import math import pytest import numpy as np from numpy.testing import assert_allclose from scipy.conftest import array_api_compatible from scipy._lib._array_api import array_namespace, is_array_api_strict from scipy._lib._array_api_no_0d import (xp_assert_equal, xp_assert_close, xp_assert_less) from scipy.special import logsumexp, softmax from scipy.special._logsumexp import _wrap_radians dtypes = ['float32', 'float64', 'int32', 'int64', 'complex64', 'complex128'] integral_dtypes = ['int32', 'int64'] @array_api_compatible @pytest.mark.usefixtures("skip_xp_backends") @pytest.mark.skip_xp_backends('jax.numpy', reason="JAX arrays do not support item assignment") def test_wrap_radians(xp): x = xp.asarray([-math.pi-1, -math.pi, -1, -1e-300, 0, 1e-300, 1, math.pi, math.pi+1]) ref = xp.asarray([math.pi-1, math.pi, -1, -1e-300, 0, 1e-300, 1, math.pi, -math.pi+1]) res = _wrap_radians(x, xp) xp_assert_close(res, ref, atol=0) @array_api_compatible @pytest.mark.usefixtures("skip_xp_backends") @pytest.mark.skip_xp_backends('jax.numpy', reason="JAX arrays do not support item assignment") class TestLogSumExp: def test_logsumexp(self, xp): # Test with zero-size array a = xp.asarray([]) desired = xp.asarray(-xp.inf) xp_assert_equal(logsumexp(a), desired) # Test whether logsumexp() function correctly handles large inputs. a = xp.arange(200., dtype=xp.float64) desired = xp.log(xp.sum(xp.exp(a))) xp_assert_close(logsumexp(a), desired) # Now test with large numbers b = xp.asarray([1000., 1000.]) desired = xp.asarray(1000.0 + math.log(2.0)) xp_assert_close(logsumexp(b), desired) n = 1000 b = xp.full((n,), 10000) desired = xp.asarray(10000.0 + math.log(n)) xp_assert_close(logsumexp(b), desired) x = xp.asarray([1e-40] * 1000000) logx = xp.log(x) X = xp.stack([x, x]) logX = xp.stack([logx, logx]) xp_assert_close(xp.exp(logsumexp(logX)), xp.sum(X)) xp_assert_close(xp.exp(logsumexp(logX, axis=0)), xp.sum(X, axis=0)) xp_assert_close(xp.exp(logsumexp(logX, axis=1)), xp.sum(X, axis=1)) # Handling special values properly inf = xp.asarray([xp.inf]) nan = xp.asarray([xp.nan]) xp_assert_equal(logsumexp(inf), inf[0]) xp_assert_equal(logsumexp(-inf), -inf[0]) xp_assert_equal(logsumexp(nan), nan[0]) xp_assert_equal(logsumexp(xp.asarray([-xp.inf, -xp.inf])), -inf[0]) # Handling an array with different magnitudes on the axes a = xp.asarray([[1e10, 1e-10], [-1e10, -np.inf]]) ref = xp.asarray([1e10, -1e10]) xp_assert_close(logsumexp(a, axis=-1), ref) # Test keeping dimensions xp_test = array_namespace(a) # `torch` needs `expand_dims` ref = xp_test.expand_dims(ref, axis=-1) xp_assert_close(logsumexp(a, axis=-1, keepdims=True), ref) # Test multiple axes xp_assert_close(logsumexp(a, axis=(-1, -2)), xp.asarray(1e10)) def test_logsumexp_b(self, xp): a = xp.arange(200., dtype=xp.float64) b = xp.arange(200., 0., -1.) desired = xp.log(xp.sum(b*xp.exp(a))) xp_assert_close(logsumexp(a, b=b), desired) a = xp.asarray([1000, 1000]) b = xp.asarray([1.2, 1.2]) desired = xp.asarray(1000 + math.log(2 * 1.2)) xp_assert_close(logsumexp(a, b=b), desired) x = xp.asarray([1e-40] * 100000) b = xp.linspace(1, 1000, 100000) logx = xp.log(x) X = xp.stack((x, x)) logX = xp.stack((logx, logx)) B = xp.stack((b, b)) xp_assert_close(xp.exp(logsumexp(logX, b=B)), xp.sum(B * X)) xp_assert_close(xp.exp(logsumexp(logX, b=B, axis=0)), xp.sum(B * X, axis=0)) xp_assert_close(xp.exp(logsumexp(logX, b=B, axis=1)), xp.sum(B * X, axis=1)) def test_logsumexp_sign(self, xp): a = xp.asarray([1, 1, 1]) b = xp.asarray([1, -1, -1]) r, s = logsumexp(a, b=b, return_sign=True) xp_assert_close(r, xp.asarray(1.)) xp_assert_equal(s, xp.asarray(-1.)) def test_logsumexp_sign_zero(self, xp): a = xp.asarray([1, 1]) b = xp.asarray([1, -1]) r, s = logsumexp(a, b=b, return_sign=True) assert not xp.isfinite(r) assert not xp.isnan(r) assert r < 0 assert s == 0 def test_logsumexp_sign_shape(self, xp): a = xp.ones((1, 2, 3, 4)) b = xp.ones_like(a) r, s = logsumexp(a, axis=2, b=b, return_sign=True) assert r.shape == s.shape == (1, 2, 4) r, s = logsumexp(a, axis=(1, 3), b=b, return_sign=True) assert r.shape == s.shape == (1,3) def test_logsumexp_complex_sign(self, xp): a = xp.asarray([1 + 1j, 2 - 1j, -2 + 3j]) r, s = logsumexp(a, return_sign=True) expected_sumexp = xp.sum(xp.exp(a)) # This is the numpy>=2.0 convention for np.sign expected_sign = expected_sumexp / xp.abs(expected_sumexp) xp_assert_close(s, expected_sign) xp_assert_close(s * xp.exp(r), expected_sumexp) def test_logsumexp_shape(self, xp): a = xp.ones((1, 2, 3, 4)) b = xp.ones_like(a) r = logsumexp(a, axis=2, b=b) assert r.shape == (1, 2, 4) r = logsumexp(a, axis=(1, 3), b=b) assert r.shape == (1, 3) def test_logsumexp_b_zero(self, xp): a = xp.asarray([1, 10000]) b = xp.asarray([1, 0]) xp_assert_close(logsumexp(a, b=b), xp.asarray(1.)) def test_logsumexp_b_shape(self, xp): a = xp.zeros((4, 1, 2, 1)) b = xp.ones((3, 1, 5)) logsumexp(a, b=b) @pytest.mark.parametrize('arg', (1, [1, 2, 3])) @pytest.mark.skip_xp_backends(np_only=True) def test_xp_invalid_input(self, arg, xp): assert logsumexp(arg) == logsumexp(np.asarray(np.atleast_1d(arg))) @pytest.mark.skip_xp_backends(np_only=True, reason="Lists correspond with NumPy backend") def test_list(self, xp): a = [1000, 1000] desired = xp.asarray(1000.0 + math.log(2.0), dtype=np.float64) xp_assert_close(logsumexp(a), desired) @pytest.mark.parametrize('dtype', dtypes) def test_dtypes_a(self, dtype, xp): dtype = getattr(xp, dtype) a = xp.asarray([1000., 1000.], dtype=dtype) xp_test = array_namespace(a) # torch needs compatible `isdtype` desired_dtype = (xp.asarray(1.).dtype if xp_test.isdtype(dtype, 'integral') else dtype) # true for all libraries tested desired = xp.asarray(1000.0 + math.log(2.0), dtype=desired_dtype) xp_assert_close(logsumexp(a), desired) @pytest.mark.parametrize('dtype_a', dtypes) @pytest.mark.parametrize('dtype_b', dtypes) def test_dtypes_ab(self, dtype_a, dtype_b, xp): xp_dtype_a = getattr(xp, dtype_a) xp_dtype_b = getattr(xp, dtype_b) a = xp.asarray([2, 1], dtype=xp_dtype_a) b = xp.asarray([1, -1], dtype=xp_dtype_b) xp_test = array_namespace(a, b) # torch needs compatible result_type if is_array_api_strict(xp): xp_float_dtypes = [dtype for dtype in [xp_dtype_a, xp_dtype_b] if not xp_test.isdtype(dtype, 'integral')] if len(xp_float_dtypes) < 2: # at least one is integral xp_float_dtypes.append(xp.asarray(1.).dtype) desired_dtype = xp_test.result_type(*xp_float_dtypes) else: # True for all libraries tested desired_dtype = xp_test.result_type(xp_dtype_a, xp_dtype_b, xp.float32) desired = xp.asarray(math.log(math.exp(2) - math.exp(1)), dtype=desired_dtype) xp_assert_close(logsumexp(a, b=b), desired) def test_gh18295(self, xp): # gh-18295 noted loss of precision when real part of one element is much # larger than the rest. Check that this is resolved. a = xp.asarray([0.0, -40.0]) res = logsumexp(a) ref = xp.logaddexp(a[0], a[1]) xp_assert_close(res, ref) @pytest.mark.parametrize('dtype', ['complex64', 'complex128']) def test_gh21610(self, xp, dtype): # gh-21610 noted that `logsumexp` could return imaginary components # outside the range (-pi, pi]. Check that this is resolved. # While working on this, I noticed that all other tests passed even # when the imaginary component of the result was zero. This suggested # the need of a stronger test with imaginary dtype. rng = np.random.default_rng(324984329582349862) dtype = getattr(xp, dtype) shape = (10, 100) x = rng.uniform(1, 40, shape) + 1.j * rng.uniform(1, 40, shape) x = xp.asarray(x, dtype=dtype) res = logsumexp(x, axis=1) ref = xp.log(xp.sum(xp.exp(x), axis=1)) max = xp.full_like(xp.imag(res), xp.asarray(xp.pi)) xp_assert_less(xp.abs(xp.imag(res)), max) xp_assert_close(res, ref) out, sgn = logsumexp(x, return_sign=True, axis=1) ref = xp.sum(xp.exp(x), axis=1) xp_assert_less(xp.abs(xp.imag(sgn)), max) xp_assert_close(out, xp.real(xp.log(ref))) xp_assert_close(sgn, ref/xp.abs(ref)) def test_gh21709_small_imaginary(self, xp): # Test that `logsumexp` does not lose relative precision of # small imaginary components x = xp.asarray([0, 0.+2.2204460492503132e-17j]) res = logsumexp(x) # from mpmath import mp # mp.dps = 100 # x, y = mp.mpc(0), mp.mpc('0', '2.2204460492503132e-17') # ref = complex(mp.log(mp.exp(x) + mp.exp(y))) ref = xp.asarray(0.6931471805599453+1.1102230246251566e-17j) xp_assert_close(xp.real(res), xp.real(ref)) xp_assert_close(xp.imag(res), xp.imag(ref), atol=0, rtol=1e-15) class TestSoftmax: def test_softmax_fixtures(self): assert_allclose(softmax([1000, 0, 0, 0]), np.array([1, 0, 0, 0]), rtol=1e-13) assert_allclose(softmax([1, 1]), np.array([.5, .5]), rtol=1e-13) assert_allclose(softmax([0, 1]), np.array([1, np.e])/(1 + np.e), rtol=1e-13) # Expected value computed using mpmath (with mpmath.mp.dps = 200) and then # converted to float. x = np.arange(4) expected = np.array([0.03205860328008499, 0.08714431874203256, 0.23688281808991013, 0.6439142598879722]) assert_allclose(softmax(x), expected, rtol=1e-13) # Translation property. If all the values are changed by the same amount, # the softmax result does not change. assert_allclose(softmax(x + 100), expected, rtol=1e-13) # When axis=None, softmax operates on the entire array, and preserves # the shape. assert_allclose(softmax(x.reshape(2, 2)), expected.reshape(2, 2), rtol=1e-13) def test_softmax_multi_axes(self): assert_allclose(softmax([[1000, 0], [1000, 0]], axis=0), np.array([[.5, .5], [.5, .5]]), rtol=1e-13) assert_allclose(softmax([[1000, 0], [1000, 0]], axis=1), np.array([[1, 0], [1, 0]]), rtol=1e-13) # Expected value computed using mpmath (with mpmath.mp.dps = 200) and then # converted to float. x = np.array([[-25, 0, 25, 50], [1, 325, 749, 750]]) expected = np.array([[2.678636961770877e-33, 1.9287498479371314e-22, 1.3887943864771144e-11, 0.999999999986112], [0.0, 1.9444526359919372e-185, 0.2689414213699951, 0.7310585786300048]]) assert_allclose(softmax(x, axis=1), expected, rtol=1e-13) assert_allclose(softmax(x.T, axis=0), expected.T, rtol=1e-13) # 3-d input, with a tuple for the axis. x3d = x.reshape(2, 2, 2) assert_allclose(softmax(x3d, axis=(1, 2)), expected.reshape(2, 2, 2), rtol=1e-13)