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#! /usr/bin/env python
##############################################################################
## DendroPy Phylogenetic Computing Library.
##
## Copyright 2010-2015 Jeet Sukumaran and Mark T. Holder.
## All rights reserved.
##
## See "LICENSE.rst" for terms and conditions of usage.
##
## If you use this work or any portion thereof in published work,
## please cite it as:
##
## Sukumaran, J. and M. T. Holder. 2010. DendroPy: a Python library
## for phylogenetic computing. Bioinformatics 26: 1569-1571.
##
##############################################################################
"""
Tests statistical routines.
"""
import unittest
from dendropy.test.support import dendropytest
from dendropy.calculate import statistics
from dendropy.utility import messaging
_LOG = messaging.get_logger(__name__)
class HpdCalculationTests(dendropytest.ExtendedTestCase):
"""
Test reference values as given by ``hpd.emp``, in the "TeachingDemos" package
of R.
"""
def testEmpiricalUnimodalHpd1(self):
# Normal[mu=100, sd=1)
v = [100.93356, 100.66576, 99.44097, 100.60761, 103.65723, 101.15563,
99.09657, 100.39654, 98.77339, 101.13712, 99.33979, 99.99060,
100.39395, 101.68240, 100.99664, 99.17798, 100.83020, 98.90373,
100.30441, 99.49553, 100.52652, 99.76291, 99.95605, 99.63605,
99.21535, 100.51619, 100.55036, 101.21747, 101.04181, 97.76084,
100.19069, 99.46182, 100.47579, 99.56889, 100.23977, 101.22907,
97.85931, 100.86051, 99.56121, 100.44109, 100.02328, 98.62446,
100.11008, 100.12700, 99.27087, 100.72895, 99.06796, 99.38019,
99.79908, 100.82761, 101.26901, 99.88911, 98.09761, 99.16706,
98.98752, 100.10088, 100.58883, 99.42982, 101.90322, 101.22817,
101.36052, 97.70629, 100.15950, 99.39458, 100.19414, 103.43317,
100.32429, 98.90429, 101.28049, 99.82948, 100.96041, 99.46024,
98.22509, 101.63878, 100.66998, 101.82238, 99.49847, 100.41055,
98.71792, 99.66001, 98.53177, 99.11997, 100.14802, 98.96423,
101.93145, 100.09478, 100.85930, 99.82181, 101.50284, 99.93301,
99.57168, 98.19978, 100.90708, 99.25086, 101.74170, 99.86034,
99.85785, 99.89154, 99.62313, 99.41994,]
#==> 101.82238 97.70629
#==> 101.90322 97.76084
#==> 101.93145 97.85931
#==> 103.43317 98.09761
#==> 103.65723 98.19978
#n= 100
#nn= 5
#xx= [4.11609, 4.142380000000003, 4.0721400000000045, 5.335560000000001, 5.457449999999994]
#m= 4.07214
#nnn= 100
#(97.85931, 101.93145)
c1, c2 = statistics.empirical_hpd(v)
self.assertAlmostEqual(c1, 97.85931)
self.assertAlmostEqual(c2, 101.93145)
def testEmpiricalUnimodalHpd2(self):
# Exp(rate=0.2)
v = [3.27592276968062, 0.471030483022332, 8.69292160732502,
5.31655522508031, 11.6689748180798, 3.74156305545426,
0.930466635618359, 4.02394197251564, 0.0273082678142286,
2.19627505168319, 11.2686246344702, 3.12780772801489,
16.3526409110966, 1.03131624741206, 4.43873460812746,
1.16054141893983, 1.37002475326881, 4.03690286425358,
2.75003841612488, 0.247246073558927, 2.97294339863583,
9.91361622656596, 1.40643152873963, 5.06202565485096,
2.56700876867399, 5.10566710939115, 8.30197051456789,
0.439280721062038, 11.3532735680448, 1.46181986900046,
11.1246174474465, 2.24797004368156, 1.79919427493587,
8.79207140509944, 4.81857897692776, 2.30751369846985,
0.589188064119702, 3.36240844568238, 9.85515167894673,
13.7341997859286, 3.04674943210557, 10.2497380129517,
15.3365677214208, 0.322058985475451, 2.13952575810254,
8.7431202231924, 9.48776975232077, 0.437449288806399,
2.91444693226367, 0.234506344422698, 2.30315598892048,
11.9319818628238, 1.30209191970236, 1.34823656175286,
25.9922393489827, 9.88916845991366, 4.32954248951232,
0.748464160133153, 1.30975685780868, 10.16635726164,
12.2592059050905, 0.469188864149385, 1.23079363489524,
40.8792947675279, 5.14233190545297, 6.33412759730077,
4.14186116397752, 0.811017339583486, 2.73471124237403,
9.42033216315222, 6.48358419050878, 3.18536503706127,
3.99172384842717, 0.936779121402651, 9.05760801355255,
5.50938969922668, 1.06717714807019, 8.42135253320348,
3.84890870635814, 0.382886157387499, 6.31485156693912,
0.300180648919195, 0.8748722959183, 1.82131360052153,
3.14994857879356, 0.281196870910665, 7.2329476564647,
2.68667792435735, 0.364864277653396, 0.757411941885948,
5.50616672241545, 4.88404127282506, 0.167293788399547,
8.03142971525326, 10.5768193447809, 14.8404745685177,
1.30770040210336, 25.8265917826642, 1.59898946760222,
4.81477369067675,]
# n= 100
# nn= 5
# P1= 15.33657 16.35264 25.82659 25.99224 40.87929
# P2= 0.02730827 0.1672938 0.2345063 0.2472461 0.2811969
# xx= 15.30926 16.18535 25.59209 25.74499 40.5981
# m= 15.30926
# nnn= 1
# FINAL = 0.02730827 15.33657
# [1] 0.02730827 15.33656772
c1, c2 = statistics.empirical_hpd(v)
self.assertAlmostEqual(c1, 0.02730827)
self.assertAlmostEqual(c2, 15.33656772)
def testEmpiricalUnimodalHpd3(self):
# Gamma(shape=5.5, rate=100)
v = [0.0380707918890542, 0.0613501755118962, 0.0349990175822757,
0.0619137725677135, 0.07861308334536, 0.0480553266749484,
0.062862553519841, 0.0682992193072175, 0.0498105967259703,
0.0391473475922808, 0.0814239076471267, 0.0622768940091115,
0.0278766690168117, 0.0317487156549716, 0.0586667309884353,
0.0610901783693829, 0.0614272435233303, 0.0467353725415623,
0.0235002000890242, 0.085772673901534, 0.0556214310452847,
0.0670344572022403, 0.0544400125583679, 0.0538488966212504,
0.05294861204774, 0.0487265157882631, 0.0319744057916896,
0.0727994868817337, 0.0406117459082881, 0.0411118268978343,
0.0500761307970585, 0.0308194535724841, 0.0657552493534245,
0.100523723943228, 0.0465808929090943, 0.0460932186699443,
0.0561270845816648, 0.0600098984413655, 0.039155736440776,
0.0477087458173384, 0.0662527620357706, 0.0259218058062224,
0.0240999453565313, 0.0403149976175261, 0.0397058239610132,
0.080726331847454, 0.084357840225122, 0.0469807175107997,
0.0629060978549567, 0.0815708340371883, 0.0662480716451838,
0.0291424513010887, 0.0423492520899737, 0.0400760974537379,
0.0988931209604346, 0.0334625360347498, 0.0481980311926021,
0.0326792585090408, 0.0454491423001323, 0.020993064627905,
0.0435735408306696, 0.0408747071998941, 0.0152619235644154,
0.0749659776042904, 0.0568986969556779, 0.0238240850033704,
0.0546832244279347, 0.0793788099421741, 0.0366737460311167,
0.0122826115173667, 0.0542719395504513, 0.0426583849776426,
0.0211571623626521, 0.097984660746214, 0.0909562231889738,
0.0317473196033018, 0.0683970866878872, 0.0249627875602813,
0.081633395263259, 0.050187713841904, 0.09452301382497,
0.0832417097555666, 0.0784842034909532, 0.0329463277742707,
0.134071786835307, 0.0672633924985841, 0.0492264776710421,
0.0346193998786818, 0.0608703914888914, 0.0479141586724897,
0.0653849788769291, 0.0363831431722953, 0.0978132293790966,
0.0663011935255327, 0.0245590323775349, 0.0438722027031532,
0.0294721189654155, 0.0482169372325583, 0.0372503987850244,
0.049380448859450]
# n= 100
# nn= 5
# P1= 0.09781323 0.09798466 0.09889312 0.1005237 0.1340718
# P2= 0.01228261 0.01526192 0.02099306 0.02115716 0.0235002
# xx= 0.08553062 0.08272274 0.07790006 0.07936656 0.1105716
# m= 0.07790006
# nnn= 3
# FINAL = 0.02099306 0.09889312
# [1] 0.02099306 0.09889312
c1, c2 = statistics.empirical_hpd(v)
self.assertAlmostEqual(c1, 0.02099306)
self.assertAlmostEqual(c2, 0.09889312)
class TestMedian(unittest.TestCase):
"""
Test from: http://wiki.python.org/moin/SimplePrograms.
"""
def testMedian(self):
self.assertEqual(statistics.median([2, 9, 9, 7, 9, 2, 4, 5, 8]), 7)
class TestVarianceCovariance(unittest.TestCase):
def setUp(self):
# vlen = 30
# ndim = 5
# data = []
# data.append([random.gauss(random.randint(0, 1000), 1000) for i in range(vlen)])
# for dim in range(ndim-1):
# u = random.uniform(0, 1)
# if u > 0.8:
# data.append([x * 3 for x in data[0]])
# elif u > 0.6:
# data.append([x + random.gauss(0, x/100) for x in data[0]])
# elif u > 0.4:
# data.append([x + random.gauss(0, x/10) for x in data[0]])
# elif u > 0.2:
# data.append([random.gauss(0, random.randint(1, 100)) for x in data[0]])
# print data
self.data = [[-387.0725787021329, 931.5293654488856, 546.94301742877,
-1308.9393303633315, 1811.352775963276, 451.3538641126903,
562.9659558111259, 2279.483383601514, -908.0885971464554,
-650.165321672863, -426.0293691171515, 1109.1183877724106,
35.16260780005632, 1453.566295339867, 2838.575344737274,
370.1667315279002, -853.2876360550472, 1171.341723677777,
556.5194253749042, 275.59547544853393, 1936.6411793187876,
-146.60284069858278, 227.34032009264192, 294.9677652833037,
-230.43349352689938, 2272.2745879401054, -522.4676539536883,
880.3216676214797, -364.3858002091546, 4.674611872631715],
[-388.4042113486994, 927.1172167918467, 538.8506889384198,
-1298.3326898912524, 1813.4425528719585, 449.9792508848036,
566.6065457390224, 2275.5404727189675, -911.1644303228873,
-637.7793275095457, -426.24850592012865, 1116.7861772441804,
34.677032164373, 1435.260152533119, 2859.8928263857206,
367.6125468449959, -864.1297741225864, 1170.321476247361,
554.8054179855712, 271.657749074347, 1921.1532376931864,
-145.65499088854472, 226.57461475353222, 298.7472447593899,
-231.0886348421088, 2292.785060285147, -528.8141997687727,
880.8322517812744, -367.48567832266133, 4.599758786967388],
[-1161.2177361063987, 2794.588096346657, 1640.82905228631,
-3926.8179910899944, 5434.0583278898275, 1354.061592338071,
1688.8978674333778, 6838.450150804542, -2724.2657914393662,
-1950.495965018589, -1278.0881073514545, 3327.355163317232,
105.48782340016896, 4360.698886019602, 8515.726034211822,
1110.5001945837007, -2559.8629081651416, 3514.0251710333314,
1669.5582761247128, 826.7864263456017, 5809.923537956363,
-439.80852209574834, 682.0209602779257, 884.9032958499112,
-691.3004805806981, 6816.823763820316, -1567.402961861065,
2640.965002864439, -1093.1574006274636, 14.023835617895145],
[-389.0970757367656, 930.0845285660921, 546.6471157339992,
-1325.4845049714904, 1807.0225831671107, 451.97595156242477,
563.1808453852201, 2275.359502238535, -910.6620730299588,
-639.8911116399893, -430.4296686299347, 1114.0085423914036,
35.23322927194568, 1445.7289312962391, 2869.2649737548804,
369.61107326701136, -847.7524690958505, 1180.5581555467884,
558.6182051869164, 270.71734809287057, 1953.153593413107,
-148.16228159208333, 228.94407431058426, 296.62535613622003,
-232.98333550881344, 2267.1784698610254, -515.4738926823279,
874.9725307590513, -360.1574033066678, 4.7265309567945994]]
# import numpy
# expected_cov = numpy.cov(numpy.array(data),rowvar=0).tolist()
# print expected_cov
self.expected_cov = [[149393.17790377847, -360424.96906892554, -211940.40550363238,
505544.04928701016, -700254.966766187, -174502.80419746446,
-217345.74407933108, -881568.5997736979, 350625.3243410929,
252753.2580470269, 164369.7501328118, -427881.97570378595,
-13617.530634341638, -563503.0643466829, -1093807.4471157312,
-143274.32024934815, 329464.18420184636, -452213.78708996583,
-215077.8426113635, -107087.45068333478, -748475.3164486786,
56624.942130779986, -87816.4837208772, -113659.46065397991,
88859.94740941831, -877271.1179979955, 201980.68894789586,
-340566.08097309095, 140911.57157102908, -1808.2870504090968],
[-360424.96906892554, 869569.9362145537, 511337.65185982996,
-1219681.7066146561, 1689442.2338632138, 421008.1622157625,
524366.7087900256, 2126887.1168150404, -845917.5496523898,
-609812.9697163638, -396557.36555995565, 1032301.8444213009,
32854.22747731646, 1359535.4531227027, 2638892.0982596218,
345667.84863406006, -794860.8161464253, 1091011.1989148206,
518899.4015696987, 258366.84703955788, 1805784.8802174286,
-136613.94859184456, 211866.75720555347, 274211.2373116087,
-214382.2903332192, 2116495.277061747, -487298.17819055147,
821655.4956393185, -339963.90830350405, 4362.735925535438],
[-211940.40550363238, 511337.65185982996, 300691.95320246654,
-717234.9644576052, 993436.5475125475, 247567.57305548087,
308338.74556175485, 1250675.074863846, -497422.68334818585,
-358596.5629816347, -233190.50326784851, 607018.0135966156,
19319.94031851559, 799465.1231295253, 1551742.404717372,
203265.87160003383, -467383.8843663716, 641555.1887777617,
305132.059903797, 151928.88274220875, 1061887.3462284554,
-80335.43600964258, 124586.13005423953, 161240.75009037546,
-126064.20956241484, 1244532.2694496606, -286532.5812771456,
483153.3495236603, -199901.83344425834, 2565.5529679555852],
[505544.04928701016, -1219681.7066146561, -717234.9644576052,
1710856.9192995324, -2369616.693280398, -590520.9262912686,
-735476.3899937997, -2983204.334641759, 1186502.1830001853,
855325.270463226, 556238.3789052436, -1447924.970738861,
-46083.75449593974, -1906929.2316904257, -3701435.8716964982,
-484845.3566280408, 1114827.964160791, -1530318.2381011278,
-727832.8495215549, -362379.6028049886, -2532950.829680498,
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4122.182167280981, -1705.4815430793697, 21.890454372860443]]
def testVarianceCovariance1(self):
cov = statistics.variance_covariance(self.data)
for i, x in enumerate(cov):
for j, y in enumerate(x):
self.assertAlmostEqual(cov[i][j], self.expected_cov[i][j])
def testVarianceCovariance2(self):
d = [[-323.9573971686496, 315.7388065925112, -439.6717600886799,
-1178.099816177854, 534.643723366918, 1432.26163863866,
-497.1855740226206, -1301.8090901379649, -757.2159368960788,
1019.1610261218987], [-971.8721915059489, 947.2164197775336,
-1319.0152802660396, -3534.299448533562, 1603.9311701007541,
4296.7849159159805, -1491.5567220678618, -3905.427270413895,
-2271.6478106882364, 3057.483078365696], [1805.2578794408694,
-110.00822001898491, 3403.866092254204, -7.164802263774928,
1090.216811454231, -1328.8920608696994, 1313.2108525086446,
-20191.95994589982, -2217.3808792199297,
-14735.400560599832], [-394.27706884544017,
305.72735899534194, -386.17544812632764,
-1312.6418677447905, 554.652417355839,
1429.310268304489, -479.9816099694797,
-1474.7086736016736, -766.5610040209765,
943.9067418319103], [-91.76220598952864,
136.88060210863958, -85.06584754543456,
-81.68026472600144, 26.24124439892005,
-0.4363035110954008, 9.600832668565268,
-13.610656002675592, -56.73800195687172,
10.062534396465715]]
e = [[1118051.315834594, -340504.4676922032, 1930944.9443670718,
1089311.6226191486, -702.760833078737, -1907420.4159428228,
1043769.6960229203, -7881480.1714532245, -303512.8258235939,
-7557633.140329254], [-340504.4676922032, 153014.53369854396,
-566748.0815504972, -545103.1972692355, 131399.1886553155,
811301.8312219149, -373506.9853324348, 1559586.2728247487,
-113040.33582529923, 2056440.4519370624], [1930944.9443670718,
-566748.0815504972, 3350039.66106187, 1776176.7004303827,
62345.622800847406, -3185282.8296726383,
1777391.1979210868, -14030883.204065276,
-623124.0396947996, -13181274.97885164],
[1089311.6226191486, -545103.1972692355, 1776176.7004303827,
2033255.6374553614, -594563.6823540081,
-2903121.0040589883, 1268999.4533419132,
-3864821.0472551202, 631450.3221457871,
-6251946.061145776], [-702.760833078737, 131399.1886553155,
62345.622800847406, -594563.6823540081,
363149.79842651676, 640030.6375209386,
-154836.23379737284, -2326341.9245344824,
-566971.7171338849, -674414.9016981383],
[-1907420.4159428228, 811301.8312219149,
-3185282.8296726383, -2903121.0040589883,
640030.6375209386, 4381775.401023215,
-2054062.3922582623, 9356357.877914747,
-479593.4464370444, 11710459.142730745],
[1043769.6960229203, -373506.9853324348,
1777391.1979210868, 1268999.4533419132,
-154836.23379737284, -2054062.3922582623,
1041077.3129029109, -6374584.529610114,
-42690.656074846236, -6773734.4112940645],
[-7881480.1714532245, 1559586.2728247487,
-14030883.204065276, -3864821.0472551202,
-2326341.9245344824, 9356357.877914747,
-6374584.529610114, 70562391.7586506,
5780752.083342586, 57672359.799883455],
[-303512.8258235939, -113040.33582529923,
-623124.0396947996, 631450.3221457871,
-566971.7171338849, -479593.4464370444,
-42690.656074846236, 5780752.083342586,
968375.1765316972, 3112971.715860271],
[-7557633.140329254, 2056440.4519370624,
-13181274.97885164, -6251946.061145776,
-674414.9016981383, 11710459.142730745,
-6773734.4112940645, 57672359.799883455,
3112971.715860271, 52393351.00087271]]
cov = statistics.variance_covariance(d)
for i, x in enumerate(cov):
for j, y in enumerate(x):
self.assertAlmostEqual(cov[i][j], e[i][j])
class FishersExactTests(dendropytest.ExtendedTestCase):
"""
Fisher's exact test.
"""
def setUp(self):
self.table = [[12, 5], [29, 2]]
def testLeftTail(self):
ft = statistics.FishersExactTest(self.table)
p = ft.left_tail_p()
self.assertAlmostEqual(p, 0.044554737835078267)
def testRightTail(self):
ft = statistics.FishersExactTest(self.table)
p = ft.right_tail_p()
self.assertAlmostEqual(p, 0.99452520602190897)
def testTwoTail(self):
ft = statistics.FishersExactTest(self.table)
p = ft.two_tail_p()
self.assertAlmostEqual(p, 0.08026855207410688)
if __name__ == "__main__":
unittest.main()
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