class TestInversion(with_metaclass(DecoratorMeta, object)):
decorators = [(dec.slow, None), (check_version, (sympy, '0.7')),
(check_version, (mp, '0.19'))]
def test_log(self):
with mp.workdps(30):
logcoeffs = mp.taylor(lambda x: mp.log(1 + x), 0, 10)
expcoeffs = mp.taylor(lambda x: mp.exp(x) - 1, 0, 10)
invlogcoeffs = lagrange_inversion(logcoeffs)
mp_assert_allclose(invlogcoeffs, expcoeffs)
def test_sin(self):
with mp.workdps(30):
sincoeffs = mp.taylor(mp.sin, 0, 10)
asincoeffs = mp.taylor(mp.asin, 0, 10)
invsincoeffs = lagrange_inversion(sincoeffs)
mp_assert_allclose(invsincoeffs, asincoeffs, atol=1e-30)
class TestInversion(with_metaclass(DecoratorMeta, object)):
decorators = [(dec.slow, None),
(check_version, (sympy, '0.7')),
(check_version, (mp, '0.19'))]
@dec.knownfailureif(_is_32bit_platform, "rtol only 2e-9, see gh-6938")
def test_log(self):
with mp.workdps(30):
logcoeffs = mp.taylor(lambda x: mp.log(1 + x), 0, 10)
expcoeffs = mp.taylor(lambda x: mp.exp(x) - 1, 0, 10)
invlogcoeffs = lagrange_inversion(logcoeffs)
mp_assert_allclose(invlogcoeffs, expcoeffs)
@dec.knownfailureif(_is_32bit_platform, "rtol only 1e-15, see gh-6938")
def test_sin(self):
with mp.workdps(30):
sincoeffs = mp.taylor(mp.sin, 0, 10)
asincoeffs = mp.taylor(mp.asin, 0, 10)
invsincoeffs = lagrange_inversion(sincoeffs)
mp_assert_allclose(invsincoeffs, asincoeffs, atol=1e-30)
class TestCDFlib(with_metaclass(DecoratorMeta, object)):
decorators = [(dec.slow, None), (check_version, (mpmath, '0.19'))]
@knownfailure_overridable()
def test_bdtrik(self):
_assert_inverts(
sp.bdtrik,
_binomial_cdf,
0,
[ProbArg(), IntArg(1, 1000), ProbArg()],
rtol=1e-4)
def test_bdtrin(self):
_assert_inverts(
sp.bdtrin,
_binomial_cdf,
1,
[IntArg(1, 1000), ProbArg(), ProbArg()],
rtol=1e-4,
endpt_atol=[None, None, 1e-6])
def test_btdtria(self):
_assert_inverts(
sp.btdtria,
lambda a, b, x: mpmath.betainc(a, b, x2=x, regularized=True),
0, [
ProbArg(),
Arg(0, 1e3, inclusive_a=False),
Arg(0, 1, inclusive_a=False, inclusive_b=False)
],
rtol=1e-6)
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-20, 1e-20])
@knownfailure_overridable()
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_gdtria(self):
_assert_inverts(
sp.gdtria,
lambda a, b, x: mpmath.gammainc(b, b=a * x, regularized=True),
0, [
ProbArg(),
Arg(0, 1e3, inclusive_a=False),
Arg(0, 1e4, inclusive_a=False)
],
rtol=1e-7,
endpt_atol=[None, 1e-10, 1e-10])
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-10, 1e-10])
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)
@knownfailure_overridable()
def test_stdtridf(self):
_assert_inverts(sp.stdtridf,
_student_t_cdf,
0, [ProbArg(), Arg()],
rtol=1e-7)
def test_stdtrit(self):
_assert_inverts(sp.stdtrit,
_student_t_cdf,
1, [IntArg(1, 100), ProbArg()],
rtol=1e-7,
endpt_atol=[None, 1e-10])
def test_chdtriv(self):
_assert_inverts(
sp.chdtriv,
lambda v, x: mpmath.gammainc(v / 2, b=x / 2, regularized=True),
0, [ProbArg(), IntArg(1, 100)],
rtol=1e-4)
@knownfailure_overridable()
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)
@knownfailure_overridable()
def test_chndtrinc(self):
# Use a larger atol since mpmath is doing numerical integration
_assert_inverts(
sp.chndtrinc,
_noncentral_chi_cdf,
2, [Arg(0, 100, inclusive_a=False),
IntArg(1, 100),
ProbArg()],
n=1000,
rtol=1e-4,
atol=1e-15)
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_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_neg_shape(self):
_assert_inverts(
sp.tklmbda,
_tukey_lmbda_quantile,
0, [ProbArg(), Arg(-np.inf, 0, inclusive_b=False)],
spfunc_first=False,
rtol=1e-5,
endpt_atol=[1e-9, None])
@knownfailure_overridable()
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)