code: import sys
  import hashlib
  
  import pytest
  
  import numpy as np
  from numpy.linalg import LinAlgError
  from numpy.testing import (
      assert_, assert_raises, assert_equal, assert_allclose,
      assert_warns, assert_no_warnings, assert_array_equal,
      assert_array_almost_equal, suppress_warnings)
  
  from numpy.random import Generator, MT19937, SeedSequence
  
  random = Generator(MT19937())
  
  JUMP_TEST_DATA = [
      {
          "seed": 0,
          "steps": 10,
          "initial": {"key_md5": "64eaf265d2203179fb5ffb73380cd589", "pos": 9},
          "jumped": {"key_md5": "8cb7b061136efceef5217a9ce2cc9a5a", "pos": 598},
      },
      {
          "seed":384908324,
          "steps":312,
          "initial": {"key_md5": "e99708a47b82ff51a2c7b0625b81afb5", "pos": 311},
          "jumped": {"key_md5": "2ecdbfc47a895b253e6e19ccb2e74b90", "pos": 276},
      },
      {
          "seed": [839438204, 980239840, 859048019, 821],
          "steps": 511,
          "initial": {"key_md5": "9fcd6280df9199785e17e93162ce283c", "pos": 510},
          "jumped": {"key_md5": "433b85229f2ed853cde06cd872818305", "pos": 475},
      },
  ]
  
  @pytest.fixture(scope='module', params=[True, False])
  def endpoint(request):
      return request.param
  
  
  class TestSeed:
      def test_scalar(self):
          s = Generator(MT19937(0))
          assert_equal(s.integers(1000), 479)
          s = Generator(MT19937(4294967295))
          assert_equal(s.integers(1000), 324)
  
      def test_array(self):
          s = Generator(MT19937(range(10)))
          assert_equal(s.integers(1000), 465)
          s = Generator(MT19937(np.arange(10)))
          assert_equal(s.integers(1000), 465)
          s = Generator(MT19937([0]))
          assert_equal(s.integers(1000), 479)
          s = Generator(MT19937([4294967295]))
          assert_equal(s.integers(1000), 324)
  
      def test_seedsequence(self):
          s = MT19937(SeedSequence(0))
          assert_equal(s.random_raw(1), 2058676884)
  
      def test_invalid_scalar(self):
          # seed must be an unsigned 32 bit integer
          assert_raises(TypeError, MT19937, -0.5)
          assert_raises(ValueError, MT19937, -1)
  
      def test_invalid_array(self):
          # seed must be an unsigned integer
          assert_raises(TypeError, MT19937, [-0.5])
          assert_raises(ValueError, MT19937, [-1])
          assert_raises(ValueError, MT19937, [1, -2, 4294967296])
  
      def test_noninstantized_bitgen(self):
          assert_raises(ValueError, Generator, MT19937)
  
  
  class TestBinomial:
      def test_n_zero(self):
          # Tests the corner case of n == 0 for the binomial distribution.
          # binomial(0, p) should be zero for any p in [0, 1].
          # This test addresses issue #3480.
          zeros = np.zeros(2, dtype='int')
          for p in [0, .5, 1]:
              assert_(random.binomial(0, p) == 0)
              assert_array_equal(random.binomial(zeros, p), zeros)
  
      def test_p_is_nan(self):
          # Issue #4571.
          assert_raises(ValueError, random.binomial, 1, np.nan)
  
  
  class TestMultinomial:
      def test_basic(self):
          random.multinomial(100, [0.2, 0.8])
  
      def test_zero_probability(self):
          random.multinomial(100, [0.2, 0.8, 0.0, 0.0, 0.0])
  
      def test_int_negative_interval(self):
          assert_(-5 <= random.integers(-5, -1) < -1)
          x = random.integers(-5, -1, 5)
          assert_(np.all(-5 <= x))
          assert_(np.all(x < -1))
  
      def test_size(self):
          # gh-3173
          p = [0.5, 0.5]
          assert_equal(random.multinomial(1, p, np.uint32(1)).shape, (1, 2))
          assert_equal(random.multinomial(1, p, np.uint32(1)).shape, (1, 2))
          assert_equal(random.multinomial(1, p, np.uint32(1)).shape, (1, 2))
          assert_equal(random.multinomial(1, p, [2, 2]).shape, (2, 2, 2))
          assert_equal(random.multinomial(1, p, (2, 2)).shape, (2, 2, 2))
          assert_equal(random.multinomial(1, p, np.array((2, 2))).shape,
                       (2, 2, 2))
  
          assert_raises(TypeError, random.multinomial, 1, p,
                        float(1))
  
      def test_invalid_prob(self):
          assert_raises(ValueError, random.multinomial, 100, [1.1, 0.2])
          assert_raises(ValueError, random.multinomial, 100, [-.1, 0.9])
  
      def test_invalid_n(self):
          assert_raises(ValueError, random.multinomial, -1, [0.8, 0.2])
          assert_raises(ValueError, random.multinomial, [-1] * 10, [0.8, 0.2])
  
      def test_p_non_contiguous(self):
          p = np.arange(15.)
          p /= np.sum(p[1::3])
          pvals = p[1::3]
          random = Generator(MT19937(1432985819))
          non_contig = random.multinomial(100, pvals=pvals)
          random = Generator(MT19937(1432985819))
          contig = random.multinomial(100, pvals=np.ascontiguousarray(pvals))
          assert_array_equal(non_contig, contig)
  
      def test_multidimensional_pvals(self):
          assert_raises(ValueError, random.multinomial, 10, [[0, 1]])
          assert_raises(ValueError, random.multinomial, 10, [[0], [1]])
          assert_raises(ValueError, random.multinomial, 10, [[[0], [1]], [[1], [0]]])
          assert_raises(ValueError, random.multinomial, 10, np.array([[0, 1], [1, 0]]))
  
  
  class TestMultivariateHypergeometric:
  
      def setup(self):
          self.seed = 8675309
  
      def test_argument_validation(self):
          # Error cases...
  
          # `colors` must be a 1-d sequence
          assert_raises(ValueError, random.multivariate_hypergeometric,
                        10, 4)
  
          # Negative nsample
          assert_raises(ValueError, random.multivariate_hypergeometric,
                        [2, 3, 4], -1)
  
          # Negative color
          assert_raises(ValueError, random.multivariate_hypergeometric,
                        [-1, 2, 3], 2)
  
          # nsample exceeds sum(colors)
          assert_raises(ValueError, random.multivariate_hypergeometric,
                        [2, 3, 4], 10)
  
          # nsample exceeds sum(colors) (edge case of empty colors)
          assert_raises(ValueError, random.multivariate_hypergeometric,
                        [], 1)
  
          # Validation errors associated with very large values in colors.
          assert_raises(ValueError, random.multivariate_hypergeometric,
                        [999999999, 101], 5, 1, 'marginals')
  
          int64_info = np.iinfo(np.int64)
          max_int64 = int64_info.max
          max_int64_index = max_int64 // int64_info.dtype.itemsize
          assert_raises(ValueError, random.multivariate_hypergeometric,
                        [max_int64_index - 100, 101], 5, 1, 'count')
  
      @pytest.mark.parametrize('method', ['count', 'marginals'])
      def test_edge_cases(self, method):
          # Set the seed, but in fact, all the results in this test are
          # deterministic, so we don't really need this.
          random = Generator(MT19937(self.seed))
  
          x = random.multivariate_hypergeometric([0, 0, 0], 0, method=method)
          assert_array_equal(x, [0, 0, 0])
  
          x = random.multivariate_hypergeometric([], 0, method=method)
          assert_array_equal(x, [])
  
          x = random.multivariate_hypergeometric([], 0, size=1, method=method)
          assert_array_equal(x, np.empty((1, 0), dtype=np.int64))
  
          x = random.multivariate_hypergeometric([1, 2, 3], 0, method=method)
          assert_array_equal(x, [0, 0, 0])
  
          x = random.multivariate_hypergeometric([9, 0, 0], 3, method=method)
          assert_array_equal(x, [3, 0, 0])
  
          colors = [1, 1, 0, 1, 1]
          x = random.multivariate_hypergeometric(colors, sum(colors),
                                                 method=method)
          assert_array_equal(x, colors)
  
          x = random.multivariate_hypergeometric([3, 4, 5], 12, size=3,
                                                 method=method)
          assert_array_equal(x, [[3, 4, 5]]*3)
  
      # Cases for nsample:
      #     nsample < 10
      #     10 <= nsample < colors.sum()/2
      #     colors.sum()/2 < nsample < colors.sum() - 10
      #     colors.sum() - 10 < nsample < colors.sum()
      @pytest.mark.parametrize('nsample', [8, 25, 45, 55])
      @pytest.mark.parametrize('method', ['count', 'marginals'])
      @pytest.mark.parametrize('size', [5, (2, 3), 150000])
      def test_typical_cases(self, nsample, method, size):
          random = Generator(MT19937(self.seed))
  
          colors = np.array([10, 5, 20, 25])
          sample = random.multivariate_hypergeometric(colors, nsample, size,
                                                      method=method)
          if isinstance(size, int):
              expected_shape = (size,) + colors.shape
          else:
              expected_shape = size + colors.shape
          assert_equal(sample.shape, expected_shape)
          assert_((sample >= 0).all())
          assert_((sample <= colors).all())
          assert_array_equal(sample.sum(axis=-1),
                             np.full(size, fill_value=nsample, dtype=int))
          if isinstance(size, int) and size >= 100000:
              # This sample is large enough to compare its mean to
              # the expected values.
              assert_allclose(sample.mean(axis=0),
                              nsample * colors / colors.sum(),
                              rtol=1e-3, atol=0.005)
  
      def test_repeatability1(self):
          random = Generator(MT19937(self.seed))
          sample = random.multivariate_hypergeometric([3, 4, 5], 5, size=5,
                                                      method='count')
          expected = np.array([[2, 1, 2],
                               [2, 1, 2],
                               [1, 1, 3],
                               [2, 0, 3],
                               [2, 1, 2]])
          assert_array_equal(sample, expected)
  
      def test_repeatability2(self):
          random = Generator(MT19937(self.seed))
          sample = random.multivariate_hypergeometric([20, 30, 50], 50,
                                                      size=5,
                                                      method='marginals')
          expected = np.array([[ 9, 17, 24],
                               [ 7, 13, 30],
                               [ 9, 15, 26],
                               [ 9, 17, 24],
                               [12, 14, 24]])
          assert_array_equal(sample, expected)
  
      def test_repeatability3(self):
          random = Generator(MT19937(self.seed))
          sample = random.multivariate_hypergeometric([20, 30, 50], 12,
                                                      size=5,
                                                      method='marginals')
          expected = np.array([[2, 3, 7],
                               [5, 3, 4],
                               [2, 5, 5],
                               [5, 3, 4],
                               [1, 5, 6]])
          assert_array_equal(sample, expected)
  
  
  class TestSetState:
      def setup(self):
          self.seed = 1234567890
          self.rg = Generator(MT19937(self.seed))
          self.bit_generator = self.rg.bit_generator
          self.state = self.bit_generator.state
          self.legacy_state = (self.state['bit_generator'],
                               self.state['state']['key'],
                               self.state['state']['pos'])
  
      def test_gaussian_reset(self):
          # Make sure the cached every-other-Gaussian is reset.
          old = self.rg.standard_normal(size=3)
          self.bit_generator.state = self.state
          new = self.rg.standard_normal(size=3)
          assert_(np.all(old == new))
  
      def test_gaussian_reset_in_media_res(self):
          # When the state is saved with a cached Gaussian, make sure the
          # cached Gaussian is restored.
  
          self.rg.standard_normal()
          state = self.bit_generator.state
          old = self.rg.standard_normal(size=3)
          self.bit_generator.state = state
          new = self.rg.standard_normal(size=3)
          assert_(np.all(old == new))
  
      def test_negative_binomial(self):
          # Ensure that the negative binomial results take floating point
          # arguments without truncation.
          self.rg.negative_binomial(0.5, 0.5)
  
  
  class TestIntegers:
      rfunc = random.integers
  
      # valid integer/boolean types
      itype = [bool, np.int8, np.uint8, np.int16, np.uint16,
               np.int32, np.uint32, np.int64, np.uint64]
  
      def test_unsupported_type(self, endpoint):
          assert_raises(TypeError, self.rfunc, 1, endpoint=endpoint, dtype=float)
  
      def test_bounds_checking(self, endpoint):
          for dt in self.itype:
              lbnd = 0 if dt is bool else np.iinfo(dt).min
              ubnd = 2 if dt is bool else np.iinfo(dt).max + 1
              ubnd = ubnd - 1 if endpoint else ubnd
              assert_raises(ValueError, self.rfunc, lbnd - 1, ubnd,
                            endpoint=endpoint, dtype=dt)
              assert_raises(ValueError, self.rfunc, lbnd, ubnd + 1,
                            endpoint=endpoint, dtype=dt)
              assert_raises(ValueError, self.rfunc, ubnd, lbnd,
                            endpoint=endpoint, dtype=dt)
              assert_raises(ValueError, self.rfunc, 1, 0, endpoint=endpoint,
                            dtype=dt)
  
              assert_raises(ValueError, self.rfunc, [lbnd - 1], ubnd,
                            endpoint=endpoint, dtype=dt)
              assert_raises(ValueError, self.rfunc, [lbnd], [ubnd + 1],
                            endpoint=endpoint, dtype=dt)
              assert_raises(ValueError, self.rfunc, [ubnd], [lbnd],
                            endpoint=endpoint, dtype=dt)
              assert_raises(ValueError, self.rfunc, 1, [0],
                            endpoint=endpoint, dtype=dt)
  
      def test_bounds_checking_array(self, endpoint):
          for dt in self.itype:
              lbnd = 0 if dt is bool else np.iinfo(dt).min
              ubnd = 2 if dt is bool else np.iinfo(dt).max + (not endpoint)
  
              assert_raises(ValueError, self.rfunc, [lbnd - 1] * 2, [ubnd] * 2,
                            endpoint=endpoint, dtype=dt)
              assert_raises(ValueError, self.rfunc, [lbnd] * 2,
                            [ubnd + 1] * 2, endpoint=endpoint, dtype=dt)
              assert_raises(ValueError, self.rfunc, ubnd, [lbnd] * 2,
                            endpoint=endpoint, dtype=dt)
              assert_raises(ValueError, self.rfunc, [1] * 2, 0,
                            endpoint=endpoint, dtype=dt)
  
      def test_rng_zero_and_extremes(self, endpoint):
          for dt in self.itype:
              lbnd = 0 if dt is bool else np.iinfo(dt).min
              ubnd = 2 if dt is bool else np.iinfo(dt).max + 1
              ubnd = ubnd - 1 if endpoint else ubnd
              is_open = not endpoint
  
              tgt = ubnd - 1
              assert_equal(self.rfunc(tgt, tgt + is_open, size=1000,
                                      endpoint=endpoint, dtype=dt), tgt)
              assert_equal(self.rfunc([tgt], tgt + is_open, size=1000,
                                      endpoint=endpoint, dtype=dt), tgt)
  
              tgt = lbnd
              assert_equal(self.rfunc(tgt, tgt + is_open, size=1000,
                                      endpoint=endpoint, dtype=dt), tgt)
              assert_equal(self.rfunc(tgt, [tgt + is_open], size=1000,
                                      endpoint=endpoint, dtype=dt), tgt)
  
              tgt = (lbnd + ubnd) // 2
              assert_equal(self.rfunc(tgt, tgt + is_open, size=1000,
                                      endpoint=endpoint, dtype=dt), tgt)
              assert_equal(self.rfunc([tgt], [tgt + is_open],
                                      size=1000, endpoint=endpoint, dtype=dt),
                           tgt)
  
      def test_rng_zero_and_extremes_array(self, endpoint):
          size = 1000
          for dt in self.itype:
              lbnd = 0 if dt is bool else np.iinfo(dt).min
              ubnd = 2 if dt is bool else np.iinfo(dt).max + 1
              ubnd = ubnd - 1 if endpoint else ubnd
  
              tgt = ubnd - 1
              assert_equal(self.rfunc([tgt], [tgt + 1],
                                      size=size, dtype=dt), tgt)
              assert_equal(self.rfunc(
                  [tgt] * size, [tgt + 1] * size, dtype=dt), tgt)
              assert_equal(self.rfunc(
                  [tgt] * size, [tgt + 1] * size, size=size, dtype=dt), tgt)
  
              tgt = lbnd
              assert_equal(self.rfunc([tgt], [tgt + 1],
                                      size=size, dtype=dt), tgt)
              assert_equal(self.rfunc(
                  [tgt] * size, [tgt + 1] * size, dtype=dt), tgt)
              assert_equal(self.rfunc(
                  [tgt] * size, [tgt + 1] * size, size=size, dtype=dt), tgt)
  
              tgt = (lbnd + ubnd) // 2
              assert_equal(self.rfunc([tgt], [tgt + 1],
                                      size=size, dtype=dt), tgt)
              assert_equal(self.rfunc(
                  [tgt] * size, [tgt + 1] * size, dtype=dt), tgt)
              assert_equal(self.rfunc(
                  [tgt] * size, [tgt + 1] * size, size=size, dtype=dt), tgt)
  
      def test_full_range(self, endpoint):
          # Test for ticket #1690
  
          for dt in self.itype:
              lbnd = 0 if dt is bool else np.iinfo(dt).min
              ubnd = 2 if dt is bool else np.iinfo(dt).max + 1
              ubnd = ubnd - 1 if endpoint else ubnd
  
              try:
                  self.rfunc(lbnd, ubnd, endpoint=endpoint, dtype=dt)
              except Exception as e:
                  raise AssertionError("No error should have been raised, "
                                       "but one was with the following "
                                       "message:\n\n%s" % str(e))
  
      def test_full_range_array(self, endpoint):
          # Test for ticket #1690
  
          for dt in self.itype:
              lbnd = 0 if dt is bool else np.iinfo(dt).min
              ubnd = 2 if dt is bool else np.iinfo(dt).max + 1
              ubnd = ubnd - 1 if endpoint else ubnd
  
              try:
                  self.rfunc([lbnd] * 2, [ubnd], endpoint=endpoint, dtype=dt)
              except Exception as e:
                  raise AssertionError("No error should have been raised, "
                                       "but one was with the following "
                                       "message:\n\n%s" % str(e))
  
      def test_in_bounds_fuzz(self, endpoint):
          # Don't use fixed seed
          random = Generator(MT19937())
  
          for dt in self.itype[1:]:
              for ubnd in [4, 8, 16]:
                  vals = self.rfunc(2, ubnd - endpoint, size=2 ** 16,
                                    endpoint=endpoint, dtype=dt)
                  assert_(vals.max() < ubnd)
                  assert_(vals.min() >= 2)
  
          vals = self.rfunc(0, 2 - endpoint, size=2 ** 16, endpoint=endpoint,
                            dtype=bool)
          assert_(vals.max() < 2)
          assert_(vals.min() >= 0)
  
      def test_scalar_array_equiv(self, endpoint):
          for dt in self.itype:
              lbnd = 0 if dt is bool else np.iinfo(dt).min
              ubnd = 2 if dt is bool else np.iinfo(dt).max + 1
              ubnd = ubnd - 1 if endpoint else ubnd
  
              size = 1000
              random = Generator(MT19937(1234))
              scalar = random.integers(lbnd, ubnd, size=size, endpoint=endpoint,
                                  dtype=dt)
  
              random = Generator(MT19937(1234))
              scalar_array = random.integers([lbnd], [ubnd], size=size,
                                        endpoint=endpoint, dtype=dt)
  
              random = Generator(MT19937(1234))
              array = random.integers([lbnd] * size, [ubnd] *
                                 size, size=size, endpoint=endpoint, dtype=dt)
              assert_array_equal(scalar, scalar_array)
              assert_array_equal(scalar, array)
  
      def test_repeatability(self, endpoint):
          # We use a md5 hash of generated sequences of 1000 samples
          # in the range [0, 6) for all but bool, where the range
          # is [0, 2). Hashes are for little endian numbers.
          tgt = {'bool':   'b3300e66d2bb59e493d255d47c3a6cbe',
                 'int16':  '39624ead49ad67e37545744024d2648b',
                 'int32':  '5c4810373f979336c6c0c999996e47a1',
                 'int64':  'ab126c15edff26f55c50d2b7e37391ac',
                 'int8':   'ba71ccaffeeeb9eeb1860f8075020b9c',
                 'uint16': '39624ead49ad67e37545744024d2648b',
                 'uint32': '5c4810373f979336c6c0c999996e47a1',
                 'uint64': 'ab126c15edff26f55c50d2b7e37391ac',
                 'uint8':  'ba71ccaffeeeb9eeb1860f8075020b9c'}
  
          for dt in self.itype[1:]:
              random = Generator(MT19937(1234))
  
              # view as little endian for hash
              if sys.byteorder == 'little':
                  val = random.integers(0, 6 - endpoint, size=1000, endpoint=endpoint,
                                   dtype=dt)
              else:
                  val = random.integers(0, 6 - endpoint, size=1000, endpoint=endpoint,
                                   dtype=dt).byteswap()
  
              res = hashlib.md5(val).hexdigest()
              assert_(tgt[np.dtype(dt).name] == res)
  
          # bools do not depend on endianness
          random = Generator(MT19937(1234))
          val = random.integers(0, 2 - endpoint, size=1000, endpoint=endpoint,
                           dtype=bool).view(np.int8)
          res = hashlib.md5(val).hexdigest()
          assert_(tgt[np.dtype(bool).name] == res)
  
      def test_repeatability_broadcasting(self, endpoint):
          for dt in self.itype:
              lbnd = 0 if dt in (bool, np.bool_) else np.iinfo(dt).min
              ubnd = 2 if dt in (bool, np.bool_) else np.iinfo(dt).max + 1
              ubnd = ubnd - 1 if endpoint else ubnd
  
              # view as little endian for hash
              random = Generator(MT19937(1234))
              val = random.integers(lbnd, ubnd, size=1000, endpoint=endpoint,
                               dtype=dt)
  
              random = Generator(MT19937(1234))
              val_bc = random.integers([lbnd] * 1000, ubnd, endpoint=endpoint,
                                  dtype=dt)
  
              assert_array_equal(val, val_bc)
  
              random = Generator(MT19937(1234))
              val_bc = random.integers([lbnd] * 1000, [ubnd] * 1000,
                                  endpoint=endpoint, dtype=dt)
  
              assert_array_equal(val, val_bc)
  
      @pytest.mark.parametrize(
          'bound, expected',
          [(2**32 - 1, np.array([517043486, 1364798665, 1733884389, 1353720612,
                                 3769704066, 1170797179, 4108474671])),
           (2**32, np.array([517043487, 1364798666, 1733884390, 1353720613,
                             3769704067, 1170797180, 4108474672])),
           (2**32 + 1, np.array([517043487, 1733884390, 3769704068, 4108474673,
                                 1831631863, 1215661561, 3869512430]))]
      )
      def test_repeatability_32bit_boundary(self, bound, expected):
          for size in [None, len(expected)]:
              random = Generator(MT19937(1234))
              x = random.integers(bound, size=size)
              assert_equal(x, expected if size is not None else expected[0])
  
      def test_repeatability_32bit_boundary_broadcasting(self):
          desired = np.array([[[1622936284, 3620788691, 1659384060],
                               [1417365545,  760222891, 1909653332],
                               [3788118662,  660249498, 4092002593]],
                              [[3625610153, 2979601262, 3844162757],
                               [ 685800658,  120261497, 2694012896],
                               [1207779440, 1586594375, 3854335050]],
                              [[3004074748, 2310761796, 3012642217],
                               [2067714190, 2786677879, 1363865881],
                               [ 791663441, 1867303284, 2169727960]],
                              [[1939603804, 1250951100,  298950036],
                               [1040128489, 3791912209, 3317053765],
                               [3155528714,   61360675, 2305155588]],
                              [[ 817688762, 1335621943, 3288952434],
                               [1770890872, 1102951817, 1957607470],
                               [3099996017,  798043451,   48334215]]])
          for size in [None, (5, 3, 3)]:
              random = Generator(MT19937(12345))
              x = random.integers([[-1], [0], [1]],
                                  [2**32 - 1, 2**32, 2**32 + 1],
                                  size=size)
              assert_array_equal(x, desired if size is not None else desired[0])
  
      def test_int64_uint64_broadcast_exceptions(self, endpoint):
          configs = {np.uint64: ((0, 2**65), (-1, 2**62), (10, 9), (0, 0)),
                     np.int64: ((0, 2**64), (-(2**64), 2**62), (10, 9), (0, 0),
                                (-2**63-1, -2**63-1))}
          for dtype in configs:
              for config in configs[dtype]:
                  low, high = config
                  high = high - endpoint
                  low_a = np.array([[low]*10])
                  high_a = np.array([high] * 10)
                  assert_raises(ValueError, random.integers, low, high,
                                endpoint=endpoint, dtype=dtype)
                  assert_raises(ValueError, random.integers, low_a, high,
                                endpoint=endpoint, dtype=dtype)
                  assert_raises(ValueError, random.integers, low, high_a,
                                endpoint=endpoint, dtype=dtype)
                  assert_raises(ValueError, random.integers, low_a, high_a,
                                endpoint=endpoint, dtype=dtype)
  
                  low_o = np.array([[low]*10], dtype=object)
                  high_o = np.array([high] * 10, dtype=object)
                  assert_raises(ValueError, random.integers, low_o, high,
                                endpoint=endpoint, dtype=dtype)
                  assert_raises(ValueError, random.integers, low, high_o,
                                endpoint=endpoint, dtype=dtype)
                  assert_raises(ValueError, random.integers, low_o, high_o,
                                endpoint=endpoint, dtype=dtype)
  
      def test_int64_uint64_corner_case(self, endpoint):
          # When stored in Numpy arrays, `lbnd` is casted
          # as np.int64, and `ubnd` is casted as np.uint64.
          # Checking whether `lbnd` >= `ubnd` used to be
          # done solely via direct comparison, which is incorrect
          # because when Numpy tries to compare both numbers,
          # it casts both to np.float64 because there is
          # no integer superset of np.int64 and np.uint64. However,
          # `ubnd` is too large to be represented in np.float64,
          # causing it be round down to np.iinfo(np.int64).max,
          # leading to a ValueError because `lbnd` now equals
          # the new `ubnd`.
  
          dt = np.int64
          tgt = np.iinfo(np.int64).max
          lbnd = np.int64(np.iinfo(np.int64).max)
          ubnd = np.uint64(np.iinfo(np.int64).max + 1 - endpoint)
  
          # None of these function calls should
          # generate a ValueError now.
          actual = random.integers(lbnd, ubnd, endpoint=endpoint, dtype=dt)
          assert_equal(actual, tgt)
  
      def test_respect_dtype_singleton(self, endpoint):
          # See gh-7203
          for dt in self.itype:
              lbnd = 0 if dt is bool else np.iinfo(dt).min
              ubnd = 2 if dt is bool else np.iinfo(dt).max + 1
              ubnd = ubnd - 1 if endpoint else ubnd
              dt = np.bool_ if dt is bool else dt
  
              sample = self.rfunc(lbnd, ubnd, endpoint=endpoint, dtype=dt)
              assert_equal(sample.dtype, dt)
  
          for dt in (bool, int, np.compat.long):
              lbnd = 0 if dt is bool else np.iinfo(dt).min
              ubnd = 2 if dt is bool else np.iinfo(dt).max + 1
              ubnd = ubnd - 1 if endpoint else ubnd
  
              # gh-7284: Ensure that we get Python data types
              sample = self.rfunc(lbnd, ubnd, endpoint=endpoint, dtype=dt)
              assert not hasattr(sample, 'dtype')
              assert_equal(type(sample), dt)
  
      def test_respect_dtype_array(self, endpoint):
          # See gh-7203
          for dt in self.itype:
              lbnd = 0 if dt is bool else np.iinfo(dt).min
              ubnd = 2 if dt is bool else np.iinfo(dt).max + 1
              ubnd = ubnd - 1 if endpoint else ubnd
              dt = np.bool_ if dt is bool else dt
  
              sample = self.rfunc([lbnd], [ubnd], endpoint=endpoint, dtype=dt)
              assert_equal(sample.dtype, dt)
              sample = self.rfunc([lbnd] * 2, [ubnd] * 2, endpoint=endpoint,
                                  dtype=dt)
              assert_equal(sample.dtype, dt)
  
      def test_zero_size(self, endpoint):
          # See gh-7203
          for dt in self.itype:
              sample = self.rfunc(0, 0, (3, 0, 4), endpoint=endpoint, dtype=dt)
              assert sample.shape == (3, 0, 4)
              assert sample.dtype == dt
              assert self.rfunc(0, -10, 0, endpoint=endpoint,
                                dtype=dt).shape == (0,)
              assert_equal(random.integers(0, 0, size=(3, 0, 4)).shape,
                           (3, 0, 4))
              assert_equal(random.integers(0, -10, size=0).shape, (0,))
              assert_equal(random.integers(10, 10, size=0).shape, (0,))
  
      def test_error_byteorder(self):
          other_byteord_dt = '<i4' if sys.byteorder == 'big' else '>i4'
          with pytest.raises(ValueError):
              random.integers(0, 200, size=10, dtype=other_byteord_dt)
  
      # chi2max is the maximum acceptable chi-squared value.
      @pytest.mark.slow
      @pytest.mark.parametrize('sample_size,high,dtype,chi2max',
          [(5000000, 5, np.int8, 125.0),          # p-value ~4.6e-25
           (5000000, 7, np.uint8, 150.0),         # p-value ~7.7e-30
           (10000000, 2500, np.int16, 3300.0),    # p-value ~3.0e-25
           (50000000, 5000, np.uint16, 6500.0),   # p-value ~3.5e-25
          ])
      def test_integers_small_dtype_chisquared(self, sample_size, high,
                                               dtype, chi2max):
          # Regression test for gh-14774.
          samples = random.integers(high, size=sample_size, dtype=dtype)
  
          values, counts = np.unique(samples, return_counts=True)
          expected = sample_size / high
          chi2 = ((counts - expected)**2 / expected).sum()
          assert chi2 < chi2max
  
  
  class TestRandomDist:
      # Make sure the random distribution returns the correct value for a
      # given seed
  
      def setup(self):
          self.seed = 1234567890
  
      def test_integers(self):
          random = Generator(MT19937(self.seed))
          actual = random.integers(-99, 99, size=(3, 2))
          desired = np.array([[-80, -56], [41, 37], [-83, -16]])
          assert_array_equal(actual, desired)
  
      def test_integers_masked(self):
          # Test masked rejection sampling algorithm to generate array of
          # uint32 in an interval.
          random = Generator(MT19937(self.seed))
          actual = random.integers(0, 99, size=(3, 2), dtype=np.uint32)
          desired = np.array([[9, 21], [70, 68], [8, 41]], dtype=np.uint32)
          assert_array_equal(actual, desired)
  
      def test_integers_closed(self):
          random = Generator(MT19937(self.seed))
          actual = random.integers(-99, 99, size=(3, 2), endpoint=True)
          desired = np.array([[-80, -56], [ 41, 38], [-83, -15]])
          assert_array_equal(actual, desired)
  
      def test_integers_max_int(self):
          # Tests whether integers with closed=True can generate the
          # maximum allowed Python int that can be converted
          # into a C long. Previous implementations of this
          # method have thrown an OverflowError when attempting
          # to generate this integer.
          actual = random.integers(np.iinfo('l').max, np.iinfo('l').max,
                                   endpoint=True)
  
          desired = np.iinfo('l').max
          assert_equal(actual, desired)
  
      def test_random(self):
          random = Generator(MT19937(self.seed))
          actual = random.random((3, 2))
          desired = np.array([[0.096999199829214, 0.707517457682192],
                              [0.084364834598269, 0.767731206553125],
                              [0.665069021359413, 0.715487190596693]])
          assert_array_almost_equal(actual, desired, decimal=15)
  
          random = Generator(MT19937(self.seed))
          actual = random.random()
          assert_array_almost_equal(actual, desired[0, 0], decimal=15)
  
      def test_random_float(self):
          random = Generator(MT19937(self.seed))
          actual = random.random((3, 2))
          desired = np.array([[0.0969992 , 0.70751746],
                              [0.08436483, 0.76773121],
                              [0.66506902, 0.71548719]])
          assert_array_almost_equal(actual, desired, decimal=7)
  
      def test_random_float_scalar(self):
          random = Generator(MT19937(self.seed))
          actual = random.random(dtype=np.float32)
          desired = 0.0969992
          assert_array_almost_equal(actual, desired, decimal=7)
  
      def test_random_unsupported_type(self):
          assert_raises(TypeError, random.random, dtype='int32')
  
      def test_choice_uniform_replace(self):
          random = Generator(MT19937(self.seed))
          actual = random.choice(4, 4)
          desired = np.array([0, 0, 2, 2], dtype=np.int64)
          assert_array_equal(actual, desired)
  
      def test_choice_nonuniform_replace(self):
          random = Generator(MT19937(self.seed))
          actual = random.choice(4, 4, p=[0.4, 0.4, 0.1, 0.1])
          desired = np.array([0, 1, 0, 1], dtype=np.int64)
          assert_array_equal(actual, desired)
  
      def test_choice_uniform_noreplace(self):
          random = Generator(MT19937(self.seed))
          actual = random.choice(4, 3, replace=False)
          desired = np.array([2, 0, 3], dtype=np.int64)
          assert_array_equal(actual, desired)
          actual = random.choice(4, 4, replace=False, shuffle=False)
          desired = np.arange(4, dtype=np.int64)
          assert_array_equal(actual, desired)
  
      def test_choice_nonuniform_noreplace(self):
          random = Generator(MT19937(self.seed))
          actual = random.choice(4, 3, replace=False, p=[0.1, 0.3, 0.5, 0.1])
          desired = np.array([0, 2, 3], dtype=np.int64)
          assert_array_equal(actual, desired)
  
      def test_choice_noninteger(self):
          random = Generator(MT19937(self.seed))
          actual = random.choice(['a', 'b', 'c', 'd'], 4)
          desired = np.array(['a', 'a', 'c', 'c'])
          assert_array_equal(actual, desired)
  
      def test_choice_multidimensional_default_axis(self):
          random = Generator(MT19937(self.seed))
          actual = random.choice([[0, 1], [2, 3], [4, 5], [6, 7]], 3)
          desired = np.array([[0, 1], [0, 1], [4, 5]])
          assert_array_equal(actual, desired)
  
      def test_choice_multidimensional_custom_axis(self):
          random = Generator(MT19937(self.seed))
          actual = random.choice([[0, 1], [2, 3], [4, 5], [6, 7]], 1, axis=1)
          desired = np.array([[0], [2], [4], [6]])
          assert_array_equal(actual, desired)
  
      def test_choice_exceptions(self):
          sample = random.choice
          assert_raises(ValueError, sample, -1, 3)
          assert_raises(ValueError, sample, 3., 3)
          assert_raises(ValueError, sample, [], 3)
          assert_raises(ValueError, sample, [1, 2, 3, 4], 3,
                        p=[[0.25, 0.25], [0.25, 0.25]])
          assert_raises(ValueError, sample, [1, 2], 3, p=[0.4, 0.4, 0.2])
          assert_raises(ValueError, sample, [1, 2], 3, p=[1.1, -0.1])
          assert_raises(ValueError, sample, [1, 2], 3, p=[0.4, 0.4])
          assert_raises(ValueError, sample, [1, 2, 3], 4, replace=False)
          # gh-13087
          assert_raises(ValueError, sample, [1, 2, 3], -2, replace=False)
          assert_raises(ValueError, sample, [1, 2, 3], (-1,), replace=False)
          assert_raises(ValueError, sample, [1, 2, 3], (-1, 1), replace=False)
          assert_raises(ValueError, sample, [1, 2, 3], 2,
                        replace=False, p=[1, 0, 0])
  
      def test_choice_return_shape(self):
          p = [0.1, 0.9]
          # Check scalar
          assert_(np.isscalar(random.choice(2, replace=True)))
          assert_(np.isscalar(random.choice(2, replace=False)))
          assert_(np.isscalar(random.choice(2, replace=True, p=p)))
          assert_(np.isscalar(random.choice(2, replace=False, p=p)))
          assert_(np.isscalar(random.choice([1, 2], replace=True)))
          assert_(random.choice([None], replace=True) is None)
          a = np.array([1, 2])
          arr = np.empty(1, dtype=object)
          arr[0] = a
          assert_(random.choice(arr, replace=True) is a)
  
          # Check 0-d array
          s = tuple()
          assert_(not np.isscalar(random.choice(2, s, replace=True)))
          assert_(not np.isscalar(random.choice(2, s, replace=False)))
          assert_(not np.isscalar(random.choice(2, s, replace=True, p=p)))
          assert_(not np.isscalar(random.choice(2, s, replace=False, p=p)))
          assert_(not np.isscalar(random.choice([1, 2], s, replace=True)))
          assert_(random.choice([None], s, replace=True).ndim == 0)
          a = np.array([1, 2])
          arr = np.empty(1, dtype=object)
          arr[0] = a
          assert_(random.choice(arr, s, replace=True).item() is a)
  
          # Check multi dimensional array
          s = (2, 3)
          p = [0.1, 0.1, 0.1, 0.1, 0.4, 0.2]
          assert_equal(random.choice(6, s, replace=True).shape, s)
          assert_equal(random.choice(6, s, replace=False).shape, s)
          assert_equal(random.choice(6, s, replace=True, p=p).shape, s)
          assert_equal(random.choice(6, s, replace=False, p=p).shape, s)
          assert_equal(random.choice(np.arange(6), s, replace=True).shape, s)
  
          # Check zero-size
          assert_equal(random.integers(0, 0, size=(3, 0, 4)).shape, (3, 0, 4))
          assert_equal(random.integers(0, -10, size=0).shape, (0,))
          assert_equal(random.integers(10, 10, size=0).shape, (0,))
          assert_equal(random.choice(0, size=0).shape, (0,))
          assert_equal(random.choice([], size=(0,)).shape, (0,))
          assert_equal(random.choice(['a', 'b'], size=(3, 0, 4)).shape,
                       (3, 0, 4))
          assert_raises(ValueError, random.choice, [], 10)
  
      def test_choice_nan_probabilities(self):
          a = np.array([42, 1, 2])
          p = [None, None, None]
          assert_raises(ValueError, random.choice, a, p=p)
  
      def test_choice_p_non_contiguous(self):
          p = np.ones(10) / 5
          p[1::2] = 3.0
          random = Generator(MT19937(self.seed))
          non_contig = random.choice(5, 3, p=p[::2])
          random = Generator(MT19937(self.seed))
          contig = random.choice(5, 3, p=np.ascontiguousarray(p[::2]))
          assert_array_equal(non_contig, contig)
  
      def test_choice_return_type(self):
          # gh 9867
          p = np.ones(4) / 4.
          actual = random.choice(4, 2)
          assert actual.dtype == np.int64
          actual = random.choice(4, 2, replace=False)
          assert actual.dtype == np.int64
          actual = random.choice(4, 2, p=p)
          assert actual.dtype == np.int64
          actual = random.choice(4, 2, p=p, replace=False)
          assert actual.dtype == np.int64
  
      def test_choice_large_sample(self):
          choice_hash = 'd44962a0b1e92f4a3373c23222244e21'
          random = Generator(MT19937(self.seed))
          actual = random.choice(10000, 5000, replace=False)
          if sys.byteorder != 'little':
              actual = actual.byteswap()
          res = hashlib.md5(actual.view(np.int8)).hexdigest()
          assert_(choice_hash == res)
  
      def test_bytes(self):
          random = Generator(MT19937(self.seed))
          actual = random.bytes(10)
          desired = b'\x86\xf0\xd4\x18\xe1\x81\t8%\xdd'
          assert_equal(actual, desired)
  
      def test_shuffle(self):
          # Test lists, arrays (of various dtypes), and multidimensional versions
          # of both, c-contiguous or not:
          for conv in [lambda x: np.array([]),
                       lambda x: x,
                       lambda x: np.asarray(x).astype(np.int8),
                       lambda x: np.asarray(x).astype(np.float32),
                       lambda x: np.asarray(x).astype(np.complex64),
                       lambda x: np.asarray(x).astype(object),
                       lambda x: [(i, i) for i in x],
                       lambda x: np.asarray([[i, i] for i in x]),
                       lambda x: np.vstack([x, x]).T,
                       # gh-11442
                       lambda x: (np.asarray([(i, i) for i in x],
                                             [("a", int), ("b", int)])
                                  .view(np.recarray)),
                       # gh-4270
                       lambda x: np.asarray([(i, i) for i in x],
                                            [("a", object, (1,)),
                                             ("b", np.int32, (1,))])]:
              random = Generator(MT19937(self.seed))
              alist = conv([1, 2, 3, 4, 5, 6, 7, 8, 9, 0])
              random.shuffle(alist)
              actual = alist
              desired = conv([4, 1, 9, 8, 0, 5, 3, 6, 2, 7])
              assert_array_equal(actual, desired)
  
      def test_shuffle_custom_axis(self):
          random = Generator(MT19937(self.seed))
          actual = np.arange(16).reshape((4, 4))
          random.shuffle(actual, axis=1)
          desired = np.array([[ 0,  3,  1,  2],
                              [ 4,  7,  5,  6],
                              [ 8, 11,  9, 10],
                              [12, 15, 13, 14]])
          assert_array_equal(actual, desired)
          random = Generator(MT19937(self.seed))
          actual = np.arange(16).reshape((4, 4))
          random.shuffle(actual, axis=-1)
          assert_array_equal(actual, desired)
  
      def test_shuffle_axis_nonsquare(self):
          y1 = np.arange(20).reshape(2, 10)
          y2 = y1.copy()
          random = Generator(MT19937(self.seed))
          random.shuffle(y1, axis=1)
          random = Generator(MT19937(self.seed))
          random.shuffle(y2.T)
          assert_array_equal(y1, y2)
  
      def test_shuffle_masked(self):
          # gh-3263
          a = np.ma.masked_values(np.reshape(range(20), (5, 4)) % 3 - 1, -1)
          b = np.ma.masked_values(np.arange(20) % 3 - 1, -1)
          a_orig = a.copy()
          b_orig = b.copy()
          for i in range(50):
              random.shuffle(a)
              assert_equal(
                  sorted(a.data[~a.mask]), sorted(a_orig.data[~a_orig.mask]))
              random.shuffle(b)
              assert_equal(
                  sorted(b.data[~b.mask]), sorted(b_orig.data[~b_orig.mask]))
  
      def test_shuffle_exceptions(self):
          random = Generator(MT19937(self.seed))
          arr = np.arange(10)
          assert_raises(np.AxisError, random.shuffle, arr, 1)
          arr = np.arange(9).reshape((3, 3))
          assert_raises(np.AxisError, random.shuffle, arr, 3)
          assert_raises(TypeError, random.shuffle, arr, slice(1, 2, None))
          arr = [[1, 2, 3], [4, 5, 6]]
          assert_raises(NotImplementedError, random.shuffle, arr, 1)
  
      def test_permutation(self):
          random = Generator(MT19937(self.seed))
          alist = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0]
          actual = random.permutation(alist)
          desired = [4, 1, 9, 8, 0, 5, 3, 6, 2, 7]
          assert_array_equal(actual, desired)
  
          random = Generator(MT19937(self.seed))
          arr_2d = np.atleast_2d([1, 2, 3, 4, 5, 6, 7, 8, 9, 0]).T
          actual = random.permutation(arr_2d)
          assert_array_equal(actual, np.atleast_2d(desired).T)
          
          bad_x_str = "abcd"
          assert_raises(np.AxisError, random.permutation, bad_x_str)
  
          bad_x_float = 1.2
          assert_raises(np.AxisError, random.permutation, bad_x_float)
  
          random = Generator(MT19937(self.seed))
          integer_val = 10
          desired = [3, 0, 8, 7, 9, 4, 2, 5, 1, 6]
  
          actual = random.permutation(integer_val)
          assert_array_equal(actual, desired)
  
      def test_permutation_custom_axis(self):
          a = np.arange(16).reshape((4, 4))
          desired = np.array([[ 0,  3,  1,  2],
                              [ 4,  7,  5,  6],
                              [ 8, 11,  9, 10],
                              [12, 15, 13, 14]])
          random = Generator(MT19937(self.seed))
          actual = random.permutation(a, axis=1)
          assert_array_equal(actual, desired)
          random = Generator(MT19937(self.seed))
          actual = random.permutation(a, axis=-1)
          assert_array_equal(actual, desired)
  
      def test_permutation_exceptions(self):
          random = Generator(MT19937(self.seed))
          arr = np.arange(10)
          assert_raises(np.AxisError, random.permutation, arr, 1)
          arr = np.arange(9).reshape((3, 3))
          assert_raises(np.AxisError, random.permutation, arr, 3)
          assert_raises(TypeError, random.permutation, arr, slice(1, 2, None))
  
      def test_beta(self):
          random = Generator(MT19937(self.seed))
          actual = random.beta(.1, .9, size=(3, 2))
          desired = np.array(
              [[1.083029353267698e-10, 2.449965303168024e-11],
               [2.397085162969853e-02, 3.590779671820755e-08],
               [2.830254190078299e-04, 1.744709918330393e-01]])
          assert_array_almost_equal(actual, desired, decimal=15)
  
      def test_binomial(self):
          random = Generator(MT19937(self.seed))
          actual = random.binomial(100.123, .456, size=(3, 2))
          desired = np.array([[42, 41],
                              [42, 48],
                              [44, 50]])
          assert_array_equal(actual, desired)
  
          random = Generator(MT19937(self.seed))
          actual = random.binomial(100.123, .456)
          desired = 42
          assert_array_equal(actual, desired)
  
      def test_chisquare(self):
          random = Generator(MT19937(self.seed))
          actual = random.chisquare(50, size=(3, 2))
          desired = np.array([[32.9850547060149, 39.0219480493301],
                              [56.2006134779419, 57.3474165711485],
                              [55.4243733880198, 55.4209797925213]])
          assert_array_almost_equal(actual, desired, decimal=13)
  
      def test_dirichlet(self):
          random = Generator(MT19937(self.seed))
          alpha = np.array([51.72840233779265162, 39.74494232180943953])
          actual = random.dirichlet(alpha, size=(3, 2))
          desired = np.array([[[0.5439892869558927,  0.45601071304410745],
                               [0.5588917345860708,  0.4411082654139292 ]],
                              [[0.5632074165063435,  0.43679258349365657],
                               [0.54862581112627,    0.45137418887373015]],
                              [[0.49961831357047226, 0.5003816864295278 ],
                               [0.52374806183482,    0.47625193816517997]]])
          assert_array_almost_equal(actual, desired, decimal=15)
          bad_alpha = np.array([5.4e-01, -1.0e-16])
          assert_raises(ValueError, random.dirichlet, bad_alpha)
  
          random = Generator(MT19937(self.seed))
          alpha = np.array([51.72840233779265162, 39.74494232180943953])
          actual = random.dirichlet(alpha)
          assert_array_almost_equal(actual, desired[0, 0], decimal=15)
  
      def test_dirichlet_size(self):
          # gh-3173
          p = np.array([51.72840233779265162, 39.74494232180943953])
          assert_equal(random.dirichlet(p, np.uint32(1)).shape, (1, 2))
          assert_equal(random.dirichlet(p, np.uint32(1)).shape, (1, 2))
          assert_equal(random.dirichlet(p, np.uint32(1)).shape, (1, 2))
          assert_equal(random.dirichlet(p, [2, 2]).shape, (2, 2, 2))
          assert_equal(random.dirichlet(p, (2, 2)).shape, (2, 2, 2))
          assert_equal(random.dirichlet(p, np.array((2, 2))).shape, (2, 2, 2))
  
          assert_raises(TypeError, random.dirichlet, p, float(1))
  
      def test_dirichlet_bad_alpha(self):
          # gh-2089
          alpha = np.array([5.4e-01, -1.0e-16])
          assert_raises(ValueError, random.dirichlet, alpha)
  
          # gh-15876
          assert_raises(ValueError, random.dirichlet, [[5, 1]])
          assert_raises(ValueError, random.dirichlet, [[5], [1]])
          assert_raises(ValueError, random.dirichlet, [[[5], [1]], [[1], [5]]])
          assert_raises(ValueError, random.dirichlet, np.array([[5, 1], [1, 5]]))
  
      def test_dirichlet_alpha_non_contiguous(self):
          a = np.array([51.72840233779265162, -1.0, 39.74494232180943953])
          alpha = a[::2]
          random = Generator(MT19937(self.seed))
          non_contig = random.dirichlet(alpha, size=(3, 2))
          random = Generator(MT19937(self.seed))
          contig = random.dirichlet(np.ascontiguousarray(alpha),
                                    size=(3, 2))
          assert_array_almost_equal(non_contig, contig)
  
      def test_dirichlet_small_alpha(self):
          eps = 1.0e-9  # 1.0e-10 -> runtime x 10; 1e-11 -> runtime x 200, etc.
          alpha = eps * np.array([1., 1.0e-3])
          random = Generator(MT19937(self.seed))
          actual = random.dirichlet(alpha, size=(3, 2))
          expected = np.array([
              [[1., 0.],
               [1., 0.]],
              [[1., 0.],
               [1., 0.]],
              [[1., 0.],
               [1., 0.]]
          ])
          assert_array_almost_equal(actual, expected, decimal=15)
  
      @pytest.mark.slow
      def test_dirichlet_moderately_small_alpha(self):
          # Use alpha.max() < 0.1 to trigger stick breaking code path
          alpha = np.array([0.02, 0.04, 0.03])
          exact_mean = alpha / alpha.sum()
          random = Generator(MT19937(self.seed))
          sample = random.dirichlet(alpha, size=20000000)
          sample_mean = sample.mean(axis=0)
          assert_allclose(sample_mean, exact_mean, rtol=1e-3)
  
      def test_exponential(self):
          random = Generator(MT19937(self.seed))
          actual = random.exponential(1.1234, size=(3, 2))
          desired = np.array([[0.098845481066258, 1.560752510746964],
                              [0.075730916041636, 1.769098974710777],
                              [1.488602544592235, 2.49684815275751 ]])
          assert_array_almost_equal(actual, desired, decimal=15)
  
      def test_exponential_0(self):
          assert_equal(random.exponential(scale=0), 0)
          assert_raises(ValueError, random.exponential, scale=-0.)
  
      def test_f(self):
          random = Generator(MT19937(self.seed))
          actual = random.f(12, 77, size=(3, 2))
          desired = np.array([[0.461720027077085, 1.100441958872451],
                              [1.100337455217484, 0.91421736740018 ],
                              [0.500811891303113, 0.826802454552058]])
          assert_array_almost_equal(actual, desired, decimal=15)
  
      def test_gamma(self):
          random = Generator(MT19937(self.seed))
          actual = random.gamma(5, 3, size=(3, 2))
          desired = np.array([[ 5.03850858902096,  7.9228656732049 ],
                              [18.73983605132985, 19.57961681699238],
                              [18.17897755150825, 18.17653912505234]])
          assert_array_almost_equal(actual, desired, decimal=14)
  
      def test_gamma_0(self):
          assert_equal(random.gamma(shape=0, scale=0), 0)
          assert_raises(ValueError, random.gamma, shape=-0., scale=-0.)
  
      def test_geometric(self):
          random = Generator(MT19937(self.seed))
          actual = random.geometric(.123456789, size=(3, 2))
          desired = np.array([[ 1, 10],
                              [ 1, 12],
                              [ 9, 10]])
          assert_array_equal(actual, desired)
  
      def test_geometric_exceptions(self):
          assert_raises(ValueError, random.geometric, 1.1)
          assert_raises(ValueError, random.geometric, [1.1] * 10)
          assert_raises(ValueError, random.geometric, -0.1)
          assert_raises(ValueError, random.geometric, [-0.1] * 10)
          with np.errstate(invalid='ignore'):
              assert_raises(ValueError, random.geometric, np.nan)
              assert_raises(ValueError, random.geometric, [np.nan] * 10)
  
      def test_gumbel(self):
          random = Generator(MT19937(self.seed))
          actual = random.gumbel(loc=.123456789, scale=2.0, size=(3, 2))
          desired = np.array([[ 4.688397515056245, -0.289514845417841],
                              [ 4.981176042584683, -0.633224272589149],
                              [-0.055915275687488, -0.333962478257953]])
          assert_array_almost_equal(actual, desired, decimal=15)
  
      def test_gumbel_0(self):
          assert_equal(random.gumbel(scale=0), 0)
          assert_raises(ValueError, random.gumbel, scale=-0.)
  
      def test_hypergeometric(self):
          random = Generator(MT19937(self.seed))
          actual = random.hypergeometric(10.1, 5.5, 14, size=(3, 2))
          desired = np.array([[ 9, 9],
                              [ 9, 9],
                              [10, 9]])
          assert_array_equal(actual, desired)
  
          # Test nbad = 0
          actual = random.hypergeometric(5, 0, 3, size=4)
          desired = np.array([3, 3, 3, 3])
          assert_array_equal(actual, desired)
  
          actual = random.hypergeometric(15, 0, 12, size=4)
          desired = np.array([12, 12, 12, 12])
          assert_array_equal(actual, desired)
  
          # Test ngood = 0
          actual = random.hypergeometric(0, 5, 3, size=4)
          desired = np.array([0, 0, 0, 0])
          assert_array_equal(actual, desired)
  
          actual = random.hypergeometric(0, 15, 12, size=4)
          desired = np.array([0, 0, 0, 0])
          assert_array_equal(actual, desired)
  
      def test_laplace(self):
          random = Generator(MT19937(self.seed))
          actual = random.laplace(loc=.123456789, scale=2.0, size=(3, 2))
          desired = np.array([[-3.156353949272393,  1.195863024830054],
                              [-3.435458081645966,  1.656882398925444],
                              [ 0.924824032467446,  1.251116432209336]])
          assert_array_almost_equal(actual, desired, decimal=15)
  
      def test_laplace_0(self):
          assert_equal(random.laplace(scale=0), 0)
          assert_raises(ValueError, random.laplace, scale=-0.)
  
      def test_logistic(self):
          random = Generator(MT19937(self.seed))
          actual = random.logistic(loc=.123456789, scale=2.0, size=(3, 2))
          desired = np.array([[-4.338584631510999,  1.890171436749954],
                              [-4.64547787337966 ,  2.514545562919217],
                              [ 1.495389489198666,  1.967827627577474]])
          assert_array_almost_equal(actual, desired, decimal=15)
  
      def test_lognormal(self):
          random = Generator(MT19937(self.seed))
          actual = random.lognormal(mean=.123456789, sigma=2.0, size=(3, 2))
          desired = np.array([[ 0.0268252166335, 13.9534486483053],
                              [ 0.1204014788936,  2.2422077497792],
                              [ 4.2484199496128, 12.0093343977523]])
          assert_array_almost_equal(actual, desired, decimal=13)
  
      def test_lognormal_0(self):
          assert_equal(random.lognormal(sigma=0), 1)
          assert_raises(ValueError, random.lognormal, sigma=-0.)
  
      def test_logseries(self):
          random = Generator(MT19937(self.seed))
          actual = random.logseries(p=.923456789, size=(3, 2))
          desired = np.array([[14, 17],
                              [3, 18],
                              [5, 1]])
          assert_array_equal(actual, desired)
  
      def test_logseries_exceptions(self):
          with np.errstate(invalid='ignore'):
              assert_raises(ValueError, random.logseries, np.nan)
              assert_raises(ValueError, random.logseries, [np.nan] * 10)
  
      def test_multinomial(self):
          random = Generator(MT19937(self.seed))
          actual = random.multinomial(20, [1 / 6.] * 6, size=(3, 2))
          desired = np.array([[[1, 5, 1, 6, 4, 3],
                               [4, 2, 6, 2, 4, 2]],
                              [[5, 3, 2, 6, 3, 1],
                               [4, 4, 0, 2, 3, 7]],
                              [[6, 3, 1, 5, 3, 2],
                               [5, 5, 3, 1, 2, 4]]])
          assert_array_equal(actual, desired)
  
      @pytest.mark.parametrize("method", ["svd", "eigh", "cholesky"])
      def test_multivariate_normal(self, method):
          random = Generator(MT19937(self.seed))
          mean = (.123456789, 10)
          cov = [[1, 0], [0, 1]]
          size = (3, 2)
          actual = random.multivariate_normal(mean, cov, size, method=method)
          desired = np.array([[[-1.747478062846581,  11.25613495182354  ],
                               [-0.9967333370066214, 10.342002097029821 ]],
                              [[ 0.7850019631242964, 11.181113712443013 ],
                               [ 0.8901349653255224,  8.873825399642492 ]],
                              [[ 0.7130260107430003,  9.551628690083056 ],
                               [ 0.7127098726541128, 11.991709234143173 ]]])
  
          assert_array_almost_equal(actual, desired, decimal=15)
  
          # Check for default size, was raising deprecation warning
          actual = random.multivariate_normal(mean, cov, method=method)
          desired = np.array([0.233278563284287, 9.424140804347195])
          assert_array_almost_equal(actual, desired, decimal=15)
          # Check that non symmetric covariance input raises exception when
          # check_valid='raises' if using default svd method.
          mean = [0, 0]
          cov = [[1, 2], [1, 2]]
          assert_raises(ValueError, random.multivariate_normal, mean, cov,
                        check_valid='raise')
  
          # Check that non positive-semidefinite covariance warns with
          # RuntimeWarning
          cov = [[1, 2], [2, 1]]
          assert_warns(RuntimeWarning, random.multivariate_normal, mean, cov)
          assert_warns(RuntimeWarning, random.multivariate_normal, mean, cov,
                       method='eigh')
          assert_raises(LinAlgError, random.multivariate_normal, mean, cov,
                        method='cholesky')
  
          # and that it doesn't warn with RuntimeWarning check_valid='ignore'
          assert_no_warnings(random.multivariate_normal, mean, cov,
                             check_valid='ignore')
  
          # and that it raises with RuntimeWarning check_valid='raises'
          assert_raises(ValueError, random.multivariate_normal, mean, cov,
                        check_valid='raise')
          assert_raises(ValueError, random.multivariate_normal, mean, cov,
                        check_valid='raise', method='eigh')
  
          # check degenerate samples from singular covariance matrix
          cov = [[1, 1], [1, 1]]
          if method in ('svd', 'eigh'):
              samples = random.multivariate_normal(mean, cov, size=(3, 2),
                                                   method=method)
              assert_array_almost_equal(samples[..., 0], samples[..., 1],
                                        decimal=6)
          else:
              assert_raises(LinAlgError, random.multivariate_normal, mean, cov,
                            method='cholesky')
  
          cov = np.array([[1, 0.1], [0.1, 1]], dtype=np.float32)
          with suppress_warnings() as sup:
              random.multivariate_normal(mean, cov, method=method)
              w = sup.record(RuntimeWarning)
              assert len(w) == 0
  
          mu = np.zeros(2)
          cov = np.eye(2)
          assert_raises(ValueError, random.multivariate_normal, mean, cov,
                        check_valid='other')
          assert_raises(ValueError, random.multivariate_normal,
                        np.zeros((2, 1, 1)), cov)
          assert_raises(ValueError, random.multivariate_normal,
                        mu, np.empty((3, 2)))
          assert_raises(ValueError, random.multivariate_normal,
                        mu, np.eye(3))
  
      @pytest.mark.parametrize("method", ["svd", "eigh", "cholesky"])
      def test_multivariate_normal_basic_stats(self, method):
          random = Generator(MT19937(self.seed))
          n_s = 1000
          mean = np.array([1, 2])
          cov = np.array([[2, 1], [1, 2]])
          s = random.multivariate_normal(mean, cov, size=(n_s,), method=method)
          s_center = s - mean
          cov_emp = (s_center.T @ s_center) / (n_s - 1)
          # these are pretty loose and are only designed to detect major errors
          assert np.all(np.abs(s_center.mean(-2)) < 0.1)
          assert np.all(np.abs(cov_emp - cov) < 0.2)
  
      def test_negative_binomial(self):
          random = Generator(MT19937(self.seed))
          actual = random.negative_binomial(n=100, p=.12345, size=(3, 2))
          desired = np.array([[543, 727],
                              [775, 760],
                              [600, 674]])
          assert_array_equal(actual, desired)
  
      def test_negative_binomial_exceptions(self):
          with np.errstate(invalid='ignore'):
              assert_raises(ValueError, random.negative_binomial, 100, np.nan)
              assert_raises(ValueError, random.negative_binomial, 100,
                            [np.nan] * 10)
  
      def test_negative_binomial_p0_exception(self):
          # Verify that p=0 raises an exception.
          with assert_raises(ValueError):
              x = random.negative_binomial(1, 0)
  
      def test_noncentral_chisquare(self):
          random = Generator(MT19937(self.seed))
          actual = random.noncentral_chisquare(df=5, nonc=5, size=(3, 2))
          desired = np.array([[ 1.70561552362133, 15.97378184942111],
                              [13.71483425173724, 20.17859633310629],
                              [11.3615477156643 ,  3.67891108738029]])
          assert_array_almost_equal(actual, desired, decimal=14)
  
          actual = random.noncentral_chisquare(df=.5, nonc=.2, size=(3, 2))
          desired = np.array([[9.41427665607629e-04, 1.70473157518850e-04],
                              [1.14554372041263e+00, 1.38187755933435e-03],
                              [1.90659181905387e+00, 1.21772577941822e+00]])
          assert_array_almost_equal(actual, desired, decimal=14)
  
          random = Generator(MT19937(self.seed))
          actual = random.noncentral_chisquare(df=5, nonc=0, size=(3, 2))
          desired = np.array([[0.82947954590419, 1.80139670767078],
                              [6.58720057417794, 7.00491463609814],
                              [6.31101879073157, 6.30982307753005]])
          assert_array_almost_equal(actual, desired, decimal=14)
  
      def test_noncentral_f(self):
          random = Generator(MT19937(self.seed))
          actual = random.noncentral_f(dfnum=5, dfden=2, nonc=1,
                                       size=(3, 2))
          desired = np.array([[0.060310671139  , 0.23866058175939],
                              [0.86860246709073, 0.2668510459738 ],
                              [0.23375780078364, 1.88922102885943]])
          assert_array_almost_equal(actual, desired, decimal=14)
  
      def test_noncentral_f_nan(self):
          random = Generator(MT19937(self.seed))
          actual = random.noncentral_f(dfnum=5, dfden=2, nonc=np.nan)
          assert np.isnan(actual)
  
      def test_normal(self):
          random = Generator(MT19937(self.seed))
          actual = random.normal(loc=.123456789, scale=2.0, size=(3, 2))
          desired = np.array([[-3.618412914693162,  2.635726692647081],
                              [-2.116923463013243,  0.807460983059643],
                              [ 1.446547137248593,  2.485684213886024]])
          assert_array_almost_equal(actual, desired, decimal=15)
  
      def test_normal_0(self):
          assert_equal(random.normal(scale=0), 0)
          assert_raises(ValueError, random.normal, scale=-0.)
  
      def test_pareto(self):
          random = Generator(MT19937(self.seed))
          actual = random.pareto(a=.123456789, size=(3, 2))
          desired = np.array([[1.0394926776069018e+00, 7.7142534343505773e+04],
                              [7.2640150889064703e-01, 3.4650454783825594e+05],
                              [4.5852344481994740e+04, 6.5851383009539105e+07]])
          # For some reason on 32-bit x86 Ubuntu 12.10 the [1, 0] entry in this
          # matrix differs by 24 nulps. Discussion:
          #   https://mail.python.org/pipermail/numpy-discussion/2012-September/063801.html
          # Consensus is that this is probably some gcc quirk that affects
          # rounding but not in any important way, so we just use a looser
          # tolerance on this test:
          np.testing.assert_array_almost_equal_nulp(actual, desired, nulp=30)
  
      def test_poisson(self):
          random = Generator(MT19937(self.seed))
          actual = random.poisson(lam=.123456789, size=(3, 2))
          desired = np.array([[0, 0],
                              [0, 0],
                              [0, 0]])
          assert_array_equal(actual, desired)
  
      def test_poisson_exceptions(self):
          lambig = np.iinfo('int64').max
          lamneg = -1
          assert_raises(ValueError, random.poisson, lamneg)
          assert_raises(ValueError, random.poisson, [lamneg] * 10)
          assert_raises(ValueError, random.poisson, lambig)
          assert_raises(ValueError, random.poisson, [lambig] * 10)
          with np.errstate(invalid='ignore'):
              assert_raises(ValueError, random.poisson, np.nan)
              assert_raises(ValueError, random.poisson, [np.nan] * 10)
  
      def test_power(self):
          random = Generator(MT19937(self.seed))
          actual = random.power(a=.123456789, size=(3, 2))
          desired = np.array([[1.977857368842754e-09, 9.806792196620341e-02],
                              [2.482442984543471e-10, 1.527108843266079e-01],
                              [8.188283434244285e-02, 3.950547209346948e-01]])
          assert_array_almost_equal(actual, desired, decimal=15)
  
      def test_rayleigh(self):
          random = Generator(MT19937(self.seed))
          actual = random.rayleigh(scale=10, size=(3, 2))
          desired = np.array([[ 4.51734079831581, 15.6802442485758 ],
                              [ 4.19850651287094, 17.08718809823704],
                              [14.7907457708776 , 15.85545333419775]])
          assert_array_almost_equal(actual, desired, decimal=14)
  
      def test_rayleigh_0(self):
          assert_equal(random.rayleigh(scale=0), 0)
          assert_raises(ValueError, random.rayleigh, scale=-0.)
  
      def test_standard_cauchy(self):
          random = Generator(MT19937(self.seed))
          actual = random.standard_cauchy(size=(3, 2))
          desired = np.array([[-1.489437778266206, -3.275389641569784],
                              [ 0.560102864910406, -0.680780916282552],
                              [-1.314912905226277,  0.295852965660225]])
          assert_array_almost_equal(actual, desired, decimal=15)
  
      def test_standard_exponential(self):
          random = Generator(MT19937(self.seed))
          actual = random.standard_exponential(size=(3, 2), method='inv')
          desired = np.array([[0.102031839440643, 1.229350298474972],
                              [0.088137284693098, 1.459859985522667],
                              [1.093830802293668, 1.256977002164613]])
          assert_array_almost_equal(actual, desired, decimal=15)
  
      def test_standard_expoential_type_error(self):
          assert_raises(TypeError, random.standard_exponential, dtype=np.int32)
  
      def test_standard_gamma(self):
          random = Generator(MT19937(self.seed))
          actual = random.standard_gamma(shape=3, size=(3, 2))
          desired = np.array([[0.62970724056362, 1.22379851271008],
                              [3.899412530884  , 4.12479964250139],
                              [3.74994102464584, 3.74929307690815]])
          assert_array_almost_equal(actual, desired, decimal=14)
  
      def test_standard_gammma_scalar_float(self):
          random = Generator(MT19937(self.seed))
          actual = random.standard_gamma(3, dtype=np.float32)
          desired = 2.9242148399353027
          assert_array_almost_equal(actual, desired, decimal=6)
  
      def test_standard_gamma_float(self):
          random = Generator(MT19937(self.seed))
          actual = random.standard_gamma(shape=3, size=(3, 2))
          desired = np.array([[0.62971, 1.2238 ],
                              [3.89941, 4.1248 ],
                              [3.74994, 3.74929]])
          assert_array_almost_equal(actual, desired, decimal=5)
  
      def test_standard_gammma_float_out(self):
          actual = np.zeros((3, 2), dtype=np.float32)
          random = Generator(MT19937(self.seed))
          random.standard_gamma(10.0, out=actual, dtype=np.float32)
          desired = np.array([[10.14987,  7.87012],
                               [ 9.46284, 12.56832],
                               [13.82495,  7.81533]], dtype=np.float32)
          assert_array_almost_equal(actual, desired, decimal=5)
  
          random = Generator(MT19937(self.seed))
          random.standard_gamma(10.0, out=actual, size=(3, 2), dtype=np.float32)
          assert_array_almost_equal(actual, desired, decimal=5)
  
      def test_standard_gamma_unknown_type(self):
          assert_raises(TypeError, random.standard_gamma, 1.,
                        dtype='int32')
  
      def test_out_size_mismatch(self):
          out = np.zeros(10)
          assert_raises(ValueError, random.standard_gamma, 10.0, size=20,
                        out=out)
          assert_raises(ValueError, random.standard_gamma, 10.0, size=(10, 1),
                        out=out)
  
      def test_standard_gamma_0(self):
          assert_equal(random.standard_gamma(shape=0), 0)
          assert_raises(ValueError, random.standard_gamma, shape=-0.)
  
      def test_standard_normal(self):
          random = Generator(MT19937(self.seed))
          actual = random.standard_normal(size=(3, 2))
          desired = np.array([[-1.870934851846581,  1.25613495182354 ],
                              [-1.120190126006621,  0.342002097029821],
                              [ 0.661545174124296,  1.181113712443012]])
          assert_array_almost_equal(actual, desired, decimal=15)
  
      def test_standard_normal_unsupported_type(self):
          assert_raises(TypeError, random.standard_normal, dtype=np.int32)
  
      def test_standard_t(self):
          random = Generator(MT19937(self.seed))
          actual = random.standard_t(df=10, size=(3, 2))
          desired = np.array([[-1.484666193042647,  0.30597891831161 ],
                              [ 1.056684299648085, -0.407312602088507],
                              [ 0.130704414281157, -2.038053410490321]])
          assert_array_almost_equal(actual, desired, decimal=15)
  
      def test_triangular(self):
          random = Generator(MT19937(self.seed))
          actual = random.triangular(left=5.12, mode=10.23, right=20.34,
                                     size=(3, 2))
          desired = np.array([[ 7.86664070590917, 13.6313848513185 ],
                              [ 7.68152445215983, 14.36169131136546],
                              [13.16105603911429, 13.72341621856971]])
          assert_array_almost_equal(actual, desired, decimal=14)
  
      def test_uniform(self):
          random = Generator(MT19937(self.seed))
          actual = random.uniform(low=1.23, high=10.54, size=(3, 2))
          desired = np.array([[2.13306255040998 , 7.816987531021207],
                              [2.015436610109887, 8.377577533009589],
                              [7.421792588856135, 7.891185744455209]])
          assert_array_almost_equal(actual, desired, decimal=15)
  
      def test_uniform_range_bounds(self):
          fmin = np.finfo('float').min
          fmax = np.finfo('float').max
  
          func = random.uniform
          assert_raises(OverflowError, func, -np.inf, 0)
          assert_raises(OverflowError, func, 0, np.inf)
          assert_raises(OverflowError, func, fmin, fmax)
          assert_raises(OverflowError, func, [-np.inf], [0])
          assert_raises(OverflowError, func, [0], [np.inf])
  
          # (fmax / 1e17) - fmin is within range, so this should not throw
          # account for i386 extended precision DBL_MAX / 1e17 + DBL_MAX >
          # DBL_MAX by increasing fmin a bit
          random.uniform(low=np.nextafter(fmin, 1), high=fmax / 1e17)
  
      def test_scalar_exception_propagation(self):
          # Tests that exceptions are correctly propagated in distributions
          # when called with objects that throw exceptions when converted to
          # scalars.
          #
          # Regression test for gh: 8865
  
          class ThrowingFloat(np.ndarray):
              def __float__(self):
                  raise TypeError
  
          throwing_float = np.array(1.0).view(ThrowingFloat)
          assert_raises(TypeError, random.uniform, throwing_float,
                        throwing_float)
  
          class ThrowingInteger(np.ndarray):
              def __int__(self):
                  raise TypeError
  
          throwing_int = np.array(1).view(ThrowingInteger)
          assert_raises(TypeError, random.hypergeometric, throwing_int, 1, 1)
  
      def test_vonmises(self):
          random = Generator(MT19937(self.seed))
          actual = random.vonmises(mu=1.23, kappa=1.54, size=(3, 2))
          desired = np.array([[ 1.107972248690106,  2.841536476232361],
                              [ 1.832602376042457,  1.945511926976032],
                              [-0.260147475776542,  2.058047492231698]])
          assert_array_almost_equal(actual, desired, decimal=15)
  
      def test_vonmises_small(self):
          # check infinite loop, gh-4720
          random = Generator(MT19937(self.seed))
          r = random.vonmises(mu=0., kappa=1.1e-8, size=10**6)
          assert_(np.isfinite(r).all())
  
      def test_vonmises_nan(self):
          random = Generator(MT19937(self.seed))
          r = random.vonmises(mu=0., kappa=np.nan)
          assert_(np.isnan(r))
  
      def test_wald(self):
          random = Generator(MT19937(self.seed))
          actual = random.wald(mean=1.23, scale=1.54, size=(3, 2))
          desired = np.array([[0.26871721804551, 3.2233942732115 ],
                              [2.20328374987066, 2.40958405189353],
                              [2.07093587449261, 0.73073890064369]])
          assert_array_almost_equal(actual, desired, decimal=14)
  
      def test_weibull(self):
          random = Generator(MT19937(self.seed))
          actual = random.weibull(a=1.23, size=(3, 2))
          desired = np.array([[0.138613914769468, 1.306463419753191],
                              [0.111623365934763, 1.446570494646721],
                              [1.257145775276011, 1.914247725027957]])
          assert_array_almost_equal(actual, desired, decimal=15)
  
      def test_weibull_0(self):
          random = Generator(MT19937(self.seed))
          assert_equal(random.weibull(a=0, size=12), np.zeros(12))
          assert_raises(ValueError, random.weibull, a=-0.)
  
      def test_zipf(self):
          random = Generator(MT19937(self.seed))
          actual = random.zipf(a=1.23, size=(3, 2))
          desired = np.array([[  1,   1],
                              [ 10, 867],
                              [354,   2]])
          assert_array_equal(actual, desired)
  
  
  class TestBroadcast:
      # tests that functions that broadcast behave
      # correctly when presented with non-scalar arguments
      def setup(self):
          self.seed = 123456789
  
  
      def test_uniform(self):
          random = Generator(MT19937(self.seed))
          low = [0]
          high = [1]
          uniform = random.uniform
          desired = np.array([0.16693771389729, 0.19635129550675, 0.75563050964095])
  
          random = Generator(MT19937(self.seed))
          actual = random.uniform(low * 3, high)
          assert_array_almost_equal(actual, desired, decimal=14)
  
          random = Generator(MT19937(self.seed))
          actual = random.uniform(low, high * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
  
      def test_normal(self):
          loc = [0]
          scale = [1]
          bad_scale = [-1]
          random = Generator(MT19937(self.seed))
          desired = np.array([-0.38736406738527,  0.79594375042255,  0.0197076236097])
  
          random = Generator(MT19937(self.seed))
          actual = random.normal(loc * 3, scale)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, random.normal, loc * 3, bad_scale)
  
          random = Generator(MT19937(self.seed))
          normal = random.normal
          actual = normal(loc, scale * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, normal, loc, bad_scale * 3)
  
      def test_beta(self):
          a = [1]
          b = [2]
          bad_a = [-1]
          bad_b = [-2]
          desired = np.array([0.18719338682602, 0.73234824491364, 0.17928615186455])
  
          random = Generator(MT19937(self.seed))
          beta = random.beta
          actual = beta(a * 3, b)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, beta, bad_a * 3, b)
          assert_raises(ValueError, beta, a * 3, bad_b)
  
          random = Generator(MT19937(self.seed))
          actual = random.beta(a, b * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
  
      def test_exponential(self):
          scale = [1]
          bad_scale = [-1]
          desired = np.array([0.67245993212806, 0.21380495318094, 0.7177848928629])
  
          random = Generator(MT19937(self.seed))
          actual = random.exponential(scale * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, random.exponential, bad_scale * 3)
  
      def test_standard_gamma(self):
          shape = [1]
          bad_shape = [-1]
          desired = np.array([0.67245993212806, 0.21380495318094, 0.7177848928629])
  
          random = Generator(MT19937(self.seed))
          std_gamma = random.standard_gamma
          actual = std_gamma(shape * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, std_gamma, bad_shape * 3)
  
      def test_gamma(self):
          shape = [1]
          scale = [2]
          bad_shape = [-1]
          bad_scale = [-2]
          desired = np.array([1.34491986425611, 0.42760990636187, 1.4355697857258])
  
          random = Generator(MT19937(self.seed))
          gamma = random.gamma
          actual = gamma(shape * 3, scale)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, gamma, bad_shape * 3, scale)
          assert_raises(ValueError, gamma, shape * 3, bad_scale)
  
          random = Generator(MT19937(self.seed))
          gamma = random.gamma
          actual = gamma(shape, scale * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, gamma, bad_shape, scale * 3)
          assert_raises(ValueError, gamma, shape, bad_scale * 3)
  
      def test_f(self):
          dfnum = [1]
          dfden = [2]
          bad_dfnum = [-1]
          bad_dfden = [-2]
          desired = np.array([0.07765056244107, 7.72951397913186, 0.05786093891763])
  
          random = Generator(MT19937(self.seed))
          f = random.f
          actual = f(dfnum * 3, dfden)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, f, bad_dfnum * 3, dfden)
          assert_raises(ValueError, f, dfnum * 3, bad_dfden)
  
          random = Generator(MT19937(self.seed))
          f = random.f
          actual = f(dfnum, dfden * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, f, bad_dfnum, dfden * 3)
          assert_raises(ValueError, f, dfnum, bad_dfden * 3)
  
      def test_noncentral_f(self):
          dfnum = [2]
          dfden = [3]
          nonc = [4]
          bad_dfnum = [0]
          bad_dfden = [-1]
          bad_nonc = [-2]
          desired = np.array([2.02434240411421, 12.91838601070124, 1.24395160354629])
  
          random = Generator(MT19937(self.seed))
          nonc_f = random.noncentral_f
          actual = nonc_f(dfnum * 3, dfden, nonc)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert np.all(np.isnan(nonc_f(dfnum, dfden, [np.nan] * 3)))
  
          assert_raises(ValueError, nonc_f, bad_dfnum * 3, dfden, nonc)
          assert_raises(ValueError, nonc_f, dfnum * 3, bad_dfden, nonc)
          assert_raises(ValueError, nonc_f, dfnum * 3, dfden, bad_nonc)
  
          random = Generator(MT19937(self.seed))
          nonc_f = random.noncentral_f
          actual = nonc_f(dfnum, dfden * 3, nonc)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, nonc_f, bad_dfnum, dfden * 3, nonc)
          assert_raises(ValueError, nonc_f, dfnum, bad_dfden * 3, nonc)
          assert_raises(ValueError, nonc_f, dfnum, dfden * 3, bad_nonc)
  
          random = Generator(MT19937(self.seed))
          nonc_f = random.noncentral_f
          actual = nonc_f(dfnum, dfden, nonc * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, nonc_f, bad_dfnum, dfden, nonc * 3)
          assert_raises(ValueError, nonc_f, dfnum, bad_dfden, nonc * 3)
          assert_raises(ValueError, nonc_f, dfnum, dfden, bad_nonc * 3)
  
      def test_noncentral_f_small_df(self):
          random = Generator(MT19937(self.seed))
          desired = np.array([0.04714867120827, 0.1239390327694])
          actual = random.noncentral_f(0.9, 0.9, 2, size=2)
          assert_array_almost_equal(actual, desired, decimal=14)
  
      def test_chisquare(self):
          df = [1]
          bad_df = [-1]
          desired = np.array([0.05573640064251, 1.47220224353539, 2.9469379318589])
  
          random = Generator(MT19937(self.seed))
          actual = random.chisquare(df * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, random.chisquare, bad_df * 3)
  
      def test_noncentral_chisquare(self):
          df = [1]
          nonc = [2]
          bad_df = [-1]
          bad_nonc = [-2]
          desired = np.array([0.07710766249436, 5.27829115110304, 0.630732147399])
  
          random = Generator(MT19937(self.seed))
          nonc_chi = random.noncentral_chisquare
          actual = nonc_chi(df * 3, nonc)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, nonc_chi, bad_df * 3, nonc)
          assert_raises(ValueError, nonc_chi, df * 3, bad_nonc)
  
          random = Generator(MT19937(self.seed))
          nonc_chi = random.noncentral_chisquare
          actual = nonc_chi(df, nonc * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, nonc_chi, bad_df, nonc * 3)
          assert_raises(ValueError, nonc_chi, df, bad_nonc * 3)
  
      def test_standard_t(self):
          df = [1]
          bad_df = [-1]
          desired = np.array([-1.39498829447098, -1.23058658835223, 0.17207021065983])
  
          random = Generator(MT19937(self.seed))
          actual = random.standard_t(df * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, random.standard_t, bad_df * 3)
  
      def test_vonmises(self):
          mu = [2]
          kappa = [1]
          bad_kappa = [-1]
          desired = np.array([2.25935584988528, 2.23326261461399, -2.84152146503326])
  
          random = Generator(MT19937(self.seed))
          actual = random.vonmises(mu * 3, kappa)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, random.vonmises, mu * 3, bad_kappa)
  
          random = Generator(MT19937(self.seed))
          actual = random.vonmises(mu, kappa * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, random.vonmises, mu, bad_kappa * 3)
  
      def test_pareto(self):
          a = [1]
          bad_a = [-1]
          desired = np.array([0.95905052946317, 0.2383810889437 , 1.04988745750013])
  
          random = Generator(MT19937(self.seed))
          actual = random.pareto(a * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, random.pareto, bad_a * 3)
  
      def test_weibull(self):
          a = [1]
          bad_a = [-1]
          desired = np.array([0.67245993212806, 0.21380495318094, 0.7177848928629])
  
          random = Generator(MT19937(self.seed))
          actual = random.weibull(a * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, random.weibull, bad_a * 3)
  
      def test_power(self):
          a = [1]
          bad_a = [-1]
          desired = np.array([0.48954864361052, 0.19249412888486, 0.51216834058807])
  
          random = Generator(MT19937(self.seed))
          actual = random.power(a * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, random.power, bad_a * 3)
  
      def test_laplace(self):
          loc = [0]
          scale = [1]
          bad_scale = [-1]
          desired = np.array([-1.09698732625119, -0.93470271947368, 0.71592671378202])
  
          random = Generator(MT19937(self.seed))
          laplace = random.laplace
          actual = laplace(loc * 3, scale)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, laplace, loc * 3, bad_scale)
  
          random = Generator(MT19937(self.seed))
          laplace = random.laplace
          actual = laplace(loc, scale * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, laplace, loc, bad_scale * 3)
  
      def test_gumbel(self):
          loc = [0]
          scale = [1]
          bad_scale = [-1]
          desired = np.array([1.70020068231762, 1.52054354273631, -0.34293267607081])
  
          random = Generator(MT19937(self.seed))
          gumbel = random.gumbel
          actual = gumbel(loc * 3, scale)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, gumbel, loc * 3, bad_scale)
  
          random = Generator(MT19937(self.seed))
          gumbel = random.gumbel
          actual = gumbel(loc, scale * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, gumbel, loc, bad_scale * 3)
  
      def test_logistic(self):
          loc = [0]
          scale = [1]
          bad_scale = [-1]
          desired = np.array([-1.607487640433, -1.40925686003678, 1.12887112820397])
  
          random = Generator(MT19937(self.seed))
          actual = random.logistic(loc * 3, scale)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, random.logistic, loc * 3, bad_scale)
  
          random = Generator(MT19937(self.seed))
          actual = random.logistic(loc, scale * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, random.logistic, loc, bad_scale * 3)
          assert_equal(random.logistic(1.0, 0.0), 1.0)
  
      def test_lognormal(self):
          mean = [0]
          sigma = [1]
          bad_sigma = [-1]
          desired = np.array([0.67884390500697, 2.21653186290321, 1.01990310084276])
  
          random = Generator(MT19937(self.seed))
          lognormal = random.lognormal
          actual = lognormal(mean * 3, sigma)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, lognormal, mean * 3, bad_sigma)
  
          random = Generator(MT19937(self.seed))
          actual = random.lognormal(mean, sigma * 3)
          assert_raises(ValueError, random.lognormal, mean, bad_sigma * 3)
  
      def test_rayleigh(self):
          scale = [1]
          bad_scale = [-1]
          desired = np.array([0.60439534475066, 0.66120048396359, 1.67873398389499])
  
          random = Generator(MT19937(self.seed))
          actual = random.rayleigh(scale * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, random.rayleigh, bad_scale * 3)
  
      def test_wald(self):
          mean = [0.5]
          scale = [1]
          bad_mean = [0]
          bad_scale = [-2]
          desired = np.array([0.38052407392905, 0.50701641508592, 0.484935249864])
  
          random = Generator(MT19937(self.seed))
          actual = random.wald(mean * 3, scale)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, random.wald, bad_mean * 3, scale)
          assert_raises(ValueError, random.wald, mean * 3, bad_scale)
  
          random = Generator(MT19937(self.seed))
          actual = random.wald(mean, scale * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, random.wald, bad_mean, scale * 3)
          assert_raises(ValueError, random.wald, mean, bad_scale * 3)
  
      def test_triangular(self):
          left = [1]
          right = [3]
          mode = [2]
          bad_left_one = [3]
          bad_mode_one = [4]
          bad_left_two, bad_mode_two = right * 2
          desired = np.array([1.57781954604754, 1.62665986867957, 2.30090130831326])
  
          random = Generator(MT19937(self.seed))
          triangular = random.triangular
          actual = triangular(left * 3, mode, right)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, triangular, bad_left_one * 3, mode, right)
          assert_raises(ValueError, triangular, left * 3, bad_mode_one, right)
          assert_raises(ValueError, triangular, bad_left_two * 3, bad_mode_two,
                        right)
  
          random = Generator(MT19937(self.seed))
          triangular = random.triangular
          actual = triangular(left, mode * 3, right)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, triangular, bad_left_one, mode * 3, right)
          assert_raises(ValueError, triangular, left, bad_mode_one * 3, right)
          assert_raises(ValueError, triangular, bad_left_two, bad_mode_two * 3,
                        right)
  
          random = Generator(MT19937(self.seed))
          triangular = random.triangular
          actual = triangular(left, mode, right * 3)
          assert_array_almost_equal(actual, desired, decimal=14)
          assert_raises(ValueError, triangular, bad_left_one, mode, right * 3)
          assert_raises(ValueError, triangular, left, bad_mode_one, right * 3)
          assert_raises(ValueError, triangular, bad_left_two, bad_mode_two,
                        right * 3)
  
          assert_raises(ValueError, triangular, 10., 0., 20.)
          assert_raises(ValueError, triangular, 10., 25., 20.)
          assert_raises(ValueError, triangular, 10., 10., 10.)
  
      def test_binomial(self):
          n = [1]
          p = [0.5]
          bad_n = [-1]
          bad_p_one = [-1]
          bad_p_two = [1.5]
          desired = np.array([0, 0, 1])
  
          random = Generator(MT19937(self.seed))
          binom = random.binomial
          actual = binom(n * 3, p)
          assert_array_equal(actual, desired)
          assert_raises(ValueError, binom, bad_n * 3, p)
          assert_raises(ValueError, binom, n * 3, bad_p_one)
          assert_raises(ValueError, binom, n * 3, bad_p_two)
  
          random = Generator(MT19937(self.seed))
          actual = random.binomial(n, p * 3)
          assert_array_equal(actual, desired)
          assert_raises(ValueError, binom, bad_n, p * 3)
          assert_raises(ValueError, binom, n, bad_p_one * 3)
          assert_raises(ValueError, binom, n, bad_p_two * 3)
  
      def test_negative_binomial(self):
          n = [1]
          p = [0.5]
          bad_n = [-1]
          bad_p_one = [-1]
          bad_p_two = [1.5]
          desired = np.array([0, 2, 1], dtype=np.int64)
  
          random = Generator(MT19937(self.seed))
          neg_binom = random.negative_binomial
          actual = neg_binom(n * 3, p)
          assert_array_equal(actual, desired)
          assert_raises(ValueError, neg_binom, bad_n * 3, p)
          assert_raises(ValueError, neg_binom, n * 3, bad_p_one)
          assert_raises(ValueError, neg_binom, n * 3, bad_p_two)
  
          random = Generator(MT19937(self.seed))
          neg_binom = random.negative_binomial
          actual = neg_binom(n, p * 3)
          assert_array_equal(actual, desired)
          assert_raises(ValueError, neg_binom, bad_n, p * 3)
          assert_raises(ValueError, neg_binom, n, bad_p_one * 3)
          assert_raises(ValueError, neg_binom, n, bad_p_two * 3)
  
      def test_poisson(self):
  
          lam = [1]
          bad_lam_one = [-1]
          desired = np.array([0, 0, 3])
  
          random = Generator(MT19937(self.seed))
          max_lam = random._poisson_lam_max
          bad_lam_two = [max_lam * 2]
          poisson = random.poisson
          actual = poisson(lam * 3)
          assert_array_equal(actual, desired)
          assert_raises(ValueError, poisson, bad_lam_one * 3)
          assert_raises(ValueError, poisson, bad_lam_two * 3)
  
      def test_zipf(self):
          a = [2]
          bad_a = [0]
          desired = np.array([1, 8, 1])
  
          random = Generator(MT19937(self.seed))
          zipf = random.zipf
          actual = zipf(a * 3)
          assert_array_equal(actual, desired)
          assert_raises(ValueError, zipf, bad_a * 3)
          with np.errstate(invalid='ignore'):
              assert_raises(ValueError, zipf, np.nan)
              assert_raises(ValueError, zipf, [0, 0, np.nan])
  
      def test_geometric(self):
          p = [0.5]
          bad_p_one = [-1]
          bad_p_two = [1.5]
          desired = np.array([1, 1, 3])
  
          random = Generator(MT19937(self.seed))
          geometric = random.geometric
          actual = geometric(p * 3)
          assert_array_equal(actual, desired)
          assert_raises(ValueError, geometric, bad_p_one * 3)
          assert_raises(ValueError, geometric, bad_p_two * 3)
  
      def test_hypergeometric(self):
          ngood = [1]
          nbad = [2]
          nsample = [2]
          bad_ngood = [-1]
          bad_nbad = [-2]
          bad_nsample_one = [-1]
          bad_nsample_two = [4]
          desired = np.array([0, 0, 1])
  
          random = Generator(MT19937(self.seed))
          actual = random.hypergeometric(ngood * 3, nbad, nsample)
          assert_array_equal(actual, desired)
          assert_raises(ValueError, random.hypergeometric, bad_ngood * 3, nbad, nsample)
          assert_raises(ValueError, random.hypergeometric, ngood * 3, bad_nbad, nsample)
          assert_raises(ValueError, random.hypergeometric, ngood * 3, nbad, bad_nsample_one)
          assert_raises(ValueError, random.hypergeometric, ngood * 3, nbad, bad_nsample_two)
  
          random = Generator(MT19937(self.seed))
          actual = random.hypergeometric(ngood, nbad * 3, nsample)
          assert_array_equal(actual, desired)
          assert_raises(ValueError, random.hypergeometric, bad_ngood, nbad * 3, nsample)
          assert_raises(ValueError, random.hypergeometric, ngood, bad_nbad * 3, nsample)
          assert_raises(ValueError, random.hypergeometric, ngood, nbad * 3, bad_nsample_one)
          assert_raises(ValueError, random.hypergeometric, ngood, nbad * 3, bad_nsample_two)
  
          random = Generator(MT19937(self.seed))
          hypergeom = random.hypergeometric
          actual = hypergeom(ngood, nbad, nsample * 3)
          assert_array_equal(actual, desired)
          assert_raises(ValueError, hypergeom, bad_ngood, nbad, nsample * 3)
          assert_raises(ValueError, hypergeom, ngood, bad_nbad, nsample * 3)
          assert_raises(ValueError, hypergeom, ngood, nbad, bad_nsample_one * 3)
          assert_raises(ValueError, hypergeom, ngood, nbad, bad_nsample_two * 3)
  
          assert_raises(ValueError, hypergeom, -1, 10, 20)
          assert_raises(ValueError, hypergeom, 10, -1, 20)
          assert_raises(ValueError, hypergeom, 10, 10, -1)
          assert_raises(ValueError, hypergeom, 10, 10, 25)
  
          # ValueError for arguments that are too big.
          assert_raises(ValueError, hypergeom, 2**30, 10, 20)
          assert_raises(ValueError, hypergeom, 999, 2**31, 50)
          assert_raises(ValueError, hypergeom, 999, [2**29, 2**30], 1000)
  
      def test_logseries(self):
          p = [0.5]
          bad_p_one = [2]
          bad_p_two = [-1]
          desired = np.array([1, 1, 1])
  
          random = Generator(MT19937(self.seed))
          logseries = random.logseries
          actual = logseries(p * 3)
          assert_array_equal(actual, desired)
          assert_raises(ValueError, logseries, bad_p_one * 3)
          assert_raises(ValueError, logseries, bad_p_two * 3)
  
      def test_multinomial(self):
          random = Generator(MT19937(self.seed))
          actual = random.multinomial([5, 20], [1 / 6.] * 6, size=(3, 2))
          desired = np.array([[[0, 0, 2, 1, 2, 0],
                               [2, 3, 6, 4, 2, 3]],
                              [[1, 0, 1, 0, 2, 1],
                               [7, 2, 2, 1, 4, 4]],
                              [[0, 2, 0, 1, 2, 0],
                               [3, 2, 3, 3, 4, 5]]], dtype=np.int64)
          assert_array_equal(actual, desired)
  
          random = Generator(MT19937(self.seed))
          actual = random.multinomial([5, 20], [1 / 6.] * 6)
          desired = np.array([[0, 0, 2, 1, 2, 0],
                              [2, 3, 6, 4, 2, 3]], dtype=np.int64)
          assert_array_equal(actual, desired)
  
  
  class TestThread:
      # make sure each state produces the same sequence even in threads
      def setup(self):
          self.seeds = range(4)
  
      def check_function(self, function, sz):
          from threading import Thread
  
          out1 = np.empty((len(self.seeds),) + sz)
          out2 = np.empty((len(self.seeds),) + sz)
  
          # threaded generation
          t = [Thread(target=function, args=(Generator(MT19937(s)), o))
               for s, o in zip(self.seeds, out1)]
          [x.start() for x in t]
          [x.join() for x in t]
  
          # the same serial
          for s, o in zip(self.seeds, out2):
              function(Generator(MT19937(s)), o)
  
          # these platforms change x87 fpu precision mode in threads
          if np.intp().dtype.itemsize == 4 and sys.platform == "win32":
              assert_array_almost_equal(out1, out2)
          else:
              assert_array_equal(out1, out2)
  
      def test_normal(self):
          def gen_random(state, out):
              out[...] = state.normal(size=10000)
  
          self.check_function(gen_random, sz=(10000,))
  
      def test_exp(self):
          def gen_random(state, out):
              out[...] = state.exponential(scale=np.ones((100, 1000)))
  
          self.check_function(gen_random, sz=(100, 1000))
  
      def test_multinomial(self):
          def gen_random(state, out):
              out[...] = state.multinomial(10, [1 / 6.] * 6, size=10000)
  
          self.check_function(gen_random, sz=(10000, 6))
  
  
  # See Issue #4263
  class TestSingleEltArrayInput:
      def setup(self):
          self.argOne = np.array([2])
          self.argTwo = np.array([3])
          self.argThree = np.array([4])
          self.tgtShape = (1,)
  
      def test_one_arg_funcs(self):
          funcs = (random.exponential, random.standard_gamma,
                   random.chisquare, random.standard_t,
                   random.pareto, random.weibull,
                   random.power, random.rayleigh,
                   random.poisson, random.zipf,
                   random.geometric, random.logseries)
  
          probfuncs = (random.geometric, random.logseries)
  
          for func in funcs:
              if func in probfuncs:  # p < 1.0
                  out = func(np.array([0.5]))
  
              else:
                  out = func(self.argOne)
  
              assert_equal(out.shape, self.tgtShape)
  
      def test_two_arg_funcs(self):
          funcs = (random.uniform, random.normal,
                   random.beta, random.gamma,
                   random.f, random.noncentral_chisquare,
                   random.vonmises, random.laplace,
                   random.gumbel, random.logistic,
                   random.lognormal, random.wald,
                   random.binomial, random.negative_binomial)
  
          probfuncs = (random.binomial, random.negative_binomial)
  
          for func in funcs:
              if func in probfuncs:  # p <= 1
                  argTwo = np.array([0.5])
  
              else:
                  argTwo = self.argTwo
  
              out = func(self.argOne, argTwo)
              assert_equal(out.shape, self.tgtShape)
  
              out = func(self.argOne[0], argTwo)
              assert_equal(out.shape, self.tgtShape)
  
              out = func(self.argOne, argTwo[0])
              assert_equal(out.shape, self.tgtShape)
  
      def test_integers(self, endpoint):
          itype = [np.bool_, np.int8, np.uint8, np.int16, np.uint16,
                   np.int32, np.uint32, np.int64, np.uint64]
          func = random.integers
          high = np.array([1])
          low = np.array([0])
  
          for dt in itype:
              out = func(low, high, endpoint=endpoint, dtype=dt)
              assert_equal(out.shape, self.tgtShape)
  
              out = func(low[0], high, endpoint=endpoint, dtype=dt)
              assert_equal(out.shape, self.tgtShape)
  
              out = func(low, high[0], endpoint=endpoint, dtype=dt)
              assert_equal(out.shape, self.tgtShape)
  
      def test_three_arg_funcs(self):
          funcs = [random.noncentral_f, random.triangular,
                   random.hypergeometric]
  
          for func in funcs:
              out = func(self.argOne, self.argTwo, self.argThree)
              assert_equal(out.shape, self.tgtShape)
  
              out = func(self.argOne[0], self.argTwo, self.argThree)
              assert_equal(out.shape, self.tgtShape)
  
              out = func(self.argOne, self.argTwo[0], self.argThree)
              assert_equal(out.shape, self.tgtShape)
  
  
  @pytest.mark.parametrize("config", JUMP_TEST_DATA)
  def test_jumped(config):
      # Each config contains the initial seed, a number of raw steps
      # the md5 hashes of the initial and the final states' keys and
      # the position of of the initial and the final state.
      # These were produced using the original C implementation.
      seed = config["seed"]
      steps = config["steps"]
  
      mt19937 = MT19937(seed)
      # Burn step
      mt19937.random_raw(steps)
      key = mt19937.state["state"]["key"]
      if sys.byteorder == 'big':
          key = key.byteswap()
      md5 = hashlib.md5(key)
      assert mt19937.state["state"]["pos"] == config["initial"]["pos"]
      assert md5.hexdigest() == config["initial"]["key_md5"]
  
      jumped = mt19937.jumped()
      key = jumped.state["state"]["key"]
      if sys.byteorder == 'big':
          key = key.byteswap()
      md5 = hashlib.md5(key)
      assert jumped.state["state"]["pos"] == config["jumped"]["pos"]
      assert md5.hexdigest() == config["jumped"]["key_md5"]
  
apis: numpy.sum numpy.ones numpy.testing.assert_equal numpy.dtype numpy.asarray numpy.testing.assert_no_warnings numpy.nextafter numpy.testing.assert_warns numpy.ascontiguousarray numpy.isfinite numpy.vstack numpy.abs numpy.testing.assert_array_equal numpy.uint32 numpy.random.SeedSequence numpy.isnan numpy.unique numpy.eye numpy.atleast_2d numpy.zeros numpy.testing.suppress_warnings numpy.arange numpy.testing.assert_array_almost_equal_nulp numpy.testing.assert_array_almost_equal numpy.all numpy.finfo numpy.intp numpy.testing.assert_raises numpy.empty numpy.errstate numpy.iinfo numpy.testing.assert_allclose numpy.array numpy.full numpy.random.MT19937 numpy.testing.assert_