1;
clear all;

t0 = clock (); % we will use this latter to calculate elapsed time


% load useful functions;
useful_functions;

% some physical constants
useful_constants;

% load atom energy levels and decay description
four_levels;
%three_levels;
%two_levels;

% load EM field description
field_description;

Nfreq=length(modulation_freq);



%tune probe frequency
detuning_p=0;
N_detun_steps=100;
detuning_p_min=-1;
detuning_p_max=-detuning_p_min;
detuning_freq=zeros(1,N_detun_steps+1);
kappa_p      =zeros(1,N_detun_steps+1);
kappa_m      =zeros(1,N_detun_steps+1);

wp0=w12;
wp=wp0+detuning_p_min;
wm=wd-(wp-wd);
%modulation_freq=[0,  wp, wd, wm,   -wp, -wd, -wm,  wp-wd, wd-wp];
%E_field        =[0,  Ep, Ed, Em,   Epc, Edc, Emc,  0,     0    ];
modulation_freq=[0,  wp, wd, -wp, -wd,  wp-wd, wd-wp];
E_field        =[0,  Ep, Ed,  Epc, Edc, 0,     0    ];
Nfreq=length(modulation_freq);

% now we create Liouville indexes list
[N, rhoLiouville_w, rhoLiouville_r, rhoLiouville_c]=unfold_density_matrix(Nlevels,Nfreq);
rhoLiouville=zeros(N,1);

% calculate E_field independent properties of athe atom
% to be used as sub matrix templates for Liouville operator matrix
[L0m, polarizability_m]=L0_and_polarization_submatrices( ...
		Nlevels, ...
		H0, g_decay, g_dephasing, dipole_elements ...
		);
% Liouville operator matrix construction
L=Liouville_operator_matrix( 
		N, 
		L0m, polarizability_m,
		E_field, 
		modulation_freq, rhoLiouville_w, rhoLiouville_r, rhoLiouville_c
		);


%use the fact that sum(rho_ii)=1 to constrain solution
[rhoLiouville_dot, L]=constrain_rho_and_match_L(
		N, L,
		modulation_freq, rhoLiouville_w, rhoLiouville_r, rhoLiouville_c);


%solving for density matrix vector
rhoLiouville=L\rhoLiouville_dot;


L_new=L;
rhoLiouville_new=rhoLiouville;

% uncomment to update reference file
% save 'L_and_rhoL_referenced.mat' L

diff_with_reference=sum(sum(abs(L_new-L)))

elapsed_time = etime (clock (), t0)