function [ possible_lens_placement, possible_lens_set, possible_sample_energy, n_possible_lens_placement, index  ] = mode_match( q0, qf, Ltot, lambda, lens_permutations )
%MODE_MATCH Summary of this function goes here
%   Detailed explanation goes here

n_perms = size(lens_permutations,1);
n_shuffles=20; %number of random placements of lenses

%Initialize sample arrays
N = n_perms * n_shuffles;
possible_lens_placement = zeros(N,3);
possible_lens_set = zeros(N,3);
possible_sample_energy = zeros(N,1);
initial_rand_lens_placement=zeros(N,3);

lens_size = .03; % physical size of the lens

for ip = 1:n_perms
    f3=lens_permutations(ip,3);
    x3=Ltot-f3; % last lense transfer collimated region to focused spot
    for is = 1:n_shuffles
        possible_lens_set((ip-1)*n_shuffles + is,:) = lens_permutations(ip,:);

        initial_rand_lens_placement_tmp = sort(lens_size+(x3-2*lens_size)*rand(1,2));
        initial_rand_lens_placement((ip-1)*n_shuffles + is,:) = [initial_rand_lens_placement_tmp, x3];
    end
end

parfor i = 1:N
      
        fitness_simplified=@(x) fitness(q0, qf, Ltot, x, possible_lens_set(i,:), lambda );
        [x_sol, energy]=fminsearch(fitness_simplified, initial_rand_lens_placement(i,:), optimset('TolX',1e-8,'TolFun',1e-8,'MaxFunEvals',1e8,'MaxIter',200));
        
        possible_lens_placement(i,:) =x_sol;
        possible_sample_energy(i) = energy;

end

%Sorting possible solution according to energy
[possible_sample_energy, index] = sort(possible_sample_energy);
possible_lens_placement = possible_lens_placement(index,:);
possible_lens_set = possible_lens_set(index,:);

%Truncate other possible solutions to an accuracy of n decimal places
n=4; 
possible_lens_placement_trunc = round(possible_lens_placement*10^n)./10^n;
[possible_lens_placement_uniq, index] = unique(possible_lens_placement_trunc,'rows','stable'); %Unique solutions only

n_possible_lens_placement = min(5,size(possible_lens_placement_uniq,1));

end