def likelihood(x, m=None, Cinv=None, sigma=1, detC=None):
"""return likelihood of x for the normal density N(m, sigma**2 * Cinv**-1)"""
# testing: MC integrate must be one: mean(p(x_i)) * volume(where x_i are uniformely sampled)
# for i in xrange(3): print mean([cma.likelihood(20*r-10, dim * [0], None, 3) for r in rand(10000,dim)]) * 20**dim
if m is None:
dx = x
else:
dx = x - m # array(x) - array(m)
n = len(x)
s2pi = (2 * np.pi)**(n / 2.)
if Cinv is None:
return exp(-sum(dx**2) / sigma**2 / 2) / s2pi / sigma**n
if detC is None:
detC = 1. / np.linalg.linalg.det(Cinv)
return exp(-np.dot(dx, np.dot(Cinv, dx)) / sigma**2 / 2) / s2pi / abs(detC)**0.5 / sigma**n
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