def test_gdtrib(self):
# Use small values of a and x or mpmath doesn't converge
_assert_inverts(
sp.gdtrib,
lambda a, b, x: mpmath.gammainc(b, b=a*x, regularized=True),
1, [Arg(0, 1e2, inclusive_a=False), ProbArg(),
Arg(0, 1e3, inclusive_a=False)], rtol=1e-5)
def test_gdtrix(self):
_assert_inverts(
sp.gdtrix,
lambda a, b, x: mpmath.gammainc(b, b=a*x, regularized=True),
2, [Arg(0, 1e3, inclusive_a=False), Arg(0, 1e3, inclusive_a=False),
ProbArg()], rtol=1e-7,
endpt_atol=[None, 1e-7, 1e-10])
def test_btdtria(self):
_assert_inverts(
sp.btdtria,
lambda a, b, x: mpmath.betainc(a, b, x2=x, regularized=True),
0, [ProbArg(), Arg(0, 1e2, inclusive_a=False),
Arg(0, 1, inclusive_a=False, inclusive_b=False)],
rtol=1e-6)
def test_chndtridf(self):
# Use a larger atol since mpmath is doing numerical integration
_assert_inverts(
sp.chndtridf,
_noncentral_chi_cdf,
1, [Arg(0, 100, inclusive_a=False), ProbArg(),
Arg(0, 100, inclusive_a=False)],
n=1000, rtol=1e-4, atol=1e-15)
def test_btdtrib(self):
# Use small values of a or mpmath doesn't converge
_assert_inverts(
sp.btdtrib,
lambda a, b, x: mpmath.betainc(a, b, x2=x, regularized=True),
1, [Arg(0, 1e2, inclusive_a=False), ProbArg(),
Arg(0, 1, inclusive_a=False, inclusive_b=False)],
rtol=1e-7, endpt_atol=[None, 1e-18, 1e-15])
def test_gammainc():
# Quick check that the gammainc in
# special._precompute.gammainc_data agrees with mpmath's
# gammainc.
assert_mpmath_equal(gammainc,
lambda a, x: mp.gammainc(a, b=x, regularized=True),
[Arg(0, 100, inclusive_a=False), Arg(0, 100)],
nan_ok=False, rtol=1e-17, n=50, dps=50)
def test_gammaincc():
# Check that the gammaincc in special._precompute.gammainc_data
# agrees with mpmath's gammainc.
assert_mpmath_equal(lambda a, x: gammaincc(a, x, dps=1000),
lambda a, x: mp.gammainc(a, a=x, regularized=True),
[Arg(20, 100), Arg(20, 100)],
nan_ok=False, rtol=1e-17, n=50, dps=1000)
# Test the fast integer path
assert_mpmath_equal(gammaincc,
lambda a, x: mp.gammainc(a, a=x, regularized=True),
[IntArg(1, 100), Arg(0, 100)],
nan_ok=False, rtol=1e-17, n=50, dps=50)
def test_tklmbda_neg_shape(self):
_assert_inverts(
sp.tklmbda,
_tukey_lmbda_quantile,
0, [ProbArg(), Arg(-25, 0, inclusive_b=False)],
spfunc_first=False, rtol=1e-5,
endpt_atol=[1e-9, 1e-5])
def test_tklmbda_zero_shape(self):
# When lmbda = 0 the CDF has a simple closed form
one = mpmath.mpf(1)
assert_mpmath_equal(
lambda x: sp.tklmbda(x, 0),
lambda x: one/(mpmath.exp(-x) + one),
[Arg()], rtol=1e-7)
def test_tklmbda_pos_shape(self):
_assert_inverts(sp.tklmbda,
_tukey_lmbda_quantile,
0,
[ProbArg(), Arg(0, 100, inclusive_a=False)],
spfunc_first=False,
rtol=1e-5)
def test_stdtr(self):
# Ideally the left endpoint for Arg() should be 0.
assert_mpmath_equal(
sp.stdtr,
_student_t_cdf,
[IntArg(1, 100), Arg(1e-10, np.inf)],
rtol=1e-7)
def test_chndtrix(self):
# Use a larger atol since mpmath is doing numerical integration
_assert_inverts(
sp.chndtrix,
_noncentral_chi_cdf,
0, [ProbArg(), IntArg(1, 100), Arg(0, 100, inclusive_a=False)],
n=1000, rtol=1e-4, atol=1e-15,
endpt_atol=[1e-6, None, None])
def test_fdtridfd(self):
_assert_inverts(
sp.fdtridfd,
_f_cdf,
1, [IntArg(1, 100),
ProbArg(),
Arg(0, 100, inclusive_a=False)],
rtol=1e-7)
def test_stdtridf(self):
_assert_inverts(
sp.stdtridf,
_student_t_cdf,
0, [ProbArg(), Arg()], rtol=1e-7)
