# 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.
# ==============================================================================
"""Tests for Student t distribution."""

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

import importlib
import math

import numpy as np

from tensorflow.python.framework import constant_op
from tensorflow.python.framework import random_seed
from tensorflow.python.ops import math_ops
from tensorflow.python.ops import nn_ops
from tensorflow.python.ops.distributions import student_t
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")


class StudentTTest(test.TestCase):

  def testStudentPDFAndLogPDF(self):
    with self.test_session():
      batch_size = 6
      df = constant_op.constant([3.] * batch_size)
      mu = constant_op.constant([7.] * batch_size)
      sigma = constant_op.constant([8.] * batch_size)
      df_v = 3.
      mu_v = 7.
      sigma_v = 8.
      t = np.array([-2.5, 2.5, 8., 0., -1., 2.], dtype=np.float32)
      student = student_t.StudentT(df, loc=mu, scale=-sigma)

      log_pdf = student.log_prob(t)
      self.assertEquals(log_pdf.get_shape(), (6,))
      log_pdf_values = log_pdf.eval()
      pdf = student.prob(t)
      self.assertEquals(pdf.get_shape(), (6,))
      pdf_values = pdf.eval()

      if not stats:
        return

      expected_log_pdf = stats.t.logpdf(t, df_v, loc=mu_v, scale=sigma_v)
      expected_pdf = stats.t.pdf(t, df_v, loc=mu_v, scale=sigma_v)
      self.assertAllClose(expected_log_pdf, log_pdf_values)
      self.assertAllClose(np.log(expected_pdf), log_pdf_values)
      self.assertAllClose(expected_pdf, pdf_values)
      self.assertAllClose(np.exp(expected_log_pdf), pdf_values)

  def testStudentLogPDFMultidimensional(self):
    with self.test_session():
      batch_size = 6
      df = constant_op.constant([[1.5, 7.2]] * batch_size)
      mu = constant_op.constant([[3., -3.]] * batch_size)
      sigma = constant_op.constant([[-math.sqrt(10.), math.sqrt(15.)]] *
                                   batch_size)
      df_v = np.array([1.5, 7.2])
      mu_v = np.array([3., -3.])
      sigma_v = np.array([np.sqrt(10.), np.sqrt(15.)])
      t = np.array([[-2.5, 2.5, 4., 0., -1., 2.]], dtype=np.float32).T
      student = student_t.StudentT(df, loc=mu, scale=sigma)
      log_pdf = student.log_prob(t)
      log_pdf_values = log_pdf.eval()
      self.assertEqual(log_pdf.get_shape(), (6, 2))
      pdf = student.prob(t)
      pdf_values = pdf.eval()
      self.assertEqual(pdf.get_shape(), (6, 2))

      if not stats:
        return
      expected_log_pdf = stats.t.logpdf(t, df_v, loc=mu_v, scale=sigma_v)
      expected_pdf = stats.t.pdf(t, df_v, loc=mu_v, scale=sigma_v)
      self.assertAllClose(expected_log_pdf, log_pdf_values)
      self.assertAllClose(np.log(expected_pdf), log_pdf_values)
      self.assertAllClose(expected_pdf, pdf_values)
      self.assertAllClose(np.exp(expected_log_pdf), pdf_values)

  def testStudentCDFAndLogCDF(self):
    with self.test_session():
      batch_size = 6
      df = constant_op.constant([3.] * batch_size)
      mu = constant_op.constant([7.] * batch_size)
      sigma = constant_op.constant([-8.] * batch_size)
      df_v = 3.
      mu_v = 7.
      sigma_v = 8.
      t = np.array([-2.5, 2.5, 8., 0., -1., 2.], dtype=np.float32)
      student = student_t.StudentT(df, loc=mu, scale=sigma)

      log_cdf = student.log_cdf(t)
      self.assertEquals(log_cdf.get_shape(), (6,))
      log_cdf_values = log_cdf.eval()
      cdf = student.cdf(t)
      self.assertEquals(cdf.get_shape(), (6,))
      cdf_values = cdf.eval()

      if not stats:
        return
      expected_log_cdf = stats.t.logcdf(t, df_v, loc=mu_v, scale=sigma_v)
      expected_cdf = stats.t.cdf(t, df_v, loc=mu_v, scale=sigma_v)
      self.assertAllClose(expected_log_cdf, log_cdf_values, atol=0., rtol=1e-5)
      self.assertAllClose(
          np.log(expected_cdf), log_cdf_values, atol=0., rtol=1e-5)
      self.assertAllClose(expected_cdf, cdf_values, atol=0., rtol=1e-5)
      self.assertAllClose(
          np.exp(expected_log_cdf), cdf_values, atol=0., rtol=1e-5)

  def testStudentEntropy(self):
    df_v = np.array([[2., 3., 7.]])  # 1x3
    mu_v = np.array([[1., -1, 0]])  # 1x3
    sigma_v = np.array([[1., -2., 3.]]).T  # transposed => 3x1
    with self.test_session():
      student = student_t.StudentT(df=df_v, loc=mu_v, scale=sigma_v)
      ent = student.entropy()
      ent_values = ent.eval()

    # Help scipy broadcast to 3x3
    ones = np.array([[1, 1, 1]])
    sigma_bc = np.abs(sigma_v) * ones
    mu_bc = ones.T * mu_v
    df_bc = ones.T * df_v
    if not stats:
      return
    expected_entropy = stats.t.entropy(
        np.reshape(df_bc, [-1]),
        loc=np.reshape(mu_bc, [-1]),
        scale=np.reshape(sigma_bc, [-1]))
    expected_entropy = np.reshape(expected_entropy, df_bc.shape)
    self.assertAllClose(expected_entropy, ent_values)

  def testStudentSample(self):
    with self.test_session():
      df = constant_op.constant(4.)
      mu = constant_op.constant(3.)
      sigma = constant_op.constant(-math.sqrt(10.))
      df_v = 4.
      mu_v = 3.
      sigma_v = np.sqrt(10.)
      n = constant_op.constant(200000)
      student = student_t.StudentT(df=df, loc=mu, scale=sigma)
      samples = student.sample(n, seed=123456)
      sample_values = samples.eval()
      n_val = 200000
      self.assertEqual(sample_values.shape, (n_val,))
      self.assertAllClose(sample_values.mean(), mu_v, rtol=1e-2, atol=0)
      self.assertAllClose(
          sample_values.var(),
          sigma_v**2 * df_v / (df_v - 2),
          rtol=1e-2,
          atol=0)
      self._checkKLApprox(df_v, mu_v, sigma_v, sample_values)

  # Test that sampling with the same seed twice gives the same results.
  def testStudentSampleMultipleTimes(self):
    with self.test_session():
      df = constant_op.constant(4.)
      mu = constant_op.constant(3.)
      sigma = constant_op.constant(math.sqrt(10.))
      n = constant_op.constant(100)

      random_seed.set_random_seed(654321)
      student = student_t.StudentT(
          df=df, loc=mu, scale=sigma, name="student_t1")
      samples1 = student.sample(n, seed=123456).eval()

      random_seed.set_random_seed(654321)
      student2 = student_t.StudentT(
          df=df, loc=mu, scale=sigma, name="student_t2")
      samples2 = student2.sample(n, seed=123456).eval()

      self.assertAllClose(samples1, samples2)

  def testStudentSampleSmallDfNoNan(self):
    with self.test_session():
      df_v = [1e-1, 1e-5, 1e-10, 1e-20]
      df = constant_op.constant(df_v)
      n = constant_op.constant(200000)
      student = student_t.StudentT(df=df, loc=1., scale=1.)
      samples = student.sample(n, seed=123456)
      sample_values = samples.eval()
      n_val = 200000
      self.assertEqual(sample_values.shape, (n_val, 4))
      self.assertTrue(np.all(np.logical_not(np.isnan(sample_values))))

  def testStudentSampleMultiDimensional(self):
    with self.test_session():
      batch_size = 7
      df = constant_op.constant([[3., 7.]] * batch_size)
      mu = constant_op.constant([[3., -3.]] * batch_size)
      sigma = constant_op.constant([[math.sqrt(10.), math.sqrt(15.)]] *
                                   batch_size)
      df_v = [3., 7.]
      mu_v = [3., -3.]
      sigma_v = [np.sqrt(10.), np.sqrt(15.)]
      n = constant_op.constant(200000)
      student = student_t.StudentT(df=df, loc=mu, scale=sigma)
      samples = student.sample(n, seed=123456)
      sample_values = samples.eval()
      self.assertEqual(samples.get_shape(), (200000, batch_size, 2))
      self.assertAllClose(
          sample_values[:, 0, 0].mean(), mu_v[0], rtol=1e-2, atol=0)
      self.assertAllClose(
          sample_values[:, 0, 0].var(),
          sigma_v[0]**2 * df_v[0] / (df_v[0] - 2),
          rtol=1e-1,
          atol=0)
      self._checkKLApprox(df_v[0], mu_v[0], sigma_v[0], sample_values[:, 0, 0])
      self.assertAllClose(
          sample_values[:, 0, 1].mean(), mu_v[1], rtol=1e-2, atol=0)
      self.assertAllClose(
          sample_values[:, 0, 1].var(),
          sigma_v[1]**2 * df_v[1] / (df_v[1] - 2),
          rtol=1e-1,
          atol=0)
      self._checkKLApprox(df_v[0], mu_v[0], sigma_v[0], sample_values[:, 0, 1])

  def _checkKLApprox(self, df, mu, sigma, samples):
    n = samples.size
    np.random.seed(137)
    if not stats:
      return
    sample_scipy = stats.t.rvs(df, loc=mu, scale=sigma, size=n)
    covg = 0.99
    r = stats.t.interval(covg, df, loc=mu, scale=sigma)
    bins = 100
    hist, _ = np.histogram(samples, bins=bins, range=r)
    hist_scipy, _ = np.histogram(sample_scipy, bins=bins, range=r)
    self.assertGreater(hist.sum(), n * (covg - .01))
    self.assertGreater(hist_scipy.sum(), n * (covg - .01))
    hist_min1 = hist + 1.  # put at least one item in each bucket
    hist_norm = hist_min1 / hist_min1.sum()
    hist_scipy_min1 = hist_scipy + 1.  # put at least one item in each bucket
    hist_scipy_norm = hist_scipy_min1 / hist_scipy_min1.sum()
    kl_appx = np.sum(np.log(hist_scipy_norm / hist_norm) * hist_scipy_norm)
    self.assertLess(kl_appx, 1)

  def testBroadcastingParams(self):

    def _check(student):
      self.assertEqual(student.mean().get_shape(), (3,))
      self.assertEqual(student.variance().get_shape(), (3,))
      self.assertEqual(student.entropy().get_shape(), (3,))
      self.assertEqual(student.log_prob(2.).get_shape(), (3,))
      self.assertEqual(student.prob(2.).get_shape(), (3,))
      self.assertEqual(student.sample(37, seed=123456).get_shape(), (37, 3,))

    _check(student_t.StudentT(df=[2., 3., 4.,], loc=2., scale=1.))
    _check(student_t.StudentT(df=7., loc=[2., 3., 4.,], scale=1.))
    _check(student_t.StudentT(df=7., loc=3., scale=[2., 3., 4.,]))

  def testBroadcastingPdfArgs(self):

    def _assert_shape(student, arg, shape):
      self.assertEqual(student.log_prob(arg).get_shape(), shape)
      self.assertEqual(student.prob(arg).get_shape(), shape)

    def _check(student):
      _assert_shape(student, 2., (3,))
      xs = np.array([2., 3., 4.], dtype=np.float32)
      _assert_shape(student, xs, (3,))
      xs = np.array([xs])
      _assert_shape(student, xs, (1, 3))
      xs = xs.T
      _assert_shape(student, xs, (3, 3))

    _check(student_t.StudentT(df=[2., 3., 4.,], loc=2., scale=1.))
    _check(student_t.StudentT(df=7., loc=[2., 3., 4.,], scale=1.))
    _check(student_t.StudentT(df=7., loc=3., scale=[2., 3., 4.,]))

    def _check2d(student):
      _assert_shape(student, 2., (1, 3))
      xs = np.array([2., 3., 4.], dtype=np.float32)
      _assert_shape(student, xs, (1, 3))
      xs = np.array([xs])
      _assert_shape(student, xs, (1, 3))
      xs = xs.T
      _assert_shape(student, xs, (3, 3))

    _check2d(student_t.StudentT(df=[[2., 3., 4.,]], loc=2., scale=1.))
    _check2d(student_t.StudentT(df=7., loc=[[2., 3., 4.,]], scale=1.))
    _check2d(student_t.StudentT(df=7., loc=3., scale=[[2., 3., 4.,]]))

    def _check2d_rows(student):
      _assert_shape(student, 2., (3, 1))
      xs = np.array([2., 3., 4.], dtype=np.float32)  # (3,)
      _assert_shape(student, xs, (3, 3))
      xs = np.array([xs])  # (1,3)
      _assert_shape(student, xs, (3, 3))
      xs = xs.T  # (3,1)
      _assert_shape(student, xs, (3, 1))

    _check2d_rows(student_t.StudentT(df=[[2.], [3.], [4.]], loc=2., scale=1.))
    _check2d_rows(student_t.StudentT(df=7., loc=[[2.], [3.], [4.]], scale=1.))
    _check2d_rows(student_t.StudentT(df=7., loc=3., scale=[[2.], [3.], [4.]]))

  def testMeanAllowNanStatsIsFalseWorksWhenAllBatchMembersAreDefined(self):
    with self.test_session():
      mu = [1., 3.3, 4.4]
      student = student_t.StudentT(df=[3., 5., 7.], loc=mu, scale=[3., 2., 1.])
      mean = student.mean().eval()
      self.assertAllClose([1., 3.3, 4.4], mean)

  def testMeanAllowNanStatsIsFalseRaisesWhenBatchMemberIsUndefined(self):
    with self.test_session():
      mu = [1., 3.3, 4.4]
      student = student_t.StudentT(
          df=[0.5, 5., 7.], loc=mu, scale=[3., 2., 1.],
          allow_nan_stats=False)
      with self.assertRaisesOpError("x < y"):
        student.mean().eval()

  def testMeanAllowNanStatsIsTrueReturnsNaNForUndefinedBatchMembers(self):
    with self.test_session():
      mu = [-2, 0., 1., 3.3, 4.4]
      sigma = [5., 4., 3., 2., 1.]
      student = student_t.StudentT(
          df=[0.5, 1., 3., 5., 7.], loc=mu, scale=sigma,
          allow_nan_stats=True)
      mean = student.mean().eval()
      self.assertAllClose([np.nan, np.nan, 1., 3.3, 4.4], mean)

  def testVarianceAllowNanStatsTrueReturnsNaNforUndefinedBatchMembers(self):
    with self.test_session():
      # df = 0.5 ==> undefined mean ==> undefined variance.
      # df = 1.5 ==> infinite variance.
      df = [0.5, 1.5, 3., 5., 7.]
      mu = [-2, 0., 1., 3.3, 4.4]
      sigma = [5., 4., 3., 2., 1.]
      student = student_t.StudentT(
          df=df, loc=mu, scale=sigma, allow_nan_stats=True)
      var = student.variance().eval()
      ## scipy uses inf for variance when the mean is undefined.  When mean is
      # undefined we say variance is undefined as well.  So test the first
      # member of var, making sure it is NaN, then replace with inf and compare
      # to scipy.
      self.assertTrue(np.isnan(var[0]))
      var[0] = np.inf

      if not stats:
        return
      expected_var = [
          stats.t.var(d, loc=m, scale=s) for (d, m, s) in zip(df, mu, sigma)
      ]
      self.assertAllClose(expected_var, var)

  def testVarianceAllowNanStatsFalseGivesCorrectValueForDefinedBatchMembers(
      self):
    with self.test_session():
      # df = 1.5 ==> infinite variance.
      df = [1.5, 3., 5., 7.]
      mu = [0., 1., 3.3, 4.4]
      sigma = [4., 3., 2., 1.]
      student = student_t.StudentT(df=df, loc=mu, scale=sigma)
      var = student.variance().eval()

      if not stats:
        return
      expected_var = [
          stats.t.var(d, loc=m, scale=s) for (d, m, s) in zip(df, mu, sigma)
      ]
      self.assertAllClose(expected_var, var)

  def testVarianceAllowNanStatsFalseRaisesForUndefinedBatchMembers(self):
    with self.test_session():
      # df <= 1 ==> variance not defined
      student = student_t.StudentT(
          df=1., loc=0., scale=1., allow_nan_stats=False)
      with self.assertRaisesOpError("x < y"):
        student.variance().eval()

    with self.test_session():
      # df <= 1 ==> variance not defined
      student = student_t.StudentT(
          df=0.5, loc=0., scale=1., allow_nan_stats=False)
      with self.assertRaisesOpError("x < y"):
        student.variance().eval()

  def testStd(self):
    with self.test_session():
      # Defined for all batch members.
      df = [3.5, 5., 3., 5., 7.]
      mu = [-2.2]
      sigma = [5., 4., 3., 2., 1.]
      student = student_t.StudentT(df=df, loc=mu, scale=sigma)
      # Test broadcast of mu across shape of df/sigma
      stddev = student.stddev().eval()
      mu *= len(df)

      if not stats:
        return
      expected_stddev = [
          stats.t.std(d, loc=m, scale=s) for (d, m, s) in zip(df, mu, sigma)
      ]
      self.assertAllClose(expected_stddev, stddev)

  def testMode(self):
    with self.test_session():
      df = [0.5, 1., 3]
      mu = [-1, 0., 1]
      sigma = [5., 4., 3.]
      student = student_t.StudentT(df=df, loc=mu, scale=sigma)
      # Test broadcast of mu across shape of df/sigma
      mode = student.mode().eval()
      self.assertAllClose([-1., 0, 1], mode)

  def testPdfOfSample(self):
    with self.test_session() as sess:
      student = student_t.StudentT(df=3., loc=np.pi, scale=1.)
      num = 20000
      samples = student.sample(num, seed=123456)
      pdfs = student.prob(samples)
      mean = student.mean()
      mean_pdf = student.prob(student.mean())
      sample_vals, pdf_vals, mean_val, mean_pdf_val = sess.run(
          [samples, pdfs, student.mean(), mean_pdf])
      self.assertEqual(samples.get_shape(), (num,))
      self.assertEqual(pdfs.get_shape(), (num,))
      self.assertEqual(mean.get_shape(), ())
      self.assertNear(np.pi, np.mean(sample_vals), err=0.02)
      self.assertNear(np.pi, mean_val, err=1e-6)
      # Verify integral over sample*pdf ~= 1.
      self._assertIntegral(sample_vals, pdf_vals, err=2e-3)
      if not stats:
        return
      self.assertNear(stats.t.pdf(np.pi, 3., loc=np.pi), mean_pdf_val, err=1e-6)

  def testPdfOfSampleMultiDims(self):
    with self.test_session() as sess:
      student = student_t.StudentT(df=[7., 11.], loc=[[5.], [6.]], scale=3.)
      self.assertAllEqual([], student.event_shape)
      self.assertAllEqual([], student.event_shape_tensor().eval())
      self.assertAllEqual([2, 2], student.batch_shape)
      self.assertAllEqual([2, 2], student.batch_shape_tensor().eval())
      num = 50000
      samples = student.sample(num, seed=123456)
      pdfs = student.prob(samples)
      sample_vals, pdf_vals = sess.run([samples, pdfs])
      self.assertEqual(samples.get_shape(), (num, 2, 2))
      self.assertEqual(pdfs.get_shape(), (num, 2, 2))
      self.assertNear(5., np.mean(sample_vals[:, 0, :]), err=.03)
      self.assertNear(6., np.mean(sample_vals[:, 1, :]), err=.03)
      self._assertIntegral(sample_vals[:, 0, 0], pdf_vals[:, 0, 0], err=0.02)
      self._assertIntegral(sample_vals[:, 0, 1], pdf_vals[:, 0, 1], err=0.02)
      self._assertIntegral(sample_vals[:, 1, 0], pdf_vals[:, 1, 0], err=0.02)
      self._assertIntegral(sample_vals[:, 1, 1], pdf_vals[:, 1, 1], err=0.02)
      if not stats:
        return
      self.assertNear(
          stats.t.var(7., loc=0., scale=3.),  # loc d.n. effect var
          np.var(sample_vals[:, :, 0]),
          err=.4)
      self.assertNear(
          stats.t.var(11., loc=0., scale=3.),  # loc d.n. effect var
          np.var(sample_vals[:, :, 1]),
          err=.4)

  def _assertIntegral(self, sample_vals, pdf_vals, err=1.5e-3):
    s_p = zip(sample_vals, pdf_vals)
    prev = (sample_vals.min() - 1000, 0)
    total = 0
    for k in sorted(s_p, key=lambda x: x[0]):
      pair_pdf = (k[1] + prev[1]) / 2
      total += (k[0] - prev[0]) * pair_pdf
      prev = k
    self.assertNear(1., total, err=err)

  def testNegativeDofFails(self):
    with self.test_session():
      student = student_t.StudentT(df=[2, -5.], loc=0., scale=1.,
                                   validate_args=True, name="S")
      with self.assertRaisesOpError(r"Condition x > 0 did not hold"):
        student.mean().eval()

  def testStudentTWithAbsDfSoftplusScale(self):
    with self.test_session():
      df = constant_op.constant([-3.2, -4.6])
      mu = constant_op.constant([-4.2, 3.4])
      sigma = constant_op.constant([-6.4, -8.8])
      student = student_t.StudentTWithAbsDfSoftplusScale(
          df=df, loc=mu, scale=sigma)
      self.assertAllClose(
          math_ops.floor(math_ops.abs(df)).eval(), student.df.eval())
      self.assertAllClose(mu.eval(), student.loc.eval())
      self.assertAllClose(nn_ops.softplus(sigma).eval(), student.scale.eval())


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