Vehicle-cpp/hkpc/software/scipy/special/tests/test_exponential_integrals.py

import pytest

import numpy as np
from numpy.testing import assert_allclose
import scipy.special as sc


class TestExp1:

    def test_branch_cut(self):
        assert np.isnan(sc.exp1(-1))
        assert sc.exp1(complex(-1, 0)).imag == (
            -sc.exp1(complex(-1, -0.0)).imag
        )

        assert_allclose(
            sc.exp1(complex(-1, 0)),
            sc.exp1(-1 + 1e-20j),
            atol=0,
            rtol=1e-15
        )
        assert_allclose(
            sc.exp1(complex(-1, -0.0)),
            sc.exp1(-1 - 1e-20j),
            atol=0,
            rtol=1e-15
        )

    def test_834(self):
        # Regression test for #834
        a = sc.exp1(-complex(19.9999990))
        b = sc.exp1(-complex(19.9999991))
        assert_allclose(a.imag, b.imag, atol=0, rtol=1e-15)


class TestExpi:

    @pytest.mark.parametrize('result', [
        sc.expi(complex(-1, 0)),
        sc.expi(complex(-1, -0.0)),
        sc.expi(-1)
    ])
    def test_branch_cut(self, result):
        desired = -0.21938393439552027368  # Computed using Mpmath
        assert_allclose(result, desired, atol=0, rtol=1e-14)

    def test_near_branch_cut(self):
        lim_from_above = sc.expi(-1 + 1e-20j)
        lim_from_below = sc.expi(-1 - 1e-20j)
        assert_allclose(
            lim_from_above.real,
            lim_from_below.real,
            atol=0,
            rtol=1e-15
        )
        assert_allclose(
            lim_from_above.imag,
            -lim_from_below.imag,
            atol=0,
            rtol=1e-15
        )

    def test_continuity_on_positive_real_axis(self):
        assert_allclose(
            sc.expi(complex(1, 0)),
            sc.expi(complex(1, -0.0)),
            atol=0,
            rtol=1e-15
        )


class TestExpn:

    def test_out_of_domain(self):
        assert all(np.isnan([sc.expn(-1, 1.0), sc.expn(1, -1.0)]))