gem.utility.utilities.calc_Lambda

gem.utility.utilities.calc_Lambda(R, Lambda_c, Delta_p, D, H_list)

Compute Lambda matrix from R, D, Lambda_c and Delta. It comes from the same equation as for Lambda_c. Lambda is expressed as

\[\Lambda = \sum_s l_s h_s\]

where \(h_s\) are a set of matrices that forms a basis for the space of Hermitian matrices with dimension :math:`

u`. They are given in H_list. The elements \(l_s\) are obtained by calculating

\[l_s = -l^c_s - \sum_{cblpha} \]

rac{partial}{partial d^P_s} left[ Delta ( 1 - Delta ) ]^{1/2}_{cb} ( D R^T)_{bc}

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

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