ants.utils.polar_decomposition

polar_decomposition(X)[source]

Perform a polar decomposition of a matrix.

The polar decomposition of a matrix X is a factorization of the form:

X = P @ Z

where P is an orthogonal projection matrix and Z is an orthogonal matrix.

Parameters:

X (numpy.ndarray) – Input matrix to decompose. Should be a square matrix.

Returns:

A dictionary containing: - “P”: the orthogonal projection matrix. - “Z”: the orthogonal part of the decomposition. - “Xtilde”: the reconstructed matrix from the decomposition (Xtilde = P @ Z).

Return type:

dict