# TODO: Test robust skewness
# TODO: Test robust kurtosis
import numpy as np
import pandas as pd
from numpy.testing import (assert_almost_equal, assert_raises, TestCase)
from statsmodels.stats.stattools import (omni_normtest, jarque_bera,
                                         durbin_watson, _medcouple_1d, medcouple,
                                         robust_kurtosis, robust_skewness)
from statsmodels.stats.adnorm import normal_ad

#a random array, rounded to 4 decimals
x = np.array([-0.1184, -1.3403, 0.0063, -0.612, -0.3869, -0.2313, -2.8485,
              -0.2167, 0.4153, 1.8492, -0.3706, 0.9726, -0.1501, -0.0337,
              -1.4423, 1.2489, 0.9182, -0.2331, -0.6182, 0.183])


def test_durbin_watson():
    #benchmark values from R car::durbinWatsonTest(x)
    #library("car")
    #> durbinWatsonTest(x)
    #[1] 1.95298958377419
    #> durbinWatsonTest(x**2)
    #[1] 1.848802400319998
    #> durbinWatsonTest(x[2:20]+0.5*x[1:19])
    #[1] 1.09897993228779
    #> durbinWatsonTest(x[2:20]+0.8*x[1:19])
    #[1] 0.937241876707273
    #> durbinWatsonTest(x[2:20]+0.9*x[1:19])
    #[1] 0.921488912587806
    st_R = 1.95298958377419
    assert_almost_equal(durbin_watson(x), st_R, 14)

    st_R = 1.848802400319998
    assert_almost_equal(durbin_watson(x**2), st_R, 14)

    st_R = 1.09897993228779
    assert_almost_equal(durbin_watson(x[1:] + 0.5 * x[:-1]), st_R, 14)

    st_R = 0.937241876707273
    assert_almost_equal(durbin_watson(x[1:] + 0.8 * x[:-1]), st_R, 14)

    st_R = 0.921488912587806
    assert_almost_equal(durbin_watson(x[1:] + 0.9 * x[:-1]), st_R, 14)


def test_omni_normtest():
    #tests against R fBasics
    from scipy import stats

    st_pv_R = np.array(
              [[3.994138321207883, -1.129304302161460,  1.648881473704978],
               [0.1357325110375005, 0.2587694866795507, 0.0991719192710234]])

    nt = omni_normtest(x)
    assert_almost_equal(nt, st_pv_R[:, 0], 14)

    st = stats.skewtest(x)
    assert_almost_equal(st, st_pv_R[:, 1], 14)

    kt = stats.kurtosistest(x)
    assert_almost_equal(kt, st_pv_R[:, 2], 11)

    st_pv_R = np.array(
              [[34.523210399523926,  4.429509162503833,  3.860396220444025],
               [3.186985686465249e-08, 9.444780064482572e-06, 1.132033129378485e-04]])

    x2 = x**2
    #TODO: fix precision in these test with relative tolerance
    nt = omni_normtest(x2)
    assert_almost_equal(nt, st_pv_R[:, 0], 12)

    st = stats.skewtest(x2)
    assert_almost_equal(st, st_pv_R[:, 1], 12)

    kt = stats.kurtosistest(x2)
    assert_almost_equal(kt, st_pv_R[:, 2], 12)


def test_omni_normtest_axis():
    #test axis of omni_normtest
    x = np.random.randn(25, 3)
    nt1 = omni_normtest(x)
    nt2 = omni_normtest(x, axis=0)
    nt3 = omni_normtest(x.T, axis=1)
    assert_almost_equal(nt2, nt1, decimal=13)
    assert_almost_equal(nt3, nt1, decimal=13)


def test_jarque_bera():
    #tests against R fBasics
    st_pv_R = np.array([1.9662677226861689, 0.3741367669648314])
    jb = jarque_bera(x)[:2]
    assert_almost_equal(jb, st_pv_R, 14)

    st_pv_R = np.array([78.329987305556, 0.000000000000])
    jb = jarque_bera(x**2)[:2]
    assert_almost_equal(jb, st_pv_R, 13)

    st_pv_R = np.array([5.7135750796706670, 0.0574530296971343])
    jb = jarque_bera(np.log(x**2))[:2]
    assert_almost_equal(jb, st_pv_R, 14)

    st_pv_R = np.array([2.6489315748495761, 0.2659449923067881])
    jb = jarque_bera(np.exp(-x**2))[:2]
    assert_almost_equal(jb, st_pv_R, 14)


def test_shapiro():
    #tests against R fBasics
    #testing scipy.stats
    from scipy.stats import shapiro

    st_pv_R = np.array([0.939984787255526, 0.239621898000460])
    sh = shapiro(x)
    assert_almost_equal(sh, st_pv_R, 4)

    #st is ok -7.15e-06, pval agrees at -3.05e-10
    st_pv_R = np.array([5.799574255943298e-01, 1.838456834681376e-06 * 1e4])
    sh = shapiro(x**2) * np.array([1, 1e4])
    assert_almost_equal(sh, st_pv_R, 5)

    st_pv_R = np.array([0.91730442643165588, 0.08793704167882448])
    sh = shapiro(np.log(x**2))
    assert_almost_equal(sh, st_pv_R, 5)

    #diff is [  9.38773155e-07,   5.48221246e-08]
    st_pv_R = np.array([0.818361863493919373, 0.001644620895206969])
    sh = shapiro(np.exp(-x**2))
    assert_almost_equal(sh, st_pv_R, 5)


def test_adnorm():
    #tests against R fBasics
    st_pv = []
    st_pv_R = np.array([0.5867235358882148, 0.1115380760041617])
    ad = normal_ad(x)
    assert_almost_equal(ad, st_pv_R, 12)
    st_pv.append(st_pv_R)

    st_pv_R = np.array([2.976266267594575e+00, 8.753003709960645e-08])
    ad = normal_ad(x**2)
    assert_almost_equal(ad, st_pv_R, 11)
    st_pv.append(st_pv_R)

    st_pv_R = np.array([0.4892557856308528, 0.1968040759316307])
    ad = normal_ad(np.log(x**2))
    assert_almost_equal(ad, st_pv_R, 12)
    st_pv.append(st_pv_R)

    st_pv_R = np.array([1.4599014654282669312, 0.0006380009232897535])
    ad = normal_ad(np.exp(-x**2))
    assert_almost_equal(ad, st_pv_R, 12)
    st_pv.append(st_pv_R)

    ad = normal_ad(np.column_stack((x, x**2, np.log(x**2), np.exp(-x**2))).T,
                   axis=1)
    assert_almost_equal(ad, np.column_stack(st_pv), 11)


def test_durbin_watson_pandas():
    x = np.random.randn(50)
    x_series = pd.Series(x)
    assert_almost_equal(durbin_watson(x), durbin_watson(x_series), decimal=13)


class TestStattools(TestCase):
    @classmethod
    def setup_class(cls):
        x = np.random.standard_normal(1000)
        e1, e2, e3, e4, e5, e6, e7 = np.percentile(x, (12.5, 25.0, 37.5, 50.0, 62.5, 75.0, 87.5))
        c05, c50, c95 = np.percentile(x, (5.0, 50.0, 95.0))
        f025, f25, f75, f975 = np.percentile(x, (2.5, 25.0, 75.0, 97.5))
        mean = np.mean
        kr1 = mean(((x - mean(x)) / np.std(x))**4.0) - 3.0
        kr2 = ((e7 - e5) + (e3 - e1)) / (e6 - e2) - 1.2330951154852172
        kr3 = (mean(x[x > c95]) - mean(x[x < c05])) / (mean(x[x > c50]) - mean(x[x < c50])) - 2.5852271228708048
        kr4 = (f975 - f025) / (f75 - f25) - 2.9058469516701639
        cls.kurtosis_x = x
        cls.expected_kurtosis = np.array([kr1, kr2, kr3, kr4])
        cls.kurtosis_constants = np.array([3.0,1.2330951154852172,2.5852271228708048,2.9058469516701639])

    def test_medcouple_no_axis(self):
        x = np.reshape(np.arange(100.0), (50, 2))
        mc = medcouple(x, axis=None)
        assert_almost_equal(mc, medcouple(x.ravel()))

    def test_medcouple_1d(self):
        x = np.reshape(np.arange(100.0),(50,2))
        assert_raises(ValueError, _medcouple_1d, x)

    def test_medcouple_symmetric(self):
        mc = medcouple(np.arange(5.0))
        assert_almost_equal(mc, 0)


    def test_medcouple_nonzero(self):
        mc = medcouple(np.array([1, 2, 7, 9, 10.0]))
        assert_almost_equal(mc, -0.3333333)


    def test_medcouple_symmetry(self):
        x = np.random.standard_normal(100)
        mcp = medcouple(x)
        mcn = medcouple(-x)
        assert_almost_equal(mcp + mcn, 0)


    def test_durbin_watson(self):
        x = np.random.standard_normal(100)
        dw = sum(np.diff(x)**2.0) / np.dot(x, x)
        assert_almost_equal(dw, durbin_watson(x))


    def test_durbin_watson_2d(self):
        shape = (1, 10)
        x = np.random.standard_normal(100)
        dw = sum(np.diff(x)**2.0) / np.dot(x, x)
        x = np.tile(x[:, None], shape)
        assert_almost_equal(np.squeeze(dw * np.ones(shape)), durbin_watson(x))


    def test_durbin_watson_3d(self):
        shape = (10, 1, 10)
        x = np.random.standard_normal(100)
        dw = sum(np.diff(x)**2.0) / np.dot(x, x)
        x = np.tile(x[None, :, None], shape)
        assert_almost_equal(np.squeeze(dw * np.ones(shape)), durbin_watson(x, axis=1))


    def test_robust_skewness_1d(self):
        x = np.arange(21.0)
        sk = robust_skewness(x)
        assert_almost_equal(np.array(sk), np.zeros(4))

    def test_robust_skewness_1d_2d(self):
        x = np.random.randn(21)
        y = x[:, None]
        sk_x = robust_skewness(x)
        sk_y = robust_skewness(y, axis=None)
        assert_almost_equal(np.array(sk_x), np.array(sk_y))

    def test_robust_skewness_symmetric(self):
        x = np.random.standard_normal(100)
        x = np.hstack([x, np.zeros(1), -x])
        sk = robust_skewness(x)
        assert_almost_equal(np.array(sk), np.zeros(4))


    def test_robust_skewness_3d(self):
        x = np.random.standard_normal(100)
        x = np.hstack([x, np.zeros(1), -x])
        x = np.tile(x, (10, 10, 1))
        sk_3d = robust_skewness(x, axis=2)
        result = np.zeros((10, 10))
        for sk in sk_3d:
            assert_almost_equal(sk, result)

    def test_robust_kurtosis_1d_2d(self):
        x = np.random.randn(100)
        y = x[:, None]
        kr_x = np.array(robust_kurtosis(x))
        kr_y = np.array(robust_kurtosis(y, axis=None))
        assert_almost_equal(kr_x, kr_y)

    def test_robust_kurtosis(self):
        x = self.kurtosis_x
        assert_almost_equal(np.array(robust_kurtosis(x)), self.expected_kurtosis)

    def test_robust_kurtosis_3d(self):
        x = np.tile(self.kurtosis_x, (10, 10, 1))
        kurtosis = np.array(robust_kurtosis(x, axis=2))
        for i, r in enumerate(self.expected_kurtosis):
            assert_almost_equal(r * np.ones((10, 10)), kurtosis[i])


    def test_robust_kurtosis_excess_false(self):
        x = self.kurtosis_x
        expected = self.expected_kurtosis + self.kurtosis_constants
        kurtosis = np.array(robust_kurtosis(x, excess=False))
        assert_almost_equal(expected, kurtosis)

    def test_robust_kurtosis_ab(self):
        """Test custom alpha, beta in kr3"""
        x = self.kurtosis_x
        alpha, beta = (10.0, 45.0)
        kurtosis = robust_kurtosis(self.kurtosis_x, ab=(alpha,beta), excess=False)
        num = np.mean(x[x>np.percentile(x,100.0 - alpha)]) - np.mean(x[x<np.percentile(x,alpha)])
        denom = np.mean(x[x>np.percentile(x,100.0 - beta)]) - np.mean(x[x<np.percentile(x,beta)])
        assert_almost_equal(kurtosis[2], num/denom)

    def test_robust_kurtosis_dg(self):
        """Test custom delta, gamma in kr4"""
        x = self.kurtosis_x
        delta, gamma = (10.0, 45.0)
        kurtosis = robust_kurtosis(self.kurtosis_x, dg=(delta,gamma), excess=False)
        q = np.percentile(x,[delta, 100.0-delta, gamma, 100.0-gamma])
        assert_almost_equal(kurtosis[3], (q[1] - q[0]) / (q[3] - q[2]))


if __name__ == "__main__":