File size: 4,292 Bytes
570b87b | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 | """Phase 2: Wigner-D HOA rotation accuracy and speed."""
from __future__ import annotations
import sys
import time
from pathlib import Path
import numpy as np
sys.path.insert(0, str(Path(__file__).resolve().parents[1]))
from hoa64.analysis import angular_error_deg, doa_from_intensity
from hoa64.encode import encode_points
from hoa64.rotate import rotate_matrix_order1, rotate_source_directions, rotate_yaw_pitch_roll
from hoa64.wigner import hoa_rotation_matrix, rotation_matrix_zyx, apply_hoa_rotation
def test_order1_wigner_matches_cartesian():
a = encode_points([25.0], [-12.0], [1.0])
for yaw, pitch, roll in [(90, 0, 0), (0, 45, 0), (30, -20, 15), (180, 0, 0)]:
a_w = rotate_yaw_pitch_roll(
a, yaw=yaw, pitch=pitch, roll=roll, max_order=1, method="wigner"
)
a_c = rotate_matrix_order1(a, yaw=yaw, pitch=pitch, roll=roll)
np.testing.assert_allclose(a_w[:4], a_c[:4], atol=1e-9, rtol=1e-9)
def test_wigner_matches_plane_wave_reencode():
"""Ground truth: rotate source direction, re-encode."""
cases = [
(0.0, 0.0, 90.0, 0.0, 0.0),
(40.0, -15.0, 35.0, 0.0, 0.0),
(10.0, 20.0, 0.0, 40.0, 0.0),
(-70.0, 5.0, 20.0, -25.0, 30.0),
]
for az0, el0, yaw, pitch, roll in cases:
a0 = encode_points([az0], [el0], [1.0], max_order=7)
az1, el1 = rotate_source_directions(az0, el0, yaw=yaw, pitch=pitch, roll=roll)
a_gt = encode_points([float(az1)], [float(el1)], [1.0], max_order=7)
a_w = rotate_yaw_pitch_roll(
a0, yaw=yaw, pitch=pitch, roll=roll, max_order=7, method="wigner"
)
# Relative error on full 64-vector
denom = np.linalg.norm(a_gt) + 1e-15
rel = np.linalg.norm(a_w[:64] - a_gt[:64]) / denom
assert rel < 1e-6, (
f"rel={rel:.3e} for src=({az0},{el0}) rot=({yaw},{pitch},{roll})"
)
def test_wigner_orthogonal_blocks():
R = rotation_matrix_zyx(33.0, -17.0, 8.0, degrees=True)
M = hoa_rotation_matrix(R, max_order=7)
# Each order block should be orthogonal (rotation)
for n in range(0, 8):
i0 = n * n
dim = 2 * n + 1
B = M[i0 : i0 + dim, i0 : i0 + dim]
I = B.T @ B
np.testing.assert_allclose(I, np.eye(dim), atol=1e-8)
def test_wigner_faster_than_dense():
a = encode_points([15.0], [10.0], [1.0], max_order=7)
# warm-up
rotate_yaw_pitch_roll(a, yaw=20.0, pitch=10.0, roll=5.0, method="wigner")
rotate_yaw_pitch_roll(
a, yaw=20.0, pitch=10.0, roll=5.0, method="dense", n_azi=48, n_el=24
)
t0 = time.perf_counter()
for _ in range(50):
rotate_yaw_pitch_roll(a, yaw=20.0, pitch=10.0, roll=5.0, method="wigner")
t_w = time.perf_counter() - t0
t0 = time.perf_counter()
for _ in range(5):
rotate_yaw_pitch_roll(
a, yaw=20.0, pitch=10.0, roll=5.0, method="dense", n_azi=48, n_el=24
)
t_d = time.perf_counter() - t0
# per-call times
tw = t_w / 50
td = t_d / 5
# Wigner should be substantially faster (typically 50–1000×)
assert tw < td, f"wigner {tw:.4f}s not faster than dense {td:.4f}s"
print(f" timing: wigner={tw*1e3:.3f} ms/call dense={td*1e3:.3f} ms/call speedup={td/tw:.0f}x")
def test_stream_rotation_CT():
# (C,T) path
from hoa64.encode import encode_plane_waves
t = np.linspace(0, 1, 32, endpoint=False)
sig = np.sin(2 * np.pi * 3 * t)[None, :]
hoa = encode_plane_waves([0.0], [0.0], sig, max_order=3)
out = rotate_yaw_pitch_roll(hoa, yaw=90.0, max_order=3, method="wigner")
assert out.shape[0] >= 16
# DOA of first frame energy via products
W, Y, Z, X = out[0], out[1], out[2], out[3]
I = np.array([np.mean(W * X), np.mean(W * Y), np.mean(W * Z)])
n = np.linalg.norm(I)
assert n > 1e-9
if __name__ == "__main__":
test_order1_wigner_matches_cartesian()
print("OK test_order1_wigner_matches_cartesian")
test_wigner_matches_plane_wave_reencode()
print("OK test_wigner_matches_plane_wave_reencode")
test_wigner_orthogonal_blocks()
print("OK test_wigner_orthogonal_blocks")
test_wigner_faster_than_dense()
print("OK test_wigner_faster_than_dense")
test_stream_rotation_CT()
print("OK test_stream_rotation_CT")
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