```#!/usr/bin/env python
"""Tests of statistical probability distribution integrals.

Currently using tests against calculations in R, spreadsheets being unreliable.
"""

from cogent.util.unit_test import TestCase, main
from cogent.maths.stats.distribution import z_low, z_high, zprob, chi_low, \
chi_high, t_low, t_high, tprob, poisson_high, poisson_low, poisson_exact, \
binomial_high, binomial_low, binomial_exact, f_low, f_high, fprob, \
stdtr, bdtr, bdtrc, pdtr, pdtrc, fdtr, fdtrc, gdtr, gdtrc, chdtri, stdtri,\
pdtri, bdtri, fdtri, gdtri

__author__ = "Rob Knight"
__credits__ = ["Gavin Huttley", "Rob Knight", "Sandra Smit"]
__version__ = "1.5.3-dev"
__maintainer__ = "Rob Knight"
__status__ = "Production"

class DistributionsTests(TestCase):
"""Tests of particular statistical distributions."""

def setUp(self):
self.values = [0, 0.01, 0.1, 0.5, 1, 2, 5, 10, 20, 30, 50, 200]
self.negvalues = [-i for i in self.values]
self.df = [1, 10, 100]

def test_z_low(self):
"""z_low should match R's pnorm() function"""
probs = [
0.5000000, 0.5039894, 0.5398278, 0.6914625, 0.8413447,
0.9772499, 0.9999997, 1.0000000, 1.0000000, 1.0000000,
1.0000000, 1.0000000,
]
negprobs = [
5.000000e-01, 4.960106e-01, 4.601722e-01, 3.085375e-01,
1.586553e-01, 2.275013e-02, 2.866516e-07, 7.619853e-24,
2.753624e-89, 4.906714e-198, 0.000000e+00, 0.000000e+00]

for z, p in zip(self.values, probs):
self.assertFloatEqual(z_low(z), p)
for z, p in zip(self.negvalues, negprobs):
self.assertFloatEqual(z_low(z), p)

def test_z_high(self):
"""z_high should match R's pnorm(lower.tail=FALSE) function"""

negprobs = [
0.5000000, 0.5039894, 0.5398278, 0.6914625, 0.8413447,
0.9772499, 0.9999997, 1.0000000, 1.0000000, 1.0000000,
1.0000000, 1.0000000,
]
probs = [
5.000000e-01, 4.960106e-01, 4.601722e-01, 3.085375e-01,
1.586553e-01, 2.275013e-02, 2.866516e-07, 7.619853e-24,
2.753624e-89, 4.906714e-198, 0.000000e+00, 0.000000e+00]

for z, p in zip(self.values, probs):
self.assertFloatEqual(z_high(z), p)
for z, p in zip(self.negvalues, negprobs):
self.assertFloatEqual(z_high(z), p)

def test_zprob(self):
"""zprob should match twice the z_high probability for abs(z)"""

probs = [2*i for i in [
5.000000e-01, 4.960106e-01, 4.601722e-01, 3.085375e-01,
1.586553e-01, 2.275013e-02, 2.866516e-07, 7.619853e-24,
2.753624e-89, 4.906714e-198, 0.000000e+00, 0.000000e+00]]

for z, p in zip(self.values, probs):
self.assertFloatEqual(zprob(z), p)
for z, p in zip(self.negvalues, probs):
self.assertFloatEqual(zprob(z), p)

def test_chi_low(self):
"""chi_low should match R's pchisq() function"""

probs = {
1:  [   0.00000000, 0.07965567, 0.24817037, 0.52049988, 0.68268949,
0.84270079, 0.97465268, 0.99843460, 0.99999226, 0.99999996,
1.00000000, 1.00000000
],
10: [   0.000000e+00, 2.593339e-14, 2.497951e-09, 6.611711e-06,
1.721156e-04, 3.659847e-03, 1.088220e-01, 5.595067e-01,
9.707473e-01, 9.991434e-01, 9.999997e-01, 1.000000e+00,
],
100: [  0.000000e+00, 2.906006e-180, 2.780588e-130, 2.029952e-95,
1.788777e-80, 1.233751e-65, 2.238699e-46, 2.181059e-32,
1.854727e-19, 9.056126e-13, 6.953305e-06, 1.000000e-00
],
}
for df in self.df:
for x, p in zip(self.values, probs[df]):
self.assertFloatEqual(chi_low(x, df), p)

def test_chi_high(self):
"""chi_high should match R's pchisq(lower.tail=FALSE) function"""
probs = {
1:  [   1.000000e+00, 9.203443e-01, 7.518296e-01, 4.795001e-01,
3.173105e-01, 1.572992e-01, 2.534732e-02, 1.565402e-03,
7.744216e-06, 4.320463e-08, 1.537460e-12, 2.088488e-45,
],
10: [   1.000000e+00, 1.000000e-00, 1.000000e-00, 9.999934e-01,
9.998279e-01, 9.963402e-01, 8.911780e-01, 4.404933e-01,
2.925269e-02, 8.566412e-04, 2.669083e-07, 1.613931e-37,
],
100:[   1.00000e+00, 1.00000e+00, 1.00000e+00, 1.00000e+00,
1.00000e+00, 1.00000e+00, 1.00000e+00, 1.00000e+00,
1.00000e+00, 1.00000e+00, 9.99993e-01, 1.17845e-08,
],
}

for df in self.df:
for x, p in zip(self.values, probs[df]):
self.assertFloatEqual(chi_high(x, df), p)

def test_t_low(self):
"""t_low should match R's pt() function"""
probs = {
1:  [   0.5000000, 0.5031830, 0.5317255, 0.6475836, 0.7500000,
0.8524164, 0.9371670, 0.9682745, 0.9840977, 0.9893936,
0.9936347, 0.9984085,
],
10: [   0.5000000, 0.5038910, 0.5388396, 0.6860532, 0.8295534,
0.9633060, 0.9997313, 0.9999992, 1.0000000, 1.0000000,
1.0000000, 1.0000000,
],
100:[   0.5000000, 0.5039794, 0.5397277, 0.6909132, 0.8401379,
0.9758939, 0.9999988, 1.0000000, 1.0000000, 1.0000000,
1.0000000, 1.0000000,
],
}

negprobs = {
1:  [   0.500000000, 0.496817007, 0.468274483, 0.352416382,
0.250000000, 0.147583618, 0.062832958, 0.031725517,
0.015902251, 0.010606402, 0.006365349, 0.001591536,
],
10: [   5.000000e-01, 4.961090e-01, 4.611604e-01, 3.139468e-01,
1.704466e-01, 3.669402e-02, 2.686668e-04, 7.947766e-07,
1.073031e-09, 1.980896e-11, 1.237155e-13, 1.200254e-19,
],
100:[   5.000000e-01, 4.960206e-01, 4.602723e-01, 3.090868e-01,
1.598621e-01, 2.410609e-02, 1.225087e-06, 4.950844e-17,
4.997134e-37, 4.190166e-52, 7.236082e-73, 2.774197e-132,
],
}

for df in self.df:
for x, p in zip(self.values, probs[df]):
self.assertFloatEqualRel(t_low(x, df), p, eps=1e-4)
for x, p in zip(self.negvalues, negprobs[df]):
self.assertFloatEqualRel(t_low(x, df), p, eps=1e-4)

def test_t_high(self):
"""t_high should match R's pt(lower.tail=FALSE) function"""
negprobs = {
1:  [   0.5000000, 0.5031830, 0.5317255, 0.6475836, 0.7500000,
0.8524164, 0.9371670, 0.9682745, 0.9840977, 0.9893936,
0.9936347, 0.9984085,
],
10: [   0.5000000, 0.5038910, 0.5388396, 0.6860532, 0.8295534,
0.9633060, 0.9997313, 0.9999992, 1.0000000, 1.0000000,
1.0000000, 1.0000000,
],
100:[   0.5000000, 0.5039794, 0.5397277, 0.6909132, 0.8401379,
0.9758939, 0.9999988, 1.0000000, 1.0000000, 1.0000000,
1.0000000, 1.0000000,
],
}

probs = {
1:  [   0.500000000, 0.496817007, 0.468274483, 0.352416382,
0.250000000, 0.147583618, 0.062832958, 0.031725517,
0.015902251, 0.010606402, 0.006365349, 0.001591536,
],
10: [   5.000000e-01, 4.961090e-01, 4.611604e-01, 3.139468e-01,
1.704466e-01, 3.669402e-02, 2.686668e-04, 7.947766e-07,
1.073031e-09, 1.980896e-11, 1.237155e-13, 1.200254e-19,
],
100:[   5.000000e-01, 4.960206e-01, 4.602723e-01, 3.090868e-01,
1.598621e-01, 2.410609e-02, 1.225087e-06, 4.950844e-17,
4.997134e-37, 4.190166e-52, 7.236082e-73, 2.774197e-132,
],
}

for df in self.df:
for x, p in zip(self.values, probs[df]):
self.assertFloatEqualRel(t_high(x, df), p, eps=1e-4)
for x, p in zip(self.negvalues, negprobs[df]):
self.assertFloatEqualRel(t_high(x, df), p, eps=1e-4)

def test_tprob(self):
"""tprob should match twice the t_high probability for abs(t)"""

probs = {
1:  [ 2*i for i in
[   0.500000000, 0.496817007, 0.468274483, 0.352416382,
0.250000000, 0.147583618, 0.062832958, 0.031725517,
0.015902251, 0.010606402, 0.006365349, 0.001591536,
]],
10: [ 2*i for i in
[   5.000000e-01, 4.961090e-01, 4.611604e-01, 3.139468e-01,
1.704466e-01, 3.669402e-02, 2.686668e-04, 7.947766e-07,
1.073031e-09, 1.980896e-11, 1.237155e-13, 1.200254e-19,
]],
100:[ 2*i for i in
[   5.000000e-01, 4.960206e-01, 4.602723e-01, 3.090868e-01,
1.598621e-01, 2.410609e-02, 1.225087e-06, 4.950844e-17,
4.997134e-37, 4.190166e-52, 7.236082e-73, 2.774197e-132,
]],
}
for df in self.df:
for x, p in zip(self.values, probs[df]):
self.assertFloatEqualRel(tprob(x, df), p, eps=1e-4)

def test_poisson_low(self):
"""Lower tail of poisson should match R for integer successes"""
#WARNING: Results only guaranteed for integer successes: floating
#point _should_ yield reasonable values, but R rounds to int.
expected = {
(0, 0): 1,
(0, 0.75): 0.4723666,
(0, 1): 0.3678794,
(0, 5): 0.006737947,
(0, 113.7): 4.175586e-50,
(2, 0): 1,
(2, 3): 0.4231901,
(2, 17.8): 3.296636e-06,
(17, 29.6): 0.008753318,
(180, 0): 1,
(180, 137.4):0.999784,
(180, 318):2.436995e-17,
(180, 1024):8.266457e-233,
}
for (key, value) in expected.items():
self.assertFloatEqual(poisson_low(*key), value)

def test_poisson_high(self):
"""Upper tail of poisson should match R for integer successes"""
#WARNING: Results only guaranteed for integer successes: floating
#point _should_ yield reasonable values, but R rounds to int.
expected = {
(0, 0): 0,
(0, 0.75): 0.5276334,
(0, 1): 0.6321206,
(0, 5): 0.993262,
(0, 113.7): 1,
(2, 0): 0,
(2, 3): 0.5768099,
(2, 17.8): 0.9999967,
(17, 29.6): 0.9912467,
(180, 0): 0,
(180, 137.4):0.0002159856,
(180, 318):1,
(180, 1024):1,
}
for (key, value) in expected.items():
self.assertFloatEqual(poisson_high(*key), value)

def test_poisson_exact(self):
"""Poisson exact should match expected values from R"""
expected = {
(0, 0): 1,
(0, 0.75): 0.4723666,
(0, 1): 0.3678794,
(0, 5): 0.006737947,
(0, 113.7): 4.175586e-50,
(2, 0): 0,
(2, 3): 0.2240418,
(2, 17.8): 2.946919e-06,
(17, 29.6): 0.004034353,
(180, 0): 0,
(180, 137.4):7.287501e-05,
(180, 318):1.067247e-17,
(180, 1024):6.815085e-233,
}
for (key, value) in expected.items():
self.assertFloatEqual(poisson_exact(*key), value)

def test_binomial_high(self):
"""Binomial high should match values from R for integer successes"""
expected = {
(0, 1, 0.5): 0.5,
(1, 1, 0.5): 0,
(1, 1, 0.0000001): 0,
(1, 1, 0.9999999): 0,
(3, 5, 0.75):0.6328125,
(0, 60, 0.5): 1,
(129, 130, 0.5):7.34684e-40,
(299, 300, 0.099): 4.904089e-302,
(9, 27, 0.0003): 4.958496e-29,
(1032, 2050, 0.5): 0.3702155,
(-1, 3, 0.1): 1,            #if successes less than 0, return 1
(-0.5, 3, 0.1):1,
}
for (key, value) in expected.items():
self.assertFloatEqualRel(binomial_high(*key), value, 1e-4)
#should reject if successes > trials or successes < -1
self.assertRaises(ValueError, binomial_high, 7, 5, 0.5)

def test_binomial_low(self):
"""Binomial low should match values from R for integer successes"""
expected = {
(0, 1, 0.5): 0.5,
(1, 1, 0.5): 1,
(1, 1, 0.0000001): 1,
(1, 1, 0.9999999): 1,
(26, 50, .5): 0.6641,
(3, 5, 0.75):0.3671875,
(0, 60, 0.5): 8.673617e-19,
(129, 130, 0.5):1,
(299, 300, 0.099): 1,
(9, 27, 0.0003): 1,
(1032, 2050, 0.5): 0.6297845,
}
for (key, value) in expected.items():
self.assertFloatEqualRel(binomial_low(*key), value, 1e-4)

def test_binomial_series(self):
"""binomial_exact should match values from R on a whole series"""
expected = map(float, "0.0282475249 0.1210608210 0.2334744405 0.2668279320 0.2001209490 0.1029193452 0.0367569090 0.0090016920 0.0014467005 0.0001377810 0.0000059049".split())

for i in range(len(expected)):
self.assertFloatEqual(binomial_exact(i, 10, 0.3), expected[i])

def test_binomial_exact(self):
"""binomial_exact should match values from R for integer successes"""
expected = {
(0, 1, 0.5): 0.5,
(1, 1, 0.5): 0.5,
(1, 1, 0.0000001): 1e-07,
(1, 1, 0.9999999): 0.9999999,
(3, 5, 0.75):0.2636719,
(0, 60, 0.5): 8.673617e-19,
(129, 130, 0.5):9.550892e-38,
(299, 300, 0.099): 1.338965e-298,
(9, 27, 0.0003): 9.175389e-26,
(1032, 2050, 0.5): 0.01679804,
}
for (key, value) in expected.items():
self.assertFloatEqualRel(binomial_exact(*key), value, 1e-4)

def test_binomial_exact_floats(self):
"""binomial_exact should be within limits for floating point numbers
"""
expected = {
(18.3, 100, 0.2): (0.09089812, 0.09807429),
(2.7,1050,0.006): (0.03615498, 0.07623827),
(2.7,1050,0.06): (1.365299e-25, 3.044327e-24),
(2,100.5,0.6): (7.303533e-37, 1.789727e-36),
(10,100.5,.5):(7.578011e-18,1.365543e-17),
(0.2, 60, 0.5): (8.673617e-19, 5.20417e-17),
(.5,5,.3):(0.16807,0.36015),
}

for (key, value) in expected.items():
min_val, max_val = value
assert min_val < binomial_exact(*key) < max_val
#self.assertFloatEqualRel(binomial_exact(*key), value, 1e-4)

def test_binomial_exact_errors(self):
"""binomial_exact should raise errors on invalid input"""
self.assertRaises(ValueError, binomial_exact,10.2, 5, 0.33)
self.assertRaises(ValueError, binomial_exact,-2, 5, 0.33)
self.assertRaises(ValueError, binomial_exact, 10, 50, -2)
self.assertRaises(ValueError, binomial_exact, 10, 50, 3)

def test_f_high(self):
"""F high should match values from R for integer successes"""
expected = {
(1, 1, 0): 1,
(1, 1, 1): 0.5,
(1, 1, 20): 0.1400487,
(1, 1, 1000000): 0.0006366196,
(1, 10, 0): 1,
(1,10, 5): 0.0493322,
(1, 10, 20): 0.001193467,
(10, 1, 0):1,
(10, 10, 14.7): 0.0001062585,
(13.7, 11.9, 3.8): 0.01340347,  #test non-integer degrees of freedom
#used following series to track down a bug after a failed test case
(28, 29, 2): 0.03424088,
(28, 29, 10): 1.053019e-08,
(28, 29, 20): 1.628245e-12,
(28, 29, 300): 5.038791e-29,
(28, 35, 1): 0.4946777,
(28, 37, 1): 0.4934486,
(28, 38, 1): 0.4928721,
(28, 38.001, 1): 0.4928716,
(28, 38.5, 1): 0.4925927,
(28, 39, 1): 0.492319,
(28, 39, 10): 1.431901e-10,
(28, 39, 20): 1.432014e-15,
(28, 39, 30): 1.059964e-18,
(28, 39, 50): 8.846678e-23,
(28, 39, 10): 1.431901e-10,
(28, 39, 300): 1.226935e-37,
(28, 39, 50): 8.846678e-23,
(28,39,304.7): 9.08154e-38,
(28.4, 39.2, 304.7): 5.573927e-38,
(1032, 2050, 0): 1,
(1032, 2050, 4.15): 1.23535e-165,
(1032, 2050, 0.5): 1,
(1032, 2050, 0.1): 1,
}
e = expected.items()
e.sort()
for (key, value) in e:
self.assertFloatEqualRel(f_high(*key), value)

def test_f_low(self):
"""F low should match values from R for integer successes"""
expected = {
(1, 1, 0): 0,
(1, 1, 1): 0.5,
(1, 1, 20): 0.8599513,
(1, 1, 1000000): 0.9993634,
(1, 10, 0): 0,
(1,10, 5): 0.9506678,
(1, 10, 20): 0.9988065,
(10, 1, 0):0,
(10, 10, 14.7): 0.9998937,
(28.4, 39.2, 304.7): 1,
(1032, 2050, 0): 0,
(1032, 2050, 4.15): 1,
(1032, 2050, 0.5): 7.032663e-35,
(1032, 2050, 0.1): 1.70204e-278,
}
for (key, value) in expected.items():
self.assertFloatEqualRel(f_low(*key), value)

def test_fprob(self):
"""fprob should return twice the tail on a particular side"""
error = 1e-4
#right-hand side
self.assertFloatEqualAbs(fprob(10,10,1.2), 0.7788, eps=error)
#left-hand side
self.assertFloatEqualAbs(fprob(10,10,1.2, side='left'), 1.2212,
eps=error)
self.assertRaises(ValueError, fprob, 10,10,-3)
self.assertRaises(ValueError, fprob, 10, 10, 1, 'non_valid_side')

def test_stdtr(self):
"""stdtr should match cephes results"""
t = [-10, -3.1, -0.5, -0.01, 0, 1, 0.5, 10]
k = [2, 10, 100]
exp = [
0.00492622851166,
7.94776587798e-07,
4.9508444923e-17,
0.0451003650651,
0.00562532860804,
0.00125696358826,
0.333333333333,
0.313946802871,
0.309086782915,
0.496464554479,
0.496108987495,
0.496020605117,
0.5,
0.5,
0.5,
0.788675134595,
0.829553433849,
0.840137922108,
0.666666666667,
0.686053197129,
0.690913217085,
0.995073771488,
0.999999205223,
1.0,
]
index = 0
for i in t:
for j in k:
self.assertFloatEqual(stdtr(j,i), exp[index])
index += 1

def test_bdtr(self):
"""bdtr should match cephes results"""
k_s = [0,1,2,3,5]
n_s = [5,10,1000]
p_s = [1e-10, .1, .5, .9, .999999]
exp = [
0.9999999995,
0.59049,
0.03125,
1e-05,
1.00000000014e-30,
0.999999999,
0.3486784401,
0.0009765625,
1e-10,
1.00000000029e-60,
0.9999999,
1.74787125172e-46,
9.33263618503e-302,
0.0,
0.0,
1.0,
0.91854,
0.1875,
0.00046,
4.99999600058e-24,
1.0,
0.7360989291,
0.0107421875,
9.1e-09,
9.99999100259e-54,
1.0,
1.9595578811e-44,
9.34196882121e-299,
0.0,
0.0,
1.0,
0.99144,
0.5,
0.00856,
9.99998500087e-18,
1.0,
0.9298091736,
0.0546875,
3.736e-07,
4.49999200104e-47,
1.0,
1.09744951737e-42,
4.67099374325e-296,
0.0,
0.0,
1.0,
0.99954,
0.8125,
0.08146,
9.99998000059e-12,
1.0,
0.9872048016,
0.171875,
9.1216e-06,
1.19999685024e-40,
1.0,
4.09381247279e-41,
1.5554471507e-293,
0.0,
0.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
0.9998530974,
0.623046875,
0.0016349374,
2.51998950038e-28,
1.0,
2.55654569306e-38,
7.7385053063e-289,
0.0,
0.0,
]
index = 0
for k in k_s:
for n in n_s:
for p in p_s:
self.assertFloatEqual(bdtr(k,n,p), exp[index])
index += 1

def test_bdtrc(self):
"""bdtrc should give same results as cephes"""
k_s = [0,1,2,3,5]
n_s = [5,10,1000]
p_s = [1e-10, .1, .5, .9, .999999]

exp = [
4.999999999e-10,
0.40951,
0.96875,
0.99999,
1.0,
9.9999999955e-10,
0.6513215599,
0.9990234375,
0.9999999999,
1.0,
9.9999995005e-08,
1.0,
1.0,
1.0,
1.0,
9.999999998e-20,
0.08146,
0.8125,
0.99954,
1.0,
4.4999999976e-19,
0.2639010709,
0.9892578125,
0.9999999909,
1.0,
4.99499966766e-15,
1.0,
1.0,
1.0,
1.0,
9.9999999985e-30,
0.00856,
0.5,
0.99144,
1.0,
1.19999999937e-28,
0.0701908264,
0.9453125,
0.9999996264,
1.0,
1.66166987575e-22,
1.0,
1.0,
1.0,
1.0,
4.9999999996e-40,
0.00046,
0.1875,
0.91854,
0.99999999999,
2.09999999899e-38,
0.0127951984,
0.828125,
0.9999908784,
1.0,
4.14171214499e-30,
1.0,
1.0,
1.0,
1.0,
0.0,
0.0,
0.0,
0.0,
0.0,
2.09999999928e-58,
0.0001469026,
0.376953125,
0.9983650626,
1.0,
1.36817318242e-45,
1.0,
1.0,
1.0,
1.0,
]
index = 0
for k in k_s:
for n in n_s:
for p in p_s:
self.assertFloatEqual(bdtrc(k,n,p), exp[index])
index += 1

def test_pdtr(self):
"""pdtr should match cephes results"""
k_s = [0,1,2,5,10]
m_s = [1e-9, 0.1,0.5,1,2,31]
exp = [
0.999999999 ,
0.904837418036 ,
0.606530659713 ,
0.367879441171 ,
0.135335283237 ,
3.44247710847e-14 ,
1.0 ,
0.99532115984 ,
0.909795989569 ,
0.735758882343 ,
0.40600584971 ,
1.10159267471e-12 ,
1.0 ,
0.99984534693 ,
0.985612322033 ,
0.919698602929 ,
0.676676416183 ,
1.76426951809e-11 ,
1.0 ,
0.999999998725 ,
0.999985835063 ,
0.999405815182 ,
0.983436391519 ,
9.72616712615e-09 ,
1.0 ,
1.0 ,
0.999999999992 ,
0.999999989952 ,
0.999991691776 ,
1.12519146046e-05 ,

]
index = 0
for k in k_s:
for m in m_s:
self.assertFloatEqual(pdtr(k,m), exp[index])
index += 1

def test_pdtrc(self):
"""pdtrc should match cephes results"""
k_s = [0,1,2,5,10]
m_s = [1e-9, 0.1,0.5,1,2,31]
exp = [
9.999999995e-10 ,
0.095162581964 ,
0.393469340287 ,
0.632120558829 ,
0.864664716763 ,
1.0 ,
4.99999999667e-19 ,
0.00467884016044 ,
0.090204010431 ,
0.264241117657 ,
0.59399415029 ,
0.999999999999 ,
1.66666666542e-28 ,
0.000154653070265 ,
0.014387677967 ,
0.0803013970714 ,
0.323323583817 ,
0.999999999982 ,
1.3888888877e-57 ,
1.27489869223e-09 ,
1.41649373223e-05 ,
0.000594184817582 ,
0.0165636084806 ,
0.999999990274 ,
2.50521083625e-107 ,
2.28584493079e-19 ,
7.74084073923e-12 ,
1.00477663757e-08 ,
8.30822436848e-06 ,
0.999988748085 ,
]
index = 0
for k in k_s:
for m in m_s:
self.assertFloatEqual(pdtrc(k,m), exp[index])
index += 1

def test_fdtr(self):
"""fdtr should match cephes results"""
a_s = [1, 2, 10, 1000]
b_s = a_s
x_s = [0, 0.01, 0.5, 10, 521.4]
exp = [
0.0,
0.0634510348611,
0.391826552031,
0.805017770958,
0.972137685271,
0.0,
0.0705345615859,
0.4472135955,
0.912870929175,
0.998087586699,
0.0,
0.0776792814356,
0.504352495617,
0.989880440265,
0.999999999415,
0.0,
0.0796356309764,
0.520335137562,
0.998387447605,
1.0,
0.0,
0.00985245702333,
0.292893218813,
0.781782109764,
0.96904781206,
0.0,
0.00990099009901,
0.333333333333,
0.909090909091,
0.99808575804,
0.0,
0.00994027888402,
0.379078676941,
0.995884773663,
0.999999999923,
0.0,
0.00995006724716,
0.393317789705,
0.999949891187,
1.0,
0.0,
1.5895531756e-06,
0.18766987087,
0.758331535711,
0.965930763936,
0.0,
2.44851927021e-07,
0.185934432082,
0.90573080983,
0.998084291751,
0.0,
1.15978163168e-08,
0.144845806026,
0.999428447457,
0.999999999997,
0.0,
2.54720538101e-09,
0.109321108726,
1.0,
1.0,
0.0,
1.66707029586e-22,
0.157610464133,
0.751895627261,
0.965077362955,
0.0,
2.56671102571e-40,
0.135876263477,
0.904846465249,
0.998083928382,
0.0,
5.1131107462e-143,
0.030392376141,
0.999825108037,
0.999999999999,
0.0,
0.0,
9.96002853277e-28,
1.0,
1.0,
]
index = 0
for a in a_s:
for b in b_s:
for x in x_s:
self.assertFloatEqual(fdtr(a,b,x), exp[index])
index += 1

def test_fdtrc(self):
"""fdtrc should match cephes results"""
a_s = [1, 2, 10, 1000]
b_s = a_s
x_s = [0, 0.01, 0.5, 10, 521.4]
exp = [
1.0,
0.936548965139,
0.608173447969,
0.194982229042,
0.0278623147287,
1.0,
0.929465438414,
0.5527864045,
0.0871290708247,
0.00191241330122,
1.0,
0.922320718564,
0.495647504383,
0.0101195597354,
5.85364343244e-10,
1.0,
0.920364369024,
0.479664862438,
0.00161255239482,
3.24963344513e-93,
1.0,
0.990147542977,
0.707106781187,
0.218217890236,
0.0309521879405,
1.0,
0.990099009901,
0.666666666667,
0.0909090909091,
0.00191424196018,
1.0,
0.990059721116,
0.620921323059,
0.00411522633745,
7.73162209771e-11,
1.0,
0.990049932753,
0.606682210295,
5.01088134545e-05,
7.71037335669e-156,
1.0,
0.999998410447,
0.81233012913,
0.241668464289,
0.0340692360638,
1.0,
0.999999755148,
0.814065567918,
0.0942691901701,
0.00191570824928,
1.0,
0.999999988402,
0.855154193974,
0.000571552543402,
3.21796660031e-12,
1.0,
0.999999997453,
0.890678891274,
3.96065609687e-16,
0.0,
1.0,
1.0,
0.842389535866,
0.248104372739,
0.0349226370457,
1.0,
1.0,
0.864123736523,
0.0951535347509,
0.00191607161849,
1.0,
1.0,
0.969607623859,
0.00017489196271,
6.83862415869e-13,
1.0,
1.0,
1.0,
6.68418402018e-243,
0.0,
]
index = 0
for a in a_s:
for b in b_s:
for x in x_s:
self.assertFloatEqual(fdtrc(a,b,x), exp[index])
index += 1

def test_gdtr(self):
"""gdtr should match cephes results"""
a_s = [1, 2, 10, 1000]
b_s = a_s
x_s = [0, 0.01, 0.5, 10, 521.4]
exp = [
0.0,
0.00995016625083,
0.393469340287,
0.99995460007,
1.0,
0.0,
4.96679133403e-05,
0.090204010431,
0.999500600773,
1.0,
0.0,
2.7307942837e-27,
1.70967002935e-10,
0.542070285528,
1.0,
0.0,
0.0,
0.0,
0.0,
2.78154480191e-77,
0.0,
0.0198013266932,
0.632120558829,
0.999999997939,
1.0,
0.0,
0.00019735322711,
0.264241117657,
0.999999956716,
1.0,
0.0,
2.77103020131e-24,
1.11425478339e-07,
0.995004587692,
1.0,
0.0,
0.0,
0.0,
0.0,
0.91070640569,
0.0,
0.095162581964,
0.993262053001,
1.0,
1.0,
0.0,
0.00467884016044,
0.959572318005,
1.0,
1.0,
0.0,
2.51634780677e-17,
0.0318280573062,
1.0,
1.0,
0.0,
0.0,
0.0,
0.0,
1.0,
0.0,
0.99995460007,
1.0,
1.0,
1.0,
0.0,
0.999500600773,
1.0,
1.0,
1.0,
0.0,
0.542070285528,
1.0,
1.0,
1.0,
0.0,
0.0,
3.29827279707e-86,
1.0,
1.0,
]
index = 0
for a in a_s:
for b in b_s:
for x in x_s:
self.assertFloatEqual(gdtr(a,b,x), exp[index])
index += 1

def test_gdtrc(self):
"""gdtrc should match cephes results"""
a_s = [1, 2, 10, 1000]
b_s = a_s
x_s = [0, 0.01, 0.5, 10, 521.4]
exp = [
1.0,
0.990049833749,
0.606530659713,
4.53999297625e-05,
3.62123855523e-227,
1.0,
0.999950332087,
0.909795989569,
0.000499399227387,
1.89173502125e-224,
1.0,
1.0,
0.999999999829,
0.457929714472,
2.89188102723e-208,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
0.980198673307,
0.367879441171,
2.06115362244e-09,
0.0,
1.0,
0.999802646773,
0.735758882343,
4.32842260712e-08,
0.0,
1.0,
1.0,
0.999999888575,
0.00499541230831,
0.0,
1.0,
1.0,
1.0,
1.0,
0.0892935943104,
1.0,
0.904837418036,
0.00673794699909,
3.72007597602e-44,
0.0,
1.0,
0.99532115984,
0.0404276819945,
3.75727673578e-42,
0.0,
1.0,
1.0,
0.968171942694,
1.12534739608e-31,
0.0,
1.0,
1.0,
1.0,
1.0,
0.0,
1.0,
4.53999297625e-05,
7.12457640674e-218,
0.0,
0.0,
1.0,
0.000499399227387,
3.56941277978e-215,
0.0,
0.0,
1.0,
0.457929714472,
3.90479663912e-199,
0.0,
0.0,
1.0,
1.0,
1.0,
0.0,
0.0,
]
index = 0
for a in a_s:
for b in b_s:
for x in x_s:
self.assertFloatEqual(gdtrc(a,b,x), exp[index])
index += 1

def test_chdtri(self):
"""chdtri should match cephes results"""
k_s = [1,2,5,10,100]
p_s = [1e-50, 1e-9, .02, .5, .8, .99]
exp = [
224.384748319,
37.3248930514,
5.41189443105,
0.45493642312,
0.0641847546673,
0.00015708785791,
230.258509299,
41.4465316739,
7.82404601086,
1.38629436112,
0.446287102628,
0.020100671707,
244.127298027,
50.6921937015,
13.388222599,
4.3514601911,
2.34253430584,
0.554298076728,
262.995620961,
62.9454574206,
21.1607675413,
9.34181776559,
6.17907925604,
2.55821216019,
478.347499744,
209.317598707,
131.141676866,
99.334129236,
87.9453359228,
70.0648949254,
]
index = 0
for k in k_s:
for p in p_s:
self.assertFloatEqual(chdtri(k,p), exp[index])
index += 1

def test_stdtri(self):
"""stdtri should match cephes results"""
k_s = [1,2,5,10,100]
p_s = [1e-50, 1e-9, .02, .5, .8, .99]
exp = [
-3.18309886184e+49,
-318309886.184,
-15.8945448441,
8.1775627727e-17,
1.37638192049,
31.8205159538,
-7.07106781216e+24,
-22360.6797414,
-4.84873221444,
7.48293180888e-17,
1.06066017178,
6.96455671876,
-15683925591.1,
-98.9372246484,
-2.75650852191,
6.976003623e-17,
0.919543780236,
3.36492999891,
-256452.571877,
-20.1446977667,
-2.35931462368,
6.80574793291e-17,
0.879057828551,
2.76376945745,
-28.9584072963,
-6.59893982023,
-2.08088390123,
6.6546053747e-17,
0.845230424487,
2.3642173659,
]
index = 0
for k in k_s:
for p in p_s:
self.assertFloatEqual(stdtri(k,p), exp[index])
index += 1

def test_pdtri(self):
"""pdtri should match cephes results"""
k_s = [1,2,5,10,100]
p_s = [1e-50, 1e-9, .02, .5, .8, .99]
exp = [
119.924420375,
23.9397278656,
5.83392170192,
1.67834699002,
0.824388309033,
0.148554740253,
124.094307191,
26.6722865587,
7.51660387561,
2.67406031372,
1.53504420264,
0.436045165078,
134.901981814,
33.6746016741,
12.0269783451,
5.67016118871,
3.90366383933,
1.7852844853,
150.2138305,
43.627975401,
18.8297496417,
10.6685224038,
8.15701989758,
4.77124616939,
332.371212972,
173.368244558,
122.695978128,
100.666862949,
92.4593447729,
79.0999186597,
]
index = 0
for k in k_s:
for p in p_s:
self.assertFloatEqual(pdtri(k,p), exp[index])
index += 1

def test_bdtri(self):
"""bdtri should match cephes results"""
k_s = [0,1,2,3]
n_s = [5,10,1000]
p_s = [1e-10, .1, .5, .9, .999999]
exp = [
0.99,
0.36904265552,
0.129449436704,
0.020851637639,
2.00000080006e-07,
0.9,
0.205671765276,
0.0669670084632,
0.0104807417938,
1.00000045003e-07,
0.0227627790442,
0.00229993617745,
0.000692907009547,
0.000105354965434,
1.00000049953e-09,
0.997884361719,
0.58389037462,
0.313810170456,
0.112234958546,
0.000316327821398,
0.939678616058,
0.336847723307,
0.162262728195,
0.0545286199977,
0.00014913049349,
0.0260030189545,
0.0038841043984,
0.00167777786542,
0.000531936197341,
1.415587631e-06,
0.999784533318,
0.753363546712,
0.5,
0.246636453288,
0.00465241636163,
0.964779035441,
0.449603888674,
0.258574723285,
0.11582527803,
0.00203463563411,
0.0287538329681,
0.00531348536403,
0.00267315927217,
0.00110256069953,
1.82723947076e-05,
0.999996837712,
0.887765041454,
0.686189829544,
0.41610962538,
0.0212382182007,
0.981054188003,
0.551730832384,
0.355099967912,
0.187562296647,
0.00839131408953,
0.0312483560212,
0.00666849533707,
0.00367082709364,
0.00174586632568,
7.10965576424e-05,
]
index = 0
for k in k_s:
for n in n_s:
for p in p_s:
self.assertFloatEqual(bdtri(k,n,p), exp[index])
index += 1

def test_gdtri(self):
"""gdtri should match cephes results"""
k_s = [1,2,4,10,100]
n_s = k_s
p_s = [1e-9, .02, .5, .8, .99]
exp = [
1.0000000005e-09,
0.0202027073175,
0.69314718056,
1.60943791243,
4.60517018599,
4.47220262303e-05,
0.214699095008,
1.67834699002,
2.994308347,
6.63835206799,
0.0124777531242,
1.01623845904,
3.67206074885,
5.51504571515,
10.0451175148,
0.602134838869,
4.61834927756,
9.66871461471,
12.5187528198,
18.7831173933,
51.1433022288,
80.5501391278,
99.6668649193,
108.304391619,
124.722561491,
5.0000000025e-10,
0.0101013536588,
0.34657359028,
0.804718956217,
2.30258509299,
2.23610131152e-05,
0.107349547504,
0.839173495008,
1.4971541735,
3.319176034,
0.00623887656209,
0.50811922952,
1.83603037443,
2.75752285758,
5.02255875742,
0.301067419435,
2.30917463878,
4.83435730736,
6.25937640991,
9.39155869666,
25.5716511144,
40.2750695639,
49.8334324597,
54.1521958095,
62.3612807454,
2.50000000125e-10,
0.00505067682938,
0.17328679514,
0.402359478109,
1.1512925465,
1.11805065576e-05,
0.053674773752,
0.419586747504,
0.748577086751,
1.659588017,
0.00311943828105,
0.25405961476,
0.918015187213,
1.37876142879,
2.51127937871,
0.150533709717,
1.15458731939,
2.41717865368,
3.12968820495,
4.69577934833,
12.7858255572,
20.1375347819,
24.9167162298,
27.0760979048,
31.1806403727,
1.0000000005e-10,
0.00202027073175,
0.069314718056,
0.160943791243,
0.460517018599,
4.47220262303e-06,
0.0214699095008,
0.167834699002,
0.2994308347,
0.663835206799,
0.00124777531242,
0.101623845904,
0.367206074885,
0.551504571515,
1.00451175148,
0.0602134838869,
0.461834927756,
0.966871461471,
1.25187528198,
1.87831173933,
5.11433022288,
8.05501391278,
9.96668649193,
10.8304391619,
12.4722561491,
1.0000000005e-11,
0.000202027073175,
0.0069314718056,
0.0160943791243,
0.0460517018599,
4.47220262303e-07,
0.00214699095008,
0.0167834699002,
0.02994308347,
0.0663835206799,
0.000124777531242,
0.0101623845904,
0.0367206074885,
0.0551504571515,
0.100451175148,
0.00602134838869,
0.0461834927756,
0.0966871461471,
0.125187528198,
0.187831173933,
0.511433022288,
0.805501391278,
0.996668649193,
1.08304391619,
1.24722561491,
]
index = 0
for k in k_s:
for n in n_s:
for p in p_s:
self.assertFloatEqual(gdtri(k,n,p), exp[index])
index += 1

def test_fdtri(self):
"""fdtri should match cephes results"""
k_s = [1,2,4,10,100]
n_s = k_s
p_s = [1e-50, 1e-9, .02, .5, .8, .99]
exp = [
0.0,
2.46740096071e-18,
0.000987610197427,
1.0,
9.472135955,
4052.18069548,
0.0,
1.99999988687e-18,
0.000800320128051,
0.666666666667,
3.55555555556,
98.5025125628,
0.0,
1.77777767722e-18,
0.000711321880645,
0.548632170413,
2.35072147881,
21.1976895844,
0.0,
1.65119668161e-18,
0.000660638708985,
0.489736921158,
1.88288794493,
10.0442892734,
0.0,
1.57866975531e-18,
0.000631602221127,
0.458262714634,
1.66429288986,
6.89530103058,
0.0,
9.99999973218e-10,
0.0206164098292,
1.5,
12.0,
4999.5,
0.0,
9.99999972718e-10,
0.0204081632653,
1.0,
4.0,
99.0,
0.0,
9.99999972468e-10,
0.0203050891044,
0.828427124746,
2.472135955,
18.0,
0.0,
9.99999972318e-10,
0.0202435772829,
0.743491774985,
1.89864830731,
7.55943215755,
0.0,
9.99999972228e-10,
0.0202067893611,
0.697973989501,
1.63562099482,
4.82390980716,
0.0,
1.29104998825e-05,
0.0712270257663,
1.82271484235,
13.6443218387,
5624.58332963,
0.0,
1.58118880931e-05,
0.082357834815,
1.20710678119,
4.2360679775,
99.2493718553,
0.0,
1.82578627816e-05,
0.0917479893415,
1.0,
2.48261291932,
15.9770248526,
0.0,
2.04128031324e-05,
0.0999726146531,
0.898817134423,
1.82861100515,
5.99433866163,
0.0,
2.21407117017e-05,
0.106518545067,
0.844891468084,
1.5273126184,
3.5126840636,
0.0,
0.00213897888638,
0.130917099116,
2.04191262042,
14.7718897826,
6055.8467074,
0.0,
0.00322083313175,
0.168531162323,
1.34500479177,
4.38216390487,
99.3991959745,
0.0,
0.00448830777955,
0.207656634378,
1.11257336081,
2.45957986729,
14.5459008033,
0.0,
0.00608578074458,
0.251574092492,
1.0,
1.73159473193,
4.84914680208,
0.0,
0.00800159033308,
0.298648905106,
0.940477156977,
1.38089597558,
2.50331112688,
0.0,
3.09672866088e-11,
0.178906118636,
2.18215440197,
15.4973240414,
6334.110036,
0.0,
5.2776234633e-11,
0.2457526061,
1.43271814572,
4.47142755584,
99.4891628084,
0.0,
0.0659164713677,
0.326585865322,
1.18358397235,
2.43020291912,
13.5769915067,
0.0,
0.119865858243,
0.442669184276,
1.06329004653,
1.63265061785,
4.01371941549,
0.0,
0.289673110482,
0.661509869668,
1.0,
1.1839371445,
1.59766912303,
]
index = 0
for k in k_s:
for n in n_s:
for p in p_s:
self.assertFloatEqual(fdtri(k,n,p), exp[index])
index += 1

if __name__ == "__main__":
main()

```