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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)
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