"""Multivariate Log Gamma
Parameters
----------
a: tensor like
p: int
degrees of freedom. p > 0
"""
i = tt.arange(1, p + 1)
return p * (p - 1) * tt.log(np.pi) / 4.0 + tt.sum(
gammaln(a + (1.0 - i) / 2.0), axis=0)
def log_i0(x):
"""
Calculates the logarithm of the 0 order modified Bessel function of the first kind""
"""
return tt.switch(
tt.lt(x, 5),
tt.log1p(x**2.0 / 4.0 + x**4.0 / 64.0 + x**6.0 / 2304.0 +
x**8.0 / 147456.0 + x**10.0 / 14745600.0 +
x**12.0 / 2123366400.0),
x - 0.5 * tt.log(2.0 * np.pi * x) +
tt.log1p(1.0 / (8.0 * x) + 9.0 / (128.0 * x**2.0) + 225.0 /
(3072.0 * x**3.0) + 11025.0 / (98304.0 * x**4.0)),
)
scalar_psi = Psi(scalar.upgrade_to_float, name="scalar_psi")
psi = tt.Elemwise(scalar_psi, name="psi")
def impl(self, x):
return Psi.st_impl(x)
import theano.tensor as tt
from theano.scalar.basic_scipy import GammaLn, Psi, I0, I1
from theano import scalar
__all__ = ['gammaln', 'multigammaln', 'psi', 'i0', 'i1']
scalar_gammaln = GammaLn(scalar.upgrade_to_float, name='scalar_gammaln')
gammaln = tt.Elemwise(scalar_gammaln, name='gammaln')
def multigammaln(a, p):
"""Multivariate Log Gamma
:Parameters:
a : tensor like
p : int degrees of freedom
p > 0
"""
i = tt.arange(1, p + 1)
return (p * (p - 1) * tt.log(np.pi) / 4.
+ tt.sum(gammaln(a + (1. - i) / 2.), axis=0))
scalar_psi = Psi(scalar.upgrade_to_float, name='scalar_psi')
psi = tt.Elemwise(scalar_psi, name='psi')
scalar_i0 = I0(scalar.upgrade_to_float, name='scalar_i0')
i0 = tt.Elemwise(scalar_i0, name='i0')
scalar_i1 = I1(scalar.upgrade_to_float, name='scalar_i1')
i1 = tt.Elemwise(scalar_i1, name='i1')
def impl(self, x):
return Psi.st_impl(x)