gem.utility.utilities.calc_Lambda_c

gem.utility.utilities.calc_Lambda_c(R, Lambda, Delta_p, D, H_list)

Compute Lambda_c matrix from R, D, Lambda and Delta. It is given by

\[\Lambda_c = \sum_s l^c_s h_s\]

where \(h_s\) are a set of matrices that forms a basis for the space of Hermitian matrices with dimension \(\nu\). The elements \(l^c_s\) are obtained by calculating

\[l^c_s = -l_s - \sum_{\alpha} \text{Tr} \left[ \frac{\partial}{\partial d^P_s} \left[ \Delta ( 1 - \Delta ) ]^{1/2} ( D R^T ) \right]\]

where \(l_s\) are the elements of the decomposition of \(\Lambda = \sum_s l_s h_s\) and \(d^P_s\) of \(\Delta_p = \sum_s d_s h_s^T\).

Here, extracting the \(l_s`s from :math:\)Lambda` is done using the inverse_realHcombination function. The derivative with respect to \(d^P_s\) is done using the dF function. \(\Lambda_c\) is reconstructed using the realHcombinaison function.