linalg._procrustes

Solve the orthogonal Procrustes problem.

Module Contents

Functions

orthogonal_procrustes(A,B,check_finite=True) Compute the matrix solution of the orthogonal Procrustes problem.
orthogonal_procrustes(A, B, check_finite=True)

Compute the matrix solution of the orthogonal Procrustes problem.

Given matrices A and B of equal shape, find an orthogonal matrix R that most closely maps A to B [1]. Note that unlike higher level Procrustes analyses of spatial data, this function only uses orthogonal transformations like rotations and reflections, and it does not use scaling or translation.

A : (M, N) array_like
Matrix to be mapped.
B : (M, N) array_like
Target matrix.
check_finite : bool, optional
Whether to check that the input matrices contain only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.
R : (N, N) ndarray
The matrix solution of the orthogonal Procrustes problem. Minimizes the Frobenius norm of dot(A, R) - B, subject to dot(R.T, R) == I.
scale : float
Sum of the singular values of dot(A.T, B).
ValueError
If the input arrays are incompatibly shaped. This may also be raised if matrix A or B contains an inf or nan and check_finite is True, or if the matrix product AB contains an inf or nan.

New in version 0.15.0.

[1]Peter H. Schonemann, “A generalized solution of the orthogonal Procrustes problem”, Psychometrica – Vol. 31, No. 1, March, 1996.