153 lines
4.3 KiB
Python
153 lines
4.3 KiB
Python
import pytest
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import numpy as np
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from numpy.testing import assert_allclose, assert_array_equal
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import scipy.special as sc
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from scipy.special._testutils import FuncData
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INVALID_POINTS = [
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(1, -1),
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(0, 0),
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(-1, 1),
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(np.nan, 1),
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(1, np.nan)
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]
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class TestGammainc:
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@pytest.mark.parametrize('a, x', INVALID_POINTS)
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def test_domain(self, a, x):
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assert np.isnan(sc.gammainc(a, x))
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def test_a_eq_0_x_gt_0(self):
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assert sc.gammainc(0, 1) == 1
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@pytest.mark.parametrize('a, x, desired', [
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(np.inf, 1, 0),
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(np.inf, 0, 0),
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(np.inf, np.inf, np.nan),
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(1, np.inf, 1)
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])
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def test_infinite_arguments(self, a, x, desired):
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result = sc.gammainc(a, x)
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if np.isnan(desired):
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assert np.isnan(result)
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else:
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assert result == desired
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@pytest.mark.parametrize("x", [-np.inf, -1.0, -0.0, 0.0, np.inf, np.nan])
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def test_a_nan(self, x):
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assert np.isnan(sc.gammainc(np.nan, x))
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@pytest.mark.parametrize("a", [-np.inf, -1.0, -0.0, 0.0, np.inf, np.nan])
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def test_x_nan(self, a):
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assert np.isnan(sc.gammainc(a, np.nan))
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def test_infinite_limits(self):
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# Test that large arguments converge to the hard-coded limits
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# at infinity.
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assert_allclose(
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sc.gammainc(1000, 100),
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sc.gammainc(np.inf, 100),
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atol=1e-200, # Use `atol` since the function converges to 0.
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rtol=0
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)
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assert sc.gammainc(100, 1000) == sc.gammainc(100, np.inf)
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def test_x_zero(self):
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a = np.arange(1, 10)
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assert_array_equal(sc.gammainc(a, 0), 0)
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def test_limit_check(self):
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result = sc.gammainc(1e-10, 1)
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limit = sc.gammainc(0, 1)
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assert np.isclose(result, limit)
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def gammainc_line(self, x):
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# The line a = x where a simpler asymptotic expansion (analog
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# of DLMF 8.12.15) is available.
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c = np.array([-1/3, -1/540, 25/6048, 101/155520,
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-3184811/3695155200, -2745493/8151736420])
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res = 0
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xfac = 1
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for ck in c:
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res -= ck*xfac
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xfac /= x
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res /= np.sqrt(2*np.pi*x)
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res += 0.5
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return res
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def test_line(self):
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x = np.logspace(np.log10(25), 300, 500)
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a = x
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dataset = np.vstack((a, x, self.gammainc_line(x))).T
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FuncData(sc.gammainc, dataset, (0, 1), 2, rtol=1e-11).check()
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def test_roundtrip(self):
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a = np.logspace(-5, 10, 100)
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x = np.logspace(-5, 10, 100)
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y = sc.gammaincinv(a, sc.gammainc(a, x))
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assert_allclose(x, y, rtol=1e-10)
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class TestGammaincc:
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@pytest.mark.parametrize('a, x', INVALID_POINTS)
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def test_domain(self, a, x):
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assert np.isnan(sc.gammaincc(a, x))
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def test_a_eq_0_x_gt_0(self):
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assert sc.gammaincc(0, 1) == 0
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@pytest.mark.parametrize('a, x, desired', [
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(np.inf, 1, 1),
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(np.inf, 0, 1),
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(np.inf, np.inf, np.nan),
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(1, np.inf, 0)
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])
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def test_infinite_arguments(self, a, x, desired):
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result = sc.gammaincc(a, x)
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if np.isnan(desired):
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assert np.isnan(result)
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else:
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assert result == desired
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@pytest.mark.parametrize("x", [-np.inf, -1.0, -0.0, 0.0, np.inf, np.nan])
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def test_a_nan(self, x):
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assert np.isnan(sc.gammaincc(np.nan, x))
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@pytest.mark.parametrize("a", [-np.inf, -1.0, -0.0, 0.0, np.inf, np.nan])
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def test_x_nan(self, a):
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assert np.isnan(sc.gammaincc(a, np.nan))
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def test_infinite_limits(self):
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# Test that large arguments converge to the hard-coded limits
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# at infinity.
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assert sc.gammaincc(1000, 100) == sc.gammaincc(np.inf, 100)
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assert_allclose(
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sc.gammaincc(100, 1000),
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sc.gammaincc(100, np.inf),
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atol=1e-200, # Use `atol` since the function converges to 0.
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rtol=0
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)
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def test_limit_check(self):
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result = sc.gammaincc(1e-10,1)
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limit = sc.gammaincc(0,1)
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assert np.isclose(result, limit)
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def test_x_zero(self):
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a = np.arange(1, 10)
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assert_array_equal(sc.gammaincc(a, 0), 1)
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def test_roundtrip(self):
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a = np.logspace(-5, 10, 100)
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x = np.logspace(-5, 10, 100)
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y = sc.gammainccinv(a, sc.gammaincc(a, x))
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assert_allclose(x, y, rtol=1e-14)
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