# Copyright 2018 The JAX Authors.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from jax import lax
from jax._src.lax.lax import _const as _lax_const
from jax._src.numpy.util import promote_args_inexact
from jax._src.typing import Array, ArrayLike
[文档]
def logpdf(x: ArrayLike, loc: ArrayLike = 0, scale: ArrayLike = 1) -> Array:
r"""Laplace log probability distribution function.
JAX implementation of :obj:`scipy.stats.laplace` ``logpdf``.
The Laplace probability distribution function is given by
.. math::
f(x) = \frac{1}{2} e^{-|x|}
Args:
x: arraylike, value at which to evaluate the PDF
loc: arraylike, distribution offset parameter
scale: arraylike, distribution scale parameter
Returns:
array of logpdf values.
See Also:
- :func:`jax.scipy.stats.laplace.cdf`
- :func:`jax.scipy.stats.laplace.pdf`
"""
x, loc, scale = promote_args_inexact("laplace.logpdf", x, loc, scale)
two = _lax_const(x, 2)
linear_term = lax.div(lax.abs(lax.sub(x, loc)), scale)
return lax.neg(lax.add(linear_term, lax.log(lax.mul(two, scale))))
[文档]
def pdf(x: ArrayLike, loc: ArrayLike = 0, scale: ArrayLike = 1) -> Array:
r"""Laplace probability distribution function.
JAX implementation of :obj:`scipy.stats.laplace` ``pdf``.
The Laplace probability distribution function is given by
.. math::
f(x) = \frac{1}{2} e^{-|x|}
Args:
x: arraylike, value at which to evaluate the PDF
loc: arraylike, distribution offset parameter
scale: arraylike, distribution scale parameter
Returns:
array of pdf values.
See Also:
- :func:`jax.scipy.stats.laplace.cdf`
- :func:`jax.scipy.stats.laplace.logpdf`
"""
return lax.exp(logpdf(x, loc, scale))
[文档]
def cdf(x: ArrayLike, loc: ArrayLike = 0, scale: ArrayLike = 1) -> Array:
r"""Laplace cumulative distribution function.
JAX implementation of :obj:`scipy.stats.laplace` ``cdf``.
The cdf is defined as
.. math::
f_{cdf}(x, k) = \int_{-\infty}^x f_{pdf}(y, k)\mathrm{d}y
where :math:`f_{pdf}` is the probability density function,
:func:`jax.scipy.stats.laplace.pdf`.
Args:
x: arraylike, value at which to evaluate the CDF
loc: arraylike, distribution offset parameter
scale: arraylike, distribution scale parameter
Returns:
array of cdf values.
See Also:
- :func:`jax.scipy.stats.laplace.pdf`
- :func:`jax.scipy.stats.laplace.logpdf`
"""
x, loc, scale = promote_args_inexact("laplace.cdf", x, loc, scale)
half = _lax_const(x, 0.5)
one = _lax_const(x, 1)
zero = _lax_const(x, 0)
diff = lax.div(lax.sub(x, loc), scale)
return lax.select(lax.le(diff, zero),
lax.mul(half, lax.exp(diff)),
lax.sub(one, lax.mul(half, lax.exp(lax.neg(diff)))))
