Add mean_and_covariance_from_sigma_points

adam_core/coordinates/covariances.py

@@ -318,6 +318,34 @@ def sample_covariance_sigma_points(
     return sigma_points, W, W_cov
 
 
+def mean_and_covariance_from_sigma_points(sigma_points, W, W_cov):
+    """
+    Calculate a covariance matrix from sigma points and their corresponding weights.
+
+    Parameters
+    ----------
+    sigma_points : `~numpy.ndarray` (2 * D + 1, D)
+        Sigma points drawn from the distribution.
+    W: `~numpy.ndarray` (2 * D + 1)
+        Weights of the sigma points.
+    W_cov: `~numpy.ndarray` (2 * D + 1)
+        Weights of the sigma points to reconstruct covariance matrix.
+
+    Returns
+    -------
+    mean : `~numpy.ndarray` (D)
+        Mean calculated from the sigma points and weights.
+    cov : `~numpy.ndarray` (D, D)
+        Covariance matrix calculated from the sigma points and weights.
+    """
+    # Calculate the mean from the sigma points and weights
+    mean = np.dot(W, sigma_points)
+
+    # Calculate the covariance matrix from the sigma points and weights
+    cov = np.cov(sigma_points, aweights=W_cov, rowvar=False, bias=True)
+    return mean, cov
+
+
 def transform_covariances_sampling(
     coords: np.ndarray,
     covariances: np.ndarray,

adam_core/coordinates/tests/test_covariances.py

@@ -1,10 +1,14 @@
 import numpy as np
 
 from ...utils.helpers.orbits import make_real_orbits
-from ..covariances import CoordinateCovariances, sample_covariance_sigma_points
+from ..covariances import (
+    CoordinateCovariances,
+    mean_and_covariance_from_sigma_points,
+    sample_covariance_sigma_points,
+)
 
 
-def test_sample_covariance_sigma_points():
+def test_sigma_points():
     # Get a sample of real orbits and test that sigma point sampling
     # allows the state vector and its covariance to be reconstructed
     orbits = make_real_orbits()
@@ -25,12 +29,13 @@ def test_sample_covariance_sigma_points():
         # since beta = 0 internally
         assert W_cov[0] == 0.0
 
-        # Reconstruct the mean and covariance
-        mean_sg = np.dot(W, samples)
+        # Reconstruct the mean and covariance and test that they match
+        # the original inputs to within 1e-14
+        mean_sg, covariance_sg = mean_and_covariance_from_sigma_points(
+            samples, W, W_cov
+        )
         np.testing.assert_allclose(mean_sg, mean, rtol=0, atol=1e-14)
-
-        cov_sg = np.cov(samples, aweights=W_cov, rowvar=False, bias=True)
-        np.testing.assert_allclose(cov_sg, covariance, rtol=0, atol=1e-14)
+        np.testing.assert_allclose(covariance_sg, covariance, rtol=0, atol=1e-14)
 
 
 def test_CoordinateCovariances_from_sigmas():