pfqn_nrp.m

%{
%{
 % @file pfqn_nrp.m
 % @brief Normalizing constant via Normal Radius-Probit (NRP) approximation.
%}
%}
 
%{
%{
 % @brief Normalizing constant via Normal Radius-Probit (NRP) approximation.
 % @fn pfqn_nrp(L, N, Z, alpha, options)
 % @param L Service demand matrix.
 % @param N Population vector.
 % @param Z Think time vector.
 % @param alpha Load-dependent rate matrix.
 % @param options Solver options.
 % @return lG Logarithm of normalizing constant.
%}
%}
function [lG] = pfqn_nrp(L,N,Z,alpha,options)
if sum(N)<0
    lG=-Inf;
    return
end
if sum(N)==0
    lG=0;
    return
end
[M,R]=size(L);
Nt = sum(N);
if sum(Z)>0
    L = [L;Z];
    alpha(end+1,1:Nt)=1:Nt;
end
if M==1 && sum(Z)==0
    [~,lG] = pfqn_gld(L,N,alpha);
    return
else
    Lmax = max(L);
end
L = L./repmat(Lmax,size(L,1),1); % scale demands in [0,1]
x0 = zeros(1,R);
[~,~,lG] = laplaceapprox(@(x) infradius_hnorm(x, L, N,alpha),x0);
lG = real(lG + N*log(Lmax'));
end