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: