% =========================================================================
% Copyright (c)2006， 東南大學移動通信國家重點實驗室
% All rights reserved.
%
% 文件名稱：T_F_g_A_S_w_Jain.m
% function描述：Jain Index下的目標函數

% 當前版本： 1.0
% 作    者：梁浩
% 完成日期： 2007年6月
%==========================================================================

function  [T F g A S] = T_F_g_A_S_w_Jain(w, N, aimFair, aveSNR, lambda, precision)

lower_quadl_bond = 10^(-1);
higher_quadl_bound = 50;
sec_num_quadl = 1000;              % 分段quadl的段數
sec_size_quadl = (higher_quadl_bound - lower_quadl_bond)./sec_num_quadl;

ww = [1, w];                % ww是將w向量的第一個元素固定為1之后的結果
for i = 1:N
%     Th(i) = quadl(@IntegralGene, 10^(-3), 10^3, 10^(-6), [], N, ww, aveSNR, i);
    for sec_num = 1:sec_num_quadl
        if sec_num == 1
            Th(i) = quadl(@IntegralGene, lower_quadl_bond+(sec_num-1).*sec_size_quadl, lower_quadl_bond+sec_num.*sec_size_quadl, 10^(-6), [], N, ww, aveSNR, i);
        else
            Th(i) = Th(i) + quadl(@IntegralGene, lower_quadl_bond+(sec_num-1).*sec_size_quadl, lower_quadl_bond+sec_num.*sec_size_quadl, 10^(-6), [], N, ww, aveSNR, i);
        end
    end
end
T = 0 - sum(Th);
F = Fairness_Jain(N, Th) - aimFair;
L = T + lambda .* F;

%%% 為求梯度，將w再各個方向上按照precision散開
for gradient_num = 1:length(w)
    w_for_gradient_low(gradient_num,:) = w;
    w_for_gradient_high(gradient_num,:) = w;
    
    w_for_gradient_low(gradient_num,gradient_num) = w_for_gradient_low(gradient_num,gradient_num) - precision;     % precision為梯度求解的精度，即橫坐標間隔
    w_for_gradient_high(gradient_num,gradient_num) = w_for_gradient_high(gradient_num,gradient_num) + precision;
end

%%% 求中心點兩側點處的取值
for gradient_num = 1:length(w)
%     gradient_num
    ww_for_gradient_low = [1, w_for_gradient_low(gradient_num,:)];                % ww是將w向量的第一個元素固定為1之后的結果
    ww_for_gradient_high = [1, w_for_gradient_high(gradient_num,:)];                % ww是將w向量的第一個元素固定為1之后的結果
    
    for i = 1:N
%         Th_low(i) = quadl(@IntegralGene, 10^(-3), 10^3, 10^(-3), [], N, ww_for_gradient_low, aveSNR, i);
%         Th_high(i) = quadl(@IntegralGene, 10^(-3), 10^3, 10^(-3), [], N, ww_for_gradient_high, aveSNR, i);
        for sec_num = 1:sec_num_quadl
            if sec_num == 1
                Th_low(i) = quadl(@IntegralGene, lower_quadl_bond+(sec_num-1).*sec_size_quadl, lower_quadl_bond+sec_num.*sec_size_quadl, 10^(-6), [], N, ww_for_gradient_low, aveSNR, i);
                Th_high(i) = quadl(@IntegralGene, lower_quadl_bond+(sec_num-1).*sec_size_quadl, lower_quadl_bond+sec_num.*sec_size_quadl, 10^(-6), [], N, ww_for_gradient_high, aveSNR, i);
            else
                Th_low(i) = Th_low(i) + quadl(@IntegralGene, lower_quadl_bond+(sec_num-1).*sec_size_quadl, lower_quadl_bond+sec_num.*sec_size_quadl, 10^(-6), [], N, ww_for_gradient_low, aveSNR, i);
                Th_high(i) = Th_high(i) + quadl(@IntegralGene, lower_quadl_bond+(sec_num-1).*sec_size_quadl, lower_quadl_bond+sec_num.*sec_size_quadl, 10^(-6), [], N, ww_for_gradient_high, aveSNR, i);
            end
        end
    end
    T_low = 0 - sum(Th_low);
    F_low = Fairness_Jain(N, Th_low) - aimFair;
    L_low = T_low + lambda .* F_low;

    T_high = 0 - sum(Th_high);
    F_high = Fairness_Jain(N, Th_high) - aimFair;
    L_high = T_high + lambda .* F_high;
    
    g_temp = gradient([T_low T T_high], precision);
    A_temp = gradient([F_low F F_high], precision);
    S_temp = gradient([L_low L L_high], precision);
    
    g(gradient_num) = g_temp(2);              % 取中心差分值
    A(gradient_num) = A_temp(2);              % 取中心差分值
    S(gradient_num) = S_temp(2);              % 取中心差分值
    
    clear ww_for_gradient_low
    clear ww_for_gradient_high
end