statsmodels.multivariate.factor_rotation.procrustes¶

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

Analytically solves the following Procrustes problem:

$$\varphi (L)=\frac{1}{2}\Vert AT-H{\Vert }^2.$$

(With no further conditions on $H$)

Under the assumption that $A^{\ast }H$ has full rank, the analytical solution $T$ is given by:

$$T=(A^{\ast }H{H}^{\ast }A{)}^{-\frac{1}{2}}{A}^{\ast }H,$$

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