / 2 + alpha * mu2 + alpha**2 * var2 / 2)
    assert_allclose(quad, expected)


@pytest.mark.parametrize('mu1', [np.array([1.0, 1.3])])
@pytest.mark.parametrize('var1', [np.array([3.0, 3.5])])
@pytest.mark.parametrize('mu2', [np.array([-2.0, 0.3])])
@pytest.mark.parametrize('var2', [np.array([4.0, 4.2])])
def test_diagquad_logspace(mu1, var1, mu2, var2):
    alpha = 2.5
    num_gauss_hermite_points = 25
    quad = quadrature.ndiagquad(lambda *X: (X[0] + alpha * X[1]),
                                num_gauss_hermite_points, [mu1, mu2],
                                [var1, var2],
                                logspace=True)
    expected = mu1 + var1 / 2 + alpha * mu2 + alpha**2 * var2 / 2
    assert_allclose(quad, expected)


@pytest.mark.parametrize('mu1', [np.array([1.0, 1.3])])
@pytest.mark.parametrize('var1', [np.array([3.0, 3.5])])
def test_diagquad_with_kwarg(mu1, var1):
    alpha = np.array([2.5, -1.3])
    num_gauss_hermite_points = 25
    quad = quadrature.ndiagquad(lambda X, Y: tf.exp(X * Y),
                                num_gauss_hermite_points,
                                mu1,
                                var1,
                                Y=alpha)
    expected = np.exp(alpha * mu1 + alpha**2 * var1 / 2)
    assert_allclose(quad, expected)