def make_bessel_y1_vals():
from mpmath import bessely
x = [mpf('0.1')] + linspace(1, 15, 15)
y1 = [bessely(1, val) for val in x]
return make_special_vals('bessel_y1_vals', ('x', x), ('y1', y1))
def make_bessel_y_vals():
from mpmath import bessely
nu = [
mpf('0.5'),
mpf('1.25'),
mpf('1.5'),
mpf('1.75'),
mpf(2),
mpf('2.75'),
mpf(5),
mpf(10),
mpf(20)
]
x = [
mpf('0.2'),
mpf(1),
mpf(2),
mpf('2.5'),
mpf(3),
mpf(5),
mpf(10),
mpf(50)
]
nu, x = zip(*outer(nu, x))
y = [bessely(*vals) for vals in zip(nu, x)]
return make_special_vals('bessel_y_vals', ('nu', nu), ('x', x), ('y', y))
def make_bessel_y1_vals():
from mpmath import bessely
x = [mpf('0.1')] + linspace(1, 15, 15)
y1 = [bessely(1, val) for val in x]
return make_special_vals('bessel_y1_vals', ('x', x), ('y1', y1))
def mpbessely(v, x):
r = float(mpmath.bessely(v, x, **HYPERKW))
if abs(r) > 1e305:
# overflowing to inf a bit earlier is OK
r = np.inf * np.sign(r)
if abs(r) == 0 and x == 0:
# invalid result from mpmath, point x=0 is a divergence
return np.nan
return r
def mpbessely(v, x):
r = float(mpmath.bessely(v, x, **HYPERKW))
if abs(r) > 1e305:
# overflowing to inf a bit earlier is OK
r = np.inf * np.sign(r)
if abs(r) == 0 and x == 0:
# invalid result from mpmath, point x=0 is a divergence
return np.nan
return r
def make_bessel_y_vals():
from mpmath import bessely
nu = [mpf('0.5'), mpf('1.25'), mpf('1.5'), mpf('1.75'), mpf(2), mpf('2.75'), mpf(5), mpf(10), mpf(20)]
x = [mpf('0.2'), mpf(1), mpf(2), mpf('2.5'), mpf(3), mpf(5), mpf(10), mpf(50)]
nu, x = zip(*outer(nu, x))
y = [bessely(*vals) for vals in zip(nu, x)]
return make_special_vals('bessel_y_vals', ('nu', nu), ('x', x), ('y', y))
def sph_yn_bessel(n, z):
out = bessely(n + mpf(1)/2, z)*sqrt(pi/(2*z))
if mpmathify(z).imag == 0:
return out.real
else:
return out
def test_bessely(self):
assert_mpmath_equal(sc.yv,
_exception_to_nan(lambda v, z: mpmath.bessely(v, z, **HYPERKW)),
[Arg(-1e100, 1e100), Arg()],
n=1000)
def test_bessely(self):
assert_mpmath_equal(
sc.yv,
_exception_to_nan(lambda v, z: mpmath.bessely(v, z, **HYPERKW)),
[Arg(-1e100, 1e100), Arg()],
n=1000)
def f11(x):
# bessel_Y1
return mpmath.bessely(1, x)
def f10(x):
# bessel_Y0
return mpmath.bessely(0, x)
def mpbessely(v, x):
r = float(mpmath.bessely(v, x))
if abs(r) == 0 and x == 0:
# invalid result from mpmath, point x=0 is a divergence
return np.nan
return r
def mpbessely(v, x):
r = complex(mpmath.bessely(v, x, **HYPERKW))
if abs(r) > 1e305:
# overflowing to inf a bit earlier is OK
r = np.inf * np.sign(r)
return r
def mp_spherical_dyn(l, z):
return mpmath.sqrt(mpmath.pi /
(2 * z)) * (mpmath.bessely(l + 0.5, z, 1) -
mpmath.bessely(l + 0.5, z) / (2 * z))
def mp_spherical_yn(l, z):
return mpmath.sqrt(mpmath.pi / 2.0 / z) * mpmath.bessely(l + 0.5, z)
def sphbessely(nu, x):
from mpmath import bessely
return sqrt(pi / (2 * x)) * bessely(nu + mpf('0.5'), x)
def mpbessely(v, x):
r = complex(mpmath.bessely(v, x, **HYPERKW))
if abs(r) > 1e305:
# overflowing to inf a bit earlier is OK
r = np.inf * np.sign(r)
return r
def mpbessely(v, x):
r = float(mpmath.bessely(v, x))
if abs(r) == 0 and x == 0:
# invalid result from mpmath, point x=0 is a divergence
return np.nan
return r
def sphbessely(nu, x):
from mpmath import bessely
return sqrt(pi / (2 * x)) * bessely(nu + mpf('0.5'), x)
def sph_yn_bessel(n, z):
out = bessely(n + mpf(1) / 2, z) * sqrt(pi / (2 * z))
if mpmathify(z).imag == 0:
return out.real
else:
return out