119 lines
3.6 KiB
Python
119 lines
3.6 KiB
Python
import pytest
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import numpy as np
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from numpy.testing import assert_allclose
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import scipy.special as sc
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class TestExp1:
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def test_branch_cut(self):
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assert np.isnan(sc.exp1(-1))
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assert sc.exp1(complex(-1, 0)).imag == (
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-sc.exp1(complex(-1, -0.0)).imag
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)
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assert_allclose(
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sc.exp1(complex(-1, 0)),
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sc.exp1(-1 + 1e-20j),
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atol=0,
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rtol=1e-15
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)
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assert_allclose(
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sc.exp1(complex(-1, -0.0)),
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sc.exp1(-1 - 1e-20j),
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atol=0,
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rtol=1e-15
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)
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def test_834(self):
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# Regression test for #834
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a = sc.exp1(-complex(19.9999990))
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b = sc.exp1(-complex(19.9999991))
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assert_allclose(a.imag, b.imag, atol=0, rtol=1e-15)
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class TestScaledExp1:
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@pytest.mark.parametrize('x, expected', [(0, 0), (np.inf, 1)])
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def test_limits(self, x, expected):
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y = sc._ufuncs._scaled_exp1(x)
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assert y == expected
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# The expected values were computed with mpmath, e.g.:
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#
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# from mpmath import mp
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# mp.dps = 80
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# x = 1e-25
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# print(float(x*mp.exp(x)*np.expint(1, x)))
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#
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# prints 5.698741165994961e-24
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#
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# The method used to compute _scaled_exp1 changes at x=1
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# and x=1250, so values at those inputs, and values just
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# above and below them, are included in the test data.
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@pytest.mark.parametrize('x, expected',
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[(1e-25, 5.698741165994961e-24),
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(0.1, 0.20146425447084518),
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(0.9995, 0.5962509885831002),
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(1.0, 0.5963473623231941),
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(1.0005, 0.5964436833238044),
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(2.5, 0.7588145912149602),
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(10.0, 0.9156333393978808),
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(100.0, 0.9901942286733019),
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(500.0, 0.9980079523802055),
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(1000.0, 0.9990019940238807),
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(1249.5, 0.9992009578306811),
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(1250.0, 0.9992012769377913),
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(1250.25, 0.9992014363957858),
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(2000.0, 0.9995004992514963),
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(1e4, 0.9999000199940024),
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(1e10, 0.9999999999),
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(1e15, 0.999999999999999),
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])
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def test_scaled_exp1(self, x, expected):
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y = sc._ufuncs._scaled_exp1(x)
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assert_allclose(y, expected, rtol=2e-15)
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class TestExpi:
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@pytest.mark.parametrize('result', [
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sc.expi(complex(-1, 0)),
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sc.expi(complex(-1, -0.0)),
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sc.expi(-1)
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])
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def test_branch_cut(self, result):
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desired = -0.21938393439552027368 # Computed using Mpmath
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assert_allclose(result, desired, atol=0, rtol=1e-14)
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def test_near_branch_cut(self):
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lim_from_above = sc.expi(-1 + 1e-20j)
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lim_from_below = sc.expi(-1 - 1e-20j)
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assert_allclose(
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lim_from_above.real,
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lim_from_below.real,
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atol=0,
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rtol=1e-15
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)
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assert_allclose(
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lim_from_above.imag,
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-lim_from_below.imag,
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atol=0,
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rtol=1e-15
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)
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def test_continuity_on_positive_real_axis(self):
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assert_allclose(
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sc.expi(complex(1, 0)),
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sc.expi(complex(1, -0.0)),
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atol=0,
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rtol=1e-15
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)
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class TestExpn:
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def test_out_of_domain(self):
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assert all(np.isnan([sc.expn(-1, 1.0), sc.expn(1, -1.0)]))
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