def test_loggamma_real():
# For positive real values loggamma dispatches to lgamma, so we
# don't need to check many points
mpmath_allclose(sc.loggamma, mpmath.loggamma,
[Arg(0, np.inf, inclusive_a=False)], 50, 1e-13)
assert all(np.isnan(sc.loggamma([0, -0.5])))
def test_greater_than_40():
mpmath_allclose(
sc.ei,
mpmath.ei,
[Arg(40, 720)], # By 720 Ei has overflowed.
200,
rtol=2 * _ε,
)
def test_zeta_between_1_and_56():
mpmath_allclose(
sc.zeta,
mpmath.zeta,
[Arg(1, 56, inclusive_a=False)],
100,
rtol=_ε,
)
def test_zeta_small_arguments():
mpmath_allclose(
sc.zeta,
mpmath.zeta,
[Arg(-1, 1, inclusive_b=False)],
50,
rtol=4 * _ε,
)
def test_between_0_and_1():
mpmath_allclose(
sc.e1,
mpmath.e1,
[Arg(0, 1, inclusive_a=False)],
100,
rtol=2 * _ε,
)
def test_between_1_and_underflow():
mpmath_allclose(
sc.e1,
mpmath.e1,
[Arg(1, -MINEXP)],
200,
rtol=2 * _ε,
)
def test_between_10_and_20():
mpmath_allclose(
sc.ei,
mpmath.ei,
[Arg(10, 20)],
50,
rtol=2 * _ε,
)
def test_between_20_and_40():
mpmath_allclose(
sc.ei,
mpmath.ei,
[Arg(20, 40)],
50,
rtol=2 * _ε,
)
def test_between_6_and_10():
mpmath_allclose(
sc.ei,
mpmath.ei,
[Arg(6, 10)],
50,
rtol=2 * _ε,
)
def test_between_0_and_6():
mpmath_allclose(
sc.ei,
mpmath.ei,
[Arg(0, 6, inclusive_a=False)],
50,
rtol=4 * _ε,
)
def test_zeta_less_than_negative_1():
mpmath_allclose(
sc.zeta,
mpmath.zeta,
[Arg(-261, -1)],
300,
rtol=5e-14,
)
def test_erfcinv():
mpmath_allclose(
sc.erfcinv,
mpmath_erfcinv,
[Arg(0, 2)],
200,
2*_ε,
dps=42,
)
def test_lgamma():
def mpmath_lgamma(x):
try:
return mpmath.loggamma(x).real
except ValueError:
# Hit a pole
return np.inf
mpmath_allclose(sc.lgamma, mpmath_lgamma, [Arg()], 1000, 5e-14)
def test_loggamma_complex():
def mpmath_loggamma(x):
try:
return mpmath.loggamma(x)
except ValueError:
# Hit a pole
return complex(np.nan, np.nan)
b = 1e200
mpmath_allclose(sc.loggamma, mpmath_loggamma,
[ComplexArg(complex(-b, -b), complex(b, b))], 1000, 5e-12)
def test_gamma():
def mpmath_gamma(x):
try:
return mpmath.gamma(x)
except ValueError:
# Gamma pole
return np.nan
# Gamma overflows around 170 so there's no point in testing beyond
# that.
mpmath_allclose(sc.gamma, mpmath_gamma, [Arg(-np.inf, 180)], 1000, 1e-14)
def test_digamma():
def mpmath_digamma(x):
try:
return mpmath.digamma(x)
except ValueError:
# Hit a pole.
if x == 0.0:
return -np.copysign(np.inf, x)
else:
return np.nan
mpmath_allclose(sc.digamma, mpmath_digamma, [Arg()], 1000, 5e-14, dps=40)
def test_erfinv():
mpmath_allclose(sc.erfinv, mpmath.erfinv, [Arg(-1, 1)], 1000, 2*_ε)
def test_cospi_complex():
rtol = 16*np.finfo(float).eps
mpmath_allclose(sc.cospi, mpmath.cospi, [ComplexArg()], 1000, rtol)
def test_sinpi_real():
rtol = np.finfo(float).eps
mpmath_allclose(sc.sinpi, mpmath.sinpi, [Arg()], 1000, rtol)
def test_erfc():
rtol = 64 * np.finfo(float).eps # ~1.4e-14
mpmath_allclose(sc.erfc, mpmath.erfc, [Arg(-1e100, 1e100)], 1000, rtol)
def test_erf():
rtol = 2 * np.finfo(float).eps
mpmath_allclose(sc.erf, mpmath.erf, [Arg()], 1000, rtol)