118 lines
3.5 KiB
Python
118 lines
3.5 KiB
Python
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import pytest
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import numpy as np
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from numpy.testing import assert_, assert_equal, assert_allclose
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import scipy.special as sc
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from scipy.special._testutils import assert_func_equal
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def test_wrightomega_nan():
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pts = [complex(np.nan, 0),
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complex(0, np.nan),
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complex(np.nan, np.nan),
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complex(np.nan, 1),
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complex(1, np.nan)]
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for p in pts:
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res = sc.wrightomega(p)
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assert_(np.isnan(res.real))
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assert_(np.isnan(res.imag))
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def test_wrightomega_inf_branch():
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pts = [complex(-np.inf, np.pi/4),
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complex(-np.inf, -np.pi/4),
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complex(-np.inf, 3*np.pi/4),
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complex(-np.inf, -3*np.pi/4)]
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expected_results = [complex(0.0, 0.0),
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complex(0.0, -0.0),
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complex(-0.0, 0.0),
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complex(-0.0, -0.0)]
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for p, expected in zip(pts, expected_results):
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res = sc.wrightomega(p)
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# We can't use assert_equal(res, expected) because in older versions of
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# numpy, assert_equal doesn't check the sign of the real and imaginary
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# parts when comparing complex zeros. It does check the sign when the
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# arguments are *real* scalars.
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assert_equal(res.real, expected.real)
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assert_equal(res.imag, expected.imag)
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def test_wrightomega_inf():
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pts = [complex(np.inf, 10),
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complex(-np.inf, 10),
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complex(10, np.inf),
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complex(10, -np.inf)]
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for p in pts:
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assert_equal(sc.wrightomega(p), p)
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def test_wrightomega_singular():
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pts = [complex(-1.0, np.pi),
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complex(-1.0, -np.pi)]
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for p in pts:
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res = sc.wrightomega(p)
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assert_equal(res, -1.0)
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assert_(np.signbit(res.imag) == np.bool_(False))
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@pytest.mark.parametrize('x, desired', [
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(-np.inf, 0),
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(np.inf, np.inf),
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])
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def test_wrightomega_real_infinities(x, desired):
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assert sc.wrightomega(x) == desired
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def test_wrightomega_real_nan():
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assert np.isnan(sc.wrightomega(np.nan))
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def test_wrightomega_real_series_crossover():
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desired_error = 2 * np.finfo(float).eps
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crossover = 1e20
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x_before_crossover = np.nextafter(crossover, -np.inf)
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x_after_crossover = np.nextafter(crossover, np.inf)
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# Computed using Mpmath
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desired_before_crossover = 99999999999999983569.948
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desired_after_crossover = 100000000000000016337.948
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assert_allclose(
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sc.wrightomega(x_before_crossover),
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desired_before_crossover,
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atol=0,
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rtol=desired_error,
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)
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assert_allclose(
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sc.wrightomega(x_after_crossover),
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desired_after_crossover,
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atol=0,
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rtol=desired_error,
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)
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def test_wrightomega_exp_approximation_crossover():
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desired_error = 2 * np.finfo(float).eps
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crossover = -50
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x_before_crossover = np.nextafter(crossover, np.inf)
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x_after_crossover = np.nextafter(crossover, -np.inf)
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# Computed using Mpmath
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desired_before_crossover = 1.9287498479639314876e-22
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desired_after_crossover = 1.9287498479639040784e-22
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assert_allclose(
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sc.wrightomega(x_before_crossover),
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desired_before_crossover,
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atol=0,
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rtol=desired_error,
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)
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assert_allclose(
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sc.wrightomega(x_after_crossover),
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desired_after_crossover,
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atol=0,
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rtol=desired_error,
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)
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def test_wrightomega_real_versus_complex():
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x = np.linspace(-500, 500, 1001)
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results = sc.wrightomega(x + 0j).real
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assert_func_equal(sc.wrightomega, results, x, atol=0, rtol=1e-14)
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