change: better coherence function

src/scgenerator/physics/pulse.py

@@ -17,6 +17,7 @@ from pathlib import Path
 from typing import Literal, Tuple, TypeVar
 
 import matplotlib.pyplot as plt
+import numba
 import numpy as np
 from numpy import pi
 from numpy.fft import fft, fftshift, ifft
@@ -715,34 +716,42 @@ def spectrogram(
     return spec
 
 
-def g12(values: np.ndarray):
+def g12(values: np.ndarray, axis: int = 0):
     """
     computes the first order coherence function of a ensemble of values
 
     Parameters
     ----------
-    values : np.ndarray, shape (..., m, n, nt)
+    values : np.ndarray, shape (..., n, nt)
         complex values following sc-ordering
+    axis : int, optional
+        axis to collapse on which to compute the coherence
 
     Returns
     -------
-    np.ndarray, shape (..., n, nt)
+    np.ndarray, shape (..., nt)
         coherence function
     """
 
-    # Create all the possible pairs of values
     n = len(values)
-    field_pairs = itertools.combinations(values, 2)
-    mean_spec = np.mean(math.abs2(values), axis=-3)
+    mean_spec = np.mean(math.abs2(values), axis=axis)
+    corr = np.zeros_like(mean_spec, dtype=complex)
     mask = mean_spec > 1e-15 * mean_spec.max()
-    corr = np.zeros_like(values[0])
-    for left, right in field_pairs:
-        corr[mask] += left[mask].conj() * right[mask]
+    corr[mask] = _g12_fast(values[..., mask])
     corr[mask] = corr[mask] / (n * (n - 1) / 2 * mean_spec[mask])
-
     return np.abs(corr)
 
 
+@numba.njit()
+def _g12_fast(values: np.ndarray) -> np.ndarray:
+    corr = np.zeros_like(values[0])
+    n = len(values)
+    for i in range(n - 1):
+        for j in range(i + 1, n):
+            corr += values[i].conj() * values[j]
+    return corr
+
+
 def avg_g12(values: np.ndarray):
     """
     computes the average of the coherence function weighted by amplitude of spectrum