pywafo/wafo/stats/tests/test_mstats_basic.py

"""
Tests for the stats.mstats module (support for masked arrays)
"""
from __future__ import division, print_function, absolute_import

import warnings

import numpy as np
from numpy import nan
import numpy.ma as ma
from numpy.ma import masked, nomask

import wafo.stats.mstats as mstats
from wafo import stats
from numpy.testing import TestCase, run_module_suite
from numpy.testing.decorators import skipif
from numpy.ma.testutils import (assert_equal, assert_almost_equal,
    assert_array_almost_equal, assert_array_almost_equal_nulp, assert_,
    assert_allclose, assert_raises)


class TestMquantiles(TestCase):
    def test_mquantiles_limit_keyword(self):
        # Regression test for Trac ticket #867
        data = np.array([[6., 7., 1.],
                         [47., 15., 2.],
                         [49., 36., 3.],
                         [15., 39., 4.],
                         [42., 40., -999.],
                         [41., 41., -999.],
                         [7., -999., -999.],
                         [39., -999., -999.],
                         [43., -999., -999.],
                         [40., -999., -999.],
                         [36., -999., -999.]])
        desired = [[19.2, 14.6, 1.45],
                   [40.0, 37.5, 2.5],
                   [42.8, 40.05, 3.55]]
        quants = mstats.mquantiles(data, axis=0, limit=(0, 50))
        assert_almost_equal(quants, desired)


class TestGMean(TestCase):
    def test_1D(self):
        a = (1,2,3,4)
        actual = mstats.gmean(a)
        desired = np.power(1*2*3*4,1./4.)
        assert_almost_equal(actual, desired, decimal=14)

        desired1 = mstats.gmean(a,axis=-1)
        assert_almost_equal(actual, desired1, decimal=14)
        assert_(not isinstance(desired1, ma.MaskedArray))

        a = ma.array((1,2,3,4),mask=(0,0,0,1))
        actual = mstats.gmean(a)
        desired = np.power(1*2*3,1./3.)
        assert_almost_equal(actual, desired,decimal=14)

        desired1 = mstats.gmean(a,axis=-1)
        assert_almost_equal(actual, desired1, decimal=14)

    @skipif(not hasattr(np, 'float96'), 'cannot find float96 so skipping')
    def test_1D_float96(self):
        a = ma.array((1,2,3,4), mask=(0,0,0,1))
        actual_dt = mstats.gmean(a, dtype=np.float96)
        desired_dt = np.power(1 * 2 * 3, 1. / 3.).astype(np.float96)
        assert_almost_equal(actual_dt, desired_dt, decimal=14)
        assert_(actual_dt.dtype == desired_dt.dtype)

    def test_2D(self):
        a = ma.array(((1, 2, 3, 4), (1, 2, 3, 4), (1, 2, 3, 4)),
                     mask=((0, 0, 0, 0), (1, 0, 0, 1), (0, 1, 1, 0)))
        actual = mstats.gmean(a)
        desired = np.array((1,2,3,4))
        assert_array_almost_equal(actual, desired, decimal=14)

        desired1 = mstats.gmean(a,axis=0)
        assert_array_almost_equal(actual, desired1, decimal=14)

        actual = mstats.gmean(a, -1)
        desired = ma.array((np.power(1*2*3*4,1./4.),
                            np.power(2*3,1./2.),
                            np.power(1*4,1./2.)))
        assert_array_almost_equal(actual, desired, decimal=14)


class TestHMean(TestCase):
    def test_1D(self):
        a = (1,2,3,4)
        actual = mstats.hmean(a)
        desired = 4. / (1./1 + 1./2 + 1./3 + 1./4)
        assert_almost_equal(actual, desired, decimal=14)
        desired1 = mstats.hmean(ma.array(a),axis=-1)
        assert_almost_equal(actual, desired1, decimal=14)

        a = ma.array((1,2,3,4),mask=(0,0,0,1))
        actual = mstats.hmean(a)
        desired = 3. / (1./1 + 1./2 + 1./3)
        assert_almost_equal(actual, desired,decimal=14)
        desired1 = mstats.hmean(a,axis=-1)
        assert_almost_equal(actual, desired1, decimal=14)

    @skipif(not hasattr(np, 'float96'), 'cannot find float96 so skipping')
    def test_1D_float96(self):
        a = ma.array((1,2,3,4), mask=(0,0,0,1))
        actual_dt = mstats.hmean(a, dtype=np.float96)
        desired_dt = np.asarray(3. / (1./1 + 1./2 + 1./3),
                                dtype=np.float96)
        assert_almost_equal(actual_dt, desired_dt, decimal=14)
        assert_(actual_dt.dtype == desired_dt.dtype)

    def test_2D(self):
        a = ma.array(((1,2,3,4),(1,2,3,4),(1,2,3,4)),
                     mask=((0,0,0,0),(1,0,0,1),(0,1,1,0)))
        actual = mstats.hmean(a)
        desired = ma.array((1,2,3,4))
        assert_array_almost_equal(actual, desired, decimal=14)

        actual1 = mstats.hmean(a,axis=-1)
        desired = (4./(1/1.+1/2.+1/3.+1/4.),
                   2./(1/2.+1/3.),
                   2./(1/1.+1/4.)
                   )
        assert_array_almost_equal(actual1, desired, decimal=14)


class TestRanking(TestCase):
    def __init__(self, *args, **kwargs):
        TestCase.__init__(self, *args, **kwargs)

    def test_ranking(self):
        x = ma.array([0,1,1,1,2,3,4,5,5,6,])
        assert_almost_equal(mstats.rankdata(x),
                           [1,3,3,3,5,6,7,8.5,8.5,10])
        x[[3,4]] = masked
        assert_almost_equal(mstats.rankdata(x),
                           [1,2.5,2.5,0,0,4,5,6.5,6.5,8])
        assert_almost_equal(mstats.rankdata(x, use_missing=True),
                            [1,2.5,2.5,4.5,4.5,4,5,6.5,6.5,8])
        x = ma.array([0,1,5,1,2,4,3,5,1,6,])
        assert_almost_equal(mstats.rankdata(x),
                           [1,3,8.5,3,5,7,6,8.5,3,10])
        x = ma.array([[0,1,1,1,2], [3,4,5,5,6,]])
        assert_almost_equal(mstats.rankdata(x),
                            [[1,3,3,3,5], [6,7,8.5,8.5,10]])
        assert_almost_equal(mstats.rankdata(x, axis=1),
                           [[1,3,3,3,5], [1,2,3.5,3.5,5]])
        assert_almost_equal(mstats.rankdata(x,axis=0),
                           [[1,1,1,1,1], [2,2,2,2,2,]])


class TestCorr(TestCase):
    def test_pearsonr(self):
        # Tests some computations of Pearson's r
        x = ma.arange(10)
        with warnings.catch_warnings():
            # The tests in this context are edge cases, with perfect
            # correlation or anticorrelation, or totally masked data.
            # None of these should trigger a RuntimeWarning.
            warnings.simplefilter("error", RuntimeWarning)

            assert_almost_equal(mstats.pearsonr(x, x)[0], 1.0)
            assert_almost_equal(mstats.pearsonr(x, x[::-1])[0], -1.0)

            x = ma.array(x, mask=True)
            pr = mstats.pearsonr(x, x)
            assert_(pr[0] is masked)
            assert_(pr[1] is masked)

        x1 = ma.array([-1.0, 0.0, 1.0])
        y1 = ma.array([0, 0, 3])
        r, p = mstats.pearsonr(x1, y1)
        assert_almost_equal(r, np.sqrt(3)/2)
        assert_almost_equal(p, 1.0/3)

        # (x2, y2) have the same unmasked data as (x1, y1).
        mask = [False, False, False, True]
        x2 = ma.array([-1.0, 0.0, 1.0, 99.0], mask=mask)
        y2 = ma.array([0, 0, 3, -1], mask=mask)
        r, p = mstats.pearsonr(x2, y2)
        assert_almost_equal(r, np.sqrt(3)/2)
        assert_almost_equal(p, 1.0/3)

    def test_spearmanr(self):
        # Tests some computations of Spearman's rho
        (x, y) = ([5.05,6.75,3.21,2.66],[1.65,2.64,2.64,6.95])
        assert_almost_equal(mstats.spearmanr(x,y)[0], -0.6324555)
        (x, y) = ([5.05,6.75,3.21,2.66,np.nan],[1.65,2.64,2.64,6.95,np.nan])
        (x, y) = (ma.fix_invalid(x), ma.fix_invalid(y))
        assert_almost_equal(mstats.spearmanr(x,y)[0], -0.6324555)

        x = [2.0, 47.4, 42.0, 10.8, 60.1, 1.7, 64.0, 63.1,
              1.0, 1.4, 7.9, 0.3, 3.9, 0.3, 6.7]
        y = [22.6, 8.3, 44.4, 11.9, 24.6, 0.6, 5.7, 41.6,
              0.0, 0.6, 6.7, 3.8, 1.0, 1.2, 1.4]
        assert_almost_equal(mstats.spearmanr(x,y)[0], 0.6887299)
        x = [2.0, 47.4, 42.0, 10.8, 60.1, 1.7, 64.0, 63.1,
              1.0, 1.4, 7.9, 0.3, 3.9, 0.3, 6.7, np.nan]
        y = [22.6, 8.3, 44.4, 11.9, 24.6, 0.6, 5.7, 41.6,
              0.0, 0.6, 6.7, 3.8, 1.0, 1.2, 1.4, np.nan]
        (x, y) = (ma.fix_invalid(x), ma.fix_invalid(y))
        assert_almost_equal(mstats.spearmanr(x,y)[0], 0.6887299)

    def test_kendalltau(self):
        # Tests some computations of Kendall's tau
        x = ma.fix_invalid([5.05, 6.75, 3.21, 2.66,np.nan])
        y = ma.fix_invalid([1.65, 26.5, -5.93, 7.96, np.nan])
        z = ma.fix_invalid([1.65, 2.64, 2.64, 6.95, np.nan])
        assert_almost_equal(np.asarray(mstats.kendalltau(x,y)),
                            [+0.3333333,0.4969059])
        assert_almost_equal(np.asarray(mstats.kendalltau(x,z)),
                            [-0.5477226,0.2785987])
        #
        x = ma.fix_invalid([0, 0, 0, 0,20,20, 0,60, 0,20,
                            10,10, 0,40, 0,20, 0, 0, 0, 0, 0, np.nan])
        y = ma.fix_invalid([0,80,80,80,10,33,60, 0,67,27,
                            25,80,80,80,80,80,80, 0,10,45, np.nan, 0])
        result = mstats.kendalltau(x,y)
        assert_almost_equal(np.asarray(result), [-0.1585188, 0.4128009])

    def test_kendalltau_seasonal(self):
        # Tests the seasonal Kendall tau.
        x = [[nan,nan, 4, 2, 16, 26, 5, 1, 5, 1, 2, 3, 1],
             [4, 3, 5, 3, 2, 7, 3, 1, 1, 2, 3, 5, 3],
             [3, 2, 5, 6, 18, 4, 9, 1, 1,nan, 1, 1,nan],
             [nan, 6, 11, 4, 17,nan, 6, 1, 1, 2, 5, 1, 1]]
        x = ma.fix_invalid(x).T
        output = mstats.kendalltau_seasonal(x)
        assert_almost_equal(output['global p-value (indep)'], 0.008, 3)
        assert_almost_equal(output['seasonal p-value'].round(2),
                            [0.18,0.53,0.20,0.04])

    def test_pointbiserial(self):
        x = [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,1,0,
             0,0,0,0,1,-1]
        y = [14.8,13.8,12.4,10.1,7.1,6.1,5.8,4.6,4.3,3.5,3.3,3.2,3.0,
             2.8,2.8,2.5,2.4,2.3,2.1,1.7,1.7,1.5,1.3,1.3,1.2,1.2,1.1,
             0.8,0.7,0.6,0.5,0.2,0.2,0.1,np.nan]
        assert_almost_equal(mstats.pointbiserialr(x, y)[0], 0.36149, 5)


class TestTrimming(TestCase):

    def test_trim(self):
        a = ma.arange(10)
        assert_equal(mstats.trim(a), [0,1,2,3,4,5,6,7,8,9])
        a = ma.arange(10)
        assert_equal(mstats.trim(a,(2,8)), [None,None,2,3,4,5,6,7,8,None])
        a = ma.arange(10)
        assert_equal(mstats.trim(a,limits=(2,8),inclusive=(False,False)),
                     [None,None,None,3,4,5,6,7,None,None])
        a = ma.arange(10)
        assert_equal(mstats.trim(a,limits=(0.1,0.2),relative=True),
                     [None,1,2,3,4,5,6,7,None,None])

        a = ma.arange(12)
        a[[0,-1]] = a[5] = masked
        assert_equal(mstats.trim(a, (2,8)),
                     [None, None, 2, 3, 4, None, 6, 7, 8, None, None, None])

        x = ma.arange(100).reshape(10, 10)
        expected = [1]*10 + [0]*70 + [1]*20
        trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=None)
        assert_equal(trimx._mask.ravel(), expected)
        trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=0)
        assert_equal(trimx._mask.ravel(), expected)
        trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=-1)
        assert_equal(trimx._mask.T.ravel(), expected)

        # same as above, but with an extra masked row inserted
        x = ma.arange(110).reshape(11, 10)
        x[1] = masked
        expected = [1]*20 + [0]*70 + [1]*20
        trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=None)
        assert_equal(trimx._mask.ravel(), expected)
        trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=0)
        assert_equal(trimx._mask.ravel(), expected)
        trimx = mstats.trim(x.T, (0.1,0.2), relative=True, axis=-1)
        assert_equal(trimx.T._mask.ravel(), expected)

    def test_trim_old(self):
        x = ma.arange(100)
        assert_equal(mstats.trimboth(x).count(), 60)
        assert_equal(mstats.trimtail(x,tail='r').count(), 80)
        x[50:70] = masked
        trimx = mstats.trimboth(x)
        assert_equal(trimx.count(), 48)
        assert_equal(trimx._mask, [1]*16 + [0]*34 + [1]*20 + [0]*14 + [1]*16)
        x._mask = nomask
        x.shape = (10,10)
        assert_equal(mstats.trimboth(x).count(), 60)
        assert_equal(mstats.trimtail(x).count(), 80)

    def test_trimmedmean(self):
        data = ma.array([77, 87, 88,114,151,210,219,246,253,262,
                         296,299,306,376,428,515,666,1310,2611])
        assert_almost_equal(mstats.trimmed_mean(data,0.1), 343, 0)
        assert_almost_equal(mstats.trimmed_mean(data,(0.1,0.1)), 343, 0)
        assert_almost_equal(mstats.trimmed_mean(data,(0.2,0.2)), 283, 0)

    def test_trimmed_stde(self):
        data = ma.array([77, 87, 88,114,151,210,219,246,253,262,
                         296,299,306,376,428,515,666,1310,2611])
        assert_almost_equal(mstats.trimmed_stde(data,(0.2,0.2)), 56.13193, 5)
        assert_almost_equal(mstats.trimmed_stde(data,0.2), 56.13193, 5)

    def test_winsorization(self):
        data = ma.array([77, 87, 88,114,151,210,219,246,253,262,
                         296,299,306,376,428,515,666,1310,2611])
        assert_almost_equal(mstats.winsorize(data,(0.2,0.2)).var(ddof=1),
                            21551.4, 1)
        data[5] = masked
        winsorized = mstats.winsorize(data)
        assert_equal(winsorized.mask, data.mask)


class TestMoments(TestCase):
    # Comparison numbers are found using R v.1.5.1
    # note that length(testcase) = 4
    # testmathworks comes from documentation for the
    # Statistics Toolbox for Matlab and can be found at both
    # http://www.mathworks.com/access/helpdesk/help/toolbox/stats/kurtosis.shtml
    # http://www.mathworks.com/access/helpdesk/help/toolbox/stats/skewness.shtml
    # Note that both test cases came from here.
    testcase = [1,2,3,4]
    testmathworks = ma.fix_invalid([1.165, 0.6268, 0.0751, 0.3516, -0.6965,
                                    np.nan])
    testcase_2d = ma.array(
    np.array([[0.05245846, 0.50344235, 0.86589117, 0.36936353, 0.46961149],
           [0.11574073, 0.31299969, 0.45925772, 0.72618805, 0.75194407],
           [0.67696689, 0.91878127, 0.09769044, 0.04645137, 0.37615733],
           [0.05903624, 0.29908861, 0.34088298, 0.66216337, 0.83160998],
           [0.64619526, 0.94894632, 0.27855892, 0.0706151, 0.39962917]]),
    mask=np.array([[True, False, False, True, False],
           [True, True, True, False, True],
           [False, False, False, False, False],
           [True, True, True, True, True],
           [False, False, True, False, False]], dtype=np.bool))

    def test_moment(self):
        y = mstats.moment(self.testcase,1)
        assert_almost_equal(y,0.0,10)
        y = mstats.moment(self.testcase,2)
        assert_almost_equal(y,1.25)
        y = mstats.moment(self.testcase,3)
        assert_almost_equal(y,0.0)
        y = mstats.moment(self.testcase,4)
        assert_almost_equal(y,2.5625)

    def test_variation(self):
        y = mstats.variation(self.testcase)
        assert_almost_equal(y,0.44721359549996, 10)

    def test_skewness(self):
        y = mstats.skew(self.testmathworks)
        assert_almost_equal(y,-0.29322304336607,10)
        y = mstats.skew(self.testmathworks,bias=0)
        assert_almost_equal(y,-0.437111105023940,10)
        y = mstats.skew(self.testcase)
        assert_almost_equal(y,0.0,10)

    def test_kurtosis(self):
        # Set flags for axis = 0 and fisher=0 (Pearson's definition of kurtosis
        # for compatibility with Matlab)
        y = mstats.kurtosis(self.testmathworks,0,fisher=0,bias=1)
        assert_almost_equal(y, 2.1658856802973,10)
        # Note that MATLAB has confusing docs for the following case
        #  kurtosis(x,0) gives an unbiased estimate of Pearson's skewness
        #  kurtosis(x)  gives a biased estimate of Fisher's skewness (Pearson-3)
        #  The MATLAB docs imply that both should give Fisher's
        y = mstats.kurtosis(self.testmathworks,fisher=0, bias=0)
        assert_almost_equal(y, 3.663542721189047,10)
        y = mstats.kurtosis(self.testcase,0,0)
        assert_almost_equal(y,1.64)

        # test that kurtosis works on multidimensional masked arrays
        correct_2d = ma.array(np.array([-1.5, -3., -1.47247052385, 0.,
                                        -1.26979517952]),
                              mask=np.array([False, False, False, True,
                                             False], dtype=np.bool))
        assert_array_almost_equal(mstats.kurtosis(self.testcase_2d, 1),
                                  correct_2d)
        for i, row in enumerate(self.testcase_2d):
            assert_almost_equal(mstats.kurtosis(row), correct_2d[i])

        correct_2d_bias_corrected = ma.array(
            np.array([-1.5, -3., -1.88988209538, 0., -0.5234638463918877]),
            mask=np.array([False, False, False, True, False], dtype=np.bool))
        assert_array_almost_equal(mstats.kurtosis(self.testcase_2d, 1,
                                                  bias=False),
                                  correct_2d_bias_corrected)
        for i, row in enumerate(self.testcase_2d):
            assert_almost_equal(mstats.kurtosis(row, bias=False),
                                correct_2d_bias_corrected[i])

        # Check consistency between stats and mstats implementations
        assert_array_almost_equal_nulp(mstats.kurtosis(self.testcase_2d[2, :]),
                                       stats.kurtosis(self.testcase_2d[2, :]))

    def test_mode(self):
        a1 = [0,0,0,1,1,1,2,3,3,3,3,4,5,6,7]
        a2 = np.reshape(a1, (3,5))
        a3 = np.array([1,2,3,4,5,6])
        a4 = np.reshape(a3, (3,2))
        ma1 = ma.masked_where(ma.array(a1) > 2, a1)
        ma2 = ma.masked_where(a2 > 2, a2)
        ma3 = ma.masked_where(a3 < 2, a3)
        ma4 = ma.masked_where(ma.array(a4) < 2, a4)
        assert_equal(mstats.mode(a1, axis=None), (3,4))
        assert_equal(mstats.mode(a1, axis=0), (3,4))
        assert_equal(mstats.mode(ma1, axis=None), (0,3))
        assert_equal(mstats.mode(a2, axis=None), (3,4))
        assert_equal(mstats.mode(ma2, axis=None), (0,3))
        assert_equal(mstats.mode(a3, axis=None), (1,1))
        assert_equal(mstats.mode(ma3, axis=None), (2,1))
        assert_equal(mstats.mode(a2, axis=0), ([[0,0,0,1,1]], [[1,1,1,1,1]]))
        assert_equal(mstats.mode(ma2, axis=0), ([[0,0,0,1,1]], [[1,1,1,1,1]]))
        assert_equal(mstats.mode(a2, axis=-1), ([[0],[3],[3]], [[3],[3],[1]]))
        assert_equal(mstats.mode(ma2, axis=-1), ([[0],[1],[0]], [[3],[1],[0]]))
        assert_equal(mstats.mode(ma4, axis=0), ([[3,2]], [[1,1]]))
        assert_equal(mstats.mode(ma4, axis=-1), ([[2],[3],[5]], [[1],[1],[1]]))


class TestPercentile(TestCase):
    def setUp(self):
        self.a1 = [3,4,5,10,-3,-5,6]
        self.a2 = [3,-6,-2,8,7,4,2,1]
        self.a3 = [3.,4,5,10,-3,-5,-6,7.0]

    def test_percentile(self):
        x = np.arange(8) * 0.5
        assert_equal(mstats.scoreatpercentile(x, 0), 0.)
        assert_equal(mstats.scoreatpercentile(x, 100), 3.5)
        assert_equal(mstats.scoreatpercentile(x, 50), 1.75)

    def test_2D(self):
        x = ma.array([[1, 1, 1],
                      [1, 1, 1],
                      [4, 4, 3],
                      [1, 1, 1],
                      [1, 1, 1]])
        assert_equal(mstats.scoreatpercentile(x,50), [1,1,1])


class TestVariability(TestCase):
    """  Comparison numbers are found using R v.1.5.1
         note that length(testcase) = 4
    """
    testcase = ma.fix_invalid([1,2,3,4,np.nan])

    def test_signaltonoise(self):
        # This is not in R, so used:
        #     mean(testcase, axis=0) / (sqrt(var(testcase)*3/4))
        y = mstats.signaltonoise(self.testcase)
        assert_almost_equal(y, 2.236067977)

    def test_sem(self):
        # This is not in R, so used: sqrt(var(testcase)*3/4) / sqrt(3)
        y = mstats.sem(self.testcase)
        assert_almost_equal(y, 0.6454972244)
        n = self.testcase.count()
        assert_allclose(mstats.sem(self.testcase, ddof=0) * np.sqrt(n/(n-2)),
                        mstats.sem(self.testcase, ddof=2))

    def test_zmap(self):
        # This is not in R, so tested by using:
        #    (testcase[i]-mean(testcase,axis=0)) / sqrt(var(testcase)*3/4)
        y = mstats.zmap(self.testcase, self.testcase)
        desired_unmaskedvals = ([-1.3416407864999, -0.44721359549996,
                                 0.44721359549996, 1.3416407864999])
        assert_array_almost_equal(desired_unmaskedvals,
                                  y.data[y.mask == False], decimal=12)

    def test_zscore(self):
        # This is not in R, so tested by using:
        #     (testcase[i]-mean(testcase,axis=0)) / sqrt(var(testcase)*3/4)
        y = mstats.zscore(self.testcase)
        desired = ma.fix_invalid([-1.3416407864999, -0.44721359549996,
                                  0.44721359549996, 1.3416407864999, np.nan])
        assert_almost_equal(desired, y, decimal=12)


class TestMisc(TestCase):

    def test_obrientransform(self):
        args = [[5]*5+[6]*11+[7]*9+[8]*3+[9]*2+[10]*2,
                [6]+[7]*2+[8]*4+[9]*9+[10]*16]
        result = [5*[3.1828]+11*[0.5591]+9*[0.0344]+3*[1.6086]+2*[5.2817]+2*[11.0538],
                  [10.4352]+2*[4.8599]+4*[1.3836]+9*[0.0061]+16*[0.7277]]
        assert_almost_equal(np.round(mstats.obrientransform(*args).T,4),
                            result,4)

    def test_kstwosamp(self):
        x = [[nan,nan, 4, 2, 16, 26, 5, 1, 5, 1, 2, 3, 1],
             [4, 3, 5, 3, 2, 7, 3, 1, 1, 2, 3, 5, 3],
             [3, 2, 5, 6, 18, 4, 9, 1, 1,nan, 1, 1,nan],
             [nan, 6, 11, 4, 17,nan, 6, 1, 1, 2, 5, 1, 1]]
        x = ma.fix_invalid(x).T
        (winter,spring,summer,fall) = x.T

        assert_almost_equal(np.round(mstats.ks_twosamp(winter,spring),4),
                            (0.1818,0.9892))
        assert_almost_equal(np.round(mstats.ks_twosamp(winter,spring,'g'),4),
                            (0.1469,0.7734))
        assert_almost_equal(np.round(mstats.ks_twosamp(winter,spring,'l'),4),
                            (0.1818,0.6744))

    def test_friedmanchisq(self):
        # No missing values
        args = ([9.0,9.5,5.0,7.5,9.5,7.5,8.0,7.0,8.5,6.0],
                [7.0,6.5,7.0,7.5,5.0,8.0,6.0,6.5,7.0,7.0],
                [6.0,8.0,4.0,6.0,7.0,6.5,6.0,4.0,6.5,3.0])
        result = mstats.friedmanchisquare(*args)
        assert_almost_equal(result[0], 10.4737, 4)
        assert_almost_equal(result[1], 0.005317, 6)
        # Missing values
        x = [[nan,nan, 4, 2, 16, 26, 5, 1, 5, 1, 2, 3, 1],
             [4, 3, 5, 3, 2, 7, 3, 1, 1, 2, 3, 5, 3],
             [3, 2, 5, 6, 18, 4, 9, 1, 1,nan, 1, 1,nan],
             [nan, 6, 11, 4, 17,nan, 6, 1, 1, 2, 5, 1, 1]]
        x = ma.fix_invalid(x)
        result = mstats.friedmanchisquare(*x)
        assert_almost_equal(result[0], 2.0156, 4)
        assert_almost_equal(result[1], 0.5692, 4)


def test_regress_simple():
    # Regress a line with sinusoidal noise. Test for #1273.
    x = np.linspace(0, 100, 100)
    y = 0.2 * np.linspace(0, 100, 100) + 10
    y += np.sin(np.linspace(0, 20, 100))

    slope, intercept, r_value, p_value, sterr = mstats.linregress(x, y)
    assert_almost_equal(slope, 0.19644990055858422)
    assert_almost_equal(intercept, 10.211269918932341)


def test_theilslopes():
    # Test for basic slope and intercept.
    slope, intercept, lower, upper = mstats.theilslopes([0,1,1])
    assert_almost_equal(slope, 0.5)
    assert_almost_equal(intercept, 0.5)

    # Test for correct masking.
    y = np.ma.array([0,1,100,1], mask=[False, False, True, False])
    slope, intercept, lower, upper = mstats.theilslopes(y)
    assert_almost_equal(slope, 1./3)
    assert_almost_equal(intercept, 2./3)

    # Test of confidence intervals from example in Sen (1968).
    x = [1, 2, 3, 4, 10, 12, 18]
    y = [9, 15, 19, 20, 45, 55, 78]
    slope, intercept, lower, upper = mstats.theilslopes(y, x, 0.07)
    assert_almost_equal(slope, 4)
    assert_almost_equal(upper, 4.38, decimal=2)
    assert_almost_equal(lower, 3.71, decimal=2)


def test_plotting_positions():
    # Regression test for #1256
    pos = mstats.plotting_positions(np.arange(3), 0, 0)
    assert_array_almost_equal(pos.data, np.array([0.25, 0.5, 0.75]))


class TestNormalitytests():

    def test_vs_nonmasked(self):
        x = np.array((-2,-1,0,1,2,3)*4)**2
        assert_array_almost_equal(mstats.normaltest(x),
                                  stats.normaltest(x))
        assert_array_almost_equal(mstats.skewtest(x),
                                  stats.skewtest(x))
        assert_array_almost_equal(mstats.kurtosistest(x),
                                  stats.kurtosistest(x))

        funcs = [stats.normaltest, stats.skewtest, stats.kurtosistest]
        mfuncs = [mstats.normaltest, mstats.skewtest, mstats.kurtosistest]
        x = [1, 2, 3, 4]
        for func, mfunc in zip(funcs, mfuncs):
            assert_raises(ValueError, func, x)
            assert_raises(ValueError, mfunc, x)

    def test_axis_None(self):
        # Test axis=None (equal to axis=0 for 1-D input)
        x = np.array((-2,-1,0,1,2,3)*4)**2
        assert_allclose(mstats.normaltest(x, axis=None), mstats.normaltest(x))
        assert_allclose(mstats.skewtest(x, axis=None), mstats.skewtest(x))
        assert_allclose(mstats.kurtosistest(x, axis=None),
                        mstats.kurtosistest(x))

    def test_maskedarray_input(self):
        # Add some masked values, test result doesn't change
        x = np.array((-2,-1,0,1,2,3)*4)**2
        xm = np.ma.array(np.r_[np.inf, x, 10],
                         mask=np.r_[True, [False] * x.size, True])
        assert_allclose(mstats.normaltest(xm), stats.normaltest(x))
        assert_allclose(mstats.skewtest(xm), stats.skewtest(x))
        assert_allclose(mstats.kurtosistest(xm), stats.kurtosistest(x))

    def test_nd_input(self):
        x = np.array((-2,-1,0,1,2,3)*4)**2
        x_2d = np.vstack([x] * 2).T
        for func in [mstats.normaltest, mstats.skewtest, mstats.kurtosistest]:
            res_1d = func(x)
            res_2d = func(x_2d)
            assert_allclose(res_2d[0], [res_1d[0]] * 2)
            assert_allclose(res_2d[1], [res_1d[1]] * 2)


#TODO: for all ttest functions, add tests with masked array inputs
class TestTtest_rel():
    def test_vs_nonmasked(self):
        np.random.seed(1234567)
        outcome = np.random.randn(20, 4) + [0, 0, 1, 2]

        # 1-D inputs
        res1 = stats.ttest_rel(outcome[:, 0], outcome[:, 1])
        res2 = mstats.ttest_rel(outcome[:, 0], outcome[:, 1])
        assert_allclose(res1, res2)

        # 2-D inputs
        res1 = stats.ttest_rel(outcome[:, 0], outcome[:, 1], axis=None)
        res2 = mstats.ttest_rel(outcome[:, 0], outcome[:, 1], axis=None)
        assert_allclose(res1, res2)
        res1 = stats.ttest_rel(outcome[:, :2], outcome[:, 2:], axis=0)
        res2 = mstats.ttest_rel(outcome[:, :2], outcome[:, 2:], axis=0)
        assert_allclose(res1, res2)

        # Check default is axis=0
        res3 = mstats.ttest_rel(outcome[:, :2], outcome[:, 2:])
        assert_allclose(res2, res3)

    def test_invalid_input_size(self):
        assert_raises(ValueError, mstats.ttest_rel,
                      np.arange(10), np.arange(11))
        x = np.arange(24)
        assert_raises(ValueError, mstats.ttest_rel,
                      x.reshape(2, 3, 4), x.reshape(2, 4, 3), axis=1)
        assert_raises(ValueError, mstats.ttest_rel,
                      x.reshape(2, 3, 4), x.reshape(2, 4, 3), axis=2)

    def test_empty(self):
        res1 = mstats.ttest_rel([], [])
        assert_(np.all(np.isnan(res1)))


class TestTtest_ind():
    def test_vs_nonmasked(self):
        np.random.seed(1234567)
        outcome = np.random.randn(20, 4) + [0, 0, 1, 2]

        # 1-D inputs
        res1 = stats.ttest_ind(outcome[:, 0], outcome[:, 1])
        res2 = mstats.ttest_ind(outcome[:, 0], outcome[:, 1])
        assert_allclose(res1, res2)

        # 2-D inputs
        res1 = stats.ttest_ind(outcome[:, 0], outcome[:, 1], axis=None)
        res2 = mstats.ttest_ind(outcome[:, 0], outcome[:, 1], axis=None)
        assert_allclose(res1, res2)
        res1 = stats.ttest_ind(outcome[:, :2], outcome[:, 2:], axis=0)
        res2 = mstats.ttest_ind(outcome[:, :2], outcome[:, 2:], axis=0)
        assert_allclose(res1, res2)

        # Check default is axis=0
        res3 = mstats.ttest_ind(outcome[:, :2], outcome[:, 2:])
        assert_allclose(res2, res3)

    def test_empty(self):
        res1 = mstats.ttest_ind([], [])
        assert_(np.all(np.isnan(res1)))


class TestTtest_1samp():
    def test_vs_nonmasked(self):
        np.random.seed(1234567)
        outcome = np.random.randn(20, 4) + [0, 0, 1, 2]

        # 1-D inputs
        res1 = stats.ttest_1samp(outcome[:, 0], 1)
        res2 = mstats.ttest_1samp(outcome[:, 0], 1)
        assert_allclose(res1, res2)

        # 2-D inputs
        res1 = stats.ttest_1samp(outcome[:, 0], outcome[:, 1], axis=None)
        res2 = mstats.ttest_1samp(outcome[:, 0], outcome[:, 1], axis=None)
        assert_allclose(res1, res2)
        res1 = stats.ttest_1samp(outcome[:, :2], outcome[:, 2:], axis=0)
        res2 = mstats.ttest_1samp(outcome[:, :2], outcome[:, 2:], axis=0)
        assert_allclose(res1, res2)

        # Check default is axis=0
        res3 = mstats.ttest_1samp(outcome[:, :2], outcome[:, 2:])
        assert_allclose(res2, res3)

    def test_empty(self):
        res1 = mstats.ttest_1samp([], 1)
        assert_(np.all(np.isnan(res1)))


class TestCompareWithStats(TestCase):
    """
    Class to compare mstats results with stats results.

    It is in general assumed that scipy.stats is at a more mature stage than
    stats.mstats.  If a routine in mstats results in similar results like in
    scipy.stats, this is considered also as a proper validation of scipy.mstats
    routine.

    Different sample sizes are used for testing, as some problems between stats
    and mstats are dependent on sample size.

    Author: Alexander Loew

    NOTE that some tests fail. This might be caused by
    a) actual differences or bugs between stats and mstats
    b) numerical inaccuracies
    c) different definitions of routine interfaces

    These failures need to be checked. Current workaround is to have disabled these tests,
    but issuing reports on scipy-dev

    """
    def get_n(self):
        """ Returns list of sample sizes to be used for comparison. """
        return [1000, 100, 10, 5]

    def generate_xy_sample(self, n):
        # This routine generates numpy arrays and corresponding masked arrays
        # with the same data, but additional masked values
        np.random.seed(1234567)
        x = np.random.randn(n)
        y = x + np.random.randn(n)
        xm = np.ones(len(x) + 5) * 1e16
        ym = np.ones(len(y) + 5) * 1e16
        xm[0:len(x)] = x
        ym[0:len(y)] = y
        mask = xm > 9e15
        xm = np.ma.array(xm, mask=mask)
        ym = np.ma.array(ym, mask=mask)
        return x, y, xm, ym

    def generate_xy_sample2D(self, n, nx):
        x = np.ones((n, nx)) * np.nan
        y = np.ones((n, nx)) * np.nan
        xm = np.ones((n+5, nx)) * np.nan
        ym = np.ones((n+5, nx)) * np.nan

        for i in range(nx):
            x[:,i], y[:,i], dx, dy = self.generate_xy_sample(n)

        xm[0:n, :] = x[0:n]
        ym[0:n, :] = y[0:n]
        xm = np.ma.array(xm, mask=np.isnan(xm))
        ym = np.ma.array(ym, mask=np.isnan(ym))
        return x, y, xm, ym

    def test_linregress(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)
            res1 = stats.linregress(x, y)
            res2 = stats.mstats.linregress(xm, ym)
            assert_allclose(np.asarray(res1), np.asarray(res2))

    def test_pearsonr(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)
            r, p = stats.pearsonr(x, y)
            rm, pm = stats.mstats.pearsonr(xm, ym)

            assert_almost_equal(r, rm, decimal=14)
            assert_almost_equal(p, pm, decimal=14)

    def test_spearmanr(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)
            r, p = stats.spearmanr(x, y)
            rm, pm = stats.mstats.spearmanr(xm, ym)
            assert_almost_equal(r, rm, 14)
            assert_almost_equal(p, pm, 14)

    def test_gmean(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)
            r = stats.gmean(abs(x))
            rm = stats.mstats.gmean(abs(xm))
            assert_allclose(r, rm, rtol=1e-13)

            r = stats.gmean(abs(y))
            rm = stats.mstats.gmean(abs(ym))
            assert_allclose(r, rm, rtol=1e-13)

    def test_hmean(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)

            r = stats.hmean(abs(x))
            rm = stats.mstats.hmean(abs(xm))
            assert_almost_equal(r, rm, 10)

            r = stats.hmean(abs(y))
            rm = stats.mstats.hmean(abs(ym))
            assert_almost_equal(r, rm, 10)

    def test_skew(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)

            r = stats.skew(x)
            rm = stats.mstats.skew(xm)
            assert_almost_equal(r, rm, 10)

            r = stats.skew(y)
            rm = stats.mstats.skew(ym)
            assert_almost_equal(r, rm, 10)

    def test_moment(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)

            r = stats.moment(x)
            rm = stats.mstats.moment(xm)
            assert_almost_equal(r, rm, 10)

            r = stats.moment(y)
            rm = stats.mstats.moment(ym)
            assert_almost_equal(r, rm, 10)

    def test_signaltonoise(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)

            r = stats.signaltonoise(x)
            rm = stats.mstats.signaltonoise(xm)
            assert_almost_equal(r, rm, 10)

            r = stats.signaltonoise(y)
            rm = stats.mstats.signaltonoise(ym)
            assert_almost_equal(r, rm, 10)

    def test_betai(self):
        np.random.seed(12345)
        for i in range(10):
            a = np.random.rand() * 5.
            b = np.random.rand() * 200.
            assert_equal(stats.betai(a, b, 0.), 0.)
            assert_equal(stats.betai(a, b, 1.), 1.)
            assert_equal(stats.mstats.betai(a, b, 0.), 0.)
            assert_equal(stats.mstats.betai(a, b, 1.), 1.)
            x = np.random.rand()
            assert_almost_equal(stats.betai(a, b, x),
                                stats.mstats.betai(a, b, x), decimal=13)

    def test_zscore(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)

            #reference solution
            zx = (x - x.mean()) / x.std()
            zy = (y - y.mean()) / y.std()

            #validate stats
            assert_allclose(stats.zscore(x), zx, rtol=1e-10)
            assert_allclose(stats.zscore(y), zy, rtol=1e-10)

            #compare stats and mstats
            assert_allclose(stats.zscore(x), stats.mstats.zscore(xm[0:len(x)]),
                            rtol=1e-10)
            assert_allclose(stats.zscore(y), stats.mstats.zscore(ym[0:len(y)]),
                            rtol=1e-10)

    def test_kurtosis(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)
            r = stats.kurtosis(x)
            rm = stats.mstats.kurtosis(xm)
            assert_almost_equal(r, rm, 10)

            r = stats.kurtosis(y)
            rm = stats.mstats.kurtosis(ym)
            assert_almost_equal(r, rm, 10)

    def test_sem(self):
        # example from stats.sem doc
        a = np.arange(20).reshape(5,4)
        am = np.ma.array(a)
        r = stats.sem(a,ddof=1)
        rm = stats.mstats.sem(am, ddof=1)

        assert_allclose(r, 2.82842712, atol=1e-5)
        assert_allclose(rm, 2.82842712, atol=1e-5)

        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)
            assert_almost_equal(stats.mstats.sem(xm, axis=None, ddof=0),
                                stats.sem(x, axis=None, ddof=0), decimal=13)
            assert_almost_equal(stats.mstats.sem(ym, axis=None, ddof=0),
                                stats.sem(y, axis=None, ddof=0), decimal=13)
            assert_almost_equal(stats.mstats.sem(xm, axis=None, ddof=1),
                                stats.sem(x, axis=None, ddof=1), decimal=13)
            assert_almost_equal(stats.mstats.sem(ym, axis=None, ddof=1),
                                stats.sem(y, axis=None, ddof=1), decimal=13)

    def test_describe(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)
            r = stats.describe(x, ddof=1)
            rm = stats.mstats.describe(xm, ddof=1)
            for ii in range(6):
                assert_almost_equal(np.asarray(r[ii]),
                                    np.asarray(rm[ii]),
                                    decimal=12)

    def test_rankdata(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)
            r = stats.rankdata(x)
            rm = stats.mstats.rankdata(x)
            assert_allclose(r, rm)

    def test_tmean(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)
            assert_almost_equal(stats.tmean(x),stats.mstats.tmean(xm), 14)
            assert_almost_equal(stats.tmean(y),stats.mstats.tmean(ym), 14)

    def test_tmax(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)
            assert_almost_equal(stats.tmax(x,2.),
                                stats.mstats.tmax(xm,2.), 10)
            assert_almost_equal(stats.tmax(y,2.),
                                stats.mstats.tmax(ym,2.), 10)

    def test_tmin(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)
            assert_equal(stats.tmin(x),stats.mstats.tmin(xm))
            assert_equal(stats.tmin(y),stats.mstats.tmin(ym))

            assert_almost_equal(stats.tmin(x,lowerlimit=-1.),
                                stats.mstats.tmin(xm,lowerlimit=-1.), 10)
            assert_almost_equal(stats.tmin(y,lowerlimit=-1.),
                                stats.mstats.tmin(ym,lowerlimit=-1.), 10)

    def test_zmap(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)
            z = stats.zmap(x,y)
            zm = stats.mstats.zmap(xm,ym)
            assert_allclose(z, zm[0:len(z)], atol=1e-10)

    def test_variation(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)
            assert_almost_equal(stats.variation(x), stats.mstats.variation(xm),
                                decimal=12)
            assert_almost_equal(stats.variation(y), stats.mstats.variation(ym),
                                decimal=12)

    def test_tvar(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)
            assert_almost_equal(stats.tvar(x), stats.mstats.tvar(xm),
                                decimal=12)
            assert_almost_equal(stats.tvar(y), stats.mstats.tvar(ym),
                                decimal=12)

    def test_trimboth(self):
        a = np.arange(20)
        b = stats.trimboth(a, 0.1)
        bm = stats.mstats.trimboth(a, 0.1)
        assert_allclose(b, bm.data[~bm.mask])

    def test_tsem(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)
            assert_almost_equal(stats.tsem(x),stats.mstats.tsem(xm), decimal=14)
            assert_almost_equal(stats.tsem(y),stats.mstats.tsem(ym), decimal=14)
            assert_almost_equal(stats.tsem(x,limits=(-2.,2.)),
                                stats.mstats.tsem(xm,limits=(-2.,2.)),
                                decimal=14)

    def test_skewtest(self):
        # this test is for 1D data
        for n in self.get_n():
            if n > 8:
                x, y, xm, ym = self.generate_xy_sample(n)
                r = stats.skewtest(x)
                rm = stats.mstats.skewtest(xm)
                assert_equal(r[0], rm[0])
                # TODO this test is not performed as it is a known issue that
                # mstats returns a slightly different p-value what is a bit
                # strange is that other tests like test_maskedarray_input don't
                # fail!
                #~ assert_almost_equal(r[1], rm[1])

    def test_skewtest_2D_notmasked(self):
        # a normal ndarray is passed to the masked function
        x = np.random.random((20, 2)) * 20.
        r = stats.skewtest(x)
        rm = stats.mstats.skewtest(x)
        assert_allclose(np.asarray(r), np.asarray(rm))

    def test_skewtest_2D_WithMask(self):
        nx = 2
        for n in self.get_n():
            if n > 8:
                x, y, xm, ym = self.generate_xy_sample2D(n, nx)
                r = stats.skewtest(x)
                rm = stats.mstats.skewtest(xm)

                assert_equal(r[0][0],rm[0][0])
                assert_equal(r[0][1],rm[0][1])

    def test_normaltest(self):
        np.seterr(over='raise')
        for n in self.get_n():
            if n > 8:
                with warnings.catch_warnings():
                    warnings.filterwarnings('ignore', category=UserWarning)
                    x, y, xm, ym = self.generate_xy_sample(n)
                    r = stats.normaltest(x)
                    rm = stats.mstats.normaltest(xm)
                    assert_allclose(np.asarray(r), np.asarray(rm))

    def test_find_repeats(self):
        x = np.asarray([1,1,2,2,3,3,3,4,4,4,4]).astype('float')
        tmp = np.asarray([1,1,2,2,3,3,3,4,4,4,4,5,5,5,5]).astype('float')
        mask = (tmp == 5.)
        xm = np.ma.array(tmp, mask=mask)

        r = stats.find_repeats(x)
        rm = stats.mstats.find_repeats(xm)

        assert_equal(r,rm)

    def test_kendalltau(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)
            r = stats.kendalltau(x, y)
            rm = stats.mstats.kendalltau(xm, ym)
            assert_almost_equal(r[0], rm[0], decimal=10)
            assert_almost_equal(r[1], rm[1], decimal=7)

    def test_obrientransform(self):
        for n in self.get_n():
            x, y, xm, ym = self.generate_xy_sample(n)
            r = stats.obrientransform(x)
            rm = stats.mstats.obrientransform(xm)
            assert_almost_equal(r.T, rm[0:len(x)])


if __name__ == "__main__":
    run_module_suite()