mirror of
https://github.com/ROCm/jax.git
synced 2025-04-22 21:36:04 +00:00
90 lines
3.1 KiB
Python
90 lines
3.1 KiB
Python
# 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.
|
|
|
|
|
|
import numpy as np
|
|
|
|
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
|
|
|
|
|
|
def logpdf(x: ArrayLike, df: ArrayLike, loc: ArrayLike = 0, scale: ArrayLike = 1) -> Array:
|
|
r"""Student's T log probability distribution function.
|
|
|
|
JAX implementation of :obj:`scipy.stats.t` ``logpdf``.
|
|
|
|
The Student's T probability distribution function is given by
|
|
|
|
.. math::
|
|
|
|
f(x, \nu) = \frac{\Gamma((\nu + 1)/2)}{\sqrt{\pi\nu}\Gamma(\nu/2)}(1 + x^2/\nu)^{(\nu+1)/2}
|
|
|
|
Where :math:`\Gamma` is the :func:`~jax.scipy.special.gamma` function, and :math:`\nu > 0`
|
|
is the degrees of freedom (JAX follows the scipy convention of naming this ``df``).
|
|
|
|
Args:
|
|
x: arraylike, value at which to evaluate the PDF
|
|
df: arraylike, distribution shape parameter
|
|
loc: arraylike, distribution offset parameter
|
|
scale: arraylike, distribution scale parameter
|
|
|
|
Returns:
|
|
array of logpdf values.
|
|
|
|
See Also:
|
|
:func:`jax.scipy.stats.t.pdf`
|
|
"""
|
|
x, df, loc, scale = promote_args_inexact("t.logpdf", x, df, loc, scale)
|
|
two = _lax_const(x, 2)
|
|
scaled_x = lax.div(lax.sub(x, loc), scale)
|
|
df_over_two = lax.div(df, two)
|
|
df_plus_one_over_two = lax.add(df_over_two, _lax_const(x, 0.5))
|
|
normalize_term_const = lax.mul(lax.mul(scale, scale), _lax_const(x, np.pi))
|
|
normalize_term_tmp = lax.div(lax.log(lax.mul(normalize_term_const, df)), two)
|
|
normalize_term = lax.sub(lax.add(lax.lgamma(df_over_two), normalize_term_tmp),
|
|
lax.lgamma(df_plus_one_over_two))
|
|
quadratic = lax.div(lax.mul(scaled_x, scaled_x), df)
|
|
return lax.neg(lax.add(normalize_term, lax.mul(df_plus_one_over_two, lax.log1p(quadratic))))
|
|
|
|
|
|
def pdf(x: ArrayLike, df: ArrayLike, loc: ArrayLike = 0, scale: ArrayLike = 1) -> Array:
|
|
r"""Student's T probability distribution function.
|
|
|
|
JAX implementation of :obj:`scipy.stats.t` ``pdf``.
|
|
|
|
The Student's T probability distribution function is given by
|
|
|
|
.. math::
|
|
|
|
f(x, \nu) = \frac{\Gamma((\nu + 1)/2)}{\sqrt{\pi\nu}\Gamma(\nu/2)}(1 + x^2/\nu)^{(\nu+1)/2}
|
|
|
|
Where :math:`\Gamma` is the :func:`~jax.scipy.special.gamma` function, and :math:`\nu > 0`
|
|
is the degrees of freedom (JAX follows the scipy convention of naming this ``df``).
|
|
|
|
Args:
|
|
x: arraylike, value at which to evaluate the PDF
|
|
df: arraylike, distribution shape parameter
|
|
loc: arraylike, distribution offset parameter
|
|
scale: arraylike, distribution scale parameter
|
|
|
|
Returns:
|
|
array
|
|
|
|
See Also:
|
|
:func:`jax.scipy.stats.t.logpdf`
|
|
"""
|
|
return lax.exp(logpdf(x, df, loc, scale))
|