def test_shape(self):
n = np.array([0, 1])
z = np.linspace(0.1, 5, 10)
res = special.spherical_hankel(n, z, kind=1, derivative=True)
shape = (2, 10)
assert shape == res.shape
def _modal_strength(n, kr, config):
"""Helper function for the calculation of the modal strength for
plane waves"""
if config == 'open':
ms = 4*np.pi*pow(1.0j, n) * _special.spherical_bessel(n, kr)
elif config == 'rigid':
ms = 4*np.pi*pow(1.0j, n+1) / \
_special.spherical_hankel(n, kr, derivative=True) / (kr)**2
elif config == 'cardioid':
ms = 4*np.pi*pow(1.0j, n) * \
(_special.spherical_bessel(n, kr) -
1.0j * _special.spherical_bessel(n, kr, derivative=True))
else:
raise ValueError("Invalid configuration.")
return ms
def test_val_second_kind(self):
z = np.linspace(0.1, 5, 25)
n = [0, 1, 2]
res = special.spherical_hankel(n, z, kind=2, derivative=True)
truth = genfromtxt_complex('./tests/data/hankel_2_diff.csv', delimiter=',')
npt.assert_allclose(res, truth)
def test_kind_exception(self):
with pytest.raises(ValueError):
special.spherical_hankel([0], [1], kind=3, derivative=True)
def test_val_first_kind(self):
z = np.linspace(0.1, 5, 25)
n = np.array([0, 1, 2])
res = special.spherical_hankel(n, z, kind=1)
truth = genfromtxt_complex('./tests/data/hankel_1.csv', delimiter=',')
npt.assert_allclose(res, truth)
def radiation_from_sphere(
n_max,
rad_sphere,
k,
distance,
density_medium=1.2,
speed_of_sound=343.0):
r"""
Radiation function in SH for a vibrating sphere including the radiation
impedance and the propagation to a arbitrary distance from the sphere.
The sign and phase conventions result in a positive pressure response for
a positive cap velocity with the intensity vector pointing away from the
source.
TODO: This function does not have a test yet.
References
----------
.. [7] E. G. Williams, Fourier Acoustics. Academic Press, 1999.
.. [8] F. Zotter, A. Sontacchi, and R. Höldrich, “Modeling a spherical
loudspeaker system as multipole source,” in Proceedings of the 33rd
DAGA German Annual Conference on Acoustics, 2007, pp. 221–222.
Parameters
----------
n_max : integer, ndarray
Maximal spherical harmonic order
r_sphere : double, ndarray
Radius of the sphere
k : double, ndarray
Wave number
distance : double
Distance from the origin
density_medium : double
Density of the medium surrounding the sphere. Default is 1.2 for air.
speed_of_sound : double
Speed of sound in m/s
Returns
-------
R : double, ndarray
Radiation function in diagonal matrix form with shape
:math:`[K \times (n_{max}+1)^2~\times~(n_{max}+1)^2]`
"""
n_sh = (n_max+1)**2
k = np.atleast_1d(k)
n_bins = k.shape[0]
radiation = np.zeros((n_bins, n_sh, n_sh), dtype=np.complex)
for n in range(0, n_max+1):
hankel = _special.spherical_hankel(n, k*distance, kind=2)
hankel_prime = _special.spherical_hankel(
n, k*rad_sphere, kind=2, derivative=True)
radiation_order = -1j * hankel/hankel_prime * \
density_medium * speed_of_sound
for m in range(-n, n+1):
acn = nm2acn(n, m)
radiation[:, acn, acn] = radiation_order
return radiation