import itertools as it import math import pytest import numpy as np from scipy._lib._array_api import (is_array_api_strict, make_xp_test_case, xp_default_dtype, xp_device) from scipy._lib._array_api_no_0d import (xp_assert_equal, xp_assert_close, xp_assert_less) from scipy.special import log_softmax, logsumexp, softmax from scipy.special._logsumexp import _wrap_radians dtypes = ['float32', 'float64', 'int32', 'int64', 'complex64', 'complex128'] integral_dtypes = ['int32', 'int64'] 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) xp_assert_close(res, ref, atol=0) # numpy warning filters don't work for dask (dask/dask#3245) # (also we should not expect the numpy warning filter to work for any Array API # library) @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning") @pytest.mark.filterwarnings("ignore:divide by zero encountered:RuntimeWarning") @pytest.mark.filterwarnings("ignore:overflow encountered:RuntimeWarning") @make_xp_test_case(logsumexp) 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 ref = xp.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])) def test_xp_invalid_input(self, arg): assert logsumexp(arg) == logsumexp(np.asarray(np.atleast_1d(arg))) def test_array_like(self): a = [1000, 1000] desired = np.asarray(1000.0 + math.log(2.0)) 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) desired_dtype = (xp.asarray(1.).dtype if xp.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) if is_array_api_strict(xp): # special-case for `TypeError: array_api_strict.float32 and # and array_api_strict.int64 cannot be type promoted together` xp_float_dtypes = [dtype for dtype in [xp_dtype_a, xp_dtype_b] if not xp.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.result_type(*xp_float_dtypes) else: desired_dtype = xp.result_type(xp_dtype_a, xp_dtype_b) if xp.isdtype(desired_dtype, 'integral'): desired_dtype = xp_default_dtype(xp) 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.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) @pytest.mark.parametrize('x,y', it.product( [ -np.inf, np.inf, complex(-np.inf, 0.), complex(-np.inf, -0.), complex(-np.inf, np.inf), complex(-np.inf, -np.inf), complex(np.inf, 0.), complex(np.inf, -0.), complex(np.inf, np.inf), complex(np.inf, -np.inf), # Phase in each quadrant. complex(-np.inf, 0.7533), complex(-np.inf, 2.3562), complex(-np.inf, 3.9270), complex(-np.inf, 5.4978), complex(np.inf, 0.7533), complex(np.inf, 2.3562), complex(np.inf, 3.9270), complex(np.inf, 5.4978), ], repeat=2) ) def test_gh22601_infinite_elements(self, x, y, xp): # Test that `logsumexp` does reasonable things in the presence of # real and complex infinities. res = logsumexp(xp.asarray([x, y])) ref = xp.log(xp.sum(xp.exp(xp.asarray([x, y])))) xp_assert_equal(res, ref) def test_no_writeback(self, xp): """Test that logsumexp doesn't accidentally write back to its parameters.""" a = xp.asarray([5., 4.]) b = xp.asarray([3., 2.]) logsumexp(a) logsumexp(a, b=b) xp_assert_equal(a, xp.asarray([5., 4.])) xp_assert_equal(b, xp.asarray([3., 2.])) @pytest.mark.parametrize("x_raw", [1.0, 1.0j, []]) def test_device(self, x_raw, xp, devices): """Test input device propagation to output.""" for d in devices: x = xp.asarray(x_raw, device=d) assert xp_device(logsumexp(x)) == xp_device(x) assert xp_device(logsumexp(x, b=x)) == xp_device(x) def test_gh22903(self, xp): # gh-22903 reported that `logsumexp` produced NaN where the weight associated # with the max magnitude element was negative and `return_sign=False`, even if # the net result should be the log of a positive number. # result is log of positive number a = xp.asarray([3.06409428, 0.37251854, 3.87471931]) b = xp.asarray([1.88190708, 2.84174795, -0.85016884]) xp_assert_close(logsumexp(a, b=b), logsumexp(a, b=b, return_sign=True)[0]) # result is log of negative number b = xp.asarray([1.88190708, 2.84174795, -3.85016884]) xp_assert_close(logsumexp(a, b=b), xp.asarray(xp.nan)) @make_xp_test_case(softmax) class TestSoftmax: def test_softmax_fixtures(self, xp): xp_assert_close(softmax(xp.asarray([1000., 0., 0., 0.])), xp.asarray([1., 0., 0., 0.]), rtol=1e-13) xp_assert_close(softmax(xp.asarray([1., 1.])), xp.asarray([.5, .5]), rtol=1e-13) xp_assert_close(softmax(xp.asarray([0., 1.])), xp.asarray([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 = xp.arange(4, dtype=xp.float64) expected = xp.asarray([0.03205860328008499, 0.08714431874203256, 0.23688281808991013, 0.6439142598879722], dtype=xp.float64) xp_assert_close(softmax(x), expected, rtol=1e-13) # Translation property. If all the values are changed by the same amount, # the softmax result does not change. xp_assert_close(softmax(x + 100), expected, rtol=1e-13) # When axis=None, softmax operates on the entire array, and preserves # the shape. xp_assert_close(softmax(xp.reshape(x, (2, 2))), xp.reshape(expected, (2, 2)), rtol=1e-13) def test_softmax_multi_axes(self, xp): xp_assert_close(softmax(xp.asarray([[1000., 0.], [1000., 0.]]), axis=0), xp.asarray([[.5, .5], [.5, .5]]), rtol=1e-13) xp_assert_close(softmax(xp.asarray([[1000., 0.], [1000., 0.]]), axis=1), xp.asarray([[1., 0.], [1., 0.]]), rtol=1e-13) # Expected value computed using mpmath (with mpmath.mp.dps = 200) and then # converted to float. x = xp.asarray([[-25., 0., 25., 50.], [ 1., 325., 749., 750.]]) expected = xp.asarray([[2.678636961770877e-33, 1.9287498479371314e-22, 1.3887943864771144e-11, 0.999999999986112], [0.0, 1.9444526359919372e-185, 0.2689414213699951, 0.7310585786300048]]) xp_assert_close(softmax(x, axis=1), expected, rtol=1e-13) xp_assert_close(softmax(x.T, axis=0), expected.T, rtol=1e-13) # 3-d input, with a tuple for the axis. x3d = xp.reshape(x, (2, 2, 2)) xp_assert_close(softmax(x3d, axis=(1, 2)), xp.reshape(expected, (2, 2, 2)), rtol=1e-13) @pytest.mark.xfail_xp_backends("array_api_strict", reason="int->float promotion") def test_softmax_int_array(self, xp): xp_assert_close(softmax(xp.asarray([1000, 0, 0, 0])), xp.asarray([1., 0., 0., 0.]), rtol=1e-13) def test_softmax_scalar(self): xp_assert_close(softmax(1000), np.asarray(1.), rtol=1e-13) def test_softmax_array_like(self): xp_assert_close(softmax([1000, 0, 0, 0]), np.asarray([1., 0., 0., 0.]), rtol=1e-13) @make_xp_test_case(log_softmax) class TestLogSoftmax: def test_log_softmax_basic(self, xp): xp_assert_close(log_softmax(xp.asarray([1000., 1.])), xp.asarray([0., -999.]), rtol=1e-13) @pytest.mark.xfail_xp_backends("array_api_strict", reason="int->float promotion") def test_log_softmax_int_array(self, xp): xp_assert_close(log_softmax(xp.asarray([1000, 1])), xp.asarray([0., -999.]), rtol=1e-13) def test_log_softmax_scalar(self): xp_assert_close(log_softmax(1.0), 0.0, rtol=1e-13) def test_log_softmax_array_like(self): xp_assert_close(log_softmax([1000, 1]), np.asarray([0., -999.]), rtol=1e-13) @staticmethod def data_1d(xp): x = xp.arange(4, dtype=xp.float64) # Expected value computed using mpmath (with mpmath.mp.dps = 200) expect = [-3.4401896985611953, -2.4401896985611953, -1.4401896985611953, -0.44018969856119533] return x, xp.asarray(expect, dtype=xp.float64) @staticmethod def data_2d(xp): x = xp.reshape(xp.arange(8, dtype=xp.float64), (2, 4)) # Expected value computed using mpmath (with mpmath.mp.dps = 200) expect = [[-3.4401896985611953, -2.4401896985611953, -1.4401896985611953, -0.44018969856119533], [-3.4401896985611953, -2.4401896985611953, -1.4401896985611953, -0.44018969856119533]] return x, xp.asarray(expect, dtype=xp.float64) @pytest.mark.parametrize("offset", [0, 100]) def test_log_softmax_translation(self, offset, xp): # Translation property. If all the values are changed by the same amount, # the softmax result does not change. x, expect = self.data_1d(xp) x += offset xp_assert_close(log_softmax(x), expect, rtol=1e-13) def test_log_softmax_noneaxis(self, xp): # When axis=None, softmax operates on the entire array, and preserves # the shape. x, expect = self.data_1d(xp) x = xp.reshape(x, (2, 2)) expect = xp.reshape(expect, (2, 2)) xp_assert_close(log_softmax(x), expect, rtol=1e-13) @pytest.mark.parametrize('axis_2d, expected_2d', [ (0, np.log(0.5) * np.ones((2, 2))), (1, [[0., -999.], [0., -999.]]), ]) def test_axes(self, axis_2d, expected_2d, xp): x = xp.asarray([[1000., 1.], [1000., 1.]]) xp_assert_close(log_softmax(x, axis=axis_2d), xp.asarray(expected_2d, dtype=x.dtype), rtol=1e-13) def test_log_softmax_2d_axis1(self, xp): x, expect = self.data_2d(xp) xp_assert_close(log_softmax(x, axis=1), expect, rtol=1e-13) def test_log_softmax_2d_axis0(self, xp): x, expect = self.data_2d(xp) xp_assert_close(log_softmax(x.T, axis=0), expect.T, rtol=1e-13) def test_log_softmax_3d(self, xp): # 3D input, with a tuple for the axis. x, expect = self.data_2d(xp) x = xp.reshape(x, (2, 2, 2)) expect = xp.reshape(expect, (2, 2, 2)) xp_assert_close(log_softmax(x, axis=(1, 2)), expect, rtol=1e-13)