distribution_variances

sofia_redux.toolkit.resampling.distribution_variances(coordinates, mean=None, covariance=None, mask=None, sigma_inv=None, dof=1)

Return variance at each coordinate based on coordinate distribution.

Given a normal sample distribution \(X\), returns the variance at each sample coordinate. For example, consider a population of zero mean (\(\bar{X} = 0\)) and a standard deviation of one (\(\sigma = 1\)). Samples located at \(\bar{X} \pm \sigma\) will return a variance of 1, while samples located at \(\bar{X} \pm 2\sigma\) will return a variance of 4.

By default, the distribution variance is derived using coordinate_covariance(), and the sample mean is derived using coordinate_mean() assuming the loss of 1 degree of freedom. However, the expected value (\(E[X]\)) may be supplied with the mean optional parameter along with the covariance, and the number of lost degrees of freedom (dof).

Parameters:

coordinatesnumpy.ndarray (n_dimensions, n_samples)

The coordinates of the sample distribution.

meannumpy.ndarray (n_dimensions,), optional

The expected mean value of the distribution.

covariancenumpy.ndarray (n_dimensions, n_dimensions), optional

The covariance matrix (if known) for the sample distribution.

masknumpy.ndarray of bool (n_samples,), optional

An array of bool values where True indicates a sample should be included when calculating the mean and covariance, and False indicates that a sample should be ignored. By default, all samples are included. The output variance will still be calculated for all samples.

sigma_invnumpy.ndarray (n_dimensions, n_dimensions), optional

The inverse of the covariance matrix, optionally passed in for speed if the covariance is known, and it’s inverse has been pre-calculated.

dofint or float, optional

The lost degrees of freedom, typically 1 to indicate that the population mean is not known and is replaced by the sample mean.

Returns:

variancenumpy.ndarray (n_samples,)

The variance at each sample coordinate based on the sample distribution.