peacock-data-public-datasets-idc-cronscript
/
venv
/lib
/python3.10
/site-packages
/scipy
/special
/tests
/test_logsumexp.py
| import numpy as np | |
| from numpy.testing import (assert_almost_equal, assert_equal, assert_allclose, | |
| assert_array_almost_equal, assert_) | |
| from scipy.special import logsumexp, softmax | |
| def test_logsumexp(): | |
| # Test whether logsumexp() function correctly handles large inputs. | |
| a = np.arange(200) | |
| desired = np.log(np.sum(np.exp(a))) | |
| assert_almost_equal(logsumexp(a), desired) | |
| # Now test with large numbers | |
| b = [1000, 1000] | |
| desired = 1000.0 + np.log(2.0) | |
| assert_almost_equal(logsumexp(b), desired) | |
| n = 1000 | |
| b = np.full(n, 10000, dtype='float64') | |
| desired = 10000.0 + np.log(n) | |
| assert_almost_equal(logsumexp(b), desired) | |
| x = np.array([1e-40] * 1000000) | |
| logx = np.log(x) | |
| X = np.vstack([x, x]) | |
| logX = np.vstack([logx, logx]) | |
| assert_array_almost_equal(np.exp(logsumexp(logX)), X.sum()) | |
| assert_array_almost_equal(np.exp(logsumexp(logX, axis=0)), X.sum(axis=0)) | |
| assert_array_almost_equal(np.exp(logsumexp(logX, axis=1)), X.sum(axis=1)) | |
| # Handling special values properly | |
| assert_equal(logsumexp(np.inf), np.inf) | |
| assert_equal(logsumexp(-np.inf), -np.inf) | |
| assert_equal(logsumexp(np.nan), np.nan) | |
| assert_equal(logsumexp([-np.inf, -np.inf]), -np.inf) | |
| # Handling an array with different magnitudes on the axes | |
| assert_array_almost_equal(logsumexp([[1e10, 1e-10], | |
| [-1e10, -np.inf]], axis=-1), | |
| [1e10, -1e10]) | |
| # Test keeping dimensions | |
| assert_array_almost_equal(logsumexp([[1e10, 1e-10], | |
| [-1e10, -np.inf]], | |
| axis=-1, | |
| keepdims=True), | |
| [[1e10], [-1e10]]) | |
| # Test multiple axes | |
| assert_array_almost_equal(logsumexp([[1e10, 1e-10], | |
| [-1e10, -np.inf]], | |
| axis=(-1,-2)), | |
| 1e10) | |
| def test_logsumexp_b(): | |
| a = np.arange(200) | |
| b = np.arange(200, 0, -1) | |
| desired = np.log(np.sum(b*np.exp(a))) | |
| assert_almost_equal(logsumexp(a, b=b), desired) | |
| a = [1000, 1000] | |
| b = [1.2, 1.2] | |
| desired = 1000 + np.log(2 * 1.2) | |
| assert_almost_equal(logsumexp(a, b=b), desired) | |
| x = np.array([1e-40] * 100000) | |
| b = np.linspace(1, 1000, 100000) | |
| logx = np.log(x) | |
| X = np.vstack((x, x)) | |
| logX = np.vstack((logx, logx)) | |
| B = np.vstack((b, b)) | |
| assert_array_almost_equal(np.exp(logsumexp(logX, b=B)), (B * X).sum()) | |
| assert_array_almost_equal(np.exp(logsumexp(logX, b=B, axis=0)), | |
| (B * X).sum(axis=0)) | |
| assert_array_almost_equal(np.exp(logsumexp(logX, b=B, axis=1)), | |
| (B * X).sum(axis=1)) | |
| def test_logsumexp_sign(): | |
| a = [1,1,1] | |
| b = [1,-1,-1] | |
| r, s = logsumexp(a, b=b, return_sign=True) | |
| assert_almost_equal(r,1) | |
| assert_equal(s,-1) | |
| def test_logsumexp_sign_zero(): | |
| a = [1,1] | |
| b = [1,-1] | |
| r, s = logsumexp(a, b=b, return_sign=True) | |
| assert_(not np.isfinite(r)) | |
| assert_(not np.isnan(r)) | |
| assert_(r < 0) | |
| assert_equal(s,0) | |
| def test_logsumexp_sign_shape(): | |
| a = np.ones((1,2,3,4)) | |
| b = np.ones_like(a) | |
| r, s = logsumexp(a, axis=2, b=b, return_sign=True) | |
| assert_equal(r.shape, s.shape) | |
| assert_equal(r.shape, (1,2,4)) | |
| r, s = logsumexp(a, axis=(1,3), b=b, return_sign=True) | |
| assert_equal(r.shape, s.shape) | |
| assert_equal(r.shape, (1,3)) | |
| def test_logsumexp_complex_sign(): | |
| a = np.array([1 + 1j, 2 - 1j, -2 + 3j]) | |
| r, s = logsumexp(a, return_sign=True) | |
| expected_sumexp = np.exp(a).sum() | |
| # This is the numpy>=2.0 convention for np.sign | |
| expected_sign = expected_sumexp / abs(expected_sumexp) | |
| assert_allclose(s, expected_sign) | |
| assert_allclose(s * np.exp(r), expected_sumexp) | |
| def test_logsumexp_shape(): | |
| a = np.ones((1, 2, 3, 4)) | |
| b = np.ones_like(a) | |
| r = logsumexp(a, axis=2, b=b) | |
| assert_equal(r.shape, (1, 2, 4)) | |
| r = logsumexp(a, axis=(1, 3), b=b) | |
| assert_equal(r.shape, (1, 3)) | |
| def test_logsumexp_b_zero(): | |
| a = [1,10000] | |
| b = [1,0] | |
| assert_almost_equal(logsumexp(a, b=b), 1) | |
| def test_logsumexp_b_shape(): | |
| a = np.zeros((4,1,2,1)) | |
| b = np.ones((3,1,5)) | |
| logsumexp(a, b=b) | |
| def test_softmax_fixtures(): | |
| 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(): | |
| 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) | |