def _block_indicator(self):
num_repeat = array.size_of_shape(
self.distribution.batch_shape[-self.reinterpreted_batch_ndims:])
dim = array.size_of_shape(self.distribution.event_shape)
block_indicator = numpy.fromfunction(
lambda i, j: i // dim == j // dim,
(num_repeat * dim, num_repeat * dim)).astype(int)
if self.xp is cuda.cupy:
block_indicator = cuda.to_gpu(block_indicator)
return block_indicator
def _block_indicator(self):
num_repeat = array.size_of_shape(
self.distribution.batch_shape[-self.reinterpreted_batch_ndims:])
dim = array.size_of_shape(self.distribution.event_shape)
block_indicator = numpy.fromfunction(
lambda i, j: i // dim == j // dim,
(num_repeat * dim, num_repeat * dim)).astype(int)
if self.xp is cuda.cupy:
block_indicator = cuda.to_gpu(block_indicator)
return block_indicator
def covariance(self):
""" The covariance of the independent distribution.
By definition, the covariance of the new
distribution becomes block diagonal matrix. Let
:math:`\\Sigma_{\\mathbf{x}}` be the covariance matrix of the original
random variable :math:`\\mathbf{x} \\in \\mathbb{R}^d`, and
:math:`\\mathbf{x}^{(1)}, \\mathbf{x}^{(2)}, \\cdots \\mathbf{x}^{(m)}`
be the :math:`m` i.i.d. random variables, new covariance matrix
:math:`\\Sigma_{\\mathbf{y}}` of :math:`\\mathbf{y} =
[\\mathbf{x}^{(1)}, \\mathbf{x}^{(2)}, \\cdots, \\mathbf{x}^{(m)}] \\in
\\mathbb{R}^{md}` can be written as
.. math::
\\left[\\begin{array}{ccc}
\\Sigma_{\\mathbf{x}^{1}} & & 0 \\\\
& \\ddots & \\\\
0 & & \\Sigma_{\\mathbf{x}^{m}}
\\end{array} \\right].
Note that this relationship holds only if the covariance matrix of the
original distribution is given analytically.
Returns:
~chainer.Variable: The covariance of the distribution.
"""
num_repeat = array.size_of_shape(
self.distribution.batch_shape[-self.reinterpreted_batch_ndims:])
dim = array.size_of_shape(self.distribution.event_shape)
cov = repeat.repeat(reshape.reshape(self.distribution.covariance,
((self.batch_shape) +
(1, num_repeat, dim, dim))),
num_repeat,
axis=-4)
cov = reshape.reshape(
transpose.transpose(cov,
axes=(tuple(range(len(self.batch_shape))) +
(-4, -2, -3, -1))),
self.batch_shape + (num_repeat * dim, num_repeat * dim))
block_indicator = self.xp.reshape(
self._block_indicator,
tuple([1] * len(self.batch_shape)) + self._block_indicator.shape)
return cov * block_indicator
def covariance(self):
""" The covariance of the independent distribution.
By definition, the covariance of the new
distribution becomes block diagonal matrix. Let
:math:`\\Sigma_{\\mathbf{x}}` be the covariance matrix of the original
random variable :math:`\\mathbf{x} \\in \\mathbb{R}^d`, and
:math:`\\mathbf{x}^{(1)}, \\mathbf{x}^{(2)}, \\cdots \\mathbf{x}^{(m)}`
be the :math:`m` i.i.d. random variables, new covariance matrix
:math:`\\Sigma_{\\mathbf{y}}` of :math:`\\mathbf{y} =
[\\mathbf{x}^{(1)}, \\mathbf{x}^{(2)}, \\cdots, \\mathbf{x}^{(m)}] \\in
\\mathbb{R}^{md}` can be written as
.. math::
\\left[\\begin{array}{ccc}
\\Sigma_{\\mathbf{x}^{1}} & & 0 \\\\
& \\ddots & \\\\
0 & & \\Sigma_{\\mathbf{x}^{m}}
\\end{array} \\right].
Note that this relationship holds only if the covariance matrix of the
original distribution is given analytically.
Returns:
~chainer.Variable: The covariance of the distribution.
"""
num_repeat = array.size_of_shape(
self.distribution.batch_shape[-self.reinterpreted_batch_ndims:])
dim = array.size_of_shape(self.distribution.event_shape)
cov = repeat.repeat(
reshape.reshape(
self.distribution.covariance,
((self.batch_shape) + (1, num_repeat, dim, dim))),
num_repeat, axis=-4)
cov = reshape.reshape(
transpose.transpose(
cov, axes=(
tuple(range(len(self.batch_shape))) + (-4, -2, -3, -1))),
self.batch_shape + (num_repeat * dim, num_repeat * dim))
block_indicator = self.xp.reshape(
self._block_indicator,
tuple([1] * len(self.batch_shape)) + self._block_indicator.shape)
return cov * block_indicator
def test_size_of_shape(self):
arr = numpy.empty(self.shape)
size = array.size_of_shape(arr.shape)
size_expect = arr.size
assert type(size) == type(size_expect)
assert size == size_expect
def test_size_of_shape(self):
arr = numpy.empty(self.shape)
size = array.size_of_shape(arr.shape)
size_expect = arr.size
assert type(size) == type(size_expect)
assert size == size_expect