# 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,
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from jax import lax
import jax.numpy as jnp
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, b: ArrayLike, loc: ArrayLike = 0, scale: ArrayLike = 1) -> Array:
  r"""Pareto log probability distribution function.

  JAX implementation of :obj:`scipy.stats.pareto` ``logpdf``.

  The Pareto probability density function is given by

  .. math::

     f(x, b) = \begin{cases}
       bx^{-(b+1)} & x \ge 1\\
       0 & x < 1
     \end{cases}

  and is defined for :math:`b > 0`.

  Args:
    x: arraylike, value at which to evaluate the PDF
    b: 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.pareto.pdf`
  """
  x, b, loc, scale = promote_args_inexact("pareto.logpdf", x, b, loc, scale)
  one = _lax_const(x, 1)
  scaled_x = lax.div(lax.sub(x, loc), scale)
  normalize_term = lax.log(lax.div(scale, b))
  log_probs = lax.neg(lax.add(normalize_term, lax.mul(lax.add(b, one), lax.log(scaled_x))))
  return jnp.where(lax.lt(x, lax.add(loc, scale)), -jnp.inf, log_probs)


def pdf(x: ArrayLike, b: ArrayLike, loc: ArrayLike = 0, scale: ArrayLike = 1) -> Array:
  r"""Pareto probability distribution function.

  JAX implementation of :obj:`scipy.stats.pareto` ``pdf``.

  The Pareto probability density function is given by

  .. math::

     f(x, b) = \begin{cases}
       bx^{-(b+1)} & x \ge 1\\
       0 & x < 1
     \end{cases}

  and is defined for :math:`b > 0`.

  Args:
    x: arraylike, value at which to evaluate the PDF
    b: arraylike, distribution shape parameter
    loc: arraylike, distribution offset parameter
    scale: arraylike, distribution scale parameter

  Returns:
    array of pdf values.

  See Also:
    :func:`jax.scipy.stats.pareto.logpdf`
  """
  return lax.exp(logpdf(x, b, loc, scale))