PIGALE 1.3.9 Documentation (original) (raw)

Computes the bilinear form to be put in diagonal form from the distance matrix dis.

Computes the bilinear form:

$[ {\rm dis}\leftarrow -\frac{1}{2}\left(I-\frac{J}{\rm ni}\right){\rm dis}\left(I-\frac{J}{\rm ni}\right) ]$

from the developped formula:

$[ {\rm dis}_{i,j}\leftarrow -\frac{1}{2}\left( {\rm dis}_{i,j}-\frac{1}{\rm ni}\sum_{\alpha=1}^{\rm ni} {\rm dis}_{i,\alpha} -\frac{1}{\rm ni}\sum_{\alpha=1}^{\rm ni} {\rm dis}_{\alpha,j} +\frac{1}{{\rm ni}^2}\sum_{\alpha=1}^{\rm ni}\sum_{\beta=1}^{\rm ni}{\rm dis}_{\alpha,\beta}\right)]$