def isotropic_gaussian(shape, scale):
"""
Isotropic Gaussian with SD `scale`.
Parameters
----------
shape : tuple
Shape of noise.
scale : float
SD of noise.
"""
rv = ndist(scale=scale, loc=0.)
density = lambda x: np.product(rv.pdf(x))
grad_negative_log_density = lambda x: x / scale**2
sampler = lambda size: rv.rvs(size=shape + size)
p = np.product(shape)
constant = -0.5 * p * np.log(2 * np.pi * scale**2)
return randomization(shape,
density,
grad_negative_log_density,
sampler,
lipschitz=1./scale**2,
log_density = lambda x: -0.5 * (np.atleast_2d(x)**2).sum(1) / scale**2 + constant)
def isotropic_gaussian(shape, scale):
rv = ndist(scale=scale, loc=0.)
density = lambda x: rv.pdf(x)
grad_negative_log_density = lambda x: x / scale**2
sampler = lambda size: rv.rvs(size=shape + size)
return randomization(shape, density, grad_negative_log_density,
sampler)
def __init__(self, initial_condition, gradient_map, projection_map,
stepsize):
(self.state, self.gradient_map, self.projection_map,
self.stepsize) = (np.copy(initial_condition), gradient_map,
projection_map, stepsize)
self._shape = self.state.shape[0]
self._sqrt_step = np.sqrt(self.stepsize)
self._noise = ndist(loc=0, scale=1)
def __init__(self, initial_condition, gradient_map, proposal_scale,
stepsize, scaling):
(self.state, self.gradient_map,
self.stepsize) = (np.copy(initial_condition), gradient_map, stepsize)
self.proposal_scale = proposal_scale
self._shape = self.state.shape[0]
self._sqrt_step = np.sqrt(self.stepsize)
self._noise = ndist(loc=0, scale=1)
self.sample = np.copy(initial_condition)
self.scaling = scaling
self.proposal_sqrt = fractional_matrix_power(self.proposal_scale, 0.5)
def isotropic_gaussian(shape, scale):
"""
Isotropic Gaussian with SD `scale`.
Parameters
----------
shape : tuple
Shape of noise.
scale : float
SD of noise.
"""
if type(shape) == type(1):
shape = (shape, )
rv = ndist(scale=scale, loc=0.)
p = np.product(shape)
density = lambda x: np.product(rv.pdf(x))
cdf = lambda x: rv.cdf(x)
pdf = lambda x: rv.pdf(x)
derivative_log_density = lambda x: -x / (scale**2)
grad_negative_log_density = lambda x: x / scale**2
sampler = lambda size: rv.rvs(size=shape + size)
CGF = isotropic_gaussian_CGF(shape, scale)
CGF_conjugate = isotropic_gaussian_CGF_conjugate(shape, scale)
p = np.product(shape)
constant = 0 # -0.5 * p * np.log(2 * np.pi * scale**2)
return randomization(
shape,
density,
cdf,
pdf,
derivative_log_density,
grad_negative_log_density,
sampler,
lipschitz=1. / scale**2,
log_density=lambda x: -0.5 *
(np.atleast_2d(x)**2).sum(1) / scale**2 + constant,
CGF=CGF,
CGF_conjugate=CGF_conjugate,
cov_prec=(scale**2, 1. / scale**2))