statsmodels.multivariate.factor_rotation.procrustes

statsmodels.multivariate.factor_rotation.procrustes(A, H)

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