text: # Copyright 2016 The TensorFlow Authors. All Rights Reserved.
  #
  # 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
  #
  #     http://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 __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  
  import importlib
  
  import numpy as np
  
  from tensorflow.python.framework import constant_op
  from tensorflow.python.framework import tensor_shape
  from tensorflow.python.framework import test_util
  from tensorflow.python.ops import array_ops
  from tensorflow.python.ops import math_ops
  from tensorflow.python.ops.distributions import dirichlet as dirichlet_lib
  from tensorflow.python.platform import test
  from tensorflow.python.platform import tf_logging
  
  
  def try_import(name):  # pylint: disable=invalid-name
    module = None
    try:
      module = importlib.import_module(name)
    except ImportError as e:
      tf_logging.warning("Could not import %s: %s" % (name, str(e)))
    return module
  
  
  stats = try_import("scipy.stats")
  
  
  @test_util.run_all_in_graph_and_eager_modes
  class DirichletTest(test.TestCase):
  
    def testSimpleShapes(self):
      with self.test_session():
        alpha = np.random.rand(3)
        dist = dirichlet_lib.Dirichlet(alpha)
        self.assertEqual(3, self.evaluate(dist.event_shape_tensor()))
        self.assertAllEqual([], self.evaluate(dist.batch_shape_tensor()))
        self.assertEqual(tensor_shape.TensorShape([3]), dist.event_shape)
        self.assertEqual(tensor_shape.TensorShape([]), dist.batch_shape)
  
    def testComplexShapes(self):
      with self.test_session():
        alpha = np.random.rand(3, 2, 2)
        dist = dirichlet_lib.Dirichlet(alpha)
        self.assertEqual(2, self.evaluate(dist.event_shape_tensor()))
        self.assertAllEqual([3, 2], self.evaluate(dist.batch_shape_tensor()))
        self.assertEqual(tensor_shape.TensorShape([2]), dist.event_shape)
        self.assertEqual(tensor_shape.TensorShape([3, 2]), dist.batch_shape)
  
    def testConcentrationProperty(self):
      alpha = [[1., 2, 3]]
      with self.test_session():
        dist = dirichlet_lib.Dirichlet(alpha)
        self.assertEqual([1, 3], dist.concentration.get_shape())
        self.assertAllClose(alpha, self.evaluate(dist.concentration))
  
    def testPdfXProper(self):
      alpha = [[1., 2, 3]]
      with self.test_session():
        dist = dirichlet_lib.Dirichlet(alpha, validate_args=True)
        self.evaluate(dist.prob([.1, .3, .6]))
        self.evaluate(dist.prob([.2, .3, .5]))
        # Either condition can trigger.
        with self.assertRaisesOpError("samples must be positive"):
          self.evaluate(dist.prob([-1., 1.5, 0.5]))
        with self.assertRaisesOpError("samples must be positive"):
          self.evaluate(dist.prob([0., .1, .9]))
        with self.assertRaisesOpError(
            "sample last-dimension must sum to `1`"):
          self.evaluate(dist.prob([.1, .2, .8]))
  
    def testPdfZeroBatches(self):
      with self.test_session():
        alpha = [1., 2]
        x = [.5, .5]
        dist = dirichlet_lib.Dirichlet(alpha)
        pdf = dist.prob(x)
        self.assertAllClose(1., self.evaluate(pdf))
        self.assertEqual((), pdf.get_shape())
  
    def testPdfZeroBatchesNontrivialX(self):
      with self.test_session():
        alpha = [1., 2]
        x = [.3, .7]
        dist = dirichlet_lib.Dirichlet(alpha)
        pdf = dist.prob(x)
        self.assertAllClose(7. / 5, self.evaluate(pdf))
        self.assertEqual((), pdf.get_shape())
  
    def testPdfUniformZeroBatches(self):
      with self.test_session():
        # Corresponds to a uniform distribution
        alpha = [1., 1, 1]
        x = [[.2, .5, .3], [.3, .4, .3]]
        dist = dirichlet_lib.Dirichlet(alpha)
        pdf = dist.prob(x)
        self.assertAllClose([2., 2.], self.evaluate(pdf))
        self.assertEqual((2), pdf.get_shape())
  
    def testPdfAlphaStretchedInBroadcastWhenSameRank(self):
      with self.test_session():
        alpha = [[1., 2]]
        x = [[.5, .5], [.3, .7]]
        dist = dirichlet_lib.Dirichlet(alpha)
        pdf = dist.prob(x)
        self.assertAllClose([1., 7. / 5], self.evaluate(pdf))
        self.assertEqual((2), pdf.get_shape())
  
    def testPdfAlphaStretchedInBroadcastWhenLowerRank(self):
      with self.test_session():
        alpha = [1., 2]
        x = [[.5, .5], [.2, .8]]
        pdf = dirichlet_lib.Dirichlet(alpha).prob(x)
        self.assertAllClose([1., 8. / 5], self.evaluate(pdf))
        self.assertEqual((2), pdf.get_shape())
  
    def testPdfXStretchedInBroadcastWhenSameRank(self):
      with self.test_session():
        alpha = [[1., 2], [2., 3]]
        x = [[.5, .5]]
        pdf = dirichlet_lib.Dirichlet(alpha).prob(x)
        self.assertAllClose([1., 3. / 2], self.evaluate(pdf))
        self.assertEqual((2), pdf.get_shape())
  
    def testPdfXStretchedInBroadcastWhenLowerRank(self):
      with self.test_session():
        alpha = [[1., 2], [2., 3]]
        x = [.5, .5]
        pdf = dirichlet_lib.Dirichlet(alpha).prob(x)
        self.assertAllClose([1., 3. / 2], self.evaluate(pdf))
        self.assertEqual((2), pdf.get_shape())
  
    def testMean(self):
      with self.test_session():
        alpha = [1., 2, 3]
        dirichlet = dirichlet_lib.Dirichlet(concentration=alpha)
        self.assertEqual(dirichlet.mean().get_shape(), [3])
        if not stats:
          return
        expected_mean = stats.dirichlet.mean(alpha)
        self.assertAllClose(self.evaluate(dirichlet.mean()), expected_mean)
  
    def testCovarianceFromSampling(self):
      alpha = np.array([[1., 2, 3],
                        [2.5, 4, 0.01]], dtype=np.float32)
      dist = dirichlet_lib.Dirichlet(alpha)  # batch_shape=[2], event_shape=[3]
      x = dist.sample(int(250e3), seed=1)
      sample_mean = math_ops.reduce_mean(x, 0)
      x_centered = x - sample_mean[None, ...]
      sample_cov = math_ops.reduce_mean(math_ops.matmul(
          x_centered[..., None], x_centered[..., None, :]), 0)
      sample_var = array_ops.matrix_diag_part(sample_cov)
      sample_stddev = math_ops.sqrt(sample_var)
  
      [
          sample_mean_,
          sample_cov_,
          sample_var_,
          sample_stddev_,
          analytic_mean,
          analytic_cov,
          analytic_var,
          analytic_stddev,
      ] = self.evaluate([
          sample_mean,
          sample_cov,
          sample_var,
          sample_stddev,
          dist.mean(),
          dist.covariance(),
          dist.variance(),
          dist.stddev(),
      ])
  
      self.assertAllClose(sample_mean_, analytic_mean, atol=0., rtol=0.04)
      self.assertAllClose(sample_cov_, analytic_cov, atol=0., rtol=0.06)
      self.assertAllClose(sample_var_, analytic_var, atol=0., rtol=0.03)
      self.assertAllClose(sample_stddev_, analytic_stddev, atol=0., rtol=0.02)
  
    def testVariance(self):
      with self.test_session():
        alpha = [1., 2, 3]
        denominator = np.sum(alpha)**2 * (np.sum(alpha) + 1)
        dirichlet = dirichlet_lib.Dirichlet(concentration=alpha)
        self.assertEqual(dirichlet.covariance().get_shape(), (3, 3))
        if not stats:
          return
        expected_covariance = np.diag(stats.dirichlet.var(alpha))
        expected_covariance += [[0., -2, -3], [-2, 0, -6],
                                [-3, -6, 0]] / denominator
        self.assertAllClose(
            self.evaluate(dirichlet.covariance()), expected_covariance)
  
    def testMode(self):
      with self.test_session():
        alpha = np.array([1.1, 2, 3])
        expected_mode = (alpha - 1) / (np.sum(alpha) - 3)
        dirichlet = dirichlet_lib.Dirichlet(concentration=alpha)
        self.assertEqual(dirichlet.mode().get_shape(), [3])
        self.assertAllClose(self.evaluate(dirichlet.mode()), expected_mode)
  
    def testModeInvalid(self):
      with self.test_session():
        alpha = np.array([1., 2, 3])
        dirichlet = dirichlet_lib.Dirichlet(concentration=alpha,
                                            allow_nan_stats=False)
        with self.assertRaisesOpError("Condition x < y.*"):
          self.evaluate(dirichlet.mode())
  
    def testModeEnableAllowNanStats(self):
      with self.test_session():
        alpha = np.array([1., 2, 3])
        dirichlet = dirichlet_lib.Dirichlet(concentration=alpha,
                                            allow_nan_stats=True)
        expected_mode = np.zeros_like(alpha) + np.nan
  
        self.assertEqual(dirichlet.mode().get_shape(), [3])
        self.assertAllClose(self.evaluate(dirichlet.mode()), expected_mode)
  
    def testEntropy(self):
      with self.test_session():
        alpha = [1., 2, 3]
        dirichlet = dirichlet_lib.Dirichlet(concentration=alpha)
        self.assertEqual(dirichlet.entropy().get_shape(), ())
        if not stats:
          return
        expected_entropy = stats.dirichlet.entropy(alpha)
        self.assertAllClose(self.evaluate(dirichlet.entropy()), expected_entropy)
  
    def testSample(self):
      with self.test_session():
        alpha = [1., 2]
        dirichlet = dirichlet_lib.Dirichlet(alpha)
        n = constant_op.constant(100000)
        samples = dirichlet.sample(n)
        sample_values = self.evaluate(samples)
        self.assertEqual(sample_values.shape, (100000, 2))
        self.assertTrue(np.all(sample_values > 0.0))
        if not stats:
          return
        self.assertLess(
            stats.kstest(
                # Beta is a univariate distribution.
                sample_values[:, 0],
                stats.beta(
                    a=1., b=2.).cdf)[0],
            0.01)
  
  
  if __name__ == "__main__":
    test.main()
  