# Copyright 2022 Google LLC # # 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 """Tests for the library of QDWH-based singular value decomposition.""" import functools import jax from jax.config import config import jax.numpy as jnp import numpy as np import scipy.linalg as osp_linalg from jax._src.lax import svd from jax._src import test_util as jtu from absl.testing import absltest from absl.testing import parameterized config.parse_flags_with_absl() _JAX_ENABLE_X64 = config.x64_enabled # Input matrix data type for SvdTest. _SVD_TEST_DTYPE = np.float64 if _JAX_ENABLE_X64 else np.float32 # Machine epsilon used by SvdTest. _SVD_TEST_EPS = jnp.finfo(_SVD_TEST_DTYPE).eps # SvdTest relative tolerance. _SVD_RTOL = 1E-6 if _JAX_ENABLE_X64 else 1E-2 _MAX_LOG_CONDITION_NUM = 9 if _JAX_ENABLE_X64 else 4 @jtu.with_config(jax_numpy_rank_promotion='allow') class SvdTest(jtu.JaxTestCase): @parameterized.named_parameters(jtu.cases_from_list( { # pylint:disable=g-complex-comprehension 'testcase_name': '_m={}_by_n={}_log_cond={}_full_matrices={}'.format( m, n, log_cond, full_matrices), 'm': m, 'n': n, 'log_cond': log_cond, 'full_matrices': full_matrices} for m, n in zip([2, 8, 10, 20], [4, 6, 10, 18]) for log_cond in np.linspace(1, _MAX_LOG_CONDITION_NUM, 4) for full_matrices in [True, False])) def testSvdWithRectangularInput(self, m, n, log_cond, full_matrices): """Tests SVD with rectangular input.""" with jax.default_matmul_precision('float32'): a = np.random.uniform( low=0.3, high=0.9, size=(m, n)).astype(_SVD_TEST_DTYPE) u, s, v = osp_linalg.svd(a, full_matrices=False) cond = 10**log_cond s = jnp.linspace(cond, 1, min(m, n)) a = (u * s) @ v a = a.astype(complex) * (1 + 1j) osp_linalg_fn = functools.partial( osp_linalg.svd, full_matrices=full_matrices) actual_u, actual_s, actual_v = svd.svd(a, full_matrices=full_matrices) k = min(m, n) if m > n: unitary_u = jnp.real(actual_u.T.conj() @ actual_u) unitary_v = jnp.real(actual_v.T.conj() @ actual_v) unitary_u_size = m if full_matrices else k unitary_v_size = k else: unitary_u = jnp.real(actual_u @ actual_u.T.conj()) unitary_v = jnp.real(actual_v @ actual_v.T.conj()) unitary_u_size = k unitary_v_size = n if full_matrices else k _, expected_s, _ = osp_linalg_fn(a) svd_fn = lambda a: svd.svd(a, full_matrices=full_matrices) args_maker = lambda: [a] with self.subTest('Test JIT compatibility'): self._CompileAndCheck(svd_fn, args_maker) with self.subTest('Test unitary u.'): self.assertAllClose(np.eye(unitary_u_size), unitary_u, rtol=_SVD_RTOL, atol=2E-3) with self.subTest('Test unitary v.'): self.assertAllClose(np.eye(unitary_v_size), unitary_v, rtol=_SVD_RTOL, atol=2E-3) with self.subTest('Test s.'): self.assertAllClose( expected_s, jnp.real(actual_s), rtol=_SVD_RTOL, atol=1E-6) @parameterized.named_parameters(jtu.cases_from_list( {'testcase_name': f'_m={m}_by_n={n}', 'm': m, 'n': n} for m, n in zip([50, 6], [3, 60]))) def testSvdWithSkinnyTallInput(self, m, n): """Tests SVD with skinny and tall input.""" # Generates a skinny and tall input with jax.default_matmul_precision('float32'): np.random.seed(1235) a = np.random.randn(m, n).astype(_SVD_TEST_DTYPE) u, s, v = svd.svd(a, full_matrices=False, hermitian=False) relative_diff = np.linalg.norm(a - (u * s) @ v) / np.linalg.norm(a) np.testing.assert_almost_equal(relative_diff, 1E-6, decimal=6) @parameterized.named_parameters(jtu.cases_from_list( { # pylint:disable=g-complex-comprehension 'testcase_name': f'_m={m}_r={r}_log_cond={log_cond}', 'm': m, 'r': r, 'log_cond': log_cond} for m, r in zip([8, 8, 8, 10], [3, 5, 7, 9]) for log_cond in np.linspace(1, 3, 3))) def testSvdWithOnRankDeficientInput(self, m, r, log_cond): """Tests SVD with rank-deficient input.""" with jax.default_matmul_precision('float32'): a = jnp.triu(jnp.ones((m, m))).astype(_SVD_TEST_DTYPE) # Generates a rank-deficient input. u, s, v = jnp.linalg.svd(a, full_matrices=False) cond = 10**log_cond s = jnp.linspace(cond, 1, m) s = s.at[r:m].set(jnp.zeros((m-r,))) a = (u * s) @ v with jax.default_matmul_precision('float32'): u, s, v = svd.svd(a, full_matrices=False, hermitian=False) diff = np.linalg.norm(a - (u * s) @ v) np.testing.assert_almost_equal(diff, 1E-4, decimal=2) @parameterized.named_parameters(jtu.cases_from_list( { # pylint:disable=g-complex-comprehension 'testcase_name': '_m={}_by_n={}_log_cond={}_full_matrices={}'.format( m, n, log_cond, full_matrices), 'm': m, 'n': n, 'log_cond': log_cond, 'full_matrices': full_matrices} for m, n in zip([2, 8, 10, 20], [4, 6, 10, 18]) for log_cond in np.linspace(1, _MAX_LOG_CONDITION_NUM, 4) for full_matrices in [True, False])) def testSingularValues(self, m, n, log_cond, full_matrices): """Tests singular values.""" with jax.default_matmul_precision('float32'): a = np.random.uniform( low=0.3, high=0.9, size=(m, n)).astype(_SVD_TEST_DTYPE) u, s, v = osp_linalg.svd(a, full_matrices=False) cond = 10**log_cond s = np.linspace(cond, 1, min(m, n)) a = (u * s) @ v a = a + 1j * a # Only computes singular values. compute_uv = False osp_linalg_fn = functools.partial( osp_linalg.svd, full_matrices=full_matrices, compute_uv=compute_uv) actual_s = svd.svd(a, full_matrices=full_matrices, compute_uv=compute_uv) expected_s = osp_linalg_fn(a) svd_fn = lambda a: svd.svd(a, full_matrices=full_matrices) args_maker = lambda: [a] with self.subTest('Test JIT compatibility'): self._CompileAndCheck(svd_fn, args_maker) with self.subTest('Test s.'): self.assertAllClose(expected_s, actual_s, rtol=_SVD_RTOL, atol=1E-6) with self.subTest('Test non-increasing order.'): # Computes `actual_diff[i] = s[i+1] - s[i]`. actual_diff = jnp.diff(actual_s, append=0) np.testing.assert_array_less(actual_diff, np.zeros_like(actual_diff)) @parameterized.named_parameters([ {'testcase_name': f'_m={m}_by_n={n}_full_matrices={full_matrices}_' # pylint:disable=g-complex-comprehension f'compute_uv={compute_uv}_dtype={dtype}', 'm': m, 'n': n, 'full_matrices': full_matrices, # pylint:disable=undefined-variable 'compute_uv': compute_uv, 'dtype': dtype} # pylint:disable=undefined-variable for m, n in zip([2, 4, 8], [4, 4, 6]) for full_matrices in [True, False] for compute_uv in [True, False] for dtype in jtu.dtypes.floating + jtu.dtypes.complex ]) def testSvdOnZero(self, m, n, full_matrices, compute_uv, dtype): """Tests SVD on matrix of all zeros.""" osp_fun = functools.partial(osp_linalg.svd, full_matrices=full_matrices, compute_uv=compute_uv) lax_fun = functools.partial(svd.svd, full_matrices=full_matrices, compute_uv=compute_uv) args_maker_svd = lambda: [jnp.zeros((m, n), dtype=dtype)] self._CheckAgainstNumpy(osp_fun, lax_fun, args_maker_svd) self._CompileAndCheck(lax_fun, args_maker_svd) @parameterized.named_parameters([ {'testcase_name': f'_m={m}_by_n={n}_r={r}_c={c}_dtype={dtype}', 'm': m, 'n': n, 'r': r, 'c': c, 'dtype': dtype} for m, n, r, c in zip([2, 4, 8], [4, 4, 6], [1, 0, 1], [1, 0, 1]) for dtype in jtu.dtypes.floating ]) def testSvdOnTinyElement(self, m, n, r, c, dtype): """Tests SVD on matrix of zeros and close-to-zero entries.""" a = jnp.zeros((m, n), dtype=dtype) tiny_element = jnp.finfo(a).tiny a = a.at[r, c].set(tiny_element) @jax.jit def lax_fun(a): return svd.svd(a, full_matrices=False, compute_uv=False, hermitian=False) actual_s = lax_fun(a) k = min(m, n) expected_s = np.zeros((k,), dtype=dtype) expected_s[0] = tiny_element self.assertAllClose(expected_s, jnp.real(actual_s), rtol=_SVD_RTOL, atol=1E-6) if __name__ == '__main__': absltest.main(testLoader=jtu.JaxTestLoader())