# 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
from gpflow.util import default_float


@pytest.fixture
def mu1(): return np.array([1.0, 1.3])


@pytest.fixture
def mu2(): return np.array([-2.0, 0.3])


@pytest.fixture
def var1(): return np.array([3.0, 3.5])


@pytest.fixture
def var2(): return np.array([4.0, 4.2])


def cast(x):
    return x
    # return tf.cast(np.asarray(x), dtype=default_float())


@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):
    quad = quadrature.ndiagquad(
        [lambda *X: tf.exp(X[0])], 25,
        [cast(mu)], [cast(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([1.0, 1.3])])
@pytest.mark.parametrize('var2', [np.array([3.0, 3.5])])
def test_diagquad_2d(mu1, var1, mu2, var2):
    alpha = 2.5
    quad = quadrature.ndiagquad(
        lambda *X: tf.exp(X[0] + alpha * X[1]),
        35,  # using logspace=True we can reduce this, see test_diagquad_logspace
        [cast(mu1), cast(mu2)], [cast(var1), cast(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([1.0, 1.3])])
@pytest.mark.parametrize('var2', [np.array([3.0, 3.5])])
def test_diagquad_logspace(mu1, var1, mu2, var2):
    alpha = 2.5
    quad = quadrature.ndiagquad(
        lambda *X: (X[0] + alpha * X[1]),
        25,
        [cast(mu1), cast(mu2)], [cast(var1), cast(var2)],
        logspace=True)
    expected = mu1 + var1 / 2 + alpha * mu2 + alpha ** 2 * var2 / 2
    assert_allclose(quad, expected)



def test_diagquad_with_kwarg(mu2, var2):
    alpha = np.array([2.5, -1.3])
    quad = quadrature.ndiagquad(
        lambda X, Y: tf.exp(X * Y), 25,
        cast(mu2), cast(var2), Y=alpha)
    expected = np.exp(alpha * mu2 + alpha ** 2 * var2 / 2)
    assert_allclose(quad, expected)