208 lines
6.4 KiB
Python
208 lines
6.4 KiB
Python
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import numpy as np
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from numpy.testing import (assert_almost_equal, assert_equal, assert_allclose,
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assert_array_almost_equal, assert_)
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from scipy.special import logsumexp, softmax
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def test_logsumexp():
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# Test whether logsumexp() function correctly handles large inputs.
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a = np.arange(200)
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desired = np.log(np.sum(np.exp(a)))
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assert_almost_equal(logsumexp(a), desired)
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# Now test with large numbers
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b = [1000, 1000]
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desired = 1000.0 + np.log(2.0)
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assert_almost_equal(logsumexp(b), desired)
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n = 1000
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b = np.full(n, 10000, dtype='float64')
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desired = 10000.0 + np.log(n)
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assert_almost_equal(logsumexp(b), desired)
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x = np.array([1e-40] * 1000000)
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logx = np.log(x)
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X = np.vstack([x, x])
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logX = np.vstack([logx, logx])
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assert_array_almost_equal(np.exp(logsumexp(logX)), X.sum())
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assert_array_almost_equal(np.exp(logsumexp(logX, axis=0)), X.sum(axis=0))
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assert_array_almost_equal(np.exp(logsumexp(logX, axis=1)), X.sum(axis=1))
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# Handling special values properly
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assert_equal(logsumexp(np.inf), np.inf)
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assert_equal(logsumexp(-np.inf), -np.inf)
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assert_equal(logsumexp(np.nan), np.nan)
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assert_equal(logsumexp([-np.inf, -np.inf]), -np.inf)
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# Handling an array with different magnitudes on the axes
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assert_array_almost_equal(logsumexp([[1e10, 1e-10],
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[-1e10, -np.inf]], axis=-1),
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[1e10, -1e10])
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# Test keeping dimensions
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assert_array_almost_equal(logsumexp([[1e10, 1e-10],
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[-1e10, -np.inf]],
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axis=-1,
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keepdims=True),
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[[1e10], [-1e10]])
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# Test multiple axes
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assert_array_almost_equal(logsumexp([[1e10, 1e-10],
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[-1e10, -np.inf]],
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axis=(-1,-2)),
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1e10)
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def test_logsumexp_b():
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a = np.arange(200)
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b = np.arange(200, 0, -1)
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desired = np.log(np.sum(b*np.exp(a)))
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assert_almost_equal(logsumexp(a, b=b), desired)
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a = [1000, 1000]
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b = [1.2, 1.2]
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desired = 1000 + np.log(2 * 1.2)
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assert_almost_equal(logsumexp(a, b=b), desired)
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x = np.array([1e-40] * 100000)
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b = np.linspace(1, 1000, 100000)
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logx = np.log(x)
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X = np.vstack((x, x))
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logX = np.vstack((logx, logx))
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B = np.vstack((b, b))
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assert_array_almost_equal(np.exp(logsumexp(logX, b=B)), (B * X).sum())
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assert_array_almost_equal(np.exp(logsumexp(logX, b=B, axis=0)),
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(B * X).sum(axis=0))
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assert_array_almost_equal(np.exp(logsumexp(logX, b=B, axis=1)),
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(B * X).sum(axis=1))
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def test_logsumexp_sign():
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a = [1,1,1]
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b = [1,-1,-1]
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r, s = logsumexp(a, b=b, return_sign=True)
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assert_almost_equal(r,1)
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assert_equal(s,-1)
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def test_logsumexp_sign_zero():
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a = [1,1]
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b = [1,-1]
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r, s = logsumexp(a, b=b, return_sign=True)
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assert_(not np.isfinite(r))
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assert_(not np.isnan(r))
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assert_(r < 0)
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assert_equal(s,0)
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def test_logsumexp_sign_shape():
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a = np.ones((1,2,3,4))
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b = np.ones_like(a)
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r, s = logsumexp(a, axis=2, b=b, return_sign=True)
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assert_equal(r.shape, s.shape)
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assert_equal(r.shape, (1,2,4))
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r, s = logsumexp(a, axis=(1,3), b=b, return_sign=True)
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assert_equal(r.shape, s.shape)
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assert_equal(r.shape, (1,3))
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def test_logsumexp_complex_sign():
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a = np.array([1 + 1j, 2 - 1j, -2 + 3j])
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r, s = logsumexp(a, return_sign=True)
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expected_sumexp = np.exp(a).sum()
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# This is the numpy>=2.0 convention for np.sign
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expected_sign = expected_sumexp / abs(expected_sumexp)
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assert_allclose(s, expected_sign)
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assert_allclose(s * np.exp(r), expected_sumexp)
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def test_logsumexp_shape():
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a = np.ones((1, 2, 3, 4))
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b = np.ones_like(a)
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r = logsumexp(a, axis=2, b=b)
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assert_equal(r.shape, (1, 2, 4))
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r = logsumexp(a, axis=(1, 3), b=b)
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assert_equal(r.shape, (1, 3))
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def test_logsumexp_b_zero():
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a = [1,10000]
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b = [1,0]
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assert_almost_equal(logsumexp(a, b=b), 1)
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def test_logsumexp_b_shape():
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a = np.zeros((4,1,2,1))
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b = np.ones((3,1,5))
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logsumexp(a, b=b)
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def test_softmax_fixtures():
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assert_allclose(softmax([1000, 0, 0, 0]), np.array([1, 0, 0, 0]),
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rtol=1e-13)
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assert_allclose(softmax([1, 1]), np.array([.5, .5]), rtol=1e-13)
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assert_allclose(softmax([0, 1]), np.array([1, np.e])/(1 + np.e),
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rtol=1e-13)
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# Expected value computed using mpmath (with mpmath.mp.dps = 200) and then
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# converted to float.
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x = np.arange(4)
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expected = np.array([0.03205860328008499,
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0.08714431874203256,
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0.23688281808991013,
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0.6439142598879722])
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assert_allclose(softmax(x), expected, rtol=1e-13)
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# Translation property. If all the values are changed by the same amount,
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# the softmax result does not change.
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assert_allclose(softmax(x + 100), expected, rtol=1e-13)
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# When axis=None, softmax operates on the entire array, and preserves
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# the shape.
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assert_allclose(softmax(x.reshape(2, 2)), expected.reshape(2, 2),
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rtol=1e-13)
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def test_softmax_multi_axes():
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assert_allclose(softmax([[1000, 0], [1000, 0]], axis=0),
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np.array([[.5, .5], [.5, .5]]), rtol=1e-13)
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assert_allclose(softmax([[1000, 0], [1000, 0]], axis=1),
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np.array([[1, 0], [1, 0]]), rtol=1e-13)
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# Expected value computed using mpmath (with mpmath.mp.dps = 200) and then
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# converted to float.
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x = np.array([[-25, 0, 25, 50],
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[1, 325, 749, 750]])
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expected = np.array([[2.678636961770877e-33,
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1.9287498479371314e-22,
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1.3887943864771144e-11,
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0.999999999986112],
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[0.0,
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1.9444526359919372e-185,
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0.2689414213699951,
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0.7310585786300048]])
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assert_allclose(softmax(x, axis=1), expected, rtol=1e-13)
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assert_allclose(softmax(x.T, axis=0), expected.T, rtol=1e-13)
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# 3-d input, with a tuple for the axis.
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x3d = x.reshape(2, 2, 2)
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assert_allclose(softmax(x3d, axis=(1, 2)), expected.reshape(2, 2, 2),
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rtol=1e-13)
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