def _get_value_log(self, x, mu, v):
"""log basic 2"""
try:
return loggamma(x+v) - loggamma(x+1) - loggamma(v) + v*log(v) - v*log(v+mu) + x*log(mu) - x*log(v+mu)
except ValueError:
#print('_get_value_log ValueError', x, mu, v, file=sys.stderr)
return 1
def logbinomial(n, k):
"""
Natural logarithm of binomial(n, k).
Examples
--------
>>> import mpmath
>>> mpmath.mp.dps = 25
>>> from mpsci.fun import logbinomial
Compute the log of C(1500, 450).
>>> logbinomial(1500, 450)
mpf('912.5010192350457701746286796')
Verify that it is the expected value.
>>> mpmath.log(mpmath.binomial(1500, 450))
mpf('912.5010192350457701746286773')
"""
if n < 0:
raise ValueError('n must be nonnegative')
if k < 0:
raise ValueError('k must be nonnegative')
if k > n:
raise ValueError('k must not exceed n')
with mpmath.extradps(5):
return (mpmath.loggamma(n + 1)
- mpmath.loggamma(k + 1)
- mpmath.loggamma(mpmath.fsum([n + 1, -k])))
def log_hyper_2F1(a, b, c, w):
log_results_even = []
log_results_odd = []
for n in range(int(1 - b)):
log_resu = logbinomial(
-b,
n) + mpmath.loggamma(a + n) + mpmath.loggamma(c) - mpmath.loggamma(
c + n) - mpmath.loggamma(a) + n * mpmath.log(w)
if is_even(n):
log_results_even.append(log_resu)
else:
log_results_odd.append(log_resu)
if len(log_results_even) == 0:
return -np.inf
else:
log_results_even_partsum = custom_logsumexp_mpmath(
log_results_even, np.ones(len(log_results_even)))
if len(log_results_odd) == 0:
return log_results_even_partsum[0]
else:
log_results_odd_partsum = custom_logsumexp_mpmath(
log_results_odd, np.ones(len(log_results_odd)))
if log_results_odd_partsum[0] > log_results_even_partsum[0]:
print('Dang!')
log_result = custom_logsumexp_mpmath(
[log_results_even_partsum[0], log_results_odd_partsum[0]],
np.array([1, -1]))
return log_result[0]
def _get_value_log(self, x, mu, v):
"""log basic 2"""
try:
return loggamma(x+v) - loggamma(x+1) - loggamma(v) + v*log(v) - v*log(v+mu) + x*log(mu) - x*log(v+mu)
except ValueError:
#print('_get_value_log ValueError', x, mu, v, file=sys.stderr)
return 1
def pdf(x, df, nc):
"""
Probability density function of the noncentral t distribution.
The infinite series is estimated with `mpmath.nsum`.
"""
with mpmath.extradps(5):
x = mpmath.mpf(x)
df = mpmath.mpf(df)
nc = mpmath.mpf(nc)
if x == 0:
logp = (-nc**2 / 2 - mpmath.log(mpmath.pi) / 2 -
mpmath.log(df) / 2 + mpmath.loggamma(
(df + 1) / 2) - mpmath.loggamma(df / 2))
p = mpmath.exp(logp)
else:
logc = (df * mpmath.log(df) / 2 - nc**2 / 2 -
mpmath.loggamma(df / 2) - mpmath.log(mpmath.pi) / 2 -
(df + 1) / 2 * mpmath.log(df + x**2))
c = mpmath.exp(logc)
def _pdf_term(i):
logterm = (mpmath.loggamma(
(df + i + 1) / 2) + i * mpmath.log(x * nc) +
i * mpmath.log(2 / (df + x**2)) / 2 -
mpmath.loggamma(i + 1))
return mpmath.exp(logterm).real
s = mpmath.nsum(_pdf_term, [0, mpmath.inf])
p = c * s
return p
def test_special_printers():
from sympy.printing.lambdarepr import IntervalPrinter
def intervalrepr(expr):
return IntervalPrinter().doprint(expr)
expr = sqrt(sqrt(2) + sqrt(3)) + S.Half
func0 = lambdify((), expr, modules="mpmath", printer=intervalrepr)
func1 = lambdify((), expr, modules="mpmath", printer=IntervalPrinter)
func2 = lambdify((), expr, modules="mpmath", printer=IntervalPrinter())
mpi = type(mpmath.mpi(1, 2))
assert isinstance(func0(), mpi)
assert isinstance(func1(), mpi)
assert isinstance(func2(), mpi)
# To check Is lambdify loggamma works for mpmath or not
exp1 = lambdify(x, loggamma(x), 'mpmath')(5)
exp2 = lambdify(x, loggamma(x), 'mpmath')(1.8)
exp3 = lambdify(x, loggamma(x), 'mpmath')(15)
exp_ls = [exp1, exp2, exp3]
sol1 = mpmath.loggamma(5)
sol2 = mpmath.loggamma(1.8)
sol3 = mpmath.loggamma(15)
sol_ls = [sol1, sol2, sol3]
assert exp_ls == sol_ls
def calc_model_evidence(self):
vval = 0
mp.mp.dps = 50
for action in range(self.hparams.num_actions):
# val=1
# aa = self.a[action]
# for i in xrange(int(self.a[action]-self.a0)):
# aa-=1
# val*=aa
# val/=(2.0*math.pi)
# val/=self.b[action]
# val*=gamma(aa)
# val/=(self.b[action]**aa)
# val *= np.sqrt(np.linalg.det(self.lambda_prior * np.eye(self.hparams.context_dim + 1)) / np.linalg.det(self.precision[action]))
# val *= (self.b0 ** self.a0)
# val/= gamma(self.a0)
# vval += val
#val= 1/float((2.0 * math.pi) ** (self.a[action]-self.a0))
#val*= (float(gamma(self.a[action]))/float(gamma(self.a0)))
#val*= np.sqrt(float(np.linalg.det(self.lambda_prior * np.eye(self.hparams.context_dim + 1)))/float(np.linalg.det(self.precision[action])))
#val*= (float(self.b0**self.a0)/float(self.b[action]**self.a[action]))
val= mp.mpf(mp.fmul(mp.fneg(mp.log(mp.fmul(2.0 , mp.pi))) , mp.fsub(self.a[action],self.a0)))
val+= mp.loggamma(self.a[action])
val-= mp.loggamma(self.a0)
val+= 0.5*mp.log(np.linalg.det(self.lambda_prior * np.eye(self.hparams.context_dim + 1)))
val -= 0.5*mp.log(np.linalg.det(self.precision[action]))
val+= mp.fmul(self.a0,mp.log(self.b0))
val-= mp.fmul(self.a[action],mp.log(self.b[action]))
vval+=mp.exp(val)
vval/=float(self.hparams.num_actions)
return vval
def logchoose(ni, ki):
try:
lgn1 = loggamma(ni + 1)
lgk1 = loggamma(ki + 1)
lgnk1 = loggamma(ni - ki + 1)
except ValueError:
raise ValueError
return lgn1 - (lgnk1 + lgk1)
def logchoose(ni, ki):
try:
lgn1 = mpmath.loggamma(ni + 1)
lgk1 = mpmath.loggamma(ki + 1)
lgnk1 = mpmath.loggamma(ni - ki + 1)
except ValueError:
#print ni,ki
raise ValueError
return lgn1 - (lgnk1 + lgk1)
def var(df, nc):
"""
Variance of the noncentral t distribution.
"""
# XXX Require df > 2.
with mpmath.extradps(5):
df = mpmath.mpf(df)
nc = mpmath.mpf(nc)
c = mpmath.exp(mpmath.loggamma((df - 1) / 2) - mpmath.loggamma(df / 2))
return df / (df - 2) * (1 + nc**2) - df / 2 * nc**2 * c**2
def beta(self, a, b):
"""
Uses either mpmath's gamma or log-gamma function to compute values of the beta function.
"""
a, b = mpmath.mpf(a), mpmath.mpf(b)
if self.use_log: beta = mpmath.exp(mpmath.loggamma(a) + mpmath.loggamma(b) - mpmath.loggamma(a + b))
else: beta = mpmath.gamma(a) * mpmath.gamma(b) / mpmath.gamma(a + b)
return beta
def mean(df, nc):
"""
Mean of the noncentral t distribution.
"""
# XXX Require df > 1.
with mpmath.extradps(5):
df = mpmath.mpf(df)
nc = mpmath.mpf(nc)
logm = (mpmath.log(nc) + mpmath.log(df / 2) / 2 + mpmath.loggamma(
(df - 1) / 2) - mpmath.loggamma(df / 2))
return mpmath.exp(logm)
def betaincreg(self, a, b, x):
"""
betaincreg(a,b,x) evaluates the incomplete beta function (regularized).
It requires a, b > 0 and 0 <= x <= 1.
Code translated from: GNU Scientific Library
"""
# In terms of methods, this function requires contfractbeta(), defined above.
# HOTFIX prevent the original a, b or x from being numpy elements
a = float(a)
b = float(b)
x = float(x)
# Transpose a, x, x into mpmath objects.
a, b, x = mpmath.mpf(a), mpmath.mpf(b), mpmath.mpf(x)
def isnegint(X):
return (X < 0) & (X == mpmath.floor(X))
# Trivial cases
if (x < 0) | (x > 1):
raise ValueError(
"Bad x in betainc(a,b,x) - x must be between 0 and 1")
elif isnegint(a) | isnegint(b) | isnegint(a + b):
raise ValueError(
"Bad a or b in betainc(a,b,x) -- neither a, b nor a+b can be negative integers"
)
elif x == 0:
return 0
elif x == 1:
return 1
else:
# Factors in front of the continued fraction
lnbeta = mpmath.loggamma(a) + mpmath.loggamma(b) - mpmath.loggamma(
a + b)
prefactor = -lnbeta + a * mpmath.log(x) + b * mpmath.log(1 - x)
# Use continued fraction directly ...
if x < (a + 1) / (a + b + 2):
fraction = self.contfractbeta(a, b, x)
result = mpmath.exp(prefactor) * fraction / a
# ... or make a symmetry transformation first
else:
fraction = self.contfractbeta(b, a, 1 - x)
term = mpmath.exp(prefactor) * fraction / b
result = 1 - term
return result
def logchoose(ni, ki):
#n = max(ni, ki)
#k = min(ni, ki)
try:
lgn1 = loggamma(ni+1)
lgk1 = loggamma(ki+1)
lgnk1 = loggamma(ni-ki+1)
except ValueError:
#print ni,ki
raise ValueError
return lgn1 - (lgnk1 + lgk1)
def pofk_paramagnet(N, k):
preterm = sqrt(2. / (pi * N))
if k == 0:
exp_term = loggamma(N + 1) - loggamma(k + 1) - loggamma(N - k + 1)
elif k == N:
exp_term = loggamma(N + 1) - loggamma(k + 1) - loggamma(N - k + 1)
else:
exp_term = loggamma(N + 1) - loggamma(k + 1) - loggamma(
N - k + 1) + k * log(k / N) + (N - k) * log(1. - (k / N))
return preterm * exp(exp_term)
def logbeta(x, y):
"""
Natural logarithm of beta(x, y).
The beta function is
Gamma(x) Gamma(y)
beta(x, y) = -----------------
Gamma(x + y)
where Gamma(z) is the Gamma function.
"""
with mpmath.extradps(5):
return (mpmath.loggamma(x) + mpmath.loggamma(y) -
mpmath.loggamma(mpmath.fsum([x, y])))
def make_lgamma_vals():
from mpmath import loggamma
x = [mpf('0.01')] + linspace(mpf('0.1'), 10, 100) + [mpf(20), mpf(30)]
lga = [loggamma(val) for val in x]
return make_special_vals('lgamma_vals', ('x', x), ('lga', lga))
def make_lgamma_vals():
from mpmath import loggamma
x = [mpf('0.01')] + linspace(mpf('0.1'), 10, 100) + [mpf(20), mpf(30)]
lga = [loggamma(val) for val in x]
return make_special_vals('lgamma_vals', ('x', x), ('lga', lga))
def logpdf(x, df):
"""
Logarithm of the PDF of Student's t distribution.
"""
if df <= 0:
raise ValueError('df must be greater than 0')
with mpmath.extradps(5):
x = mpmath.mpf(x)
df = mpmath.mpf(df)
h = (df + 1) / 2
logp = (mpmath.loggamma(h)
- mpmath.log(df * mpmath.pi)/2
- mpmath.loggamma(df/2)
- h * mpmath.log1p(x**2/df))
return logp
def logpmf(k, lam):
"""
Natural log of the probability mass function of the binomial distribution.
"""
if k < 0:
return -mpmath.mp.inf
with mpmath.extradps(5):
lam = mpmath.mpf(lam)
return k * mpmath.log(lam) - lam - mpmath.loggamma(k + 1)
def logpdf(x, k, theta):
"""
Log of the PDF of the gamma distribution.
"""
_validate_k_theta(k, theta)
x = mpmath.mpf(x)
k = mpmath.mpf(k)
theta = mpmath.mpf(theta)
return (-mpmath.loggamma(k) - k*mpmath.log(theta) +
(k - 1)*mpmath.log(x) - x/theta)
def beta(self, a, b):
"""
Uses either mpmath's gamma or log-gamma function to compute values of the beta function.
"""
# HOTFIX prevent the original a, b from being numpy elements
a = float(a)
b = float(b)
a, b = mpmath.mpf(a), mpmath.mpf(b)
if self.use_log:
beta = mpmath.exp(
mpmath.loggamma(a) + mpmath.loggamma(b) -
mpmath.loggamma(a + b))
else:
beta = mpmath.gamma(a) * mpmath.gamma(b) / mpmath.gamma(a + b)
return beta
def _pdf_term(k, x, dfn, dfd, nc):
halfnc = nc / 2
halfdfn = dfn / 2
halfdfd = dfd / 2
logr = (-halfnc + k * _mp.log(halfnc) - _logbeta(halfdfd, halfdfn + k) -
_mp.loggamma(k + 1) + (halfdfn + k) *
(_mp.log(dfn) - _mp.log(dfd)) + (halfdfn + halfdfd + k) *
(_mp.log(dfd) - _mp.log(dfd + dfn * x)) +
(halfdfn - 1 + k) * _mp.log(x))
return _mp.exp(logr)
def _cdf_term(k, x, dfn, dfd, nc):
halfnc = nc / 2
halfdfn = dfn / 2
halfdfd = dfd / 2
log_coeff = _mp.fsum([k * _mp.log(halfnc), -halfnc, -_mp.loggamma(k + 1)])
coeff = _mp.exp(log_coeff)
r = coeff * _mp.betainc(a=halfdfn + k,
b=halfdfd,
x1=0,
x2=dfn * x / (dfd + dfn * x),
regularized=True)
return r
def logpdf(x, k, theta):
"""
Log of the PDF of the log-gamma distribution.
k is the shape parameter of the gamma distribution.
theta is the scale parameter of the log-gamma distribution.
"""
with mpmath.extradps(5):
x = mpmath.mpf(x)
k = mpmath.mpf(k)
theta = mpmath.mpf(theta)
z = x / theta
return (k * z - mpmath.exp(z)) - mpmath.loggamma(k) - mpmath.log(theta)
def logpdf(x, k):
"""
Logarithm of the PDF for the chi distribution.
"""
_validate_k(k)
if x < 0:
return mpmath.mp.ninf
with mpmath.extradps(5):
x = mpmath.mpf(x)
k = mpmath.mpf(k)
p = ((k - 1)*mpmath.log(x) - x**2/2 - ((k/2) - 1)*mpmath.log(2)
- mpmath.loggamma(k/2))
return p
def likelihood(Kq1, Kq2, mq1, mq2, Nq, M, a):
Kq1 = float(Kq1)
Kq2 = float(Kq2)
mq1 = float(mq1)
mq2 = float(mq2)
Nq = float(Nq)
M = float(M)
a = float(a)
term1 = loggamma(Kq1 + Kq2 +
a) + loggamma(a) - loggamma(Kq1 + a) - loggamma(Kq2 + a)
term2 = float(Kq1) * log(float(mq1) / float(mq1 + mq2)) + float(Kq2) * log(
float(mq2) / float(mq1 + mq2))
term3 = loggamma(M + (a * Nq)) + loggamma(
a * (Nq - 1)) - loggamma(M + (a * (Nq - 1))) - loggamma(a * Nq)
return term1 + term2 + term3
def logpdf(x, nu):
"""
Logarithm of the PDF for the inverse chi-square distribution.
"""
_validate_nu(nu)
if x <= 0:
return mpmath.ninf
with mpmath.extradps(5):
x = mpmath.mpf(x)
nu = mpmath.mpf(nu)
hnu = nu/2
logp = (-hnu*mpmath.log(2) + (-hnu - 1)*mpmath.log(x) - 1/(2*x)
- mpmath.loggamma(hnu))
return logp
def nll(x, k, theta):
"""
Gamma distribution negative log-likelihood.
"""
_validate_k_theta(k, theta)
k = mpmath.mpf(k)
theta = mpmath.mpf(theta)
N = len(x)
sumx = mpmath.fsum(x)
sumlnx = mpmath.fsum(mpmath.log(t) for t in x)
ll = ((k - 1)*sumlnx - sumx/theta - N*k*mpmath.log(theta) -
N*mpmath.loggamma(k))
return -ll
def logpdf(x, nu, loc, scale, scale_inv=None):
"""
Natural logarithm of the PDF for the multivariate t distribution.
`loc` must be a sequence. `scale` is the scale matrix; it
must be an instance of `mpmath.matrix`. `scale` must be
positive definite.
If given, `scale_inv` must be the inverse of `scale`.
"""
p = mpmath.mpf(len(loc))
with mpmath.extradps(5):
nu = mpmath.mpf(nu)
if scale_inv is None:
with mpmath.extradps(5):
scale_inv = mpmath.inverse(scale)
tmp = mpmath.matrix(scale.cols, 1)
for k, v in enumerate(loc):
tmp[k] = mpmath.mpf(v)
loc = tmp
tmp = mpmath.matrix(scale.cols, 1)
for k, v in enumerate(x):
tmp[k] = mpmath.mpf(v)
x = tmp
delta = x - loc
c = (nu + p) / 2
t1 = -c * mpmath.log1p((delta.T * scale_inv * delta)[0, 0] / nu)
t2 = mpmath.loggamma(c)
t3 = mpmath.loggamma(nu / 2)
t4 = (p / 2) * mpmath.log(nu)
t5 = (p / 2) * mpmath.log(mpmath.pi)
with mpmath.extradps(5):
det = mpmath.det(scale)
t6 = mpmath.log(det) / 2
return t2 - t3 - t4 - t5 - t6 + t1
def logpdf(x, nu, loc=0, scale=1):
"""
Natural logarithm of the PDF of the Nakagami distribution.
"""
_validate_params(nu, loc, scale)
if x <= 0:
return -mpmath.inf
with mpmath.extradps(5):
if x <= loc:
return mpmath.mp.zero
x = mpmath.mpf(x)
nu = mpmath.mpf(nu)
loc = mpmath.mpf(loc)
scale = mpmath.mpf(scale)
z = (x - loc)/scale
return (mpmath.log(2) + nu*mpmath.log(nu) - mpmath.loggamma(nu)
+ (2*nu-1)*mpmath.log(z) - nu*z**2 - mpmath.log(scale))
def nll(x, nu, loc, scale):
"""
Negative log-likelihood function for the Nakagami distribution.
"""
_validate_params(nu, loc, scale)
_validate_x(x, loc=loc)
n = len(x)
with mpmath.extradps(5):
nu = mpmath.mpf(nu)
loc = mpmath.mpf(loc)
scale = mpmath.mpf(scale)
z = [(t - loc)/scale for t in x]
logsum = mpmath.fsum([mpmath.log(t) for t in z])
sqsum = mpmath.fsum([t**2 for t in z])
ll = n*(mpmath.log(2) + nu*mpmath.log(nu) - mpmath.loggamma(nu)
- mpmath.log(scale)) + (2*nu - 1)*logsum - nu*sqsum
return -ll
#!/usr/bin/python
"""
"""
import sys
import mpmath as mp
import numpy as np
mp.mp.dps = 60
a_lo = float(sys.argv[1])
a_hi = float(sys.argv[2])
n = int(sys.argv[3])
for x in np.logspace(a_lo, a_hi, 1000) :
x = mp.mpf(x)
print x, mp.loggamma(x)
def f73(x):
# lngamma
try:
return mpmath.loggamma(x)
except:
return None
def dk_term(k):
k = float(k)
if k != 0: return k * log(k) - loggamma(k + 1)
else: return -loggamma(k + 1)