statsmodels.multivariate.factor_rotation.procrustes¶

statsmodels.multivariate.factor_rotation.procrustes(A, H)[source]¶

Analytically solves the following Procrustes problem:

\[\phi(L) =\frac{1}{2}\|AT-H\|^2.\]

(With no further conditions on \(H\))

Under the assumption that \(A^*H\) has full rank, the analytical solution \(T\) is given by:

\[T = (A^*HH^*A)^{-\frac{1}{2}}A^*H,\]

see Navarra, Simoncini (2010).

Parameters:¶

Anumpy matrix

non rotated factors

Hnumpy matrix

target matrix

full_rankbool (default False)

if set to true full rank is assumed

Returns:¶

The matrix \(T\).

References

[1] Navarra, Simoncini (2010) - A guide to empirical orthogonal functions for climate data analysis