# Copyright 2018 The TensorFlow Probability 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
#
#     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.
# ============================================================================
"""Tests for Wishart."""

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

# Dependency imports
import numpy as np
from scipy import linalg
import tensorflow as tf
import tensorflow_probability as tfp

from tensorflow_probability.python.internal import tensorshape_util
from tensorflow_probability.python.internal import test_util as tfp_test_util
from tensorflow.python.framework import test_util  # pylint: disable=g-direct-tensorflow-import

tfd = tfp.distributions


def make_pd(start, n):
  """Deterministically create a positive definite matrix."""
  x = np.tril(linalg.circulant(np.arange(start, start + n)))
  return np.dot(x, x.T)


def chol(x):
  """Compute Cholesky factorization."""
  return linalg.cholesky(x).T


def wishart_var(df, x):
  """Compute Wishart variance for numpy scale matrix."""
  df = np.asarray(df)[..., np.newaxis, np.newaxis]
  x = np.sqrt(df) * np.asarray(x)
  d = np.diagonal(x, axis1=-2, axis2=-1)
  return x**2 + np.matmul(
      d[..., np.newaxis], d[..., np.newaxis, :])


@test_util.run_all_in_graph_and_eager_modes
class WishartTest(tf.test.TestCase):

  def testEntropy(self):
    scale = make_pd(1., 2)
    df = 4
    w = tfd.Wishart(df, scale_tril=chol(scale))
    # sp.stats.wishart(df=4, scale=make_pd(1., 2)).entropy()
    self.assertAllClose(6.301387092430769, self.evaluate(w.entropy()))

    w = tfd.Wishart(df=1, scale_tril=[[1.]])
    # sp.stats.wishart(df=1,scale=1).entropy()
    self.assertAllClose(0.78375711047393404, self.evaluate(w.entropy()))

  def testMeanLogDetAndLogNormalizingConstant(self):

    def entropy_alt(w):
      return self.evaluate(w.log_normalization() -
                           0.5 * (w.df - w.dimension - 1.) * w.mean_log_det() +
                           0.5 * w.df * w.dimension)

    w = tfd.Wishart(df=4, scale_tril=chol(make_pd(1., 2)))
    self.assertAllClose(self.evaluate(w.entropy()), entropy_alt(w))

    w = tfd.Wishart(df=5, scale_tril=[[1.]])
    self.assertAllClose(self.evaluate(w.entropy()), entropy_alt(w))

  def testParamBroadcasting(self):
    scale = [[[1., .5], [.5, 1.]]]  # A 1-batch of 2x2 scale operators
    df = [5, 6, 7]  # A 3-batch of degrees of freedom
    wish = tfp.distributions.Wishart(df=df, scale=scale)
    self.assertAllEqual([2, 2], tensorshape_util.as_list(wish.event_shape))
    self.assertAllEqual([2, 2], self.evaluate(wish.event_shape_tensor()))
    self.assertAllEqual([3], tensorshape_util.as_list(wish.batch_shape))
    self.assertAllEqual([3], self.evaluate(wish.batch_shape_tensor()))
    self.assertAllEqual([4, 3, 2, 2], wish.sample(sample_shape=(4,)).shape)
    self.assertAllEqual([4, 3, 2, 2],
                        self.evaluate(
                            tf.shape(input=wish.sample(sample_shape=(4,)))))

  def testMean(self):
    scale = make_pd(1., 2)
    df = 4
    w = tfd.Wishart(df, scale_tril=chol(scale))
    self.assertAllEqual(df * scale, self.evaluate(w.mean()))

  def testMeanBroadcast(self):
    scale = [make_pd(1., 2), make_pd(1., 2)]
    chol_scale = np.float32([chol(s) for s in scale])
    scale = np.float32(scale)
    df = np.array([4., 3.], dtype=np.float32)
    w = tfd.Wishart(df, scale_tril=chol_scale)
    self.assertAllEqual(
        df[..., np.newaxis, np.newaxis] * scale, self.evaluate(w.mean()))

  def testMode(self):
    scale = make_pd(1., 2)
    df = 4
    w = tfd.Wishart(df, scale_tril=chol(scale))
    self.assertAllEqual((df - 2. - 1.) * scale, self.evaluate(w.mode()))

  def testStd(self):
    scale = make_pd(1., 2)
    df = 4
    w = tfd.Wishart(df, scale_tril=chol(scale))
    self.assertAllEqual(
        np.sqrt(wishart_var(df, scale)), self.evaluate(w.stddev()))

  def testVariance(self):
    scale = make_pd(1., 2)
    df = 4
    w = tfd.Wishart(df, scale_tril=chol(scale))
    self.assertAllEqual(wishart_var(df, scale), self.evaluate(w.variance()))

  def testVarianceBroadcast(self):
    scale = [make_pd(1., 2), make_pd(1., 2)]
    chol_scale = np.float32([chol(s) for s in scale])
    scale = np.float32(scale)
    df = np.array([4., 3.], dtype=np.float32)
    w = tfd.Wishart(df, scale_tril=chol_scale)
    self.assertAllEqual(wishart_var(df, scale), self.evaluate(w.variance()))

  def testSamplingEmptyDist(self):
    w = tfd.Wishart(df=[1], scale_tril=[[1.]], validate_args=True)
    self.evaluate(w[:0].sample())

  def testLogProbEmptyDist(self):
    w = tfd.Wishart(df=[1], scale_tril=[[1.]], validate_args=True)
    self.evaluate(w[:0].log_prob([[1.]]))

  def testSampleWithSameSeed(self):
    if tf.executing_eagerly():
      return
    scale = make_pd(1., 2)
    df = 4
    seed = tfp_test_util.test_seed()

    chol_w = tfd.Wishart(
        df, scale_tril=chol(scale), input_output_cholesky=False)

    x = self.evaluate(chol_w.sample(1, seed=seed))
    chol_x = [chol(x[0])]

    full_w = tfd.Wishart(df, scale, input_output_cholesky=False)
    self.assertAllClose(x, self.evaluate(full_w.sample(1, seed=seed)))

    chol_w_chol = tfd.Wishart(
        df, scale_tril=chol(scale), input_output_cholesky=True)
    self.assertAllClose(chol_x, self.evaluate(chol_w_chol.sample(1, seed=seed)))
    eigen_values = tf.linalg.diag_part(chol_w_chol.sample(1000, seed=seed))
    np.testing.assert_array_less(0., self.evaluate(eigen_values))

    full_w_chol = tfd.Wishart(df, scale=scale, input_output_cholesky=True)
    self.assertAllClose(chol_x, self.evaluate(full_w_chol.sample(1, seed=seed)))
    eigen_values = tf.linalg.diag_part(full_w_chol.sample(1000, seed=seed))
    np.testing.assert_array_less(0., self.evaluate(eigen_values))

  def testSample(self):
    # Check first and second moments.
    df = 4.
    chol_w = tfd.Wishart(
        df=df, scale_tril=chol(make_pd(1., 3)), input_output_cholesky=False)
    x = chol_w.sample(10000, seed=tfp_test_util.test_seed(hardcoded_seed=42))
    self.assertAllEqual((10000, 3, 3), x.shape)

    moment1_estimate = self.evaluate(tf.reduce_mean(input_tensor=x, axis=[0]))
    self.assertAllClose(
        self.evaluate(chol_w.mean()), moment1_estimate, rtol=0.05)

    # The Variance estimate uses the squares rather than outer-products
    # because Wishart.Variance is the diagonal of the Wishart covariance
    # matrix.
    variance_estimate = self.evaluate(
        tf.reduce_mean(input_tensor=tf.square(x), axis=[0]) -
        tf.square(moment1_estimate))
    self.assertAllClose(
        self.evaluate(chol_w.variance()), variance_estimate, rtol=0.05)

  # Test that sampling with the same seed twice gives the same results.
  def testSampleMultipleTimes(self):
    df = 4.
    n_val = 100
    seed = tfp_test_util.test_seed()

    tf.compat.v1.set_random_seed(seed)
    chol_w1 = tfd.Wishart(
        df=df,
        scale_tril=chol(make_pd(1., 3)),
        input_output_cholesky=False,
        name="wishart1")
    samples1 = self.evaluate(chol_w1.sample(n_val, seed=seed))

    tf.compat.v1.set_random_seed(seed)
    chol_w2 = tfd.Wishart(
        df=df,
        scale_tril=chol(make_pd(1., 3)),
        input_output_cholesky=False,
        name="wishart2")
    samples2 = self.evaluate(chol_w2.sample(n_val, seed=seed))

    self.assertAllClose(samples1, samples2)

  def testProb(self):
    # Generate some positive definite (pd) matrices and their Cholesky
    # factorizations.
    x = np.array(
        [make_pd(1., 2),
         make_pd(2., 2),
         make_pd(3., 2),
         make_pd(4., 2)])
    chol_x = np.array([chol(x[0]), chol(x[1]), chol(x[2]), chol(x[3])])

    # Since Wishart wasn"t added to SciPy until 0.16, we'll spot check some
    # pdfs with hard-coded results from upstream SciPy.

    log_prob_df_seq = np.array([
        # math.log(stats.wishart.pdf(x[0], df=2+0, scale=x[0]))
        -3.5310242469692907,
        # math.log(stats.wishart.pdf(x[1], df=2+1, scale=x[1]))
        -7.689907330328961,
        # math.log(stats.wishart.pdf(x[2], df=2+2, scale=x[2]))
        -10.815845159537895,
        # math.log(stats.wishart.pdf(x[3], df=2+3, scale=x[3]))
        -13.640549882916691,
    ])

    # This test checks that batches don't interfere with correctness.
    w = tfd.Wishart(
        df=[2, 3, 4, 5], scale_tril=chol_x, input_output_cholesky=True)
    self.assertAllClose(log_prob_df_seq, self.evaluate(w.log_prob(chol_x)))

    # Now we test various constructions of Wishart with different sample
    # shape.

    log_prob = np.array([
        # math.log(stats.wishart.pdf(x[0], df=4, scale=x[0]))
        -4.224171427529236,
        # math.log(stats.wishart.pdf(x[1], df=4, scale=x[0]))
        -6.3378770664093453,
        # math.log(stats.wishart.pdf(x[2], df=4, scale=x[0]))
        -12.026946850193017,
        # math.log(stats.wishart.pdf(x[3], df=4, scale=x[0]))
        -20.951582705289454,
    ])

    for w in (tfd.Wishart(
        df=4, scale_tril=chol_x[0], input_output_cholesky=False),
              tfd.Wishart(df=4, scale=x[0], input_output_cholesky=False)):
      self.assertAllEqual((2, 2), self.evaluate(w.event_shape_tensor()))
      self.assertEqual(2, self.evaluate(w.dimension))
      self.assertAllClose(log_prob[0], self.evaluate(w.log_prob(x[0])))
      self.assertAllClose(log_prob[0:2], self.evaluate(w.log_prob(x[0:2])))
      self.assertAllClose(
          np.reshape(log_prob, (2, 2)),
          self.evaluate(w.log_prob(np.reshape(x, (2, 2, 2, 2)))))
      self.assertAllClose(
          np.reshape(np.exp(log_prob), (2, 2)),
          self.evaluate(w.prob(np.reshape(x, (2, 2, 2, 2)))))
      self.assertAllEqual((2, 2),
                          w.log_prob(np.reshape(x, (2, 2, 2, 2))).shape)

    for w in (tfd.Wishart(
        df=4, scale_tril=chol_x[0], input_output_cholesky=True),
              tfd.Wishart(df=4, scale=x[0], input_output_cholesky=True)):
      self.assertAllEqual((2, 2), self.evaluate(w.event_shape_tensor()))
      self.assertEqual(2, self.evaluate(w.dimension))
      self.assertAllClose(log_prob[0], self.evaluate(w.log_prob(chol_x[0])))
      self.assertAllClose(log_prob[0:2], self.evaluate(w.log_prob(chol_x[0:2])))
      self.assertAllClose(
          np.reshape(log_prob, (2, 2)),
          self.evaluate(w.log_prob(np.reshape(chol_x, (2, 2, 2, 2)))))
      self.assertAllClose(
          np.reshape(np.exp(log_prob), (2, 2)),
          self.evaluate(w.prob(np.reshape(chol_x, (2, 2, 2, 2)))))
      self.assertAllEqual((2, 2),
                          w.log_prob(np.reshape(x, (2, 2, 2, 2))).shape)

  def testBatchShape(self):
    scale = make_pd(1., 2)
    chol_scale = chol(scale)

    w = tfd.Wishart(df=4, scale_tril=chol_scale)
    self.assertAllEqual([], w.batch_shape)
    self.assertAllEqual([], self.evaluate(w.batch_shape_tensor()))

    w = tfd.Wishart(df=[4., 4], scale_tril=np.array([chol_scale, chol_scale]))
    self.assertAllEqual([2], w.batch_shape)
    self.assertAllEqual([2], self.evaluate(w.batch_shape_tensor()))

    scale_deferred = tf.compat.v1.placeholder_with_default(
        input=chol_scale, shape=chol_scale.shape)
    w = tfd.Wishart(df=4, scale_tril=scale_deferred)
    self.assertAllEqual([], self.evaluate(w.batch_shape_tensor()))

    scale_deferred = tf.compat.v1.placeholder_with_default(
        input=np.array([chol_scale, chol_scale]), shape=None)
    w = tfd.Wishart(df=4, scale_tril=scale_deferred)
    self.assertAllEqual([2], self.evaluate(w.batch_shape_tensor()))

  def testEventShape(self):
    scale = make_pd(1., 2)
    chol_scale = chol(scale)

    w = tfd.Wishart(df=4, scale_tril=chol_scale)
    self.assertAllEqual([2, 2], w.event_shape)
    self.assertAllEqual([2, 2], self.evaluate(w.event_shape_tensor()))

    w = tfd.Wishart(df=[4., 4], scale_tril=np.array([chol_scale, chol_scale]))
    self.assertAllEqual([2, 2], w.event_shape)
    self.assertAllEqual([2, 2], self.evaluate(w.event_shape_tensor()))

    scale_deferred = tf.compat.v1.placeholder_with_default(
        input=chol_scale, shape=chol_scale.shape)
    w = tfd.Wishart(df=4, scale_tril=scale_deferred)
    self.assertAllEqual([2, 2], self.evaluate(w.event_shape_tensor()))

    scale_deferred = tf.compat.v1.placeholder_with_default(
        input=np.array([chol_scale, chol_scale]), shape=None)
    w = tfd.Wishart(df=4, scale_tril=scale_deferred)
    self.assertAllEqual([2, 2], self.evaluate(w.event_shape_tensor()))

  def testValidateArgs(self):
    x = make_pd(1., 3)
    chol_scale = chol(x)
    df_deferred = tf.compat.v1.placeholder_with_default(input=2., shape=None)
    chol_scale_deferred = tf.compat.v1.placeholder_with_default(
        input=np.float32(chol_scale), shape=chol_scale.shape)

    # In eager mode, these checks are done statically and hence
    # ValueError is returned on object construction.
    error_type = tf.errors.InvalidArgumentError
    if tf.executing_eagerly():
      error_type = ValueError

    # Check expensive, deferred assertions.
    with self.assertRaisesRegexp(error_type, "cannot be less than"):
      chol_w = tfd.Wishart(
          df=df_deferred, scale_tril=chol_scale_deferred, validate_args=True)
      self.evaluate(chol_w.log_prob(np.asarray(x, dtype=np.float32)))

    with self.assertRaisesOpError("Cholesky decomposition was not successful"):
      df_deferred = tf.compat.v1.placeholder_with_default(input=2., shape=None)
      chol_scale_deferred = tf.compat.v1.placeholder_with_default(
          input=np.ones([3, 3], dtype=np.float32), shape=[3, 3])
      chol_w = tfd.Wishart(df=df_deferred, scale=chol_scale_deferred)
      # np.ones((3, 3)) is not positive, definite.
      self.evaluate(chol_w.log_prob(np.asarray(x, dtype=np.float32)))

    with self.assertRaisesOpError("scale_tril must be square"):
      chol_w = tfd.Wishart(
          df=4.,
          scale_tril=np.array([[2., 3., 4.], [1., 2., 3.]], dtype=np.float32),
          validate_args=True)
      self.evaluate(chol_w.scale())

    # Ensure no assertions.
    df_deferred = tf.compat.v1.placeholder_with_default(input=4., shape=None)
    chol_scale_deferred = tf.compat.v1.placeholder_with_default(
        input=np.float32(chol_scale), shape=chol_scale.shape)
    chol_w = tfd.Wishart(
        df=df_deferred, scale_tril=chol_scale_deferred, validate_args=False)
    self.evaluate(chol_w.log_prob(np.asarray(x, dtype=np.float32)))

    chol_scale_deferred = tf.compat.v1.placeholder_with_default(
        input=np.ones([3, 3], dtype=np.float32), shape=[3, 3])
    chol_w = tfd.Wishart(
        df=df_deferred, scale_tril=chol_scale_deferred, validate_args=False)
    # Bogus log_prob, but since we have no checks running... c"est la vie.
    self.evaluate(chol_w.log_prob(np.asarray(x, dtype=np.float32)))

  def testStaticAsserts(self):
    x = make_pd(1., 3)
    chol_scale = chol(x)

    # Still has these assertions because they're resolveable at graph
    # construction:
    # df < rank
    with self.assertRaisesRegexp(ValueError, "cannot be less than"):
      tfd.Wishart(df=2, scale_tril=chol_scale, validate_args=False)
    # non-float dtype
    with self.assertRaisesRegexp(TypeError, "Argument tril must have dtype"):
      tfd.Wishart(
          df=4,
          scale_tril=np.asarray(chol_scale, dtype=np.int32),
          validate_args=False)

  def testSampleBroadcasts(self):
    dims = 2
    batch_shape = [2, 3]
    sample_shape = [2, 1]
    scale = np.float32([
        [[1., 0.5],
         [0.5, 1.]],
        [[0.5, 0.25],
         [0.25, 0.75]],
    ])
    scale = np.reshape(np.concatenate([scale, scale, scale], axis=0),
                       batch_shape + [dims, dims])
    wishart = tfd.Wishart(df=5, scale=scale)
    x = wishart.sample(sample_shape, seed=tfp_test_util.test_seed())
    x_ = self.evaluate(x)
    expected_shape = sample_shape + batch_shape + [dims, dims]
    self.assertAllEqual(expected_shape, x.shape)
    self.assertAllEqual(expected_shape, x_.shape)

  def testLogProbBroadcastsX(self):
    dims = 2
    batch_shape = [2, 3]
    scale = np.float32([
        [[1., 0.5],
         [0.5, 1.]],
        [[0.5, 0.25],
         [0.25, 0.75]],
    ])
    scale = np.reshape(np.concatenate([scale, scale, scale], axis=0),
                       batch_shape + [dims, dims])
    wishart = tfd.Wishart(df=5, scale=scale)
    x = np.random.randn(dims, dims)
    x = np.matmul(x, x.T)
    lp = wishart.log_prob(x)
    lp_bc = wishart.log_prob(x * np.ones([2, 3, 1, 1]))
    lp_, lp_bc_ = self.evaluate([lp, lp_bc])
    self.assertAllEqual(batch_shape, lp.shape)
    self.assertAllEqual(batch_shape, lp_.shape)
    self.assertAllEqual(batch_shape, lp_bc.shape)
    self.assertAllEqual(batch_shape, lp_bc_.shape)
    self.assertAllClose(lp_bc_, lp_)

  def testLogProbBroadcastOverDfInsideMixture(self):
    dims = 2
    scale = np.float32([[0.5, 0.25],  #
                        [0.25, 0.75]])
    df = np.arange(3., 8., dtype=np.float32)
    dist = tfd.MixtureSameFamily(
        components_distribution=tfd.Wishart(df=df, scale=scale),
        mixture_distribution=tfd.Categorical(logits=tf.zeros(df.shape)))
    x = np.random.randn(dims, dims)
    x = np.matmul(x, x.T)
    lp = dist.log_prob(x)
    lp_ = self.evaluate(lp)
    self.assertAllEqual([], dist.batch_shape)
    self.assertAllEqual([], lp.shape)
    self.assertAllEqual([], lp_.shape)

  def testStaticAssertNonFlatDfDoesntRaise(self):
    # Check we don't get ValueError: The truth value of an array with more than
    # one element is ambiguous. Use a.any() or a.all()
    tfd.Wishart(df=[[2., 2]], scale=make_pd(1., 2), validate_args=True)


if __name__ == "__main__":
  tf.test.main()
