import numpy as np
from numpy.testing import (assert_almost_equal, assert_equal, assert_allclose,
                           assert_array_almost_equal, assert_)

from scipy.special import logsumexp, softmax


def test_logsumexp():
    # Test whether logsumexp() function correctly handles large inputs.
    a = np.arange(200)
    desired = np.log(np.sum(np.exp(a)))
    assert_almost_equal(logsumexp(a), desired)

    # Now test with large numbers
    b = [1000, 1000]
    desired = 1000.0 + np.log(2.0)
    assert_almost_equal(logsumexp(b), desired)

    n = 1000
    b = np.full(n, 10000, dtype='float64')
    desired = 10000.0 + np.log(n)
    assert_almost_equal(logsumexp(b), desired)

    x = np.array([1e-40] * 1000000)
    logx = np.log(x)

    X = np.vstack([x, x])
    logX = np.vstack([logx, logx])
    assert_array_almost_equal(np.exp(logsumexp(logX)), X.sum())
    assert_array_almost_equal(np.exp(logsumexp(logX, axis=0)), X.sum(axis=0))
    assert_array_almost_equal(np.exp(logsumexp(logX, axis=1)), X.sum(axis=1))

    # Handling special values properly
    assert_equal(logsumexp(np.inf), np.inf)
    assert_equal(logsumexp(-np.inf), -np.inf)
    assert_equal(logsumexp(np.nan), np.nan)
    assert_equal(logsumexp([-np.inf, -np.inf]), -np.inf)

    # Handling an array with different magnitudes on the axes
    assert_array_almost_equal(logsumexp([[1e10, 1e-10],
                                         [-1e10, -np.inf]], axis=-1),
                              [1e10, -1e10])

    # Test keeping dimensions
    assert_array_almost_equal(logsumexp([[1e10, 1e-10],
                                         [-1e10, -np.inf]],
                                        axis=-1,
                                        keepdims=True),
                              [[1e10], [-1e10]])

    # Test multiple axes
    assert_array_almost_equal(logsumexp([[1e10, 1e-10],
                                         [-1e10, -np.inf]],
                                        axis=(-1,-2)),
                              1e10)


def test_logsumexp_b():
    a = np.arange(200)
    b = np.arange(200, 0, -1)
    desired = np.log(np.sum(b*np.exp(a)))
    assert_almost_equal(logsumexp(a, b=b), desired)

    a = [1000, 1000]
    b = [1.2, 1.2]
    desired = 1000 + np.log(2 * 1.2)
    assert_almost_equal(logsumexp(a, b=b), desired)

    x = np.array([1e-40] * 100000)
    b = np.linspace(1, 1000, 100000)
    logx = np.log(x)

    X = np.vstack((x, x))
    logX = np.vstack((logx, logx))
    B = np.vstack((b, b))
    assert_array_almost_equal(np.exp(logsumexp(logX, b=B)), (B * X).sum())
    assert_array_almost_equal(np.exp(logsumexp(logX, b=B, axis=0)),
                                (B * X).sum(axis=0))
    assert_array_almost_equal(np.exp(logsumexp(logX, b=B, axis=1)),
                                (B * X).sum(axis=1))


def test_logsumexp_sign():
    a = [1,1,1]
    b = [1,-1,-1]

    r, s = logsumexp(a, b=b, return_sign=True)
    assert_almost_equal(r,1)
    assert_equal(s,-1)


def test_logsumexp_sign_zero():
    a = [1,1]
    b = [1,-1]

    r, s = logsumexp(a, b=b, return_sign=True)
    assert_(not np.isfinite(r))
    assert_(not np.isnan(r))
    assert_(r < 0)
    assert_equal(s,0)


def test_logsumexp_sign_shape():
    a = np.ones((1,2,3,4))
    b = np.ones_like(a)

    r, s = logsumexp(a, axis=2, b=b, return_sign=True)

    assert_equal(r.shape, s.shape)
    assert_equal(r.shape, (1,2,4))

    r, s = logsumexp(a, axis=(1,3), b=b, return_sign=True)

    assert_equal(r.shape, s.shape)
    assert_equal(r.shape, (1,3))


def test_logsumexp_complex_sign():
    a = np.array([1 + 1j, 2 - 1j, -2 + 3j])

    r, s = logsumexp(a, return_sign=True)

    expected_sumexp = np.exp(a).sum()
    # This is the numpy>=2.0 convention for np.sign
    expected_sign = expected_sumexp / abs(expected_sumexp)

    assert_allclose(s, expected_sign)
    assert_allclose(s * np.exp(r), expected_sumexp)


def test_logsumexp_shape():
    a = np.ones((1, 2, 3, 4))
    b = np.ones_like(a)

    r = logsumexp(a, axis=2, b=b)
    assert_equal(r.shape, (1, 2, 4))

    r = logsumexp(a, axis=(1, 3), b=b)
    assert_equal(r.shape, (1, 3))


def test_logsumexp_b_zero():
    a = [1,10000]
    b = [1,0]

    assert_almost_equal(logsumexp(a, b=b), 1)


def test_logsumexp_b_shape():
    a = np.zeros((4,1,2,1))
    b = np.ones((3,1,5))

    logsumexp(a, b=b)


def test_softmax_fixtures():
    assert_allclose(softmax([1000, 0, 0, 0]), np.array([1, 0, 0, 0]),
                    rtol=1e-13)
    assert_allclose(softmax([1, 1]), np.array([.5, .5]), rtol=1e-13)
    assert_allclose(softmax([0, 1]), np.array([1, np.e])/(1 + np.e),
                    rtol=1e-13)

    # Expected value computed using mpmath (with mpmath.mp.dps = 200) and then
    # converted to float.
    x = np.arange(4)
    expected = np.array([0.03205860328008499,
                         0.08714431874203256,
                         0.23688281808991013,
                         0.6439142598879722])

    assert_allclose(softmax(x), expected, rtol=1e-13)

    # Translation property.  If all the values are changed by the same amount,
    # the softmax result does not change.
    assert_allclose(softmax(x + 100), expected, rtol=1e-13)

    # When axis=None, softmax operates on the entire array, and preserves
    # the shape.
    assert_allclose(softmax(x.reshape(2, 2)), expected.reshape(2, 2),
                    rtol=1e-13)


def test_softmax_multi_axes():
    assert_allclose(softmax([[1000, 0], [1000, 0]], axis=0),
                    np.array([[.5, .5], [.5, .5]]), rtol=1e-13)
    assert_allclose(softmax([[1000, 0], [1000, 0]], axis=1),
                    np.array([[1, 0], [1, 0]]), rtol=1e-13)

    # Expected value computed using mpmath (with mpmath.mp.dps = 200) and then
    # converted to float.
    x = np.array([[-25, 0, 25, 50],
                  [1, 325, 749, 750]])
    expected = np.array([[2.678636961770877e-33,
                          1.9287498479371314e-22,
                          1.3887943864771144e-11,
                          0.999999999986112],
                         [0.0,
                          1.9444526359919372e-185,
                          0.2689414213699951,
                          0.7310585786300048]])
    assert_allclose(softmax(x, axis=1), expected, rtol=1e-13)
    assert_allclose(softmax(x.T, axis=0), expected.T, rtol=1e-13)

    # 3-d input, with a tuple for the axis.
    x3d = x.reshape(2, 2, 2)
    assert_allclose(softmax(x3d, axis=(1, 2)), expected.reshape(2, 2, 2),
                    rtol=1e-13)