scipy.linalg.orthogonal_procrustes

scipy.linalg.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 [R81]. 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.

Parameters:

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.

Returns:

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).

Raises:

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.

References

[R81]

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