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Covariance Matrix Utilities

Utility functions for constructing and validating covariance matrices from standard deviations, diagonal vectors, upper-triangular packed arrays, or full matrices.

These are used by measurement models, process noise configuration, and other estimation components.

isotropic_covariance builtin 

isotropic_covariance(dim: int, sigma: float) -> ndarray

Create an isotropic covariance matrix: sigma^2 * I.

Builds a dim x dim diagonal matrix where every diagonal element is sigma^2.

Parameters:

Name Type Description Default
dim int

Matrix dimension.

 required
sigma float

Standard deviation applied to all axes.

 required

Returns:

Type Description
ndarray

numpy.ndarray: dim x dim diagonal covariance matrix.
Example 
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import brahe as bh
r = bh.isotropic_covariance(3, 10.0)
# r = diag([100, 100, 100])

diagonal_covariance builtin 

diagonal_covariance(sigmas: ndarray) -> ndarray

Create a diagonal covariance matrix from per-axis standard deviations.

Each sigma value is squared to produce the corresponding diagonal element.

Parameters:

Name Type Description Default
sigmas ndarray

Array of standard deviations, one per axis.

 required

Returns:

Type Description
ndarray

numpy.ndarray: n x n diagonal covariance matrix.
Example 
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import brahe as bh
import numpy as np
r = bh.diagonal_covariance(np.array([5.0, 10.0, 15.0]))
# r = diag([25, 100, 225])

See Also