def test_log1p(self):
"""log1p should give same results as cephes"""
p_s = [1e-10, 1e-5, 0.1, 0.8, 0.9, 0.95, 0.999, 0.9999999, 1,
1.000000001, 1.01, 2]
exp = [9.9999999995e-11, 9.99995000033e-06, 0.0953101798043,
0.587786664902, 0.641853886172, 0.667829372576, 0.692647055518,
0.69314713056, 0.69314718056, 0.69314718106, 0.698134722071,
1.09861228867, ]
for p, e in zip(p_s, exp):
np.testing.assert_allclose(log1p(p), e)
def test_log1p(self):
"""log1p should give same results as cephes"""
p_s = [
1e-10, 1e-5, 0.1, 0.8, 0.9, 0.95, 0.999, 0.9999999, 1, 1.000000001,
1.01, 2
]
exp = [
9.9999999995e-11,
9.99995000033e-06,
0.0953101798043,
0.587786664902,
0.641853886172,
0.667829372576,
0.692647055518,
0.69314713056,
0.69314718056,
0.69314718106,
0.698134722071,
1.09861228867,
]
for p, e in zip(p_s, exp):
np.testing.assert_allclose(log1p(p), e)
def bdtrc(k, n, p):
"""Complement of binomial distribution, k+1 through n.
Uses formula bdtrc(k, n, p) = betai(k+1, n-k, p)
See Cephes docs for details.
"""
p = fix_rounding_error(p)
if (p < 0) or (p > 1):
raise ValueError("Binomial p must be between 0 and 1.")
if (k < 0) or (n < k):
raise ValueError("Binomial k must be between 0 and n.")
if k == n:
return 0
dn = n - k
if k == 0:
if p < .01:
dk = -expm1(dn * log1p(-p))
else:
dk = 1 - pow(1.0 - p, dn)
else:
dk = k + 1
dk = betai(dk, dn, p)
return dk
def bdtrc(k, n, p):
"""Complement of binomial distribution, k+1 through n.
Uses formula bdtrc(k, n, p) = betai(k+1, n-k, p)
See Cephes docs for details.
"""
p = fix_rounding_error(p)
if (p < 0) or (p > 1):
raise ValueError("Binomial p must be between 0 and 1.")
if (k < 0) or (n < k):
raise ValueError("Binomial k must be between 0 and n.")
if k == n:
return 0
dn = n - k
if k == 0:
if p < .01:
dk = -expm1(dn * log1p(-p))
else:
dk = 1 - pow(1.0 - p, dn)
else:
dk = k + 1
dk = betai(dk, dn, p)
return dk
