rocm_jax/tests/lax_scipy_test.py

# Copyright 2018 The JAX Authors.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.


import collections
import functools
from functools import partial
import itertools
import unittest

from absl.testing import absltest
from absl.testing import parameterized

import numpy as np
import scipy.special as osp_special
import scipy.cluster as osp_cluster

import jax
from jax import numpy as jnp
from jax import lax
from jax import scipy as jsp
from jax.tree_util import tree_map
from jax._src import test_util as jtu
from jax.scipy import special as lsp_special
from jax.scipy import cluster as lsp_cluster
from jax._src.lax import eigh as lax_eigh

from jax.config import config
config.parse_flags_with_absl()
FLAGS = config.FLAGS

all_shapes = [(), (4,), (3, 4), (3, 1), (1, 4), (2, 1, 4)]
compatible_shapes = [[(), ()],
                     [(4,), (3, 4)],
                     [(3, 1), (1, 4)],
                     [(2, 3, 4), (2, 1, 4)]]

float_dtypes = jtu.dtypes.floating
complex_dtypes = jtu.dtypes.complex
int_dtypes = jtu.dtypes.integer

# Params for the polar tests.
polar_shapes = [(16, 12), (12, 16), (128, 128)]
n_zero_svs = [0, 4]
degeneracies = [0, 4]
geometric_spectra = [False, True]
max_svs = [0.1, 10.]
nonzero_condition_numbers = [0.1, 100000]
sides = ["right", "left"]
methods = ["qdwh", "svd"]
seeds = [1, 10]

linear_sizes = [16, 128, 256]


def _initialize_polar_test(rng, shape, n_zero_svs, degeneracy, geometric_spectrum,
                           max_sv, nonzero_condition_number, dtype):

  n_rows, n_cols = shape
  min_dim = min(shape)
  left_vecs = rng.randn(n_rows, min_dim).astype(np.float64)
  left_vecs, _ = np.linalg.qr(left_vecs)
  right_vecs = rng.randn(n_cols, min_dim).astype(np.float64)
  right_vecs, _ = np.linalg.qr(right_vecs)

  min_nonzero_sv = max_sv / nonzero_condition_number
  num_nonzero_svs = min_dim - n_zero_svs
  if geometric_spectrum:
    nonzero_svs = np.geomspace(min_nonzero_sv, max_sv, num=num_nonzero_svs,
                               dtype=np.float64)
  else:
    nonzero_svs = np.linspace(min_nonzero_sv, max_sv, num=num_nonzero_svs,
                              dtype=np.float64)
  half_point = n_zero_svs // 2
  for i in range(half_point, half_point + degeneracy):
    nonzero_svs[i] = nonzero_svs[half_point]
  svs = np.zeros(min(shape), dtype=np.float64)
  svs[n_zero_svs:] = nonzero_svs
  svs = svs[::-1]

  result = np.dot(left_vecs * svs, right_vecs.conj().T)
  result = jnp.array(result).astype(dtype)
  spectrum = jnp.array(svs).astype(dtype)
  return result, spectrum

OpRecord = collections.namedtuple(
    "OpRecord",
    ["name", "nargs", "dtypes", "rng_factory", "test_autodiff", "nondiff_argnums", "test_name"])


def op_record(name, nargs, dtypes, rng_factory, test_grad, nondiff_argnums=(), test_name=None):
  test_name = test_name or name
  nondiff_argnums = tuple(sorted(set(nondiff_argnums)))
  return OpRecord(name, nargs, dtypes, rng_factory, test_grad, nondiff_argnums, test_name)

# TODO(phawkins): we should probably separate out the function domains used for
# autodiff tests from the function domains used for equivalence testing. For
# example, logit should closely match its scipy equivalent everywhere, but we
# don't expect numerical gradient tests to pass for inputs very close to 0.

JAX_SPECIAL_FUNCTION_RECORDS = [
    op_record("betaln", 2, float_dtypes, jtu.rand_positive, False),
    op_record("betainc", 3, float_dtypes, jtu.rand_positive, False),
    op_record("digamma", 1, float_dtypes, jtu.rand_positive, True),
    op_record("gammainc", 2, float_dtypes, jtu.rand_positive, True),
    op_record("gammaincc", 2, float_dtypes, jtu.rand_positive, True),
    op_record("erf", 1, float_dtypes, jtu.rand_small_positive, True),
    op_record("erfc", 1, float_dtypes, jtu.rand_small_positive, True),
    op_record("erfinv", 1, float_dtypes, jtu.rand_small_positive, True),
    op_record("expit", 1, float_dtypes, jtu.rand_small_positive, True),
    # TODO: gammaln has slightly high error.
    op_record("gammaln", 1, float_dtypes, jtu.rand_positive, False),
    op_record("i0", 1, float_dtypes, jtu.rand_default, True),
    op_record("i0e", 1, float_dtypes, jtu.rand_default, True),
    op_record("i1", 1, float_dtypes, jtu.rand_default, True),
    op_record("i1e", 1, float_dtypes, jtu.rand_default, True),
    op_record("logit", 1, float_dtypes, partial(jtu.rand_uniform, low=0.05,
                                                high=0.95), True),
    op_record("log_ndtr", 1, float_dtypes, jtu.rand_default, True),
    op_record("ndtri", 1, float_dtypes, partial(jtu.rand_uniform, low=0.05,
                                                high=0.95),
              True),
    op_record("ndtr", 1, float_dtypes, jtu.rand_default, True),
    # TODO(phawkins): gradient of entr yields NaNs.
    op_record("entr", 1, float_dtypes, jtu.rand_default, False),
    op_record("polygamma", 2, (int_dtypes, float_dtypes), jtu.rand_positive, True, (0,)),
    op_record("xlogy", 2, float_dtypes, jtu.rand_positive, True),
    op_record("xlog1py", 2, float_dtypes, jtu.rand_default, True),
    # TODO: enable gradient test for zeta by restricting the domain of
    # of inputs to some reasonable intervals
    op_record("zeta", 2, float_dtypes, jtu.rand_positive, False),
    # TODO: float64 produces aborts on gpu, potentially related to use of jnp.piecewise
    op_record("expi", 1, [np.float32], partial(jtu.rand_not_small, offset=0.1),
              True),
    op_record("exp1", 1, [np.float32], jtu.rand_positive, True),
    op_record("expn", 2, (int_dtypes, [np.float32]), jtu.rand_positive, True, (0,)),
]


class LaxBackedScipyTests(jtu.JaxTestCase):
  """Tests for LAX-backed Scipy implementation."""

  def _GetArgsMaker(self, rng, shapes, dtypes):
    return lambda: [rng(shape, dtype) for shape, dtype in zip(shapes, dtypes)]


  @jtu.sample_product(
    [dict(shapes=shapes, axis=axis, use_b=use_b)
      for shape_group in compatible_shapes
      for use_b in [False, True]
      for shapes in itertools.product(*(
        (shape_group, shape_group) if use_b else (shape_group,)))
      for axis in range(-max(len(shape) for shape in shapes),
                         max(len(shape) for shape in shapes))
    ],
    dtype=float_dtypes + complex_dtypes + int_dtypes,
    keepdims=[False, True],
    return_sign=[False, True],
  )
  @jtu.ignore_warning(category=RuntimeWarning, message="invalid value encountered in .*")
  @jax.numpy_rank_promotion('allow')  # This test explicitly exercises implicit rank promotion.
  def testLogSumExp(self, shapes, dtype, axis,
                    keepdims, return_sign, use_b):
    if jtu.device_under_test() != "cpu":
      rng = jtu.rand_some_inf_and_nan(self.rng())
    else:
      rng = jtu.rand_default(self.rng())
    # TODO(mattjj): test autodiff
    if use_b:
      def scipy_fun(array_to_reduce, scale_array):
        res = osp_special.logsumexp(array_to_reduce, axis, keepdims=keepdims,
                                    return_sign=return_sign, b=scale_array)
        if dtype == np.int32:
          res = tree_map(lambda x: x.astype('float32'), res)
        return res

      def lax_fun(array_to_reduce, scale_array):
        return lsp_special.logsumexp(array_to_reduce, axis, keepdims=keepdims,
                                     return_sign=return_sign, b=scale_array)

      args_maker = lambda: [rng(shapes[0], dtype), rng(shapes[1], dtype)]
    else:
      def scipy_fun(array_to_reduce):
        res = osp_special.logsumexp(array_to_reduce, axis, keepdims=keepdims,
                                    return_sign=return_sign)
        if dtype == np.int32:
          res = tree_map(lambda x: x.astype('float32'), res)
        return res

      def lax_fun(array_to_reduce):
        return lsp_special.logsumexp(array_to_reduce, axis, keepdims=keepdims,
                                     return_sign=return_sign)

      args_maker = lambda: [rng(shapes[0], dtype)]
    tol = {np.float32: 1E-6, np.float64: 1E-14}
    self._CheckAgainstNumpy(scipy_fun, lax_fun, args_maker)
    self._CompileAndCheck(lax_fun, args_maker, rtol=tol, atol=tol)

  def testLogSumExpZeros(self):
    # Regression test for https://github.com/google/jax/issues/5370
    scipy_fun = lambda a, b: osp_special.logsumexp(a, b=b)
    lax_fun = lambda a, b: lsp_special.logsumexp(a, b=b)
    args_maker = lambda: [np.array([-1000, -2]), np.array([1, 0])]
    self._CheckAgainstNumpy(scipy_fun, lax_fun, args_maker)
    self._CompileAndCheck(lax_fun, args_maker)

  def testLogSumExpOnes(self):
    # Regression test for https://github.com/google/jax/issues/7390
    args_maker = lambda: [np.ones(4, dtype='float32')]
    with jax.debug_infs(True):
      self._CheckAgainstNumpy(osp_special.logsumexp, lsp_special.logsumexp, args_maker)
      self._CompileAndCheck(lsp_special.logsumexp, args_maker)

  def testLogSumExpNans(self):
    # Regression test for https://github.com/google/jax/issues/7634
    with jax.debug_nans(True):
      with jax.disable_jit():
        result = lsp_special.logsumexp(1.0)
        self.assertEqual(result, 1.0)

        result = lsp_special.logsumexp(1.0, b=1.0)
        self.assertEqual(result, 1.0)

  @parameterized.parameters(itertools.chain.from_iterable(
    jtu.sample_product_testcases(
      [dict(op=rec.name, rng_factory=rec.rng_factory,
            test_autodiff=rec.test_autodiff,
            nondiff_argnums=rec.nondiff_argnums)],
      shapes=itertools.combinations_with_replacement(all_shapes, rec.nargs),
      dtypes=(itertools.combinations_with_replacement(rec.dtypes, rec.nargs)
        if isinstance(rec.dtypes, list) else itertools.product(*rec.dtypes)),
    )
    for rec in JAX_SPECIAL_FUNCTION_RECORDS
  ))
  @jax.numpy_rank_promotion('allow')  # This test explicitly exercises implicit rank promotion.
  @jax.numpy_dtype_promotion('standard')  # This test explicitly exercises dtype promotion
  def testScipySpecialFun(self, op, rng_factory, shapes, dtypes,
                          test_autodiff, nondiff_argnums):
    scipy_op = getattr(osp_special, op)
    lax_op = getattr(lsp_special, op)
    rng = rng_factory(self.rng())
    args_maker = self._GetArgsMaker(rng, shapes, dtypes)
    args = args_maker()
    self.assertAllClose(scipy_op(*args), lax_op(*args), atol=1e-3, rtol=1e-3,
                        check_dtypes=False)
    self._CompileAndCheck(lax_op, args_maker, rtol=1e-4)

    if test_autodiff:
      def partial_lax_op(*vals):
        list_args = list(vals)
        for i in nondiff_argnums:
          list_args.insert(i, args[i])
        return lax_op(*list_args)

      assert list(nondiff_argnums) == sorted(set(nondiff_argnums))
      diff_args = [x for i, x in enumerate(args) if i not in nondiff_argnums]
      jtu.check_grads(partial_lax_op, diff_args, order=1,
                      atol=jtu.if_device_under_test("tpu", .1, 1e-3),
                      rtol=.1, eps=1e-3)

  @jtu.sample_product(
    shape=all_shapes,
    dtype=float_dtypes,
    d=[1, 2, 5],
  )
  @jax.numpy_rank_promotion('raise')
  def testMultigammaln(self, shape, dtype, d):
    def scipy_fun(a):
      return osp_special.multigammaln(a, d)

    def lax_fun(a):
      return lsp_special.multigammaln(a, d)

    rng = jtu.rand_positive(self.rng())
    args_maker = lambda: [rng(shape, dtype) + (d - 1) / 2.]
    self._CheckAgainstNumpy(scipy_fun, lax_fun, args_maker,
                            tol={np.float32: 1e-3, np.float64: 1e-14})
    self._CompileAndCheck(
        lax_fun, args_maker, rtol={
            np.float32: 3e-07,
            np.float64: 4e-15
        })

  def testIssue980(self):
    x = np.full((4,), -1e20, dtype=np.float32)
    self.assertAllClose(np.zeros((4,), dtype=np.float32),
                        lsp_special.expit(x))

  @jax.numpy_rank_promotion('raise')
  def testIssue3758(self):
    x = np.array([1e5, 1e19, 1e10], dtype=np.float32)
    q = np.array([1., 40., 30.], dtype=np.float32)
    self.assertAllClose(np.array([1., 0., 0.], dtype=np.float32), lsp_special.zeta(x, q))

  def testXlogyShouldReturnZero(self):
    self.assertAllClose(lsp_special.xlogy(0., 0.), 0., check_dtypes=False)

  def testGradOfXlogyAtZero(self):
    partial_xlogy = functools.partial(lsp_special.xlogy, 0.)
    self.assertAllClose(jax.grad(partial_xlogy)(0.), 0., check_dtypes=False)

  def testXlog1pyShouldReturnZero(self):
    self.assertAllClose(lsp_special.xlog1py(0., -1.), 0., check_dtypes=False)

  def testGradOfXlog1pyAtZero(self):
    partial_xlog1py = functools.partial(lsp_special.xlog1py, 0.)
    self.assertAllClose(jax.grad(partial_xlog1py)(-1.), 0., check_dtypes=False)

  @jtu.sample_product(
    [dict(order=order, z=z, n_iter=n_iter)
     for order, z, n_iter in zip(
         [0, 1, 2, 3, 6], [0.01, 1.1, 11.4, 30.0, 100.6], [5, 20, 50, 80, 200]
     )],
  )
  def testBesselJn(self, order, z, n_iter):
    def lax_fun(z):
      return lsp_special.bessel_jn(z, v=order, n_iter=n_iter)

    def scipy_fun(z):
      vals = [osp_special.jv(v, z) for v in range(order+1)]
      return np.array(vals)

    args_maker = lambda : [z]
    self._CheckAgainstNumpy(scipy_fun, lax_fun, args_maker, rtol=1E-6)
    self._CompileAndCheck(lax_fun, args_maker, rtol=1E-8)

  @jtu.sample_product(
    order=[3, 4],
    shape=[(2,), (3,), (4,), (3, 5), (2, 2, 3)],
    dtype=float_dtypes,
  )
  def testBesselJnRandomPositiveZ(self, order, shape, dtype):
    rng = jtu.rand_default(self.rng(), scale=1)
    points = jnp.abs(rng(shape, dtype))

    args_maker = lambda: [points]

    def lax_fun(z):
      return lsp_special.bessel_jn(z, v=order, n_iter=15)

    def scipy_fun(z):
      vals = [osp_special.jv(v, z) for v in range(order+1)]
      return np.stack(vals, axis=0)

    self._CheckAgainstNumpy(scipy_fun, lax_fun, args_maker, rtol=1E-6)
    self._CompileAndCheck(lax_fun, args_maker, rtol=1E-8)

  @jtu.sample_product(
    l_max=[1, 2, 3, 6],
    shape=[(5,), (10,)],
    dtype=float_dtypes,
  )
  def testLpmn(self, l_max, shape, dtype):
    rng = jtu.rand_uniform(self.rng(), low=-0.2, high=0.9)
    args_maker = lambda: [rng(shape, dtype)]

    lax_fun = partial(lsp_special.lpmn, l_max, l_max)

    def scipy_fun(z, m=l_max, n=l_max):
      # scipy only supports scalar inputs for z, so we must loop here.
      vals, derivs = zip(*(osp_special.lpmn(m, n, zi) for zi in z))
      return np.dstack(vals), np.dstack(derivs)

    self._CheckAgainstNumpy(scipy_fun, lax_fun, args_maker, rtol=1e-5,
                            atol=3e-3, check_dtypes=False)
    self._CompileAndCheck(lax_fun, args_maker, rtol=1E-5, atol=3e-3)

  @jtu.sample_product(
    l_max=[3, 4, 6, 32],
    shape=[(2,), (3,), (4,), (64,)],
    dtype=float_dtypes,
  )
  def testNormalizedLpmnValues(self, l_max, shape, dtype):
    rng = jtu.rand_uniform(self.rng(), low=-0.2, high=0.9)
    args_maker = lambda: [rng(shape, dtype)]

    # Note: we test only the normalized values, not the derivatives.
    lax_fun = partial(lsp_special.lpmn_values, l_max, l_max, is_normalized=True)

    def scipy_fun(z, m=l_max, n=l_max):
      # scipy only supports scalar inputs for z, so we must loop here.
      vals, _ = zip(*(osp_special.lpmn(m, n, zi) for zi in z))
      a = np.dstack(vals)

      # apply the normalization
      num_m, num_l, _ = a.shape
      a_normalized = np.zeros_like(a)
      for m in range(num_m):
        for l in range(num_l):
          c0 = (2.0 * l + 1.0) * osp_special.factorial(l - m)
          c1 = (4.0 * np.pi) * osp_special.factorial(l + m)
          c2 = np.sqrt(c0 / c1)
          a_normalized[m, l] = c2 * a[m, l]
      return a_normalized

    self._CheckAgainstNumpy(scipy_fun, lax_fun, args_maker,
                            rtol=1e-5, atol=1e-5, check_dtypes=False)
    self._CompileAndCheck(lax_fun, args_maker, rtol=1E-6, atol=1E-6)

  @jax.numpy_dtype_promotion('standard')  # This test explicitly exercises dtype promotion
  def testSphHarmAccuracy(self):
    m = jnp.arange(-3, 3)[:, None]
    n = jnp.arange(3, 6)
    n_max = 5
    theta = 0.0
    phi = jnp.pi

    expected = lsp_special.sph_harm(m, n, theta, phi, n_max)

    actual = osp_special.sph_harm(m, n, theta, phi)

    self.assertAllClose(actual, expected, rtol=1e-8, atol=9e-5)

  @jax.numpy_dtype_promotion('standard')  # This test explicitly exercises dtype promotion
  def testSphHarmOrderZeroDegreeZero(self):
    """Tests the spherical harmonics of order zero and degree zero."""
    theta = jnp.array([0.3])
    phi = jnp.array([2.3])
    n_max = 0

    expected = jnp.array([1.0 / jnp.sqrt(4.0 * np.pi)])
    actual = jnp.real(
        lsp_special.sph_harm(jnp.array([0]), jnp.array([0]), theta, phi, n_max))

    self.assertAllClose(actual, expected, rtol=1.1e-7, atol=3e-8)

  @jax.numpy_dtype_promotion('standard')  # This test explicitly exercises dtype promotion
  def testSphHarmOrderZeroDegreeOne(self):
    """Tests the spherical harmonics of order one and degree zero."""
    theta = jnp.array([2.0])
    phi = jnp.array([3.1])
    n_max = 1

    expected = jnp.sqrt(3.0 / (4.0 * np.pi)) * jnp.cos(phi)
    actual = jnp.real(
        lsp_special.sph_harm(jnp.array([0]), jnp.array([1]), theta, phi, n_max))

    self.assertAllClose(actual, expected, rtol=2e-7, atol=6e-8)

  @jax.numpy_dtype_promotion('standard')  # This test explicitly exercises dtype promotion
  def testSphHarmOrderOneDegreeOne(self):
    """Tests the spherical harmonics of order one and degree one."""
    theta = jnp.array([2.0])
    phi = jnp.array([2.5])
    n_max = 1

    expected = (-1.0 / 2.0 * jnp.sqrt(3.0 / (2.0 * np.pi)) *
                jnp.sin(phi) * jnp.exp(1j * theta))
    actual = lsp_special.sph_harm(
        jnp.array([1]), jnp.array([1]), theta, phi, n_max)

    self.assertAllClose(actual, expected, rtol=1e-8, atol=6e-8)

  @jtu.sample_product(
    [dict(l_max=l_max, num_z=num_z)
      for l_max, num_z in zip([1, 3, 8, 10], [2, 6, 7, 8])
    ],
    dtype=jtu.dtypes.all_integer,
  )
  @jax.numpy_dtype_promotion('standard')  # This test explicitly exercises dtype promotion
  def testSphHarmForJitAndAgainstNumpy(self, l_max, num_z, dtype):
    """Tests against JIT compatibility and Numpy."""
    n_max = l_max
    shape = (num_z,)
    rng = jtu.rand_int(self.rng(), -l_max, l_max + 1)

    lsp_special_fn = partial(lsp_special.sph_harm, n_max=n_max)

    def args_maker():
      m = rng(shape, dtype)
      n = abs(m)
      theta = jnp.linspace(-4.0, 5.0, num_z)
      phi = jnp.linspace(-2.0, 1.0, num_z)
      return m, n, theta, phi

    with self.subTest('Test JIT compatibility'):
      self._CompileAndCheck(lsp_special_fn, args_maker)

    with self.subTest('Test against numpy.'):
      self._CheckAgainstNumpy(osp_special.sph_harm, lsp_special_fn, args_maker)

  @jax.numpy_dtype_promotion('standard')  # This test explicitly exercises dtype promotion
  def testSphHarmCornerCaseWithWrongNmax(self):
    """Tests the corner case where `n_max` is not the maximum value of `n`."""
    m = jnp.array([2])
    n = jnp.array([10])
    n_clipped = jnp.array([6])
    n_max = 6
    theta = jnp.array([0.9])
    phi = jnp.array([0.2])

    expected = lsp_special.sph_harm(m, n, theta, phi, n_max)

    actual = lsp_special.sph_harm(m, n_clipped, theta, phi, n_max)

    self.assertAllClose(actual, expected, rtol=1e-8, atol=9e-5)

  @jtu.sample_product(
    n_zero_sv=n_zero_svs,
    degeneracy=degeneracies,
    geometric_spectrum=geometric_spectra,
    max_sv=max_svs,
    shape=polar_shapes,
    method=methods,
    side=sides,
    nonzero_condition_number=nonzero_condition_numbers,
    dtype=jtu.dtypes.inexact,
    seed=seeds,
  )
  def testPolar(
    self, n_zero_sv, degeneracy, geometric_spectrum, max_sv, shape, method,
      side, nonzero_condition_number, dtype, seed):
    """ Tests jax.scipy.linalg.polar."""
    if jtu.device_under_test() != "cpu":
      if jnp.dtype(dtype).name in ("bfloat16", "float16"):
        raise unittest.SkipTest("Skip half precision off CPU.")

    m, n = shape
    if (method == "qdwh" and ((side == "left" and m >= n) or
                              (side == "right" and m < n))):
      raise unittest.SkipTest("method=qdwh does not support these sizes")

    matrix, _ = _initialize_polar_test(self.rng(),
      shape, n_zero_sv, degeneracy, geometric_spectrum, max_sv,
      nonzero_condition_number, dtype)
    if jnp.dtype(dtype).name in ("bfloat16", "float16"):
      self.assertRaises(
        NotImplementedError, jsp.linalg.polar, matrix, method=method,
        side=side)
      return

    unitary, posdef = jsp.linalg.polar(matrix, method=method, side=side)
    if shape[0] >= shape[1]:
      should_be_eye = np.matmul(unitary.conj().T, unitary)
    else:
      should_be_eye = np.matmul(unitary, unitary.conj().T)
    tol = 500 * float(jnp.finfo(matrix.dtype).eps)
    eye_mat = np.eye(should_be_eye.shape[0], dtype=should_be_eye.dtype)
    with self.subTest('Test unitarity.'):
      self.assertAllClose(
        eye_mat, should_be_eye, atol=tol * min(shape))

    with self.subTest('Test Hermiticity.'):
      self.assertAllClose(
        posdef, posdef.conj().T, atol=tol * jnp.linalg.norm(posdef))

    ev, _ = np.linalg.eigh(posdef)
    ev = ev[np.abs(ev) > tol * np.linalg.norm(posdef)]
    negative_ev = jnp.sum(ev < 0.)
    with self.subTest('Test positive definiteness.'):
      self.assertEqual(negative_ev, 0)

    if side == "right":
      recon = jnp.matmul(unitary, posdef, precision=lax.Precision.HIGHEST)
    elif side == "left":
      recon = jnp.matmul(posdef, unitary, precision=lax.Precision.HIGHEST)
    with self.subTest('Test reconstruction.'):
      self.assertAllClose(
        matrix, recon, atol=tol * jnp.linalg.norm(matrix))

  @jtu.sample_product(
    linear_size=linear_sizes,
    dtype=jtu.dtypes.floating + jtu.dtypes.complex,
    termination_size=[1, 19],
  )
  def test_spectral_dac_eigh(self, linear_size, dtype, termination_size):
    if jtu.device_under_test() != "tpu" and termination_size != 1:
      raise unittest.SkipTest(
          "Termination sizes greater than 1 only work on TPU")

    rng = self.rng()
    H = rng.randn(linear_size, linear_size)
    H = jnp.array(0.5 * (H + H.conj().T)).astype(dtype)
    if jnp.dtype(dtype).name in ("bfloat16", "float16"):
      self.assertRaises(
        NotImplementedError, lax_eigh.eigh, H)
      return
    evs, V = lax_eigh.eigh(H, termination_size=termination_size)
    ev_exp, eV_exp = jnp.linalg.eigh(H)
    HV = jnp.dot(H, V, precision=lax.Precision.HIGHEST)
    vV = evs.astype(V.dtype)[None, :] * V
    eps = jnp.finfo(H.dtype).eps
    atol = jnp.linalg.norm(H) * eps
    self.assertAllClose(ev_exp, jnp.sort(evs), atol=20 * atol)
    self.assertAllClose(
        HV, vV, atol=atol * (140 if jnp.issubdtype(dtype, jnp.complexfloating)
                             else 30))

  @jtu.sample_product(
    n_obs=[1, 3, 5],
    n_codes=[1, 2, 4],
    n_feats=[()] + [(i,) for i in range(1, 3)],
    dtype=float_dtypes + int_dtypes, # scipy doesn't support complex
  )
  def test_vq(self, n_obs, n_codes, n_feats, dtype):
    rng = jtu.rand_default(self.rng())
    args_maker = lambda: [rng((n_obs, *n_feats), dtype), rng((n_codes, *n_feats), dtype)]
    self._CheckAgainstNumpy(osp_cluster.vq.vq, lsp_cluster.vq.vq, args_maker, check_dtypes=False)
    self._CompileAndCheck(lsp_cluster.vq.vq, args_maker)


if __name__ == "__main__":
  absltest.main(testLoader=jtu.JaxTestLoader())