diff --git a/docs/pyttadoc/ambisonics.rst b/docs/pyttadoc/ambisonics.rst
new file mode 100644
index 0000000..4585292
--- /dev/null
+++ b/docs/pyttadoc/ambisonics.rst
@@ -0,0 +1,7 @@
+.. currentmodule:: pytta
+
+Ambisonics
+==========
+
+.. automodule:: pytta.ambisonics
+   :members:
diff --git a/docs/pyttadoc/index.rst b/docs/pyttadoc/index.rst
index ca3da8d..ba9cc57 100644
--- a/docs/pyttadoc/index.rst
+++ b/docs/pyttadoc/index.rst
@@ -57,6 +57,12 @@ Modules:
     * pytta.iso3741:
         calculations according to the standard;
 
+    * pytta.vbap:
+        vector base amplitude panning for 2D and 3D loudspeaker layouts;
+
+    * pytta.ambisonics:
+        higher-order Ambisonics encoding, decoding and rotation;
+
 .. toctree::
    classes/index
    utils/index
@@ -64,4 +70,6 @@ Modules:
    functions
    generate
    rooms
+   vbap
+   ambisonics
    properties
diff --git a/docs/pyttadoc/vbap.rst b/docs/pyttadoc/vbap.rst
new file mode 100644
index 0000000..3d1b0d0
--- /dev/null
+++ b/docs/pyttadoc/vbap.rst
@@ -0,0 +1,7 @@
+.. currentmodule:: pytta
+
+VBAP
+====
+
+.. automodule:: pytta.vbap
+   :members:
diff --git a/pytta/__init__.py b/pytta/__init__.py
index d8740aa..7e39efd 100644
--- a/pytta/__init__.py
+++ b/pytta/__init__.py
@@ -72,6 +72,12 @@
     * pytta.iso3741:
         calculations according to the standard;
 
+    * pytta.vbap:
+        vector base amplitude panning for 2D and 3D loudspeaker layouts;
+
+    * pytta.ambisonics:
+        higher-order Ambisonics encoding, decoding and rotation;
+
 
 You can find usage examples in the toolbox's examples folder.
 
@@ -108,6 +114,8 @@
 from . import utils
 from . import rooms
 from . import iso3741
+from . import vbap
+from . import ambisonics
 
 from .functions import read_wav, write_wav, merge, split, \
     list_devices, print_devices, get_device_from_user,\
@@ -130,6 +138,8 @@
            'generate',
            'utils',
            'iso3741',
+           'vbap',
+           'ambisonics',
            'rooms',
 
            # Functions
diff --git a/pytta/_tdesigns.py b/pytta/_tdesigns.py
new file mode 100644
index 0000000..578a145
--- /dev/null
+++ b/pytta/_tdesigns.py
@@ -0,0 +1,1903 @@
+"""
+Spherical t-designs of degree 1 to 21 on the unit sphere, as unit vectors.
+
+A t-design of degree t is a set of points whose mean of any polynomial of
+degree t or less on the sphere equals the mean over the sphere. The designs
+are those of Hardin and Sloane, as stored in t_designs_1_21.mat of the
+Spherical-Harmonic-Transform library of Archontis Politis
+(https://github.com/polarch/Spherical-Harmonic-Transform), BSD 3-Clause
+licence, reproduced in pytta/ambisonics.py.
+
+Hardin, R. H., & Sloane, N. J. A. (1996). McLaren's improved snub cube and
+other new spherical designs in three dimensions. Discrete & Computational
+Geometry, 15(4), 429-441.
+"""
+
+T_DESIGNS = {
+    1: [
+        (1.0, 0.0, 0.0),
+        (-1.0, 0.0, 0.0),
+    ],
+    2: [
+        (0.5773502691896257, 0.5773502691896257, 0.5773502691896257),
+        (0.5773502691896257, -0.5773502691896257, -0.5773502691896257),
+        (-0.5773502691896257, 0.5773502691896257, -0.5773502691896257),
+        (-0.5773502691896257, -0.5773502691896257, 0.5773502691896257),
+    ],
+    3: [
+        (1.0, 0.0, 0.0),
+        (-1.0, 0.0, 0.0),
+        (0.0, 1.0, 0.0),
+        (0.0, -1.0, 0.0),
+        (0.0, 0.0, 1.0),
+        (0.0, 0.0, -1.0),
+    ],
+    4: [
+        (0.850650808352, 0.0, -0.525731112119),
+        (0.525731112119, -0.850650808352, 0.0),
+        (0.0, -0.525731112119, 0.850650808352),
+        (0.850650808352, 0.0, 0.525731112119),
+        (-0.525731112119, -0.850650808352, 0.0),
+        (0.0, 0.525731112119, -0.850650808352),
+        (-0.850650808352, 0.0, -0.525731112119),
+        (-0.525731112119, 0.850650808352, 0.0),
+        (0.0, 0.525731112119, 0.850650808352),
+        (-0.850650808352, 0.0, 0.525731112119),
+        (0.525731112119, 0.850650808352, 0.0),
+        (0.0, -0.525731112119, -0.850650808352),
+    ],
+    5: [
+        (0.850650808352, 0.0, -0.525731112119),
+        (0.525731112119, -0.850650808352, 0.0),
+        (0.0, -0.525731112119, 0.850650808352),
+        (0.850650808352, 0.0, 0.525731112119),
+        (-0.525731112119, -0.850650808352, 0.0),
+        (0.0, 0.525731112119, -0.850650808352),
+        (-0.850650808352, 0.0, -0.525731112119),
+        (-0.525731112119, 0.850650808352, 0.0),
+        (0.0, 0.525731112119, 0.850650808352),
+        (-0.850650808352, 0.0, 0.525731112119),
+        (0.525731112119, 0.850650808352, 0.0),
+        (0.0, -0.525731112119, -0.850650808352),
+    ],
+    6: [
+        (0.8662468181078206, 0.42251865376111153, 0.26663540151670473),
+        (0.8662468181078206, -0.42251865376111153, -0.26663540151670473),
+        (0.8662468181078206, 0.26663540151670473, -0.42251865376111153),
+        (0.8662468181078206, -0.26663540151670473, 0.42251865376111153),
+        (-0.8662468181078206, 0.42251865376111153, -0.26663540151670473),
+        (-0.8662468181078206, -0.42251865376111153, 0.26663540151670473),
+        (-0.8662468181078206, 0.26663540151670473, 0.42251865376111153),
+        (-0.8662468181078206, -0.26663540151670473, -0.42251865376111153),
+        (0.26663540151670473, 0.8662468181078206, 0.42251865376111153),
+        (-0.26663540151670473, 0.8662468181078206, -0.42251865376111153),
+        (-0.42251865376111153, 0.8662468181078206, 0.26663540151670473),
+        (0.42251865376111153, 0.8662468181078206, -0.26663540151670473),
+        (-0.26663540151670473, -0.8662468181078206, 0.42251865376111153),
+        (0.26663540151670473, -0.8662468181078206, -0.42251865376111153),
+        (0.42251865376111153, -0.8662468181078206, 0.26663540151670473),
+        (-0.42251865376111153, -0.8662468181078206, -0.26663540151670473),
+        (0.42251865376111153, 0.26663540151670473, 0.8662468181078206),
+        (-0.42251865376111153, -0.26663540151670473, 0.8662468181078206),
+        (0.26663540151670473, -0.42251865376111153, 0.8662468181078206),
+        (-0.26663540151670473, 0.42251865376111153, 0.8662468181078206),
+        (0.42251865376111153, -0.26663540151670473, -0.8662468181078206),
+        (-0.42251865376111153, 0.26663540151670473, -0.8662468181078206),
+        (0.26663540151670473, 0.42251865376111153, -0.8662468181078206),
+        (-0.26663540151670473, -0.42251865376111153, -0.8662468181078206),
+    ],
+    7: [
+        (0.8662468181078206, 0.42251865376111153, 0.26663540151670473),
+        (0.8662468181078206, -0.42251865376111153, -0.26663540151670473),
+        (0.8662468181078206, 0.26663540151670473, -0.42251865376111153),
+        (0.8662468181078206, -0.26663540151670473, 0.42251865376111153),
+        (-0.8662468181078206, 0.42251865376111153, -0.26663540151670473),
+        (-0.8662468181078206, -0.42251865376111153, 0.26663540151670473),
+        (-0.8662468181078206, 0.26663540151670473, 0.42251865376111153),
+        (-0.8662468181078206, -0.26663540151670473, -0.42251865376111153),
+        (0.26663540151670473, 0.8662468181078206, 0.42251865376111153),
+        (-0.26663540151670473, 0.8662468181078206, -0.42251865376111153),
+        (-0.42251865376111153, 0.8662468181078206, 0.26663540151670473),
+        (0.42251865376111153, 0.8662468181078206, -0.26663540151670473),
+        (-0.26663540151670473, -0.8662468181078206, 0.42251865376111153),
+        (0.26663540151670473, -0.8662468181078206, -0.42251865376111153),
+        (0.42251865376111153, -0.8662468181078206, 0.26663540151670473),
+        (-0.42251865376111153, -0.8662468181078206, -0.26663540151670473),
+        (0.42251865376111153, 0.26663540151670473, 0.8662468181078206),
+        (-0.42251865376111153, -0.26663540151670473, 0.8662468181078206),
+        (0.26663540151670473, -0.42251865376111153, 0.8662468181078206),
+        (-0.26663540151670473, 0.42251865376111153, 0.8662468181078206),
+        (0.42251865376111153, -0.26663540151670473, -0.8662468181078206),
+        (-0.42251865376111153, 0.26663540151670473, -0.8662468181078206),
+        (0.26663540151670473, 0.42251865376111153, -0.8662468181078206),
+        (-0.26663540151670473, -0.42251865376111153, -0.8662468181078206),
+    ],
+    8: [
+        (0.507475446410817, -0.306200013239571, 0.805425492011663),
+        (-0.306200013239569, 0.805425492011663, 0.507475446410817),
+        (-0.507475446410817, 0.30620001323957, 0.805425492011663),
+        (0.805425492011663, 0.507475446410817, -0.306200013239569),
+        (0.306200013239569, 0.805425492011664, -0.507475446410817),
+        (0.805425492011663, -0.507475446410817, 0.306200013239569),
+        (0.306200013239569, -0.805425492011663, 0.507475446410816),
+        (-0.805425492011663, -0.507475446410817, -0.306200013239569),
+        (-0.30620001323957, -0.805425492011664, -0.507475446410816),
+        (-0.805425492011663, 0.507475446410818, 0.306200013239569),
+        (0.507475446410817, 0.30620001323957, -0.805425492011663),
+        (-0.507475446410817, -0.30620001323957, -0.805425492011663),
+        (0.626363670265271, -0.243527775409194, -0.74051520928072),
+        (-0.243527775409195, -0.74051520928072, 0.626363670265271),
+        (-0.626363670265271, 0.243527775409194, -0.74051520928072),
+        (-0.74051520928072, 0.62636367026527, -0.243527775409195),
+        (0.243527775409195, -0.740515209280719, -0.626363670265271),
+        (-0.74051520928072, -0.62636367026527, 0.243527775409195),
+        (0.243527775409195, 0.740515209280719, 0.626363670265271),
+        (0.74051520928072, -0.62636367026527, -0.243527775409195),
+        (-0.243527775409195, 0.74051520928072, -0.626363670265271),
+        (0.74051520928072, 0.62636367026527, 0.243527775409195),
+        (0.626363670265271, 0.243527775409194, 0.74051520928072),
+        (-0.626363670265271, -0.243527775409194, 0.74051520928072),
+        (-0.286248723426035, 0.957120327092458, -0.044523564585421),
+        (0.957120327092458, -0.04452356458542, -0.286248723426035),
+        (0.286248723426035, -0.957120327092458, -0.044523564585421),
+        (-0.04452356458542, -0.286248723426035, 0.957120327092458),
+        (-0.957120327092458, -0.044523564585419, 0.286248723426035),
+        (-0.044523564585421, 0.286248723426034, -0.957120327092458),
+        (-0.957120327092458, 0.04452356458542, -0.286248723426034),
+        (0.044523564585421, 0.286248723426034, 0.957120327092458),
+        (0.957120327092458, 0.04452356458542, 0.286248723426034),
+        (0.044523564585421, -0.286248723426034, -0.957120327092458),
+        (-0.286248723426034, -0.957120327092458, 0.044523564585421),
+        (0.286248723426035, 0.957120327092458, 0.044523564585421),
+    ],
+    9: [
+        (0.9333646931993099, 0.353542188921472, -0.06195377423185971),
+        (0.9333646931993099, -0.353542188921472, 0.06195377423185971),
+        (0.9333646931993099, -0.06195377423185971, -0.353542188921472),
+        (0.9333646931993099, 0.06195377423185971, 0.353542188921472),
+        (-0.9333646931993099, 0.353542188921472, 0.06195377423185971),
+        (-0.9333646931993099, -0.353542188921472, -0.06195377423185971),
+        (-0.9333646931993099, -0.06195377423185971, 0.353542188921472),
+        (-0.9333646931993099, 0.06195377423185971, -0.353542188921472),
+        (-0.06195377423185971, 0.9333646931993099, 0.353542188921472),
+        (0.06195377423185971, 0.9333646931993099, -0.353542188921472),
+        (-0.353542188921472, 0.9333646931993099, -0.06195377423185971),
+        (0.353542188921472, 0.9333646931993099, 0.06195377423185971),
+        (0.06195377423185971, -0.9333646931993099, 0.353542188921472),
+        (-0.06195377423185971, -0.9333646931993099, -0.353542188921472),
+        (0.353542188921472, -0.9333646931993099, -0.06195377423185971),
+        (-0.353542188921472, -0.9333646931993099, 0.06195377423185971),
+        (0.353542188921472, -0.06195377423185971, 0.9333646931993099),
+        (-0.353542188921472, 0.06195377423185971, 0.9333646931993099),
+        (-0.06195377423185971, -0.353542188921472, 0.9333646931993099),
+        (0.06195377423185971, 0.353542188921472, 0.9333646931993099),
+        (0.353542188921472, 0.06195377423185971, -0.9333646931993099),
+        (-0.353542188921472, -0.06195377423185971, -0.9333646931993099),
+        (-0.06195377423185971, 0.353542188921472, -0.9333646931993099),
+        (0.06195377423185971, -0.353542188921472, -0.9333646931993099),
+        (0.7068416977125503, 0.639740098619792, 0.3018400579657685),
+        (0.7068416977125503, -0.639740098619792, -0.3018400579657685),
+        (0.7068416977125503, 0.3018400579657685, -0.639740098619792),
+        (0.7068416977125503, -0.3018400579657685, 0.639740098619792),
+        (-0.7068416977125503, 0.639740098619792, -0.3018400579657685),
+        (-0.7068416977125503, -0.639740098619792, 0.3018400579657685),
+        (-0.7068416977125503, 0.3018400579657685, 0.639740098619792),
+        (-0.7068416977125503, -0.3018400579657685, -0.639740098619792),
+        (0.3018400579657685, 0.7068416977125503, 0.639740098619792),
+        (-0.3018400579657685, 0.7068416977125503, -0.639740098619792),
+        (-0.639740098619792, 0.7068416977125503, 0.3018400579657685),
+        (0.639740098619792, 0.7068416977125503, -0.3018400579657685),
+        (-0.3018400579657685, -0.7068416977125503, 0.639740098619792),
+        (0.3018400579657685, -0.7068416977125503, -0.639740098619792),
+        (0.639740098619792, -0.7068416977125503, 0.3018400579657685),
+        (-0.639740098619792, -0.7068416977125503, -0.3018400579657685),
+        (0.639740098619792, 0.3018400579657685, 0.7068416977125503),
+        (-0.639740098619792, -0.3018400579657685, 0.7068416977125503),
+        (0.3018400579657685, -0.639740098619792, 0.7068416977125503),
+        (-0.3018400579657685, 0.639740098619792, 0.7068416977125503),
+        (0.639740098619792, -0.3018400579657685, -0.7068416977125503),
+        (-0.639740098619792, 0.3018400579657685, -0.7068416977125503),
+        (0.3018400579657685, 0.639740098619792, -0.7068416977125503),
+        (-0.3018400579657685, -0.639740098619792, -0.7068416977125503),
+    ],
+    10: [
+        (-0.753828667197017, 0.54595190806126, -0.365621190026287),
+        (0.545951908061258, -0.36562119002629, -0.753828667197017),
+        (0.753828667197016, -0.545951908061261, -0.365621190026288),
+        (-0.365621190026289, -0.753828667197017, 0.545951908061259),
+        (-0.545951908061258, -0.365621190026288, 0.753828667197018),
+        (-0.365621190026289, 0.753828667197017, -0.545951908061259),
+        (-0.545951908061258, 0.365621190026289, -0.753828667197017),
+        (0.365621190026287, 0.753828667197017, 0.54595190806126),
+        (0.545951908061259, 0.365621190026289, 0.753828667197017),
+        (0.365621190026287, -0.753828667197018, -0.545951908061259),
+        (-0.753828667197017, -0.545951908061261, 0.365621190026288),
+        (0.753828667197016, 0.545951908061261, 0.365621190026287),
+        (0.70018101936373, -0.713151065847793, 0.034089549761256),
+        (-0.713151065847794, 0.034089549761254, 0.700181019363729),
+        (-0.70018101936373, 0.713151065847793, 0.034089549761256),
+        (0.034089549761255, 0.70018101936373, -0.713151065847793),
+        (0.713151065847793, 0.034089549761254, -0.70018101936373),
+        (0.034089549761257, -0.700181019363729, 0.713151065847794),
+        (0.713151065847794, -0.034089549761255, 0.700181019363728),
+        (-0.034089549761256, -0.700181019363729, -0.713151065847794),
+        (-0.713151065847794, -0.034089549761254, -0.700181019363729),
+        (-0.034089549761257, 0.700181019363729, 0.713151065847794),
+        (0.70018101936373, 0.713151065847793, -0.034089549761257),
+        (-0.700181019363729, -0.713151065847794, -0.034089549761257),
+        (0.276230218261792, 0.077050720725736, -0.957997939953259),
+        (0.077050720725735, -0.957997939953258, 0.276230218261793),
+        (-0.276230218261792, -0.077050720725734, -0.957997939953259),
+        (-0.957997939953259, 0.276230218261791, 0.077050720725738),
+        (-0.077050720725735, -0.957997939953259, -0.276230218261792),
+        (-0.957997939953258, -0.276230218261793, -0.077050720725736),
+        (-0.077050720725736, 0.957997939953258, 0.276230218261794),
+        (0.957997939953259, -0.27623021826179, 0.077050720725737),
+        (0.077050720725734, 0.957997939953259, -0.276230218261792),
+        (0.957997939953258, 0.276230218261793, -0.077050720725738),
+        (0.276230218261793, -0.077050720725736, 0.957997939953258),
+        (-0.276230218261791, 0.077050720725735, 0.957997939953259),
+        (0.451819102555243, -0.783355937521819, 0.42686411621907),
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+}
diff --git a/pytta/ambisonics.py b/pytta/ambisonics.py
new file mode 100644
index 0000000..7dbc653
--- /dev/null
+++ b/pytta/ambisonics.py
@@ -0,0 +1,512 @@
+"""
+PyTTa Ambisonics:
+-----------------
+
+Higher-order Ambisonics (HOA): real spherical harmonics, encoding, decoding
+with five decoders, rotation and the conversions between the usual channel
+conventions.
+
+Available functions:
+
+    >>> Y = pytta.ambisonics.real_sh(order, directions)
+    >>> hoa = pytta.ambisonics.encode(signals, directions, order)
+    >>> D, order = pytta.ambisonics.decoder(ls_directions, 'allrad')
+    >>> ls = pytta.ambisonics.decode(hoa, D)
+    >>> hoa_rot = pytta.ambisonics.rotate(hoa, yaw, pitch, roll)
+
+Signals are (samples, channels) arrays. The HOA channels follow ACN ordering,
+q = n^2 + n + m (0-based), with orthonormal real spherical harmonics (N3D)
+and no Condon-Shortley phase. Directions are (points, 2) arrays of
+[azimuth, elevation] in degrees, 0 deg in front and 90 deg to the left.
+Conversions to SN3D, FuMa and SID are included, and bformat_fuma gives the
+first-order FuMa B-format of Iceberg.
+
+Origin of the code
+------------------
+
+This module is a port to Python of the MATLAB library Higher-Order-Ambisonics
+by Archontis Politis (2015), https://github.com/polarch/Higher-Order-Ambisonics
+(getRSH, encodeHOA_N3D, decodeHOA_N3D, encodeBformat, decodeBformat,
+rotateHOA_N3D, rotateBformat, convert_N3D_SN3D, convert_N3D_FuMa,
+convert_ACN_SID, getMaxREweights, getLayoutAmbisonicOrder, ambiDecoder,
+allrad, csad), with the functions it uses from his Spherical-Harmonic-
+Transform library, https://github.com/polarch/Spherical-Harmonic-Transform
+(getSHrotMtx, euler2rotationMatrix, getTdesign and its t-designs, in
+pytta/_tdesigns.py). Both are under the BSD 3-Clause licence reproduced
+below. bformat_fuma follows native_bformat_fuma of Iceberg
+(https://github.com/aguirreSL/Iceberg, BSD 3-Clause, Sergio Aguirre).
+
+References
+----------
+
+Zotter, F., & Frank, M. (2012). All-round ambisonic panning and decoding.
+Journal of the Audio Engineering Society, 60(10), 807-820.
+
+Zotter, F., Pomberger, H., & Noisternig, M. (2012). Energy-preserving
+ambisonic decoding. Acta Acustica united with Acustica, 98(1), 37-47.
+
+Epain, N., Jin, C. T., & Zotter, F. (2014). Ambisonic decoding with
+constant angular spread. Acta Acustica united with Acustica, 100(5), 928-936.
+
+Ivanic, J., & Ruedenberg, K. (1996). Rotation matrices for real spherical
+harmonics. Direct determination by recursion. Journal of Physical Chemistry,
+100(15), 6342-6347 (with the corrections of 1998).
+
+Licence of the ported code (both libraries)
+-------------------------------------------
+
+    Copyright (c) 2015, Archontis Politis
+    All rights reserved.
+
+    Redistribution and use in source and binary forms, with or without
+    modification, are permitted provided that the following conditions are
+    met:
+
+    * Redistributions of source code must retain the above copyright notice,
+      this list of conditions and the following disclaimer.
+
+    * Redistributions in binary form must reproduce the above copyright
+      notice, this list of conditions and the following disclaimer in the
+      documentation and/or other materials provided with the distribution.
+
+    * Neither the name of the copyright holder nor the names of its
+      contributors may be used to endorse or promote products derived from
+      this software without specific prior written permission.
+
+    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
+    IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
+    TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
+    PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+    HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+    SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+    TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+    PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+    LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+    NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+    SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+"""
+
+import warnings
+from math import factorial
+
+import numpy as np
+from scipy import signal as ss
+from scipy.optimize import brentq
+from scipy.spatial import ConvexHull
+from scipy.special import eval_legendre, lpmv
+
+from . import vbap
+from ._tdesigns import T_DESIGNS
+
+
+def _dirs(directions):
+    return np.atleast_2d(np.asarray(directions, dtype=float))
+
+
+def _unit(directions):
+    d = np.radians(_dirs(directions))
+    return np.column_stack([np.cos(d[:, 0]) * np.cos(d[:, 1]),
+                            np.sin(d[:, 0]) * np.cos(d[:, 1]), np.sin(d[:, 1])])
+
+
+def _directions(vectors):
+    v = np.asarray(vectors, dtype=float)
+    return np.degrees(np.column_stack([np.arctan2(v[:, 1], v[:, 0]),
+                                       np.arctan2(v[:, 2], np.hypot(v[:, 0], v[:, 1]))]))
+
+
+def _order(channels):
+    order = int(round(np.sqrt(channels))) - 1
+    if (order + 1)**2 != channels:
+        raise ValueError('HOA signals need (order + 1)^2 channels.')
+    return order
+
+
+def real_sh(order, directions):
+    """
+    Orthonormal real spherical harmonics, ACN ordering, no Condon-Shortley
+    phase (getRSH).
+
+    Returns
+    -------
+    numpy.ndarray
+        ((order + 1)^2, points).
+    """
+    d = np.radians(_dirs(directions))
+    azi, x = d[:, 0], np.sin(d[:, 1])
+    Y = np.zeros(((order + 1)**2, len(d)))
+    Y[0] = 1 / np.sqrt(4 * np.pi)
+    for n in range(1, order + 1):
+        for m in range(-n, n + 1):
+            a = abs(m)
+            norm = np.sqrt((2 * n + 1) * factorial(n - a) / (4 * np.pi * factorial(n + a)))
+            P = (-1)**a * lpmv(a, n, x)
+            trig = (np.sqrt(2) * np.cos(m * azi) if m > 0 else
+                    np.sqrt(2) * np.sin(a * azi) if m < 0 else 1.)
+            Y[n * n + n + m] = norm * P * trig
+    return Y
+
+
+def t_design(degree):
+    """
+    Spherical t-design of degree 1 to 21 (getTdesign).
+
+    Returns
+    -------
+    (numpy.ndarray, numpy.ndarray)
+        Unit vectors (points, 3) and their [azimuth, elevation] in degrees.
+    """
+    if not 1 <= degree <= 21:
+        raise ValueError('t-designs are available for degrees 1 to 21.')
+    vecs = np.array(T_DESIGNS[degree])
+    return vecs, _directions(vecs)
+
+
+def encode(signals, directions, order):
+    """
+    Encode source signals from their directions to HOA, N3D (encodeHOA_N3D).
+
+    signals: (samples, sources); returns (samples, (order + 1)^2).
+    """
+    s = np.asarray(signals, dtype=float)
+    s = s[:, None] if s.ndim == 1 else s
+    return s @ real_sh(order, directions).T
+
+
+def _filterbank(sig, cutoffs, fs):
+    # applyFilterbank: FIR of order 100 (fir1, Hamming), zero phase by
+    # dropping the 50 samples of group delay.
+    n_band, half = len(cutoffs) + 1, 50
+    pad = np.vstack([sig, np.zeros((half, sig.shape[1]))])
+    bands = []
+    for b in range(n_band):
+        if b == 0:
+            h = ss.firwin(101, cutoffs[0], fs=fs)
+        elif b == n_band - 1:
+            h = ss.firwin(101, cutoffs[-1], fs=fs, pass_zero=False)
+        else:
+            h = ss.firwin(101, [cutoffs[b - 1], cutoffs[b]], fs=fs, pass_zero=False)
+        bands.append(ss.lfilter(h, 1, pad, axis=0)[half:])
+    return bands
+
+
+def _decode(sig, D, cutoffs, fs, channels):
+    D = np.asarray(D, dtype=float)
+    D = D[:, :, None] if D.ndim == 2 else D
+    n_band = 1 if cutoffs is None else len(cutoffs) + 1
+    if D.shape[2] != n_band:
+        raise ValueError('One decoding matrix is needed for each frequency band.')
+    if n_band == 1:
+        return sig @ D[:, :channels, 0].T
+    return sum(b @ D[:, :channels, k].T
+               for k, b in enumerate(_filterbank(sig, cutoffs, fs)))
+
+
+def decode(hoa, D, cutoffs=None, fs=None):
+    """
+    Decode HOA signals with a decoding matrix (decodeHOA_N3D).
+
+    D: (loudspeakers, (order + 1)^2), or (loudspeakers, (order + 1)^2,
+    bands) with cutoffs (bands - 1 frequencies in Hz) and fs for a decoding
+    in frequency bands, split by FIR filters of order 100.
+    """
+    hoa = np.asarray(hoa, dtype=float)
+    return _decode(hoa, D, cutoffs, fs, hoa.shape[1])
+
+
+def encode_bformat(signals, directions):
+    """First-order FuMa B-format (W/sqrt(2), X, Y, Z) of sources (encodeBformat)."""
+    s = np.asarray(signals, dtype=float)
+    s = s[:, None] if s.ndim == 1 else s
+    u = _unit(directions)
+    return s @ np.column_stack([np.ones(len(u)) / np.sqrt(2), u])
+
+
+def decode_bformat(bformat, D, cutoffs=None, fs=None):
+    """Decode FuMa B-format with the first 4 columns of D (decodeBformat)."""
+    return _decode(fuma_to_n3d(bformat), D, cutoffs, fs, 4)
+
+
+def n3d_to_sn3d(sig):
+    """N3D to SN3D normalization (convert_N3D_SN3D, 'n2sn')."""
+    sig = np.asarray(sig, dtype=float)
+    n = np.floor(np.sqrt(np.arange(sig.shape[1])))
+    return sig / np.sqrt(2 * n + 1)
+
+
+def sn3d_to_n3d(sig):
+    """SN3D to N3D normalization (convert_N3D_SN3D, 'sn2n')."""
+    sig = np.asarray(sig, dtype=float)
+    n = np.floor(np.sqrt(np.arange(sig.shape[1])))
+    return sig * np.sqrt(2 * n + 1)
+
+
+_FUMA2ACN = np.array([1, 3, 4, 2, 9, 7, 5, 6, 8, 16, 14, 12, 10, 11, 13, 15]) - 1
+_NORM_FUMA2N3D = np.array([np.sqrt(2), np.sqrt(3), np.sqrt(3), np.sqrt(3),
+                           np.sqrt(15) / 2, np.sqrt(15) / 2, np.sqrt(5), np.sqrt(15) / 2,
+                           np.sqrt(15) / 2, np.sqrt(35 / 8), np.sqrt(35) / 3,
+                           np.sqrt(224 / 45), np.sqrt(7), np.sqrt(224 / 45),
+                           np.sqrt(35) / 3, np.sqrt(35 / 8)])
+
+
+def _fuma_order(sig):
+    sig = np.asarray(sig, dtype=float)
+    order = _order(sig.shape[1])
+    if order > 3:
+        warnings.warn('FuMa is defined up to third order; keeping the first 16 channels.')
+        sig, order = sig[:, :16], 3
+    return sig, (order + 1)**2
+
+
+def fuma_to_n3d(sig):
+    """FuMa (up to third order) to N3D, ACN (convert_N3D_FuMa, 'fuma2n')."""
+    sig, nsh = _fuma_order(sig)
+    return sig[:, _FUMA2ACN[:nsh]] * _NORM_FUMA2N3D[:nsh]
+
+
+def n3d_to_fuma(sig):
+    """N3D, ACN to FuMa (up to third order) (convert_N3D_FuMa, 'n2fuma')."""
+    sig, nsh = _fuma_order(sig)
+    acn2fuma = np.argsort(_FUMA2ACN)
+    norm = (1 / _NORM_FUMA2N3D)[acn2fuma]
+    return sig[:, acn2fuma[:nsh]] * norm[:nsh]
+
+
+def _sid_index(order):
+    idx = [0]
+    for n in range(1, order + 1):
+        ms = [m for k in range(1, n + 1) for m in (n - k + 1, k - n - 1)] + [0]
+        idx += [n * n + n + m for m in ms]
+    return np.array(idx)
+
+
+def acn_to_sid(sig):
+    """ACN to SID channel ordering (convert_ACN_SID, 'acn2sid')."""
+    sig = np.asarray(sig)
+    return sig[:, _sid_index(_order(sig.shape[1]))]
+
+
+def sid_to_acn(sig):
+    """SID to ACN channel ordering (convert_ACN_SID, 'sid2acn')."""
+    sig = np.asarray(sig)
+    return sig[:, np.argsort(_sid_index(_order(sig.shape[1])))]
+
+
+def bformat_fuma(sig, convention):
+    """
+    First-order FuMa B-format (W, X, Y, Z) from full-sphere Ambisonics of
+    any order, as Iceberg's native_bformat_fuma.
+
+    convention: 'fuma', 'ambix' (ACN, SN3D) or 'n3d' (ACN, N3D). The first
+    four channels hold the first order in all three, so the conversion of
+    those four is exact.
+
+    Returns
+    -------
+    (numpy.ndarray, int)
+        (samples, 4) FuMa B-format and the order of the input.
+    """
+    sig = np.asarray(sig, dtype=float)
+    if sig.ndim != 2 or sig.shape[1] < 4:
+        raise ValueError('Ambisonics B-format needs (order + 1)^2 channels, 4 or more.')
+    order = _order(sig.shape[1])
+    c = convention.lower()
+    if c == 'fuma':
+        return sig[:, :4], order
+    if c == 'ambix':
+        return np.column_stack([sig[:, 0] / np.sqrt(2), sig[:, 3], sig[:, 1], sig[:, 2]]), order
+    if c == 'n3d':
+        return np.column_stack([sig[:, 0] / np.sqrt(2), sig[:, [3, 1, 2]] / np.sqrt(3)]), order
+    raise ValueError("convention must be 'fuma', 'ambix' or 'n3d'.")
+
+
+def max_re_weights(order):
+    """
+    Max-rE weights a_n = P_n(cos(137.9 deg / (order + 1.51))), repeated per
+    channel (getMaxREweights).
+    """
+    x = np.cos(np.radians(137.9) / (order + 1.51))
+    return np.concatenate([np.full(2 * n + 1, eval_legendre(n, x))
+                           for n in range(order + 1)])
+
+
+def layout_order(ls_directions):
+    """
+    Ambisonic order a 3D loudspeaker layout supports, from the mean energy
+    spread of VBAP at the centres of its triangles (getLayoutAmbisonicOrder).
+    """
+    ls = _dirs(ls_directions)
+    U = _unit(ls)
+    centres = _directions(np.array([U[f].sum(axis=0) for f in ConvexHull(U).simplices]))
+    groups = vbap.loudspeaker_triplets(ls)
+    g = vbap.gains(centres, groups, vbap.inverse_matrices(ls, groups))
+    rE = np.linalg.norm(g**2 @ U, axis=1)
+    spread = 2 * np.degrees(np.arccos(np.clip(rE, -1, 1)))
+    order = int(np.floor(2 * 137.9 / np.mean(spread) - 1.52 + 0.5))
+    return max(order, 1)
+
+
+def _fzero(f, x0):
+    # MATLAB fzero from a starting point: widen [x0 - dx, x0 + dx] by
+    # sqrt(2) until the sign changes, then solve on that bracket.
+    dx = x0 / 50 if x0 else 1 / 50
+    a = b = x0
+    fa = fb = f(x0)
+    while (fa > 0) == (fb > 0):
+        dx *= np.sqrt(2)
+        a, fa = x0 - dx, f(x0 - dx)
+        if (fa > 0) != (fb > 0):
+            break
+        b, fb = x0 + dx, f(x0 + dx)
+    return brentq(f, min(a, b), max(a, b), xtol=1e-14, rtol=4 * np.finfo(float).eps)
+
+
+def _energy_spread(G, U):
+    E = np.sum(G**2, axis=1)
+    rE = np.linalg.norm((G**2 @ U) / E[:, None], axis=1)
+    return np.degrees(2 * np.arccos(np.clip(2 * rE - 1, -1, 1)))
+
+
+def _csad(ls, order):
+    U = _unit(ls)
+    _, tdirs = t_design(4 * order)
+    azi, ele = np.arange(-180, 181, 5.), np.arange(-90, 91, 5.)
+    grid = np.column_stack([np.tile(azi, len(ele)), np.repeat(ele, len(azi))])
+    groups = vbap.loudspeaker_triplets(ls)
+    inv = vbap.inverse_matrices(ls, groups)
+    max_spread = np.max(_energy_spread(vbap.energy_gains(grid, groups, inv), U))
+    G = np.zeros((len(ls), len(tdirs)))
+    for k, d in enumerate(tdirs):
+        def excess(x):
+            g = vbap.energy_gains(d, groups, inv, x, 32, 4)
+            return _energy_spread(g, U)[0] - max_spread
+        G[:, k] = vbap.energy_gains(d, groups, inv, _fzero(excess, max_spread), 32, 4)[0]
+    Y = real_sh(order, tdirs)
+    return G @ Y.T @ np.linalg.inv(Y @ Y.T)
+
+
+def decoder(ls_directions, method='sad', max_re=True, order=None):
+    """
+    Ambisonic decoding matrix for a loudspeaker layout (ambiDecoder).
+
+    Parameters
+    ----------
+    ls_directions : array_like
+        (loudspeakers, 2) [azimuth, elevation] in degrees.
+    method : str
+        'sad' sampling (4 pi / L Y^T), 'mmd' mode matching (pseudo-inverse),
+        'epad' energy preserving, 'allrad' all-round (VBAP of a 21-design,
+        3D layouts) or 'csad' constant angular spread (3D layouts).
+    max_re : bool
+        Apply the max-rE weights (not for 'csad'). Default True.
+    order : int, optional
+        Decoding order; by default the order the layout supports.
+
+    Returns
+    -------
+    (numpy.ndarray, int)
+        D, (loudspeakers, (order + 1)^2), and the order.
+    """
+    ls = _dirs(ls_directions)
+    if order is None:
+        order = layout_order(ls)
+    L = len(ls)
+    Y = real_sh(order, ls)
+    m = method.lower()
+    if m == 'sad':
+        D = 4 * np.pi / L * Y.T
+    elif m == 'mmd':
+        D = np.linalg.pinv(Y)
+    elif m == 'epad':
+        U, _, Vh = np.linalg.svd(Y)
+        D = 4 * np.pi / L * Vh.T[:, :(order + 1)**2] @ U.T
+    elif m == 'allrad':
+        _, tdirs = t_design(21)
+        groups = vbap.loudspeaker_triplets(ls)
+        G = vbap.gains(tdirs, groups, vbap.inverse_matrices(ls, groups)).T
+        D = 4 * np.pi / len(tdirs) * G @ real_sh(order, tdirs).T
+    elif m == 'csad':
+        D = _csad(ls, order)
+    else:
+        raise ValueError("method must be 'sad', 'mmd', 'epad', 'allrad' or 'csad'.")
+    if max_re and m != 'csad':
+        D = D * max_re_weights(order)
+    return D, order
+
+
+def _euler_zyx(alpha, beta, gamma):
+    # euler2rotationMatrix(alpha, beta, gamma, 'zyx') = Rx(gamma) Ry(beta) Rz(alpha)
+    c, s = np.cos, np.sin
+    Rz = np.array([[c(alpha), s(alpha), 0], [-s(alpha), c(alpha), 0], [0, 0, 1]])
+    Ry = np.array([[c(beta), 0, -s(beta)], [0, 1, 0], [s(beta), 0, c(beta)]])
+    Rx = np.array([[1, 0, 0], [0, c(gamma), s(gamma)], [0, -s(gamma), c(gamma)]])
+    return Rx @ Ry @ Rz
+
+
+def sh_rotation(R, order):
+    """
+    Rotation matrix of real spherical harmonics up to order, from a 3 x 3
+    rotation matrix R, by the recursion of Ivanic and Ruedenberg
+    (getSHrotMtx, real basis).
+    """
+    out = np.zeros(((order + 1)**2,) * 2)
+    out[0, 0] = 1
+    R1 = np.array([[R[1, 1], R[1, 2], R[1, 0]],
+                   [R[2, 1], R[2, 2], R[2, 0]],
+                   [R[0, 1], R[0, 2], R[0, 0]]])
+    if order == 0:
+        return out
+    out[1:4, 1:4] = R1
+    prev = R1
+
+    def P(i, l, a, b):
+        if b == -l:
+            return R1[i + 1, 2] * prev[a + l - 1, 0] + R1[i + 1, 0] * prev[a + l - 1, 2 * l - 2]
+        if b == l:
+            return R1[i + 1, 2] * prev[a + l - 1, 2 * l - 2] - R1[i + 1, 0] * prev[a + l - 1, 0]
+        return R1[i + 1, 1] * prev[a + l - 1, b + l - 1]
+
+    for l in range(2, order + 1):
+        Rl = np.zeros((2 * l + 1, 2 * l + 1))
+        for m in range(-l, l + 1):
+            for n in range(-l, l + 1):
+                d = 1 if m == 0 else 0
+                denom = (2 * l) * (2 * l - 1) if abs(n) == l else (l * l - n * n)
+                u = np.sqrt((l * l - m * m) / denom)
+                v = np.sqrt((1 + d) * (l + abs(m) - 1) * (l + abs(m)) / denom) * (1 - 2 * d) * 0.5
+                w = np.sqrt((l - abs(m) - 1) * (l - abs(m)) / denom) * (1 - d) * (-0.5)
+                if u:
+                    u *= P(0, l, m, n)
+                if v:
+                    if m == 0:
+                        v *= P(1, l, 1, n) + P(-1, l, -1, n)
+                    elif m > 0:
+                        dm = 1 if m == 1 else 0
+                        v *= P(1, l, m - 1, n) * np.sqrt(1 + dm) - P(-1, l, -m + 1, n) * (1 - dm)
+                    else:
+                        dm = 1 if m == -1 else 0
+                        v *= P(1, l, m + 1, n) * (1 - dm) + P(-1, l, -m - 1, n) * np.sqrt(1 + dm)
+                if w:
+                    w *= (P(1, l, m + 1, n) + P(-1, l, -m - 1, n) if m > 0 else
+                          P(1, l, m - 1, n) - P(-1, l, -m + 1, n))
+                Rl[m + l, n + l] = u + v + w
+        out[l * l:(l + 1)**2, l * l:(l + 1)**2] = Rl
+        prev = Rl
+    return out
+
+
+def rotate(hoa, yaw, pitch, roll):
+    """
+    Rotate a HOA sound scene, N3D, by yaw, pitch and roll in degrees
+    (rotateHOA_N3D).
+    """
+    hoa = np.asarray(hoa, dtype=float)
+    R = _euler_zyx(-np.radians(yaw), -np.radians(pitch), np.radians(roll))
+    return hoa @ sh_rotation(R, _order(hoa.shape[1])).T
+
+
+def rotate_bformat(bformat, yaw, pitch, roll):
+    """Rotate first-order FuMa B-format by yaw, pitch and roll in degrees (rotateBformat)."""
+    R = np.eye(4)
+    R[1:, 1:] = _euler_zyx(-np.radians(yaw), -np.radians(pitch), np.radians(roll))
+    return np.asarray(bformat, dtype=float) @ R.T
diff --git a/pytta/vbap.py b/pytta/vbap.py
new file mode 100644
index 0000000..0cf21a0
--- /dev/null
+++ b/pytta/vbap.py
@@ -0,0 +1,303 @@
+"""
+PyTTa VBAP:
+-----------
+
+Vector base amplitude panning (VBAP) of Pulkki (1997) for 2D and 3D
+loudspeaker layouts, and its spread version, multiple-direction amplitude
+panning (MDAP).
+
+Available functions:
+
+    >>> groups = pytta.vbap.loudspeaker_pairs(azimuths)        # 2D
+    >>> groups = pytta.vbap.loudspeaker_triplets(directions)   # 3D
+    >>> inverses = pytta.vbap.inverse_matrices(directions, groups)
+    >>> G = pytta.vbap.gains(source_directions, groups, inverses, spread=0)
+    >>> G = pytta.vbap.energy_gains(source_directions, groups, inverses)
+
+Directions are in degrees: azimuth for 2D layouts, [azimuth, elevation] for
+3D ones, with x = cos(azi) cos(elev), y = sin(azi) cos(elev) and z =
+sin(elev) (0 deg in front, 90 deg to the left). Loudspeaker indices are
+0-based.
+
+Origin of the code
+------------------
+
+This module is a port to Python of the MATLAB library
+Vector-Base-Amplitude-Panning by Archontis Politis and Ville Pulkki (2015),
+https://github.com/polarch/Vector-Base-Amplitude-Panning (findLsPairs.m,
+findLsTriplets.m, invertLsMtx.m, vbap.m, vbip.m, getSpreadSrcDirs.m), under the BSD
+3-Clause licence reproduced below. The gains follow the MATLAB code
+operation by operation.
+
+References
+----------
+
+Pulkki, V. (1997). Virtual sound source positioning using vector base
+amplitude panning. Journal of the Audio Engineering Society, 45(6), 456-466.
+
+Pulkki, V. (1999). Uniform spreading of amplitude panned virtual sources.
+Proceedings of the IEEE Workshop on Applications of Signal Processing to
+Audio and Acoustics, New Paltz, NY.
+
+Licence of the ported code
+--------------------------
+
+    Copyright (c) 2015, Archontis Politis
+    All rights reserved.
+
+    Redistribution and use in source and binary forms, with or without
+    modification, are permitted provided that the following conditions are
+    met:
+
+    * Redistributions of source code must retain the above copyright notice,
+      this list of conditions and the following disclaimer.
+
+    * Redistributions in binary form must reproduce the above copyright
+      notice, this list of conditions and the following disclaimer in the
+      documentation and/or other materials provided with the distribution.
+
+    * Neither the name of the copyright holder nor the names of its
+      contributors may be used to endorse or promote products derived from
+      this software without specific prior written permission.
+
+    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
+    IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
+    TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
+    PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+    HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+    SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+    TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+    PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+    LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+    NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+    SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+"""
+
+import numpy as np
+from scipy.spatial import ConvexHull
+
+
+def _cartesian(directions):
+    d = np.radians(np.asarray(directions, dtype=float))
+    if d.ndim == 1:
+        return np.column_stack([np.cos(d), np.sin(d)])
+    azi, elev = d[:, 0], d[:, 1]
+    return np.column_stack([np.cos(azi) * np.cos(elev),
+                            np.sin(azi) * np.cos(elev), np.sin(elev)])
+
+
+def loudspeaker_pairs(azimuths, max_aperture=None):
+    """
+    Adjacent loudspeaker pairs of a 2D layout (findLsPairs).
+
+    Parameters
+    ----------
+    azimuths : array_like
+        Loudspeaker azimuths in degrees.
+    max_aperture : float, optional
+        Pairs that span this angle in degrees or more are left out.
+
+    Returns
+    -------
+    numpy.ndarray
+        (pairs, 2) loudspeaker indices, around the circle by azimuth.
+    """
+    azimuths = np.asarray(azimuths, dtype=float)
+    order = np.argsort(azimuths, kind='stable')
+    groups = np.column_stack([order, np.roll(order, -1)])
+    if max_aperture is not None:
+        s = azimuths[np.append(order, order[0])]
+        apertures = np.diff(s)
+        apertures[-1] = 360 - abs(apertures[-1])
+        groups = groups[apertures < max_aperture]
+    return groups
+
+
+def loudspeaker_triplets(directions, max_aperture=None):
+    """
+    Loudspeaker triplets of a 3D layout (findLsTriplets).
+
+    The triplets are the faces of the convex hull of the loudspeaker
+    directions, which on the unit sphere is their Delaunay triangulation.
+    Faces whose outward normal is at 90 deg or more from their centroid are
+    left out: those are the faces that close a layout with no loudspeakers
+    below or above, through which no source direction passes.
+
+    Parameters
+    ----------
+    directions : array_like
+        (loudspeakers, 2) [azimuth, elevation] in degrees.
+    max_aperture : float, optional
+        Triplets with a side longer than this angle in degrees are left out.
+
+    Returns
+    -------
+    numpy.ndarray
+        (triplets, 3) loudspeaker indices, each triplet counter-clockwise
+        seen from outside and starting at its smallest index, sorted.
+    """
+    U = _cartesian(directions)
+    faces = []
+    for face in ConvexHull(U).simplices:
+        v = U[face]
+        n = np.cross(v[1] - v[0], v[2] - v[1])
+        if np.dot(n, v.mean(axis=0) - U.mean(axis=0)) < 0:
+            face, v, n = face[::-1], v[::-1], -n
+        # MATLAB keeps acos(dot(centroid, n)) < pi/2; a dot product of
+        # rounding size, as on a flat bottom face, rounds to pi/2 there.
+        if np.dot(v.mean(axis=0), n) > 1e-12:
+            faces.append(np.roll(face, -int(np.argmin(face))))
+    faces = np.array(faces, dtype=int)
+    if max_aperture is not None:
+        sides = np.stack([np.sum(U[faces[:, a]] * U[faces[:, b]], axis=1)
+                          for a, b in ((0, 1), (1, 2), (2, 0))], axis=1)
+        faces = faces[np.all(np.arccos(np.clip(sides, -1, 1))
+                             <= np.radians(max_aperture), axis=1)]
+    return faces[np.lexsort((faces[:, 1], faces[:, 0]))]
+
+
+def inverse_matrices(directions, groups):
+    """
+    Inverse of the matrix of loudspeaker vectors of each group (invertLsMtx).
+
+    Parameters
+    ----------
+    directions : array_like
+        Loudspeaker azimuths (2D) or [azimuth, elevation] (3D) in degrees.
+    groups : numpy.ndarray
+        Pairs or triplets from loudspeaker_pairs or loudspeaker_triplets.
+
+    Returns
+    -------
+    numpy.ndarray
+        (groups, dim, dim): the inverse of the matrix whose rows are the
+        unit vectors of the group, so that the gains of a source u are
+        u @ inverse.
+    """
+    U = _cartesian(directions)
+    return np.linalg.inv(U[np.asarray(groups)])
+
+
+def _spread_directions(direction, spread, num_src=8, num_rings=1):
+    # getSpreadSrcDirs: num_src sources across the spread in 2D; in 3D
+    # num_rings concentric rings of num_src sources and the source itself.
+    if np.ndim(direction) == 0:
+        d = np.radians(np.linspace(direction - spread / 2, direction + spread / 2,
+                                   num_src + 1))
+        return np.column_stack([np.cos(d), np.sin(d)])
+    u = _cartesian(np.atleast_2d(direction))[0]
+    u_x = np.array([[0, -u[2], u[1]], [u[2], 0, -u[0]], [-u[1], u[0], 0]])
+    theta = 2 * np.pi / num_src
+    R = (np.eye(3) * np.cos(theta) + np.sin(theta) * u_x
+         + (1 - np.cos(theta)) * np.outer(u, u))
+    base = np.zeros((num_src, 3))
+    if direction[1] > 89 or direction[1] < -89:
+        base[0] = [1, 0, 0]
+    else:
+        c = np.cross(u, [0, 0, 1])
+        base[0] = c / np.sqrt(np.sum(c**2))
+    for n in range(1, num_src):
+        base[n] = R @ base[n - 1]
+    ring = np.radians(spread / 2) / num_rings
+    rings = np.vstack([u + base * np.tan(ring * (r + 1)) for r in range(num_rings)])
+    rings = rings / np.sqrt(np.sum(rings**2, axis=1))[:, None]
+    return np.vstack([rings, u])
+
+
+def _group_gains(u, groups, inverses, first_only, energy=False):
+    # One direction: the gains of the first (3D) or last (2D) group that
+    # holds it, normalized in amplitude (VBAP) or in energy (VBIP).
+    g = np.zeros(int(groups.max()) + 1)
+    for group, inv in zip(groups, inverses):
+        g_tmp = u @ inv
+        if np.min(g_tmp) > -0.001:
+            g[group] = g_tmp / (np.sum(g_tmp) if energy else np.sqrt(np.sum(g_tmp**2)))
+            if first_only:
+                break
+    return g
+
+
+def gains(directions, groups, inverses, spread=0.):
+    """
+    VBAP gains of a set of source directions (vbap).
+
+    Parameters
+    ----------
+    directions : array_like
+        Source azimuths (2D) or (sources, 2) [azimuth, elevation] (3D) in
+        degrees.
+    groups : numpy.ndarray
+        Pairs or triplets from loudspeaker_pairs or loudspeaker_triplets.
+    inverses : numpy.ndarray
+        From inverse_matrices.
+    spread : float, optional
+        Spread in degrees for MDAP: the gains of 9 directions across the
+        spread (8 on a ring and the source in 3D) are summed. The default is
+        0, plain VBAP.
+
+    Returns
+    -------
+    numpy.ndarray
+        (sources, loudspeakers) gains, non-negative, of norm 1 per source.
+        A source outside every group (below a hemisphere layout, say) gets
+        all gains 0, as in the MATLAB code.
+    """
+    groups = np.asarray(groups)
+    three_d = groups.shape[1] == 3
+    directions = np.asarray(directions, dtype=float)
+    directions = directions.reshape(-1, 2) if three_d else directions.reshape(-1)
+    out = np.zeros((len(directions), int(groups.max()) + 1))
+    for n, d in enumerate(directions):
+        if spread:
+            g = sum(_group_gains(u, groups, inverses, three_d)
+                    for u in _spread_directions(d, spread))
+        else:
+            g = _group_gains(_cartesian(np.atleast_2d(d) if three_d else [d])[0],
+                             groups, inverses, three_d)
+        with np.errstate(invalid='ignore'):
+            out[n] = np.fmax(0, g / np.sqrt(np.sum(g**2)))
+    return out
+
+
+def energy_gains(directions, groups, inverses, spread=0., num_src=8,
+                 num_rings=1):
+    """
+    Vector base intensity panning gains (vbip).
+
+    The energies of the loudspeakers of a group, not their amplitudes,
+    weight the loudspeaker vectors into the source direction; the gains are
+    their square roots, normalized in energy.
+
+    Parameters
+    ----------
+    directions, groups, inverses
+        As in gains.
+    spread : float, optional
+        Spread in degrees: the energies of num_src directions across it (in
+        3D num_rings rings of num_src and the source) are summed.
+    num_src, num_rings : int, optional
+        Spread directions, 8 and 1 by default.
+
+    Returns
+    -------
+    numpy.ndarray
+        (sources, loudspeakers) gains, of norm 1 per source.
+    """
+    groups = np.asarray(groups)
+    three_d = groups.shape[1] == 3
+    directions = np.asarray(directions, dtype=float)
+    directions = directions.reshape(-1, 2) if three_d else directions.reshape(-1)
+    out = np.zeros((len(directions), int(groups.max()) + 1))
+    for n, d in enumerate(directions):
+        if spread:
+            e = sum(_group_gains(u, groups, inverses, three_d, energy=True)
+                    for u in _spread_directions(d, spread, num_src, num_rings))
+        else:
+            e = _group_gains(_cartesian(np.atleast_2d(d) if three_d else [d])[0],
+                             groups, inverses, three_d, energy=True)
+        with np.errstate(invalid='ignore'):
+            e = e / np.sum(e)
+        if three_d:
+            e[e < 0] = 0
+        out[n] = np.fmax(0, np.sqrt(e))
+    return out
diff --git a/tests/golden/ambisonics_polarch.mat b/tests/golden/ambisonics_polarch.mat
new file mode 100644
index 0000000..7cb2a8b
Binary files /dev/null and b/tests/golden/ambisonics_polarch.mat differ
diff --git a/tests/golden/make_ambisonics_polarch.m b/tests/golden/make_ambisonics_polarch.m
new file mode 100644
index 0000000..b12a1e9
--- /dev/null
+++ b/tests/golden/make_ambisonics_polarch.m
@@ -0,0 +1,44 @@
+% Golden data for tests/test_ambisonics.py: polarch Higher-Order-Ambisonics
+% and Vector-Base-Amplitude-Panning (Archontis Politis, BSD 3-Clause), the
+% copies that Iceberg installs. Three functions they take from polarch
+% Spherical-Harmonic-Transform are replaced by minimal versions: getTdesign
+% (the t-designs of pytta/_tdesigns.py), sphDelaunay (the faces of the
+% convex hull) and euler2rotationMatrix ('zyx'). rotateHOA_N3D is not here;
+% the test checks the rotation by a rule. Run from tests/golden with those
+% on the path.
+rng(1, 'twister');
+dirs = [rand(20,1)*360-180, asind(rand(20,1)*2-1)];
+Y4 = getRSH(4, dirs);
+sig3 = rand(8, 16) - 0.5;                            % third order, N3D ACN
+conv.n2sn = convert_N3D_SN3D(sig3, 'n2sn');
+conv.sn2n = convert_N3D_SN3D(sig3, 'sn2n');
+conv.n2fuma = convert_N3D_FuMa(sig3, 'n2fuma');
+conv.fuma2n = convert_N3D_FuMa(sig3, 'fuma2n');
+conv.acn2sid = convert_ACN_SID(sig3, 'acn2sid');
+conv.sid2acn = convert_ACN_SID(sig3, 'sid2acn');
+maxre = {getMaxREweights(1), getMaxREweights(3), getMaxREweights(5)};
+ls_hemi = [0 0; 90 0; 180 0; -90 0; 45 45; 135 45; -135 45; -45 45; 0 90];
+ls_full = [(0:90:270)' -30*ones(4,1); (0:45:315)' zeros(8,1); (30:60:330)' 45*ones(6,1); 0 90];
+order_hemi = getLayoutAmbisonicOrder(ls_hemi);
+order_full = getLayoutAmbisonicOrder(ls_full);
+D.sad = ambiDecoder(ls_full, 'sad', 1, 3);
+D.mmd = ambiDecoder(ls_full, 'mmd', 1, 3);
+D.epad = ambiDecoder(ls_full, 'epad', 0, 3);
+D.allrad = ambiDecoder(ls_full, 'allrad', 1, 3);
+D.csad = ambiDecoder(ls_full, 'csad', 1, 2);
+[D.auto, D.auto_order] = ambiDecoder(ls_full, 'sad');
+src = [30 10; -100 40];
+s2 = rand(16, 2) - 0.5;
+enc3 = encodeHOA_N3D(3, s2, src);
+rng(2, 'twister');
+hoa2 = rand(400, 9) - 0.5;   % numpy: RandomState(2).random_sample((9, 400)).T - 0.5
+Db = cat(3, ambiDecoder(ls_full,'sad',1,2), ambiDecoder(ls_full,'mmd',1,2), ambiDecoder(ls_full,'allrad',1,2));
+dec_bands = decodeHOA_N3D(hoa2, Db, [500 2000], 48000);
+bf = encodeBformat(s2, src);
+D1 = ambiDecoder(ls_full, 'sad', 1, 1);
+bf_dec = decodeBformat(bf, D1);
+rotbf = rotateBformat(bf, 30, -20, 10);
+save('ambisonics_polarch.mat', 'dirs', 'Y4', 'sig3', 'conv', 'maxre', 'ls_hemi', 'ls_full', ...
+     'order_hemi', 'order_full', 'D', 'src', 's2', 'enc3', 'Db', 'dec_bands', ...
+     'bf', 'D1', 'bf_dec', 'rotbf');
+fprintf('orders: hemisphere %d, full %d, auto %d\n', order_hemi, order_full, D.auto_order);
diff --git a/tests/golden/make_vbap_polarch.m b/tests/golden/make_vbap_polarch.m
new file mode 100644
index 0000000..e6abb89
--- /dev/null
+++ b/tests/golden/make_vbap_polarch.m
@@ -0,0 +1,20 @@
+% Golden data for tests/test_vbap.py: polarch Vector-Base-Amplitude-Panning
+% (Archontis Politis, BSD 3-Clause), the copy that Iceberg installs in
+% Toolboxes/polarch/vbap. Run from tests/golden with that folder on the path.
+% Indices are 1-based.
+ls2 = [0 30 -30 110 -110];                                   % 5.0, 2D
+ls3 = [0 0; 90 0; 180 0; -90 0; 45 45; 135 45; -135 45; -45 45; 0 90];  % hemisphere
+src2 = (-180:7.5:180)';
+[a, e] = meshgrid(-180:20:160, -10:20:90); src3 = [a(:) e(:)];
+pairs = findLsPairs(ls2);
+inv2 = invertLsMtx(ls2, pairs);
+g2 = vbap(src2, pairs, inv2);
+g2s = vbap(src2, pairs, inv2, 20);
+tri = findLsTriplets(ls3);
+inv3 = invertLsMtx(ls3, tri);
+g3 = vbap(src3, tri, inv3);
+g3s = vbap(src3, tri, inv3, 20);
+save('vbap_polarch.mat', 'ls2', 'ls3', 'src2', 'src3', 'pairs', 'inv2', 'g2', ...
+     'g2s', 'tri', 'inv3', 'g3', 'g3s');
+fprintf('%d pairs, %d triplets\n', size(pairs, 1), size(tri, 1));
+disp(tri)
diff --git a/tests/golden/vbap_polarch.mat b/tests/golden/vbap_polarch.mat
new file mode 100644
index 0000000..8a568a5
Binary files /dev/null and b/tests/golden/vbap_polarch.mat differ
diff --git a/tests/test_ambisonics.py b/tests/test_ambisonics.py
new file mode 100644
index 0000000..c95bad4
--- /dev/null
+++ b/tests/test_ambisonics.py
@@ -0,0 +1,106 @@
+"""
+Tests for pytta.ambisonics, a port of the Higher-Order-Ambisonics library
+of Archontis Politis. Each test pins one rule.
+
+The golden data come from golden/make_ambisonics_polarch.m (MATLAB R2026b
+with polarch Higher-Order-Ambisonics and Vector-Base-Amplitude-Panning).
+"""
+import os
+import unittest
+
+import numpy as np
+import scipy.io as sio
+
+from pytta import ambisonics as A
+
+GOLDEN = os.path.join(os.path.dirname(__file__), 'golden')
+
+
+class TestAmbisonics(unittest.TestCase):
+
+    def test_real_sh_are_orthonormal(self):
+        # Gauss-Legendre in elevation (12 nodes) and 24 azimuths integrate
+        # exactly every product of harmonics up to order 10, so
+        # sum w Y Y^T = I. The 21-design does the same with equal weights,
+        # (4 pi / N) Y Y^T = I, within the precision of its tabulated points,
+        # which falls with the order (4e-10 at order 4, 2.5e-6 at order 10).
+        x, w = np.polynomial.legendre.leggauss(12)
+        el, az = np.meshgrid(np.degrees(np.arcsin(x)), np.arange(24) * 15., indexing='ij')
+        Y = A.real_sh(10, np.column_stack([az.ravel(), el.ravel()]))
+        err_gl = np.abs((Y * np.repeat(w, 24) * np.pi / 12) @ Y.T - np.eye(121)).max()
+        _, dirs = A.t_design(21)
+        Y = A.real_sh(6, dirs)
+        err_td = np.abs(4 * np.pi / len(dirs) * Y @ Y.T - np.eye(49)).max()
+        print(f'\n  Gauss-Legendre, order 10: {err_gl:.1e}; 21-design, order 6: {err_td:.1e}')
+        self.assertLess(err_gl, 1e-13)
+        self.assertLess(err_td, 1e-8)
+
+    def test_first_order_is_fuma_bformat(self):
+        # FuMa B-format is W = s / sqrt(2), X, Y, Z = s times the unit
+        # vector. The first order of an N3D encoding converts to it, scaled
+        # by the 1 / sqrt(4 pi) of the orthonormal harmonics, and so does
+        # Iceberg's bformat_fuma from a third-order AmbiX, N3D or FuMa scene.
+        rng = np.random.default_rng(4)
+        s, dirs = rng.uniform(-1, 1, (32, 3)), np.array([[30, 10], [-100, 40], [170, -60]])
+        bf = A.encode_bformat(s, dirs) / np.sqrt(4 * np.pi)
+        hoa = A.encode(s, dirs, 3)
+        errs = [np.abs(A.n3d_to_fuma(hoa[:, :4]) - bf).max(),
+                np.abs(A.bformat_fuma(hoa, 'n3d')[0] - bf).max(),
+                np.abs(A.bformat_fuma(A.n3d_to_sn3d(hoa), 'ambix')[0] - bf).max(),
+                np.abs(A.bformat_fuma(A.n3d_to_fuma(hoa), 'fuma')[0] - bf).max()]
+        print('\n  ' + ', '.join(f'{e:.1e}' for e in errs))
+        self.assertLess(max(errs), 1e-14)
+        self.assertEqual(A.bformat_fuma(hoa, 'n3d')[1], 3)
+
+    def test_rotation_moves_the_encoded_direction(self):
+        # Rotating a scene with one source equals encoding the source in
+        # the rotated direction, M u, with M = Rx(roll) Ry(-pitch) Rz(-yaw);
+        # a positive yaw adds to the azimuth.
+        s, u = np.ones((1, 1)), np.array([[25., 15.]])
+        yawed = A.rotate(A.encode(s, u, 4), 40, 0, 0)
+        e_yaw = np.abs(yawed - A.encode(s, [[65., 15.]], 4)).max()
+        M = A._euler_zyx(-np.radians(30), np.radians(20), np.radians(10))
+        moved = A._directions((M @ A._unit(u)[0])[None])
+        e_any = np.abs(A.rotate(A.encode(s, u, 4), 30, -20, 10)
+                       - A.encode(s, moved, 4)).max()
+        print(f'\n  yaw only {e_yaw:.1e}, yaw pitch roll {e_any:.1e}')
+        self.assertLess(max(e_yaw, e_any), 1e-14)
+
+    def test_matches_polarch(self):
+        d = sio.loadmat(os.path.join(GOLDEN, 'ambisonics_polarch.mat'),
+                        squeeze_me=True, struct_as_record=False)
+        c, D, L, sig3 = d['conv'], d['D'], d['ls_full'], d['sig3']
+        hoa2 = np.random.RandomState(2).random_sample((9, 400)).T - 0.5
+        self.assertEqual(A.layout_order(d['ls_hemi']), d['order_hemi'])
+        self.assertEqual(A.layout_order(L), d['order_full'])
+        D_auto, order = A.decoder(L, 'sad')
+        self.assertEqual(order, D.auto_order)
+        diffs = {
+            'real_sh': (A.real_sh(4, d['dirs']), d['Y4']),
+            'n3d_to_sn3d': (A.n3d_to_sn3d(sig3), c.n2sn),
+            'sn3d_to_n3d': (A.sn3d_to_n3d(sig3), c.sn2n),
+            'n3d_to_fuma': (A.n3d_to_fuma(sig3), c.n2fuma),
+            'fuma_to_n3d': (A.fuma_to_n3d(sig3), c.fuma2n),
+            'acn_to_sid': (A.acn_to_sid(sig3), c.acn2sid),
+            'sid_to_acn': (A.sid_to_acn(sig3), c.sid2acn),
+            'max_re_weights': (np.concatenate([A.max_re_weights(o) for o in (1, 3, 5)]),
+                               np.concatenate(d['maxre'])),
+            'sad': (A.decoder(L, 'sad', True, 3)[0], D.sad),
+            'mmd': (A.decoder(L, 'mmd', True, 3)[0], D.mmd),
+            'epad': (A.decoder(L, 'epad', False, 3)[0], D.epad),
+            'allrad': (A.decoder(L, 'allrad', True, 3)[0], D.allrad),
+            'csad': (A.decoder(L, 'csad', True, 2)[0], D.csad),
+            'sad, order of the layout': (D_auto, D.auto),
+            'encode': (A.encode(d['s2'], d['src'], 3), d['enc3']),
+            'decode in 3 bands': (A.decode(hoa2, d['Db'], [500, 2000], 48000), d['dec_bands']),
+            'encode_bformat': (A.encode_bformat(d['s2'], d['src']), d['bf']),
+            'decode_bformat': (A.decode_bformat(d['bf'], d['D1']), d['bf_dec']),
+            'rotate_bformat': (A.rotate_bformat(d['bf'], 30, -20, 10), d['rotbf'])}
+        worst = {k: np.abs(a - b).max() for k, (a, b) in diffs.items()}
+        print('\n  ' + ', '.join(f'{k} {v:.1e}' for k, v in worst.items()))
+        for k, v in worst.items():
+            self.assertLess(v, 1e-13, k)
+
+
+if __name__ == '__main__':
+    unittest.main()
diff --git a/tests/test_vbap.py b/tests/test_vbap.py
new file mode 100644
index 0000000..00e5d13
--- /dev/null
+++ b/tests/test_vbap.py
@@ -0,0 +1,90 @@
+"""
+Tests for pytta.vbap, vector base amplitude panning (Pulkki 1997), a port of
+the VBAP library of Archontis Politis. Each test pins one rule.
+
+The golden data come from golden/make_vbap_polarch.m (MATLAB R2026b with
+polarch Vector-Base-Amplitude-Panning, the copy that Iceberg installs);
+their loudspeaker indices are 1-based.
+"""
+import os
+import unittest
+
+import numpy as np
+import scipy.io as sio
+
+from pytta import vbap
+
+GOLDEN = os.path.join(os.path.dirname(__file__), 'golden')
+
+
+def unit(azi, elev=0.):
+    a, e = np.radians(azi), np.radians(elev)
+    return np.array([np.cos(a) * np.cos(e), np.sin(a) * np.cos(e), np.sin(e)])
+
+
+class TestVBAP(unittest.TestCase):
+
+    def test_stereo_pair_follows_the_tangent_law(self):
+        # Loudspeakers at +-30 deg: (g1 - g2) / (g1 + g2) = tan(theta) /
+        # tan(30 deg), with g1^2 + g2^2 = 1 (Pulkki 1997, eq. 4 and 6).
+        ls = [30, -30]
+        groups = vbap.loudspeaker_pairs(ls)
+        inv = vbap.inverse_matrices(ls, groups)
+        theta = np.linspace(-29, 29, 59)
+        g = vbap.gains(theta, groups, inv)
+        law = (g[:, 0] - g[:, 1]) / (g[:, 0] + g[:, 1])
+        err = np.max(np.abs(law - np.tan(np.radians(theta)) / np.tan(np.radians(30))))
+        print(f'\n  max |tangent law error| = {err:.1e}, '
+              f'max |norm - 1| = {np.max(np.abs(np.linalg.norm(g, axis=1) - 1)):.1e}')
+        self.assertLess(err, 1e-12)
+        np.testing.assert_allclose(np.linalg.norm(g, axis=1), 1, atol=1e-12)
+
+    def test_3d_gains_point_at_the_source(self):
+        # VBAP definition: the gains of the active triplet weight the
+        # loudspeaker vectors into a vector along the source direction, all
+        # gains are non-negative and their norm is 1. A source on a
+        # loudspeaker gets that loudspeaker alone.
+        ls = np.array([[0, 0], [90, 0], [180, 0], [-90, 0], [45, 45],
+                       [135, 45], [-135, 45], [-45, 45], [0, 90]])
+        groups = vbap.loudspeaker_triplets(ls)
+        inv = vbap.inverse_matrices(ls, groups)
+        rng = np.random.default_rng(1)
+        src = np.column_stack([rng.uniform(-180, 180, 200), rng.uniform(1, 89, 200)])
+        g = vbap.gains(src, groups, inv)
+        L = np.array([unit(*d) for d in ls])
+        p = g @ L
+        u = np.array([unit(*s) for s in src])
+        cross = np.max(np.linalg.norm(np.cross(p, u), axis=1))
+        print(f'\n  max |p x u| = {cross:.1e} over 200 sources')
+        self.assertLess(cross, 1e-12)
+        self.assertTrue(np.all(g >= 0))
+        np.testing.assert_allclose(np.linalg.norm(g, axis=1), 1, atol=1e-12)
+        on = vbap.gains(ls[[4]], groups, inv)[0]
+        self.assertAlmostEqual(on[4], 1, places=12)
+        self.assertAlmostEqual(np.sum(np.delete(on, 4)**2), 0, places=12)
+
+    def test_matches_polarch(self):
+        # Same layouts and sources: pairs and triplets (1-based there), the
+        # inverse matrices (stacked by columns there) and the gains, with and
+        # without a spread of 20 deg (MDAP).
+        d = sio.loadmat(os.path.join(GOLDEN, 'vbap_polarch.mat'), squeeze_me=True)
+        pairs = vbap.loudspeaker_pairs(d['ls2'])
+        tri = vbap.loudspeaker_triplets(d['ls3'])
+        np.testing.assert_array_equal(pairs + 1, d['pairs'])
+        np.testing.assert_array_equal(tri + 1, d['tri'])
+        inv2 = vbap.inverse_matrices(d['ls2'], pairs)
+        inv3 = vbap.inverse_matrices(d['ls3'], tri)
+        diffs = {
+            'inv2': np.abs(inv2.transpose(0, 2, 1).reshape(len(pairs), -1) - d['inv2']).max(),
+            'inv3': np.abs(inv3.transpose(0, 2, 1).reshape(len(tri), -1) - d['inv3']).max(),
+            'g2': np.abs(vbap.gains(d['src2'], pairs, inv2) - d['g2']).max(),
+            'g2s': np.abs(vbap.gains(d['src2'], pairs, inv2, 20) - d['g2s']).max(),
+            'g3': np.abs(vbap.gains(d['src3'], tri, inv3) - d['g3']).max(),
+            'g3s': np.abs(vbap.gains(d['src3'], tri, inv3, 20) - d['g3s']).max()}
+        print('\n  ' + ', '.join(f'{k} {v:.1e}' for k, v in diffs.items()))
+        for v in diffs.values():
+            self.assertLess(v, 1e-12)
+
+
+if __name__ == '__main__':
+    unittest.main()