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
  • A (numpy matrix) – non rotated factors

  • H (numpy matrix) – target matrix

  • full_rank (boolean (default False)) – if set to true full rank is assumed

Returns

Return type

The matrix \(T\).

References

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