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604 lines
24 KiB
Python
604 lines
24 KiB
Python
# Copyright 2018 Google LLC
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# https://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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import collections
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import functools
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from functools import partial
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import itertools
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import unittest
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from absl.testing import absltest
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from absl.testing import parameterized
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import numpy as np
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import scipy.special as osp_special
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from jax._src import api
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from jax import numpy as jnp
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from jax import lax
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from jax import scipy as jsp
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from jax import test_util as jtu
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from jax.scipy import special as lsp_special
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import jax._src.scipy.eigh
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from jax.config import config
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config.parse_flags_with_absl()
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FLAGS = config.FLAGS
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all_shapes = [(), (4,), (3, 4), (3, 1), (1, 4), (2, 1, 4)]
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compatible_shapes = [[(), ()],
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[(4,), (3, 4)],
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[(3, 1), (1, 4)],
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[(2, 3, 4), (2, 1, 4)]]
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float_dtypes = jtu.dtypes.floating
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complex_dtypes = jtu.dtypes.complex
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int_dtypes = jtu.dtypes.integer
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# Params for the polar tests.
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polar_shapes = [(16, 12), (12, 16), (128, 128)]
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n_zero_svs = [0, 4]
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degeneracies = [0, 4]
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geometric_spectra = [False, True]
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max_svs = [0.1, 10.]
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nonzero_condition_numbers = [0.1, 100000]
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sides = ["right", "left"]
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methods = ["qdwh", "svd"]
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seeds = [1, 10]
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linear_sizes = [16, 128, 256]
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def _initialize_polar_test(shape, n_zero_svs, degeneracy, geometric_spectrum,
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max_sv, nonzero_condition_number, dtype):
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n_rows, n_cols = shape
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min_dim = min(shape)
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left_vecs = np.random.randn(n_rows, min_dim).astype(np.float64)
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left_vecs, _ = np.linalg.qr(left_vecs)
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right_vecs = np.random.randn(n_cols, min_dim).astype(np.float64)
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right_vecs, _ = np.linalg.qr(right_vecs)
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min_nonzero_sv = max_sv / nonzero_condition_number
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num_nonzero_svs = min_dim - n_zero_svs
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if geometric_spectrum:
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nonzero_svs = np.geomspace(min_nonzero_sv, max_sv, num=num_nonzero_svs,
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dtype=np.float64)
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else:
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nonzero_svs = np.linspace(min_nonzero_sv, max_sv, num=num_nonzero_svs,
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dtype=np.float64)
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half_point = n_zero_svs // 2
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for i in range(half_point, half_point + degeneracy):
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nonzero_svs[i] = nonzero_svs[half_point]
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svs = np.zeros(min(shape), dtype=np.float64)
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svs[n_zero_svs:] = nonzero_svs
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svs = svs[::-1]
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result = np.dot(left_vecs * svs, right_vecs.conj().T)
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result = jnp.array(result).astype(dtype)
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spectrum = jnp.array(svs).astype(dtype)
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return result, spectrum
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OpRecord = collections.namedtuple(
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"OpRecord",
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["name", "nargs", "dtypes", "rng_factory", "test_autodiff", "nondiff_argnums", "test_name"])
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def op_record(name, nargs, dtypes, rng_factory, test_grad, nondiff_argnums=(), test_name=None):
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test_name = test_name or name
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nondiff_argnums = tuple(sorted(set(nondiff_argnums)))
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return OpRecord(name, nargs, dtypes, rng_factory, test_grad, nondiff_argnums, test_name)
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# TODO(phawkins): we should probably separate out the function domains used for
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# autodiff tests from the function domains used for equivalence testing. For
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# example, logit should closely match its scipy equivalent everywhere, but we
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# don't expect numerical gradient tests to pass for inputs very close to 0.
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JAX_SPECIAL_FUNCTION_RECORDS = [
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op_record("betaln", 2, float_dtypes, jtu.rand_positive, False),
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op_record("betainc", 3, float_dtypes, jtu.rand_positive, False),
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op_record("digamma", 1, float_dtypes, jtu.rand_positive, True),
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op_record("gammainc", 2, float_dtypes, jtu.rand_positive, True),
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op_record("gammaincc", 2, float_dtypes, jtu.rand_positive, True),
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op_record("erf", 1, float_dtypes, jtu.rand_small_positive, True),
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op_record("erfc", 1, float_dtypes, jtu.rand_small_positive, True),
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op_record("erfinv", 1, float_dtypes, jtu.rand_small_positive, True),
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op_record("expit", 1, float_dtypes, jtu.rand_small_positive, True),
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# TODO: gammaln has slightly high error.
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op_record("gammaln", 1, float_dtypes, jtu.rand_positive, False),
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op_record("i0", 1, float_dtypes, jtu.rand_default, True),
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op_record("i0e", 1, float_dtypes, jtu.rand_default, True),
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op_record("i1", 1, float_dtypes, jtu.rand_default, True),
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op_record("i1e", 1, float_dtypes, jtu.rand_default, True),
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op_record("logit", 1, float_dtypes, partial(jtu.rand_uniform, low=0.05,
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high=0.95), True),
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op_record("log_ndtr", 1, float_dtypes, jtu.rand_default, True),
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op_record("ndtri", 1, float_dtypes, partial(jtu.rand_uniform, low=0.05,
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high=0.95),
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True),
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op_record("ndtr", 1, float_dtypes, jtu.rand_default, True),
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# TODO(phawkins): gradient of entr yields NaNs.
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op_record("entr", 1, float_dtypes, jtu.rand_default, False),
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op_record("polygamma", 2, (int_dtypes, float_dtypes), jtu.rand_positive, True, (0,)),
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op_record("xlogy", 2, float_dtypes, jtu.rand_positive, True),
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op_record("xlog1py", 2, float_dtypes, jtu.rand_default, True),
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# TODO: enable gradient test for zeta by restricting the domain of
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# of inputs to some reasonable intervals
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op_record("zeta", 2, float_dtypes, jtu.rand_positive, False),
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]
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class LaxBackedScipyTests(jtu.JaxTestCase):
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"""Tests for LAX-backed Scipy implementation."""
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def _GetArgsMaker(self, rng, shapes, dtypes):
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return lambda: [rng(shape, dtype) for shape, dtype in zip(shapes, dtypes)]
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@parameterized.named_parameters(jtu.cases_from_list(
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{"testcase_name":
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"_shapes={}_axis={}_keepdims={}_return_sign={}_use_b_{}".format(
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jtu.format_shape_dtype_string(shapes, dtype),
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axis, keepdims, return_sign, use_b),
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# TODO(b/133842870): re-enable when exp(nan) returns NaN on CPU.
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"shapes": shapes, "dtype": dtype,
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"axis": axis, "keepdims": keepdims,
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"return_sign": return_sign, "use_b": use_b}
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for shape_group in compatible_shapes for dtype in float_dtypes + complex_dtypes + int_dtypes
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for use_b in [False, True]
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for shapes in itertools.product(*(
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(shape_group, shape_group) if use_b else (shape_group,)))
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for axis in range(-max(len(shape) for shape in shapes),
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max(len(shape) for shape in shapes))
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for keepdims in [False, True]
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for return_sign in [False, True]))
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@jtu.ignore_warning(category=RuntimeWarning,
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message="invalid value encountered in .*")
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def testLogSumExp(self, shapes, dtype, axis,
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keepdims, return_sign, use_b):
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if jtu.device_under_test() != "cpu":
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rng = jtu.rand_some_inf_and_nan(self.rng())
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else:
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rng = jtu.rand_default(self.rng())
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# TODO(mattjj): test autodiff
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if use_b:
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def scipy_fun(array_to_reduce, scale_array):
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return osp_special.logsumexp(array_to_reduce, axis, keepdims=keepdims,
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return_sign=return_sign, b=scale_array)
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def lax_fun(array_to_reduce, scale_array):
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return lsp_special.logsumexp(array_to_reduce, axis, keepdims=keepdims,
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return_sign=return_sign, b=scale_array)
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args_maker = lambda: [rng(shapes[0], dtype), rng(shapes[1], dtype)]
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else:
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def scipy_fun(array_to_reduce):
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return osp_special.logsumexp(array_to_reduce, axis, keepdims=keepdims,
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return_sign=return_sign)
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def lax_fun(array_to_reduce):
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return lsp_special.logsumexp(array_to_reduce, axis, keepdims=keepdims,
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return_sign=return_sign)
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args_maker = lambda: [rng(shapes[0], dtype)]
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tol = {np.float32: 1E-6, np.float64: 1E-14}
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self._CheckAgainstNumpy(scipy_fun, lax_fun, args_maker)
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self._CompileAndCheck(lax_fun, args_maker, rtol=tol, atol=tol)
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def testLogSumExpZeros(self):
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# Regression test for https://github.com/google/jax/issues/5370
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scipy_fun = lambda a, b: osp_special.logsumexp(a, b=b)
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lax_fun = lambda a, b: lsp_special.logsumexp(a, b=b)
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args_maker = lambda: [np.array([-1000, -2]), np.array([1, 0])]
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self._CheckAgainstNumpy(scipy_fun, lax_fun, args_maker)
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self._CompileAndCheck(lax_fun, args_maker)
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@parameterized.named_parameters(itertools.chain.from_iterable(
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jtu.cases_from_list(
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{"testcase_name": jtu.format_test_name_suffix(
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rec.test_name, shapes, dtypes),
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"rng_factory": rec.rng_factory, "shapes": shapes, "dtypes": dtypes,
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"test_autodiff": rec.test_autodiff,
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"nondiff_argnums": rec.nondiff_argnums,
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"scipy_op": getattr(osp_special, rec.name),
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"lax_op": getattr(lsp_special, rec.name)}
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for shapes in itertools.combinations_with_replacement(all_shapes, rec.nargs)
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for dtypes in (itertools.combinations_with_replacement(rec.dtypes, rec.nargs)
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if isinstance(rec.dtypes, list) else itertools.product(*rec.dtypes)))
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for rec in JAX_SPECIAL_FUNCTION_RECORDS))
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def testScipySpecialFun(self, scipy_op, lax_op, rng_factory, shapes, dtypes,
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test_autodiff, nondiff_argnums):
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if (jtu.device_under_test() == "cpu" and
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(lax_op is lsp_special.gammainc or lax_op is lsp_special.gammaincc)):
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# TODO(b/173608403): re-enable test when LLVM bug is fixed.
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raise unittest.SkipTest("Skipping test due to LLVM lowering bug")
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rng = rng_factory(self.rng())
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args_maker = self._GetArgsMaker(rng, shapes, dtypes)
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args = args_maker()
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self.assertAllClose(scipy_op(*args), lax_op(*args), atol=1e-3, rtol=1e-3,
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check_dtypes=False)
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self._CompileAndCheck(lax_op, args_maker, rtol=1e-4)
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if test_autodiff:
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def partial_lax_op(*vals):
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list_args = list(vals)
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for i in nondiff_argnums:
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list_args.insert(i, args[i])
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return lax_op(*list_args)
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assert list(nondiff_argnums) == sorted(set(nondiff_argnums))
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diff_args = [x for i, x in enumerate(args) if i not in nondiff_argnums]
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jtu.check_grads(partial_lax_op, diff_args, order=1,
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atol=jtu.if_device_under_test("tpu", .1, 1e-3),
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rtol=.1, eps=1e-3)
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@parameterized.named_parameters(jtu.cases_from_list(
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{"testcase_name": "_inshape={}_d={}".format(
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jtu.format_shape_dtype_string(shape, dtype), d),
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"shape": shape, "dtype": dtype, "d": d}
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for shape in all_shapes
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for dtype in float_dtypes
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for d in [1, 2, 5]))
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def testMultigammaln(self, shape, dtype, d):
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def scipy_fun(a):
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return osp_special.multigammaln(a, d)
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def lax_fun(a):
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return lsp_special.multigammaln(a, d)
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rng = jtu.rand_positive(self.rng())
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args_maker = lambda: [rng(shape, dtype) + (d - 1) / 2.]
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self._CheckAgainstNumpy(scipy_fun, lax_fun, args_maker,
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tol={np.float32: 1e-3, np.float64: 1e-14})
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self._CompileAndCheck(lax_fun, args_maker)
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def testIssue980(self):
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x = np.full((4,), -1e20, dtype=np.float32)
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self.assertAllClose(np.zeros((4,), dtype=np.float32),
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lsp_special.expit(x))
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def testIssue3758(self):
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x = np.array([1e5, 1e19, 1e10], dtype=np.float32)
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q = np.array([1., 40., 30.], dtype=np.float32)
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self.assertAllClose(np.array([1., 0., 0.], dtype=np.float32), lsp_special.zeta(x, q))
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def testXlogyShouldReturnZero(self):
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self.assertAllClose(lsp_special.xlogy(0., 0.), 0., check_dtypes=False)
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def testGradOfXlogyAtZero(self):
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partial_xlogy = functools.partial(lsp_special.xlogy, 0.)
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self.assertAllClose(api.grad(partial_xlogy)(0.), 0., check_dtypes=False)
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def testXlog1pyShouldReturnZero(self):
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self.assertAllClose(lsp_special.xlog1py(0., -1.), 0., check_dtypes=False)
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def testGradOfXlog1pyAtZero(self):
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partial_xlog1py = functools.partial(lsp_special.xlog1py, 0.)
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self.assertAllClose(api.grad(partial_xlog1py)(-1.), 0., check_dtypes=False)
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@parameterized.named_parameters(jtu.cases_from_list(
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{"testcase_name":
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"_maxdegree={}_inputsize={}".format(l_max, num_z),
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"l_max": l_max,
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"num_z": num_z}
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for l_max, num_z in zip([1, 2, 3], [6, 7, 8])))
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def testLpmn(self, l_max, num_z):
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# Points on which the associated Legendre functions areevaluated.
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z = np.linspace(-0.2, 0.9, num_z)
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actual_p_vals, actual_p_derivatives = lsp_special.lpmn(m=l_max, n=l_max, z=z)
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# The expected results are obtained from scipy.
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expected_p_vals = np.zeros((l_max + 1, l_max + 1, num_z))
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expected_p_derivatives = np.zeros((l_max + 1, l_max + 1, num_z))
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for i in range(num_z):
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val, derivative = osp_special.lpmn(l_max, l_max, z[i])
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expected_p_vals[:, :, i] = val
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expected_p_derivatives[:, :, i] = derivative
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with self.subTest('Test values.'):
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self.assertAllClose(actual_p_vals, expected_p_vals, rtol=1e-6, atol=3.2e-6)
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with self.subTest('Test derivatives.'):
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self.assertAllClose(actual_p_derivatives,expected_p_derivatives,
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rtol=1e-6, atol=8.4e-4)
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with self.subTest('Test JIT compatibility'):
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args_maker = lambda: [z]
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lsp_special_fn = lambda z: lsp_special.lpmn(l_max, l_max, z)
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self._CompileAndCheck(lsp_special_fn, args_maker)
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@parameterized.named_parameters(jtu.cases_from_list(
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{"testcase_name":
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"_maxdegree={}_inputsize={}".format(l_max, num_z),
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"l_max": l_max,
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"num_z": num_z}
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for l_max, num_z in zip([3, 4, 6, 32], [2, 3, 4, 64])))
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def testNormalizedLpmnValues(self, l_max, num_z):
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# Points on which the associated Legendre functions areevaluated.
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z = np.linspace(-0.2, 0.9, num_z)
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is_normalized = True
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actual_p_vals = lsp_special.lpmn_values(l_max, l_max, z, is_normalized)
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# The expected results are obtained from scipy.
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expected_p_vals = np.zeros((l_max + 1, l_max + 1, num_z))
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for i in range(num_z):
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expected_p_vals[:, :, i] = osp_special.lpmn(l_max, l_max, z[i])[0]
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def apply_normalization(a):
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"""Applies normalization to the associated Legendre functions."""
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num_m, num_l, _ = a.shape
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a_normalized = np.zeros_like(a)
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for m in range(num_m):
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for l in range(num_l):
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c0 = (2.0 * l + 1.0) * osp_special.factorial(l - m)
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c1 = (4.0 * np.pi) * osp_special.factorial(l + m)
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c2 = np.sqrt(c0 / c1)
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a_normalized[m, l] = c2 * a[m, l]
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return a_normalized
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# The results from scipy are not normalized and the comparison requires
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# normalizing the results.
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expected_p_vals_normalized = apply_normalization(expected_p_vals)
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with self.subTest('Test accuracy.'):
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self.assertAllClose(actual_p_vals, expected_p_vals_normalized, rtol=1e-6, atol=3.2e-6)
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with self.subTest('Test JIT compatibility'):
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args_maker = lambda: [z]
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lsp_special_fn = lambda z: lsp_special.lpmn_values(l_max, l_max, z, is_normalized)
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self._CompileAndCheck(lsp_special_fn, args_maker)
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def testSphHarmAccuracy(self):
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m = jnp.arange(-3, 3)[:, None]
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n = jnp.arange(3, 6)
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n_max = 5
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theta = 0.0
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phi = jnp.pi
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expected = lsp_special.sph_harm(m, n, theta, phi, n_max)
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actual = osp_special.sph_harm(m, n, theta, phi)
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self.assertAllClose(actual, expected, rtol=1e-8, atol=9e-5)
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def testSphHarmOrderZeroDegreeZero(self):
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"""Tests the spherical harmonics of order zero and degree zero."""
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theta = jnp.array([0.3])
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phi = jnp.array([2.3])
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n_max = 0
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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)
|
|
|
|
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=7e-8, atol=1.5e-8)
|
|
|
|
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)
|
|
|
|
@parameterized.named_parameters(jtu.cases_from_list(
|
|
{'testcase_name': '_maxdegree={}_inputsize={}_dtype={}'.format(
|
|
l_max, num_z, dtype),
|
|
'l_max': l_max, 'num_z': num_z, 'dtype': dtype}
|
|
for l_max, num_z in zip([1, 3, 8, 10], [2, 6, 7, 8])
|
|
for dtype in jtu.dtypes.all_integer))
|
|
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)
|
|
|
|
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)
|
|
|
|
@parameterized.named_parameters(jtu.cases_from_list(
|
|
{'testcase_name':
|
|
'_shape={}'
|
|
'_n_zero_sv={}_degeneracy={}_geometric_spectrum={}'
|
|
'_max_sv={}_method={}_side={}'
|
|
'_nonzero_condition_number={}_seed={}'.format(
|
|
jtu.format_shape_dtype_string(
|
|
shape, jnp.dtype(dtype).name).replace(" ", ""),
|
|
n_zero_sv, degeneracy, geometric_spectrum, max_sv,
|
|
method, side, nonzero_condition_number, seed
|
|
),
|
|
'n_zero_sv': n_zero_sv, 'degeneracy': degeneracy,
|
|
'geometric_spectrum': geometric_spectrum,
|
|
'max_sv': max_sv, 'shape': shape, 'method': method,
|
|
'side': side, 'nonzero_condition_number': nonzero_condition_number,
|
|
'dtype': dtype, 'seed': seed}
|
|
for n_zero_sv in n_zero_svs
|
|
for degeneracy in degeneracies
|
|
for geometric_spectrum in geometric_spectra
|
|
for max_sv in max_svs
|
|
for shape in polar_shapes
|
|
for method in methods
|
|
for side in sides
|
|
for nonzero_condition_number in nonzero_condition_numbers
|
|
for dtype in jtu.dtypes.floating
|
|
for seed in 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.")
|
|
if method == "svd":
|
|
raise unittest.SkipTest("Can't use SVD mode on TPU/GPU.")
|
|
|
|
np.random.seed(seed)
|
|
matrix, _ = _initialize_polar_test(
|
|
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 = 10 * 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.'):
|
|
assert 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))
|
|
|
|
@parameterized.named_parameters(jtu.cases_from_list(
|
|
{'testcase_name':
|
|
'_linear_size_={}_seed={}_dtype={}'.format(
|
|
linear_size, seed, jnp.dtype(dtype).name
|
|
),
|
|
'linear_size': linear_size, 'seed': seed, 'dtype': dtype}
|
|
for linear_size in linear_sizes
|
|
for seed in seeds
|
|
for dtype in jtu.dtypes.floating))
|
|
def test_spectral_dac_eigh(self, linear_size, seed, dtype):
|
|
if jtu.device_under_test != "cpu":
|
|
raise unittest.SkipTest("Skip eigh off CPU for now.")
|
|
if jnp.dtype(dtype).name in ("bfloat16", "float16"):
|
|
if jtu.device_under_test() != "cpu":
|
|
raise unittest.SkipTest("Skip half precision off CPU.")
|
|
|
|
np.random.seed(seed)
|
|
H = np.random.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, jax._src.scipy.eigh.eigh, H)
|
|
return
|
|
evs, V = jax._src.scipy.eigh.eigh(H)
|
|
ev_exp, eV_exp = jnp.linalg.eigh(H)
|
|
HV = jnp.dot(H, V, precision=lax.Precision.HIGHEST)
|
|
vV = evs * 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=30 * atol)
|
|
|
|
@parameterized.named_parameters(jtu.cases_from_list(
|
|
{'testcase_name':
|
|
'_linear_size_={}_seed={}_dtype={}'.format(
|
|
linear_size, seed, jnp.dtype(dtype).name
|
|
),
|
|
'linear_size': linear_size, 'seed': seed, 'dtype': dtype}
|
|
for linear_size in linear_sizes
|
|
for seed in seeds
|
|
for dtype in jtu.dtypes.floating))
|
|
def test_spectral_dac_svd(self, linear_size, seed, dtype):
|
|
if jnp.dtype(dtype).name in ("bfloat16", "float16"):
|
|
if jtu.device_under_test() != "cpu":
|
|
raise unittest.SkipTest("Skip half precision off CPU.")
|
|
|
|
np.random.seed(seed)
|
|
A = np.random.randn(linear_size, linear_size).astype(dtype)
|
|
if jnp.dtype(dtype).name in ("bfloat16", "float16"):
|
|
self.assertRaises(
|
|
NotImplementedError, jax._src.scipy.eigh.svd, A)
|
|
return
|
|
S_expected = np.linalg.svd(A, compute_uv=False)
|
|
U, S, V = jax._src.scipy.eigh.svd(A)
|
|
recon = jnp.dot((U * S), V, precision=lax.Precision.HIGHEST)
|
|
eps = jnp.finfo(dtype).eps
|
|
eps = eps * jnp.linalg.norm(A) * 10
|
|
self.assertAllClose(np.sort(S), np.sort(S_expected), atol=eps)
|
|
self.assertAllClose(A, recon, atol=eps)
|
|
|
|
# U is unitary.
|
|
u_unitary_delta = jnp.dot(U.conj().T, U, precision=lax.Precision.HIGHEST)
|
|
u_eye = jnp.eye(u_unitary_delta.shape[0], dtype=dtype)
|
|
self.assertAllClose(u_unitary_delta, u_eye, atol=eps)
|
|
|
|
# V is unitary.
|
|
v_unitary_delta = jnp.dot(V.conj().T, V, precision=lax.Precision.HIGHEST)
|
|
v_eye = jnp.eye(v_unitary_delta.shape[0], dtype=dtype)
|
|
self.assertAllClose(v_unitary_delta, v_eye, atol=eps)
|
|
|
|
|
|
if __name__ == "__main__":
|
|
absltest.main(testLoader=jtu.JaxTestLoader())
|