text: # Copyright 2018 Google LLC
  #
  # 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 onp
  import scipy.stats as osp_stats
  
  from ... import lax
  from ...numpy import lax_numpy as np
  from ..special import gammaln, xlogy
  
  
  def _is_simplex(x):
      x_sum = np.sum(x, axis=-1)
      return np.all(x > 0, axis=-1) & (x_sum <= 1) & (x_sum > 1 - 1e-6)
  
  
  @np._wraps(osp_stats.dirichlet.logpdf, update_doc=False)
  def logpdf(x, alpha):
      args = (onp.ones((0,), lax.dtype(x)), onp.ones((1,), lax.dtype(alpha)))
      to_dtype = lax.dtype(osp_stats.dirichlet.logpdf(*args))
      x, alpha = [lax.convert_element_type(arg, to_dtype) for arg in (x, alpha)]
      one = np._constant_like(x, 1)
      normalize_term = np.sum(gammaln(alpha), axis=-1) - gammaln(np.sum(alpha, axis=-1))
      log_probs = lax.sub(np.sum(xlogy(lax.sub(alpha, one), x), axis=-1), normalize_term)
      return np.where(_is_simplex(x), log_probs, -np.inf)
  
  
  @np._wraps(osp_stats.dirichlet.pdf, update_doc=False)
  def pdf(x, alpha):
    return lax.exp(logpdf(x, alpha))
  