From 3ec03d92a528376349918291204ece285ff4631d Mon Sep 17 00:00:00 2001
From: Frank Schultz <scf175@googlemail.com>
Date: Wed, 13 Mar 2019 16:41:54 +0100
Subject: [PATCH 1/2] 2.5D Unified WFS and Far/HF NFC-InfOA Driving Functions
 for DAGA2019

---
 sfs/mono/nfchoa.py | 87 ++++++++++++++++++++++++++++++++++++++++++++++
 sfs/mono/wfs.py    | 79 +++++++++++++++++++++++++++++++++++++++++
 2 files changed, 166 insertions(+)

diff --git a/sfs/mono/nfchoa.py b/sfs/mono/nfchoa.py
index 6677d229..e2d56c1b 100644
--- a/sfs/mono/nfchoa.py
+++ b/sfs/mono/nfchoa.py
@@ -234,3 +234,90 @@ def plane_25d(omega, x0, r0, n=[0, 1, 0], max_order=None, c=None):
         d += (-1j)**abs(m) / (k * hn2[abs(m)]) * np.exp(1j * m * (phi0 - phi))
     selection = util.source_selection_all(len(x0))
     return 2*1j / r0 * d, selection, secondary_source_point(omega, c)
+
+
+def point_25d_HF(omega, x0, r0, xs, M=None, c=None,
+                 DirichletKernelFlag=True):
+    """Compute point source driving function for NFC-InfiniteOA.
+
+    This only theoretically useful driving function is used in
+
+    https://github.com/spatialaudio/sfs-with-local-wavenumber-vector-concept
+
+    For a continous SSD only one secondary source is active.
+
+    Examples
+    --------
+    .. plot::
+        :context: close-figs
+
+        d, selection, secondary_source = sfs.mono.nfchoa.point_25d_HF(
+            omega, array.x, R, xs)
+        plot(d, selection, secondary_source)
+
+    """
+    x0 = util.asarray_of_rows(x0)
+    k = util.wavenumber(omega, c)
+    xs = util.asarray_1d(xs)
+    phi, _, r = util.cart2sph(*xs)
+    phi0 = util.cart2sph(*x0.T)[0]
+    if M is None:
+        M = util.max_order_circular_harmonics(len(x0))
+    d = 0
+
+    if DirichletKernelFlag is True:
+        for m in range(-M, M + 1):
+            d += np.exp(-1j * k * r) / np.exp(-1j * k * r0) * \
+                 r0 / r * \
+                 np.exp(-1j * m * (phi0 - phi))
+        d = d / (2 * np.pi * r0)
+    else:  # this is the analytic solution for m=oo and requires an exact
+        # stationary phase source within phi0, i.e. phi==phi0 in exactly one
+        # index
+        d = (np.exp(-1j * k * r) / np.exp(-1j * k * r0) *
+             r0 / r / r0 *
+             len(x0)/2/np.pi *
+             (phi == phi0))  # choose exactly one sec source
+    selection = util.source_selection_all(len(x0))
+    return d, selection, secondary_source_point(omega, c)
+
+
+def plane_25d_HF(omega, x0, r0, n=[0, 1, 0], M=None, c=None,
+                 DirichletKernelFlag=True):
+    """Compute plane wave driving function for NFC-InfiniteOA.
+
+    This only theoretically useful driving function is used in
+
+    https://github.com/spatialaudio/sfs-with-local-wavenumber-vector-concept
+
+    For a continous SSD only one secondary source is active.
+
+    Examples
+    --------
+    .. plot::
+        :context: close-figs
+
+        d, selection, secondary_source = sfs.mono.nfchoa.plane_25d_HF(
+            omega, array.x, R, xs)
+        plot(d, selection, secondary_source)
+
+    """
+    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]
+    if M is None:
+        M = util.max_order_circular_harmonics(len(x0))
+    d = 0
+
+    if DirichletKernelFlag is True:
+        for m in range(-M, M + 1):
+            d += np.exp(1j*np.pi*m) * np.exp(1j*m*(phi0 - phi))
+        d *= (2/r0) * (r0/np.exp(-1j*k*r0))
+    else:
+        d = (1/r0 * 4*np.pi*r0 / np.exp(-1j*k*r0) *
+             len(x0)/2/np.pi *
+             (phi == (phi0-np.pi)))  # choose exactly one sec source
+    selection = util.source_selection_all(len(x0))
+    return d, selection, secondary_source_point(omega, c)
diff --git a/sfs/mono/wfs.py b/sfs/mono/wfs.py
index a05aa0fa..efb17b24 100644
--- a/sfs/mono/wfs.py
+++ b/sfs/mono/wfs.py
@@ -217,6 +217,85 @@ def point_25d(omega, x0, n0, xs, xref=[0, 0, 0], c=None, omalias=None):
     return d, selection, secondary_source_point(omega, c)
 
 
+def point_25d_Unified_WIP(omega, x0, n0, xs, xref=[0, 0, 0],
+                          c=None, omalias=None):
+    r"""Driving function for 2.5-dimensional WFS of 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 xref or contour xref(x0) for amplitude correct synthesis.
+    c : float, optional
+        Speed of sound in m/s.
+    omalias : float, optional
+        Cut angular frequency for prefilter.
+
+    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.mono.synthesize()`.
+
+    Notes
+    -----
+    Eq. (3.10), (3.11) Start, E.W. (1997): "Direct sound enhancement by wave
+    field synthesis", doctoral thesis, TU Delft
+
+    Eq. (2.137) from Schultz, F. (2016): https://doi.org/10.18453/rosdok_id00001765
+
+    .. math::
+
+        D(\x_0,\w) = \sqrt{8 \pi \, \i\wc}
+            \sqrt{\frac{|\x_\text{ref}-\x_0| \cdot
+            |\x_0-\x_\text{s}|}{|\x_\text{ref}-\x_0| + |\x_0-\x_\text{s}|}}
+            \scalarprod{\frac{\x_0-\x_\text{s}}{|\x_0-\x_\text{s}|}}{\n_0}
+            \frac{\e{-\i\wc |\x_0-\x_\text{s}|}}{4\pi\,|\x_0-\x_\text{s}|}
+
+    Examples
+    --------
+    .. plot::
+        :context: close-figs
+
+        d, selection, secondary_source = (
+            sfs.mono.wfs.point_25d_Unified_WIP(
+                omega, array.x, array.n, xs))
+        plot(4*np.pi*np.linalg.norm(xs) * 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
+    dr = xref - x0
+    s = np.linalg.norm(ds, axis=1)
+    r = np.linalg.norm(dr, axis=1)
+
+    d = (
+        preeq_25d(omega, omalias, c) *
+        np.sqrt(8 * np.pi) *
+        np.sqrt((r * s) / (r + s)) *
+        inner1d(n0, ds) / s *
+        np.exp(-1j * k * s) / (4 * np.pi * s))
+    selection = util.source_selection_point(n0, x0, xs)
+    return d, selection, secondary_source_point(omega, c)
+
+
 point_3d = _point
 
 

From c67db62da81d0e63515bbe86bdda548684851edd Mon Sep 17 00:00:00 2001
From: Frank Schultz <scf175@googlemail.com>
Date: Thu, 14 Mar 2019 00:01:13 +0100
Subject: [PATCH 2/2] FIX UP: bugfix docstring example

---
 sfs/mono/nfchoa.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/sfs/mono/nfchoa.py b/sfs/mono/nfchoa.py
index e2d56c1b..6d6dc373 100644
--- a/sfs/mono/nfchoa.py
+++ b/sfs/mono/nfchoa.py
@@ -253,7 +253,7 @@ def point_25d_HF(omega, x0, r0, xs, M=None, c=None,
 
         d, selection, secondary_source = sfs.mono.nfchoa.point_25d_HF(
             omega, array.x, R, xs)
-        plot(d, selection, secondary_source)
+        plot(d * np.linalg.norm(xs)*4*np.pi, selection, secondary_source)
 
     """
     x0 = util.asarray_of_rows(x0)
@@ -298,7 +298,7 @@ def plane_25d_HF(omega, x0, r0, n=[0, 1, 0], M=None, c=None,
         :context: close-figs
 
         d, selection, secondary_source = sfs.mono.nfchoa.plane_25d_HF(
-            omega, array.x, R, xs)
+            omega, array.x, R, npw)
         plot(d, selection, secondary_source)
 
     """