def _stats(self, mu):
var = mu
tmp = np.asarray(mu)
mu_nonzero = tmp > 0
g1 = _lazywhere(mu_nonzero, (tmp,), lambda x: sqrt(1.0/x), np.inf)
g2 = _lazywhere(mu_nonzero, (tmp,), lambda x: 1.0/x, np.inf)
return mu, var, g1, g2
def _stats(self, mu):
var = mu
tmp = np.asarray(mu)
mu_nonzero = tmp > 0
g1 = _lazywhere(mu_nonzero, (tmp, ), lambda x: sqrt(1.0 / x), np.inf)
g2 = _lazywhere(mu_nonzero, (tmp, ), lambda x: 1.0 / x, np.inf)
return mu, var, g1, g2
def _fixed_point_helper(func, x0, args, xtol, maxiter, use_accel):
p0 = x0
for i in range(maxiter):
p1 = func(p0, *args)
if use_accel:
p2 = func(p1, *args)
d = p2 - 2.0 * p1 + p0
p = _lazywhere(d != 0, (p0, p1, d), f=_del2, fillvalue=p2)
else:
p = p1
relerr = _lazywhere(p0 != 0, (p, p0), f=_relerr, fillvalue=p)
if np.all(np.abs(relerr) < xtol):
return p
p0 = p
msg = "Failed to converge after %d iterations, value is %s" % (maxiter, p)
raise RuntimeError(msg)
def _logpmf(self, x, mu, alpha, p, w):
s, p = self.convert_params(mu, alpha, p)
return _lazywhere(x != 0, (x, s, p, w),
(lambda x, s, p, w: np.log(1. - w) +
nbinom.logpmf(x, s, p)),
np.log(w + (1. - w) *
nbinom.pmf(x, s, p)))
def _fixed_point_helper(func, x0, args, xtol, maxiter, use_accel):
p0 = x0
for i in range(maxiter):
p1 = func(p0, *args)
if use_accel:
p2 = func(p1, *args)
d = p2 - 2.0 * p1 + p0
p = _lazywhere(d != 0, (p0, p1, d), f=_del2, fillvalue=p2)
else:
p = p1
relerr = _lazywhere(p0 != 0, (p, p0), f=_relerr, fillvalue=p)
if np.all(np.abs(relerr) < xtol):
return p
p0 = p
msg = "Failed to converge after %d iterations, value is %s" % (maxiter, p)
raise RuntimeError(msg)
def alphanot1func(alpha, beta, TH, aTH, bTH, cosTH, tanTH, W):
res = _lazywhere(
beta == 0,
(alpha, beta, TH, aTH, bTH, cosTH, tanTH, W),
beta0func,
f2=otherwise,
)
return res
def _logpmf(self, k, M, n, r):
cond = ((r == 0) & (k == 0))
result = _lazywhere(~cond, (k, M, n, r),
lambda k, M, n, r:
(-betaln(k+1, r) + betaln(k+r, 1) -
betaln(n-k+1, M-r-n+1) + betaln(M-r-k+1, 1) +
betaln(n+1, M-n+1) - betaln(M+1, 1)),
fillvalue=0.0)
return result
def crystalball(x,N,beta,m,mu,sig):
""" Scipy's crystalball function (doesn't exist in python2.)
https://github.com/scipy/scipy/blob/59cabc8/scipy/stats/_continuous_distns.py#L5798
"""
from scipy._lib._util import _lazywhere
x = (x - mu)/sig
rhs = lambda x, beta, m: np.exp(-x**2 / 2)
lhs = lambda x, beta, m: (m/beta)**m * np.exp(-beta**2 / 2.0) * (m/beta - beta - x)**(-m)
return N * _lazywhere(np.atleast_1d(x > -beta), (x, beta, m), f=rhs, f2=lhs)
def _logcdf(self, x, n, p):
k = floor(x)
cdf = self._cdf(k, n, p)
cond = cdf > 0.5
def f1(k, n, p):
return np.log1p(-special.betainc(k + 1, n, 1 - p))
def f2(k, n, p):
return np.log(cdf)
with np.errstate(divide='ignore'):
return _lazywhere(cond, (x, n, p), f=f1, f2=f2)
def _rvs_Z1(alpha, beta, size=None, random_state=None):
"""Simulate random variables using Nolan's methods as detailed in [NO].
"""
def alpha1func(alpha, beta, TH, aTH, bTH, cosTH, tanTH, W):
return (2 / np.pi * ((np.pi / 2 + bTH) * tanTH - beta * np.log(
(np.pi / 2 * W * cosTH) / (np.pi / 2 + bTH))))
def beta0func(alpha, beta, TH, aTH, bTH, cosTH, tanTH, W):
return (W / (cosTH / np.tan(aTH) + np.sin(TH)) *
((np.cos(aTH) + np.sin(aTH) * tanTH) / W)**(1.0 / alpha))
def otherwise(alpha, beta, TH, aTH, bTH, cosTH, tanTH, W):
# alpha is not 1 and beta is not 0
val0 = beta * np.tan(np.pi * alpha / 2)
th0 = np.arctan(val0) / alpha
val3 = W / (cosTH / np.tan(alpha * (th0 + TH)) + np.sin(TH))
res3 = val3 * (
(np.cos(aTH) + np.sin(aTH) * tanTH - val0 *
(np.sin(aTH) - np.cos(aTH) * tanTH)) / W)**(1.0 / alpha)
return res3
def alphanot1func(alpha, beta, TH, aTH, bTH, cosTH, tanTH, W):
res = _lazywhere(
beta == 0,
(alpha, beta, TH, aTH, bTH, cosTH, tanTH, W),
beta0func,
f2=otherwise,
)
return res
alpha = np.broadcast_to(alpha, size)
beta = np.broadcast_to(beta, size)
TH = uniform.rvs(loc=-np.pi / 2.0,
scale=np.pi,
size=size,
random_state=random_state)
W = expon.rvs(size=size, random_state=random_state)
aTH = alpha * TH
bTH = beta * TH
cosTH = np.cos(TH)
tanTH = np.tan(TH)
res = _lazywhere(
alpha == 1,
(alpha, beta, TH, aTH, bTH, cosTH, tanTH, W),
alpha1func,
f2=alphanot1func,
)
return res
def _fixed_point_helper(func, x0, args, xtol, maxiter, use_accel):
"""Helper function from scipy optimize"""
p0 = x0
for i in range(maxiter):
p1 = func(p0, *args)
if np.all(np.abs(p1-p0) < xtol/2.):
return p1
if use_accel and i < maxiter//2:
p2 = func(p1, *args)
d = p2 - 2.0 * p1 + p0
p = _lazywhere(d != 0, (p0, p1, d), f=_del2, fillvalue=p2)
else:
p = p1
p0 = p
msg = "Failed to converge after %d iterations, value is %s" % (maxiter, p)
raise RuntimeError(msg)
def fixedPoint(function, x0, args, tol, maxit):
p0 = x0
for i in range(maxit): #Iterar hasta el máximo de iteraciones
p1 = function(p0, *args) #Vector resultante
p=p1 #Variable temporal
fval = _lazywhere(p0 != 0, (p, p0), f=sp_helper, fillvalue=p) #Funcion aux.
if(np.all(np.abs(fval) < tol)): # Condición de convergencia
return p
p0 = p
msg = "Failed to converge after %d iterations, value is %s" % (maxit, p)
raise RuntimeError(msg)
def _logpmf(self, x, mu, alpha, p, w):
return _lazywhere(x != 0, (x, mu, alpha, p, w),
(lambda x, mu, alpha, p, w: np.log(1. - w) +
genpoisson_p.logpmf(x, mu, alpha, p)),
np.log(w + (1. - w) *
genpoisson_p.pmf(x, mu, alpha, p)))
def _logpmf(self, x, mu, w):
return _lazywhere(x != 0, (x, mu, w),
(lambda x, mu, w: np.log(1. - w) + x * np.log(mu) -
gammaln(x + 1.) - mu),
np.log(w + (1. - w) * np.exp(-mu)))
def _cdf(self, x, a):
k = floor(x)
f = lambda k, a: 1.0 - exp(-a * k) / (exp(a) + 1)
f2 = lambda k, a: exp(a * (k+1)) / (exp(a) + 1)
return _lazywhere(k >= 0, (k, a), f=f, f2=f2)
def series_density(y, mu, p, phi):
density = _lazywhere(np.array(y) > 0, (y, mu, p, phi),
f=density_otherwise,
f2=density_at_zero)
return density
def _munp(self, n, a):
return _lazywhere(
a > n + 1, (a, n),
lambda a, n: special.zeta(a - n, 1) / special.zeta(a, 1), np.inf)
def _gen_harmonic(n, a):
"""Generalized harmonic number"""
n, a = np.broadcast_arrays(n, a)
return _lazywhere(a > 1, (n, a),
f=_gen_harmonic_gt1, f2=_gen_harmonic_leq1)
def _cdf(self, x, a):
k = floor(x)
f = lambda k, a: 1.0 - exp(-a * k) / (exp(a) + 1)
f2 = lambda k, a: exp(a * (k + 1)) / (exp(a) + 1)
return _lazywhere(k >= 0, (k, a), f=f, f2=f2)
def _munp(self, n, a):
return _lazywhere(
a > n + 1, (a, n),
lambda a, n: special.zeta(a - n, 1) / special.zeta(a, 1),
np.inf)