def point_25d(omega, x0, n0, xs, *, xref=[0, 0, 0], c=None):
r"""Driving function for 2.5-dimensional SDM for a virtual point source.
Parameters
----------
omega : float
Angular frequency of point source.
x0 : (N, 3) array_like
Sequence of secondary source positions.
n0 : (N, 3) array_like
Sequence of normal vectors of secondary sources.
xs: (3,) array_like
Position of virtual point source.
xref : (3,) array_like, optional
Reference point for synthesized sound field.
c : float, optional
Speed of sound.
Returns
-------
d : (N,) numpy.ndarray
Complex weights of secondary sources.
selection : (N,) numpy.ndarray
Boolean array containing ``True`` or ``False`` depending on
whether the corresponding secondary source is "active" or not.
secondary_source_function : callable
A function that can be used to create the sound field of a
single secondary source. See `sfs.fd.synthesize()`.
Notes
-----
The secondary sources have to be located on the x-axis (y0=0).
Driving function from :cite:`Spors2010`, Eq.(24).
Examples
--------
.. plot::
:context: close-figs
d, selection, secondary_source = sfs.fd.sdm.point_25d(
omega, array.x, array.n, xs, xref=[0, -1, 0])
plot(d, selection, secondary_source)
"""
x0 = _util.asarray_of_rows(x0)
n0 = _util.asarray_of_rows(n0)
xs = _util.asarray_1d(xs)
xref = _util.asarray_1d(xref)
k = _util.wavenumber(omega, c)
ds = x0 - xs
r = _np.linalg.norm(ds, axis=1)
d = 1/2 * 1j * k * _np.sqrt(xref[1] / (xref[1] - xs[1])) * \
xs[1] / r * _hankel2(1, k * r)
selection = _util.source_selection_all(len(x0))
return d, selection, _secondary_source_point(omega, c)
def line_2d(omega, x0, n0, xs, *, c=None):
r"""Driving function for 2-dimensional WFS for a virtual line source.
Parameters
----------
omega : float
Angular frequency of line source.
x0 : (N, 3) array_like
Sequence of secondary source positions.
n0 : (N, 3) array_like
Sequence of normal vectors of secondary sources.
xs : (3,) array_like
Position of virtual line source.
c : float, optional
Speed of sound.
Returns
-------
d : (N,) numpy.ndarray
Complex weights of secondary sources.
selection : (N,) numpy.ndarray
Boolean array containing ``True`` or ``False`` depending on
whether the corresponding secondary source is "active" or not.
secondary_source_function : callable
A function that can be used to create the sound field of a
single secondary source. See `sfs.fd.synthesize()`.
Notes
-----
.. math::
D(\x_0,\w) = \frac{\i}{2} \wc
\frac{\scalarprod{\x-\x_0}{\n_0}}{|\x-\x_\text{s}|}
\Hankel{2}{1}{\wc|\x-\x_\text{s}|}
Examples
--------
.. plot::
:context: close-figs
d, selection, secondary_source = sfs.fd.wfs.line_2d(
omega, array.x, array.n, xs)
plot(d, selection, secondary_source)
"""
x0 = _util.asarray_of_rows(x0)
n0 = _util.asarray_of_rows(n0)
xs = _util.asarray_1d(xs)
k = _util.wavenumber(omega, c)
ds = x0 - xs
r = _np.linalg.norm(ds, axis=1)
d = -1j/2 * k * _inner1d(ds, n0) / r * _hankel2(1, k * r)
selection = _util.source_selection_line(n0, x0, xs)
return d, selection, _secondary_source_line(omega, c)
def line_2d(omega, x0, n0, xs, *, c=None):
r"""Driving function for 2-dimensional WFS for a virtual line source.
Parameters
----------
omega : float
Angular frequency of line source.
x0 : (N, 3) array_like
Sequence of secondary source positions.
n0 : (N, 3) array_like
Sequence of normal vectors of secondary sources.
xs : (3,) array_like
Position of virtual line source.
c : float, optional
Speed of sound.
Returns
-------
d : (N,) numpy.ndarray
Complex weights of secondary sources.
selection : (N,) numpy.ndarray
Boolean array containing ``True`` or ``False`` depending on
whether the corresponding secondary source is "active" or not.
secondary_source_function : callable
A function that can be used to create the sound field of a
single secondary source. See `sfs.fd.synthesize()`.
Notes
-----
.. math::
D(\x_0,\w) = \frac{\i}{2} \wc
\frac{\scalarprod{\x-\x_0}{\n_0}}{|\x-\x_\text{s}|}
\Hankel{2}{1}{\wc|\x-\x_\text{s}|}
Examples
--------
.. plot::
:context: close-figs
d, selection, secondary_source = sfs.fd.wfs.line_2d(
omega, array.x, array.n, xs)
plot(d, selection, secondary_source)
"""
x0 = _util.asarray_of_rows(x0)
n0 = _util.asarray_of_rows(n0)
xs = _util.asarray_1d(xs)
k = _util.wavenumber(omega, c)
ds = x0 - xs
r = _np.linalg.norm(ds, axis=1)
d = -1j / 2 * k * _inner1d(ds, n0) / r * _hankel2(1, k * r)
selection = _util.source_selection_line(n0, x0, xs)
return d, selection, _secondary_source_line(omega, c)
def plane_25d(omega, x0, n0, n=[0, 1, 0], *, xref=[0, 0, 0], c=None):
r"""Driving function for 2.5-dimensional SDM for a virtual plane wave.
Parameters
----------
omega : float
Angular frequency of plane wave.
x0 : (N, 3) array_like
Sequence of secondary source positions.
n0 : (N, 3) array_like
Sequence of normal vectors of secondary sources.
n: (3,) array_like, optional
Normal vector (traveling direction) of plane wave.
xref : (3,) array_like, optional
Reference point for synthesized sound field.
c : float, optional
Speed of sound.
Returns
-------
d : (N,) numpy.ndarray
Complex weights of secondary sources.
selection : (N,) numpy.ndarray
Boolean array containing ``True`` or ``False`` depending on
whether the corresponding secondary source is "active" or not.
secondary_source_function : callable
A function that can be used to create the sound field of a
single secondary source. See `sfs.fd.synthesize()`.
Notes
-----
The secondary sources have to be located on the x-axis (y0=0).
Eq.(3.79) from :cite:`Ahrens2012`.
Examples
--------
.. plot::
:context: close-figs
d, selection, secondary_source = sfs.fd.sdm.plane_25d(
omega, array.x, array.n, npw, xref=[0, -1, 0])
plot(d, selection, secondary_source)
"""
x0 = _util.asarray_of_rows(x0)
n0 = _util.asarray_of_rows(n0)
n = _util.normalize_vector(n)
xref = _util.asarray_1d(xref)
k = _util.wavenumber(omega, c)
d = 4j * _np.exp(-1j*k*n[1]*xref[1]) / _hankel2(0, k*n[1]*xref[1]) * \
_np.exp(-1j*k*n[0]*x0[:, 0])
selection = _util.source_selection_all(len(x0))
return d, selection, _secondary_source_point(omega, c)
def line_2d_edge_dipole_ssd(omega, x0, xs, *, alpha=_np.pi*3/2, Nc=None,
c=None):
r"""Driving function for 2-dimensional line source with edge dipole ESA.
Driving function for a virtual line source using the 2-dimensional ESA
for an edge-shaped secondary source distribution consisting of dipole line
sources.
Parameters
----------
omega : float
Angular frequency.
x0 : (N, 3) array_like
Sequence of secondary source positions.
xs : (3,) array_like
Position of synthesized line source.
alpha : float, optional
Outer angle of edge.
Nc : int, optional
Number of elements for series expansion of driving function. Estimated
if not given.
c : float, optional
Speed of sound
Returns
-------
d : (N,) numpy.ndarray
Complex weights of secondary sources.
selection : (N,) numpy.ndarray
Boolean array containing ``True`` or ``False`` depending on
whether the corresponding secondary source is "active" or not.
secondary_source_function : callable
A function that can be used to create the sound field of a
single secondary source. See `sfs.fd.synthesize()`.
Notes
-----
One leg of the secondary sources has to be located on the x-axis (y0=0),
the edge at the origin.
Derived from :cite:`Spors2016`
"""
x0 = _np.asarray(x0)
k = _util.wavenumber(omega, c)
phi_s = _np.arctan2(xs[1], xs[0])
if phi_s < 0:
phi_s = phi_s + 2 * _np.pi
r_s = _np.linalg.norm(xs)
L = x0.shape[0]
r = _np.linalg.norm(x0, axis=1)
phi = _np.arctan2(x0[:, 1], x0[:, 0])
phi = _np.where(phi < 0, phi + 2 * _np.pi, phi)
if Nc is None:
Nc = _np.ceil(2 * k * _np.max(r) * alpha / _np.pi)
epsilon = _np.ones(Nc) # weights for series expansion
epsilon[0] = 2
d = _np.zeros(L, dtype=complex)
idx = (r <= r_s)
for m in _np.arange(Nc):
nu = m * _np.pi / alpha
f = 1/epsilon[m] * _np.cos(nu*phi_s) * _np.cos(nu*phi)
d[idx] = d[idx] + f[idx] * _jn(nu, k*r[idx]) * _hankel2(nu, k*r_s)
d[~idx] = d[~idx] + f[~idx] * _jn(nu, k*r_s) * _hankel2(nu, k*r[~idx])
return -1j*_np.pi/alpha * d
def plane_2d(omega, x0, r0, n=[0, 1, 0], *, max_order=None, c=None):
r"""Driving function for 2-dimensional NFC-HOA for a virtual plane wave.
Parameters
----------
omega : float
Angular frequency of plane wave.
x0 : (N, 3) array_like
Sequence of secondary source positions.
r0 : float
Radius of circular secondary source distribution.
n : (3,) array_like, optional
Normal vector (traveling direction) of plane wave.
max_order : float, optional
Maximum order of circular harmonics used for the calculation.
c : float, optional
Speed of sound.
Returns
-------
d : (N,) numpy.ndarray
Complex weights of secondary sources.
selection : (N,) numpy.ndarray
Boolean array containing only ``True`` indicating that
all secondary source are "active" for NFC-HOA.
secondary_source_function : callable
A function that can be used to create the sound field of a
single secondary source. See `sfs.fd.synthesize()`.
Notes
-----
.. math::
D(\phi_0, \omega) =
-\frac{2\i}{\pi r_0}
\sum_{m=-M}^M
\frac{\i^{-m}}{\Hankel{2}{m}{\wc r_0}}
\e{\i m (\phi_0 - \phi_\text{pw})}
See :sfs:`d_nfchoa/#equation-fd-nfchoa-plane-2d`
Examples
--------
.. plot::
:context: close-figs
d, selection, secondary_source = sfs.fd.nfchoa.plane_2d(
omega, array.x, R, npw)
plot(d, selection, secondary_source)
"""
if max_order is None:
max_order = _util.max_order_circular_harmonics(len(x0))
x0 = _util.asarray_of_rows(x0)
k = _util.wavenumber(omega, c)
n = _util.normalize_vector(n)
phi, _, r = _util.cart2sph(*n)
phi0 = _util.cart2sph(*x0.T)[0]
d = 0
for m in range(-max_order, max_order + 1):
d += 1j**-m / _hankel2(m, k * r0) * _np.exp(1j * m * (phi0 - phi))
selection = _util.source_selection_all(len(x0))
return -2j / (_np.pi * r0) * d, selection, _secondary_source_line(omega, c)
def line_2d_edge_dipole_ssd(omega,
x0,
xs,
*,
alpha=_np.pi * 3 / 2,
Nc=None,
c=None):
r"""Driving function for 2-dimensional line source with edge dipole ESA.
Driving function for a virtual line source using the 2-dimensional ESA
for an edge-shaped secondary source distribution consisting of dipole line
sources.
Parameters
----------
omega : float
Angular frequency.
x0 : (N, 3) array_like
Sequence of secondary source positions.
xs : (3,) array_like
Position of synthesized line source.
alpha : float, optional
Outer angle of edge.
Nc : int, optional
Number of elements for series expansion of driving function. Estimated
if not given.
c : float, optional
Speed of sound
Returns
-------
d : (N,) numpy.ndarray
Complex weights of secondary sources.
selection : (N,) numpy.ndarray
Boolean array containing ``True`` or ``False`` depending on
whether the corresponding secondary source is "active" or not.
secondary_source_function : callable
A function that can be used to create the sound field of a
single secondary source. See `sfs.fd.synthesize()`.
Notes
-----
One leg of the secondary sources has to be located on the x-axis (y0=0),
the edge at the origin.
Derived from :cite:`Spors2016`
"""
x0 = _np.asarray(x0)
k = _util.wavenumber(omega, c)
phi_s = _np.arctan2(xs[1], xs[0])
if phi_s < 0:
phi_s = phi_s + 2 * _np.pi
r_s = _np.linalg.norm(xs)
L = x0.shape[0]
r = _np.linalg.norm(x0, axis=1)
phi = _np.arctan2(x0[:, 1], x0[:, 0])
phi = _np.where(phi < 0, phi + 2 * _np.pi, phi)
if Nc is None:
Nc = _np.ceil(2 * k * _np.max(r) * alpha / _np.pi)
epsilon = _np.ones(Nc) # weights for series expansion
epsilon[0] = 2
d = _np.zeros(L, dtype=complex)
idx = (r <= r_s)
for m in _np.arange(Nc):
nu = m * _np.pi / alpha
f = 1 / epsilon[m] * _np.cos(nu * phi_s) * _np.cos(nu * phi)
d[idx] = d[idx] + f[idx] * _jn(nu, k * r[idx]) * _hankel2(nu, k * r_s)
d[~idx] = d[~idx] + f[~idx] * _jn(nu, k * r_s) * _hankel2(
nu, k * r[~idx])
return -1j * _np.pi / alpha * d