% PURPOSE: Frequency-domain evaluation of kernel
%
%
% Input:     kap = poles \beta_k which are negative and real
%
%            mu  = streangths \gamma_k corresponding to kap
%
%            qR and qI = real/imaginary parts of conjugate pair poles
%
%            mR and mI = streangth of these conjugate pair poles
%
%            frequency grid for evaluations
%          
% AUTHOR :  Scott Field
%           Department of Physics
%           University of Maryland, Collge Park
%           August 31, 2013


function [full_kernel,pair_kernel,sing_kernel] = ...
    EvaluateKernelFrequency(kap,mu,qR,qI,mR,mI,frequencies)


dsing = numel(kap);
dpair = numel(qR);

y = sqrt(-1)*frequencies;

sing_kernel = zeros(size(y));
pair_kernel = zeros(size(y));


for ii=1:dsing
    
    sing_kernel = sing_kernel + mu(ii)./(y - kap(ii));
    
end


for ii=1:dpair
    
    pole = qR(ii) + sqrt(-1)*qI(ii);
    pole_str = mR(ii) + sqrt(-1)*mI(ii);    
    pair_kernel = pair_kernel + pole_str./(y - pole);
    
    pole = qR(ii) - sqrt(-1)*qI(ii);
    pole_str = mR(ii) - sqrt(-1)*mI(ii);
    pair_kernel = pair_kernel + pole_str./(y - pole);
    
end

full_kernel = pair_kernel + sing_kernel;