Error using function handles in genetic algorithm.

I am getting error:

Unrecognized function or variable 'p'.

clc; clear; close all;

Vs = 250;

k = @(p) p/Vs;
c = @(theta) Vs/sin(theta); 
w = 0.001; 
d_h = -2; 
numElements = 10;
ES = d_h/numElements;

r_s= 2000;
G_s= 1.25e8;
n_s= 0.3; 
l_s= 2*n_s*G_s/(1-2*n_s); 
a_s= sqrt((l_s+2*G_s)/r_s); 
b_s= sqrt(G_s/r_s); 
r_g= 24; 
G_g= 3e6; 
n_g= 0.17;
dl = -5; 

%% Genetic Algorithm Parameters
options = optimoptions(@ga,'PopulationSize', 30, 'MaxGenerations', 200,'PlotFcn','gaplotbestf');

% Objective Function
objective_function = @(x_optimal) calculateObjective(x_optimal, Vs, w, r_s, G_s, n_s, k(p), c(theta), r_g, G_g, n_g, dl, d_h, numElements, ES, l_s, a_s, b_s);

A = []; 
b = [];  
lb = zeros(1, numElements-2);
ub = ones(1, numElements-2);
nonlcon = [];
[x_optimal, fval] = ga(objective_function, numElements-2, A, b, [], [], lb, ub,nonlcon, options);

% function to calculate objective
function answer = calculateObjective(x_optimal, Vs, w, r_s, G_s, n_s, k, c, r_g, G_g, n_g, dl, d_h, numElements, ES, l_s, a_s, b_s);
x = [1, x_optimal, 1];
disp(x_optimal); 

% rest of the code

answer = integral2(@(theta,p)arrayfun(@(theta,p)q(theta,p),theta,p),pi/18,pi/6,2*pi,20*pi); % minimize

end

[Star Strider]

The missing ‘p’ (used in function ‘k’) is not the only problem.

The ‘answer’ integration uses function ‘q’, however ‘q’ is also nowhere to be found.

[Manoj Manoj]

The error I am getting is because of p and theta. q is some function of p and theta.

Unrecognized function or variable 'p'.

Error in matlabanswer>@(x_optimal)calculateObjective(x_optimal,Vs,w,r_s,G_s,n_s,k(p),c(theta),r_g,G_g,n_g,dl,d_h,numElements,ES,l_s,a_s,b_s) (line 27)
objective_function = @(x_optimal) calculateObjective(x_optimal, Vs, w, r_s, G_s, n_s, k(p), c(theta), r_g, G_g, n_g, dl, d_h, numElements, ES, l_s, a_s, b_s);

Error in createAnonymousFcn>@(x)fcn(x,FcnArgs{:}) (line 11)
fcn_handle = @(x) fcn(x,FcnArgs{:});

Error in makeState (line 58)
            firstMemberScore = FitnessFcn(state.Population(initScoreProvided+1,:));

Error in galincon (line 24)
state = makeState(GenomeLength,FitnessFcn,Iterate,output.problemtype,options);

Error in ga (line 414)
            [x,fval,exitFlag,output,population,scores] = galincon(FitnessFcn,nvars, ...

Error in matlabanswer (line 34)
[x_optimal, fval] = ga(objective_function, numElements-2, A, b, [], [], lb, ub,nonlcon, options);

Caused by:
    Failure in initial user-supplied fitness function evaluation. GA cannot continue.

[Torsten]

objective_function = @(x_optimal) calculateObjective(x_optimal, Vs, w, r_s, G_s, n_s, k, c, r_g, G_g, n_g, dl, d_h, numElements, ES, l_s, a_s, b_s);

instead of

objective_function = @(x_optimal) calculateObjective(x_optimal, Vs, w, r_s, G_s, n_s, k(p), c(theta), r_g, G_g, n_g, dl, d_h, numElements, ES, l_s, a_s, b_s);

Remember that in "calculateObjective", k and c will be function handles, not values. Use them correctly in function q.

[Star Strider]

The only reference I found to ‘q’ was in the ‘answer’ assignment. I still can’t find the actual function anywhere. I’d have trtied to run the code otherwise.

[Manoj Manoj]

This is the complete code

Vs = 250;
k = @(p) p/Vs;
c = @(theta) Vs/sin(theta); 
w = 0.001; 
d_h = -2; 
numElements = 10;
ES = d_h/numElements;

r_s= 2000;
G_s= 1.25e8;
n_s= 0.3; 
l_s= 2*n_s*G_s/(1-2*n_s); 
a_s= sqrt((l_s+2*G_s)/r_s); 
b_s= sqrt(G_s/r_s); 
r_g= 24; 
G_g= 3e6; 
n_g= 0.17;
dl = -5; 

%% Genetic Algorithm Parameters
options = optimoptions(@ga,'PopulationSize', 30, 'MaxGenerations', 200,'PlotFcn','gaplotbestf');

% Objective Function
objective_function = @(x_optimal) calculateObjective(x_optimal, Vs, w, r_s, G_s, n_s, k, c, r_g, G_g, n_g, dl, d_h, numElements, ES, l_s, a_s, b_s);
A = []; 
b = [];  
lb = zeros(1, numElements-2);
ub = ones(1, numElements-2);
nonlcon = [];
[x_optimal, fval] = ga(objective_function, numElements-2, A, b, [], [], lb, ub,nonlcon, options);

% function to calculate objective
function answer = calculateObjective(x_optimal, Vs, w, r_s, G_s, n_s, k, c, r_g, G_g, n_g, dl, d_h, numElements, ES, l_s, a_s, b_s);
disp(x_optimal); 

l_g= 2*n_g*G_g/(1-2*n_g); 
a_g= sqrt((l_g+2*G_g)/r_g);
b_g= sqrt(G_g/r_g); 

g_a_g= sqrt((c/a_g)^2-1);
g_b_g= sqrt((c/b_g)^2-1);


theta_g= 2*(b_g/c)^2;



    A_g = k*g_a_g*dl;
    B_g = k*g_b_g*dl;


    C_A_g= cos(A_g);
    S_A_g= sin(A_g);

    C_B_g= cos(B_g);
    S_B_g= sin(B_g);
  
    Gg_inv = [theta_g*C_A_g+(1-theta_g)*C_B_g, 1i*(g_a_g*g_b_g*theta_g*S_B_g+(theta_g-1)*S_A_g)/g_a_g, (-C_A_g+C_B_g)/(c^2*r_g), 1i*(g_a_g*g_b_g*S_B_g+S_A_g)/(c^2*g_a_g*r_g);...
       1i*(-g_a_g*g_b_g*theta_g*S_A_g+(1-theta_g)*S_B_g)/g_b_g, theta_g*C_B_g+(1-theta_g)*C_A_g, 1i*(g_a_g*g_b_g*S_A_g+S_B_g)/(c^2*g_b_g*r_g), (-C_A_g+C_B_g)/(c^2*r_g);...
       c^2*r_g*theta_g*(theta_g-1)*(C_A_g-C_B_g), 1i*c^2*r_g*(g_a_g*g_b_g*theta_g^2*S_B_g+(theta_g-1)^2*S_A_g)/g_a_g, theta_g*C_B_g+(1-theta_g)*C_A_g, 1i*(g_a_g*g_b_g*theta_g*S_B_g+(theta_g-1)*S_A_g)/g_a_g;...
       1i*c^2*r_g*(g_a_g*g_b_g*theta_g^2*S_A_g+(theta_g-1)^2*S_B_g)/g_b_g, c^2*r_g*theta_g*(theta_g-1)*(C_A_g-C_B_g), 1i*(-g_a_g*g_b_g*theta_g*S_A_g+(1-theta_g)*S_B_g)/g_b_g, theta_g*C_A_g+(1-theta_g)*C_B_g];
    

l_s= 2*n_s*G_s/(1-2*n_s);
a_s= sqrt((l_s+2*G_s)/r_s); 
b_s= sqrt(G_s/r_s);  

g_a_s= sqrt((c/a_s)^2-1);
g_b_s= sqrt((c/b_s)^2-1);


theta_s= 2*(b_s/c)^2;

    A_s = k*g_a_s*d_h;
    B_s = k*g_b_s*d_h;

    C_A_s= cos(A_s);
    S_A_s= sin(A_s);

    C_B_s= cos(B_s);
    S_B_s= sin(B_s);

    Gs_inv = [theta_s*C_A_s+(1-theta_s)*C_B_s, 1i*(g_a_s*g_b_s*theta_s*S_B_s+(theta_s-1)*S_A_s)/g_a_s, (-C_A_s+C_B_s)/(c^2*r_s), 1i*(g_a_s*g_b_s*S_B_s+S_A_s)/(c^2*g_a_s*r_s);...
       1i*(-g_a_s*g_b_s*theta_s*S_A_s+(1-theta_s)*S_B_s)/g_b_s, theta_s*C_B_s+(1-theta_s)*C_A_s, 1i*(g_a_s*g_b_s*S_A_s+S_B_s)/(c^2*g_b_s*r_s), (-C_A_s+C_B_s)/(c^2*r_s);...
       c^2*r_s*theta_s*(theta_s-1)*(C_A_s-C_B_s), 1i*c^2*r_s*(g_a_s*g_b_s*theta_s^2*S_B_s+(theta_s-1)^2*S_A_s)/g_a_s, theta_s*C_B_s+(1-theta_s)*C_A_s, 1i*(g_a_s*g_b_s*theta_s*S_B_s+(theta_s-1)*S_A_s)/g_a_s;...
       1i*c^2*r_s*(g_a_s*g_b_s*theta_s^2*S_A_s+(theta_s-1)^2*S_B_s)/g_b_s, c^2*r_s*theta_s*(theta_s-1)*(C_A_s-C_B_s), 1i*(-g_a_s*g_b_s*theta_s*S_A_s+(1-theta_s)*S_B_s)/g_b_s, theta_s*C_A_s+(1-theta_s)*C_B_s];


B= Gs_inv*Gg_inv;

B1= B(1,1);
B2= B(1,2);
B3= B(1,3);
B4= B(1,4);
B5= B(2,1);
B6= B(2,2);
B7= B(2,3);
B8= B(2,4);
B9= B(3,1);
B10= B(3,2);
B11= B(3,3);
B12= B(3,4);
B13= B(4,1);
B14= B(4,2);
B15= B(4,3);
B16= B(4,4);

c1= -(B1+B2);
c2= -(B3+B4);
c3= -(B5+B6); 
c4= -(B7+B8);
c5= -(B9+B10);
c6= -(B11+B12);
c7= -(B13+B14);
c8= -(B15+B16);

x2_inv= [(-b_bar*c3*c8+b_bar*c4*c7+c3*c6*d_bar-c4*c5*d_bar+c5*c8-c6*c7)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (b_bar*c1*c8-b_bar*c2*c7-c1*c6*d_bar+c2*c5*d_bar)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (-b_bar*c1*c4+b_bar*c2*c3+c1*c6-c2*c5)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7);...
    (a_bar*c3*c8-a_bar*c4*c7-c3*c6*c_bar+c4*c5*c_bar)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (-a_bar*c1*c8+a_bar*c2*c7+c1*c6*c_bar-c2*c5*c_bar+c5*c8-c6*c7)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (a_bar*c1*c4-a_bar*c2*c3+c3*c6-c4*c5)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7);...
    (a_bar*c4*d_bar-a_bar*c8-b_bar*c4*c_bar+c6*c_bar)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (-a_bar*c2*d_bar+b_bar*c2*c_bar-b_bar*c8+c6*d_bar)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (-c2*c_bar-c4*d_bar+c8)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (a_bar*c2+b_bar*c4-c6)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7);...
    (-a_bar*c3*d_bar+a_bar*c7+b_bar*c3*c_bar-c5*c_bar)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (a_bar*c1*d_bar-b_bar*c1*c_bar+b_bar*c7-c5*d_bar)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (c1*c_bar+c3*d_bar-c7)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (-a_bar*c1-b_bar*c3+c5)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7)];

Y2= x2_inv*(B*[0;0;-w;w]);

u_in= (B(1,4)-B(1,3))*c*w;
mag_u_in= abs(u_in);
w_in= (B(2,4)-B(2,3))*c*w;
mag_w_in= abs(w_in);
Input= sqrt(mag_u_in^2+mag_w_in^2);

u_out= c*abs(Y2(1,1));
w_out= c*abs(Y2(2,1));
Output= sqrt(u_out^2+w_out^2);

q= @(theta,p)Output/Input;
answer = integral2(@(theta,p)arrayfun(@(theta,p)q(theta,p),theta,p),pi/18,pi/6,2*pi,20*pi); % minimize

end

[Torsten]

Try this.

I wonder why your function does not depend on "x_optimal" . From your code, you will always get the same value for "answer" from the "integral2" function, and thus "ga" will terminate with the initial condition vector for x_optimal.

Vs = 250;
k = @(p) p/Vs;
c = @(theta) Vs/sin(theta); 
w = 0.001; 
d_h = -2; 
numElements = 10;
ES = d_h/numElements;
r_s= 2000;
G_s= 1.25e8;
n_s= 0.3; 
l_s= 2*n_s*G_s/(1-2*n_s); 
a_s= sqrt((l_s+2*G_s)/r_s); 
b_s= sqrt(G_s/r_s); 
r_g= 24; 
G_g= 3e6; 
n_g= 0.17;
dl = -5; 
%% Genetic Algorithm Parameters
options = optimoptions(@ga,'PopulationSize', 30, 'MaxGenerations', 200,'PlotFcn','gaplotbestf');
% Objective Function
objective_function = @(x_optimal) driver_calculateObjective(x_optimal, Vs, w, r_s, G_s, n_s, k, c, r_g, G_g, n_g, dl, d_h, numElements, ES, l_s, a_s, b_s);
A = []; 
b = [];  
lb = zeros(1, numElements-2);
ub = ones(1, numElements-2);
nonlcon = [];
[x_optimal, fval] = ga(objective_function, numElements-2, A, b, [], [], lb, ub,nonlcon, options);

function answer = driver_calculateObjective(x_optimal, Vs, w, r_s, G_s, n_s, k, c, r_g, G_g, n_g, dl, d_h, numElements, ES, l_s, a_s, b_s);
  q = @(theta,p)calculate_objective(theta,p,x_optimal,Vs, w, r_s, G_s, n_s, k(p), c(theta), r_g, G_g, n_g, dl, d_h, numElements, ES, l_s, a_s, b_s);)
  answer = integral2(@(theta,p)arrayfun(@(theta,p)q(theta,p),theta,p),pi/18,pi/6,2*pi,20*pi); % minimize
end

% function to calculate objective
function answer = calculateObjective(x_optimal, Vs, w, r_s, G_s, n_s, k, c, r_g, G_g, n_g, dl, d_h, numElements, ES, l_s, a_s, b_s);
disp(x_optimal); 
l_g= 2*n_g*G_g/(1-2*n_g); 
a_g= sqrt((l_g+2*G_g)/r_g);
b_g= sqrt(G_g/r_g); 
g_a_g= sqrt((c/a_g)^2-1);
g_b_g= sqrt((c/b_g)^2-1);
theta_g= 2*(b_g/c)^2;
    A_g = k*g_a_g*dl;
    B_g = k*g_b_g*dl;
    C_A_g= cos(A_g);
    S_A_g= sin(A_g);
    C_B_g= cos(B_g);
    S_B_g= sin(B_g);
  
    Gg_inv = [theta_g*C_A_g+(1-theta_g)*C_B_g, 1i*(g_a_g*g_b_g*theta_g*S_B_g+(theta_g-1)*S_A_g)/g_a_g, (-C_A_g+C_B_g)/(c^2*r_g), 1i*(g_a_g*g_b_g*S_B_g+S_A_g)/(c^2*g_a_g*r_g);...
       1i*(-g_a_g*g_b_g*theta_g*S_A_g+(1-theta_g)*S_B_g)/g_b_g, theta_g*C_B_g+(1-theta_g)*C_A_g, 1i*(g_a_g*g_b_g*S_A_g+S_B_g)/(c^2*g_b_g*r_g), (-C_A_g+C_B_g)/(c^2*r_g);...
       c^2*r_g*theta_g*(theta_g-1)*(C_A_g-C_B_g), 1i*c^2*r_g*(g_a_g*g_b_g*theta_g^2*S_B_g+(theta_g-1)^2*S_A_g)/g_a_g, theta_g*C_B_g+(1-theta_g)*C_A_g, 1i*(g_a_g*g_b_g*theta_g*S_B_g+(theta_g-1)*S_A_g)/g_a_g;...
       1i*c^2*r_g*(g_a_g*g_b_g*theta_g^2*S_A_g+(theta_g-1)^2*S_B_g)/g_b_g, c^2*r_g*theta_g*(theta_g-1)*(C_A_g-C_B_g), 1i*(-g_a_g*g_b_g*theta_g*S_A_g+(1-theta_g)*S_B_g)/g_b_g, theta_g*C_A_g+(1-theta_g)*C_B_g];
    
l_s= 2*n_s*G_s/(1-2*n_s);
a_s= sqrt((l_s+2*G_s)/r_s); 
b_s= sqrt(G_s/r_s);  
g_a_s= sqrt((c/a_s)^2-1);
g_b_s= sqrt((c/b_s)^2-1);
theta_s= 2*(b_s/c)^2;
    A_s = k*g_a_s*d_h;
    B_s = k*g_b_s*d_h;
    C_A_s= cos(A_s);
    S_A_s= sin(A_s);
    C_B_s= cos(B_s);
    S_B_s= sin(B_s);
    Gs_inv = [theta_s*C_A_s+(1-theta_s)*C_B_s, 1i*(g_a_s*g_b_s*theta_s*S_B_s+(theta_s-1)*S_A_s)/g_a_s, (-C_A_s+C_B_s)/(c^2*r_s), 1i*(g_a_s*g_b_s*S_B_s+S_A_s)/(c^2*g_a_s*r_s);...
       1i*(-g_a_s*g_b_s*theta_s*S_A_s+(1-theta_s)*S_B_s)/g_b_s, theta_s*C_B_s+(1-theta_s)*C_A_s, 1i*(g_a_s*g_b_s*S_A_s+S_B_s)/(c^2*g_b_s*r_s), (-C_A_s+C_B_s)/(c^2*r_s);...
       c^2*r_s*theta_s*(theta_s-1)*(C_A_s-C_B_s), 1i*c^2*r_s*(g_a_s*g_b_s*theta_s^2*S_B_s+(theta_s-1)^2*S_A_s)/g_a_s, theta_s*C_B_s+(1-theta_s)*C_A_s, 1i*(g_a_s*g_b_s*theta_s*S_B_s+(theta_s-1)*S_A_s)/g_a_s;...
       1i*c^2*r_s*(g_a_s*g_b_s*theta_s^2*S_A_s+(theta_s-1)^2*S_B_s)/g_b_s, c^2*r_s*theta_s*(theta_s-1)*(C_A_s-C_B_s), 1i*(-g_a_s*g_b_s*theta_s*S_A_s+(1-theta_s)*S_B_s)/g_b_s, theta_s*C_A_s+(1-theta_s)*C_B_s];
B= Gs_inv*Gg_inv;
B1= B(1,1);
B2= B(1,2);
B3= B(1,3);
B4= B(1,4);
B5= B(2,1);
B6= B(2,2);
B7= B(2,3);
B8= B(2,4);
B9= B(3,1);
B10= B(3,2);
B11= B(3,3);
B12= B(3,4);
B13= B(4,1);
B14= B(4,2);
B15= B(4,3);
B16= B(4,4);
c1= -(B1+B2);
c2= -(B3+B4);
c3= -(B5+B6); 
c4= -(B7+B8);
c5= -(B9+B10);
c6= -(B11+B12);
c7= -(B13+B14);
c8= -(B15+B16);
x2_inv= [(-b_bar*c3*c8+b_bar*c4*c7+c3*c6*d_bar-c4*c5*d_bar+c5*c8-c6*c7)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (b_bar*c1*c8-b_bar*c2*c7-c1*c6*d_bar+c2*c5*d_bar)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (-b_bar*c1*c4+b_bar*c2*c3+c1*c6-c2*c5)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7);...
    (a_bar*c3*c8-a_bar*c4*c7-c3*c6*c_bar+c4*c5*c_bar)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (-a_bar*c1*c8+a_bar*c2*c7+c1*c6*c_bar-c2*c5*c_bar+c5*c8-c6*c7)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (a_bar*c1*c4-a_bar*c2*c3+c3*c6-c4*c5)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7);...
    (a_bar*c4*d_bar-a_bar*c8-b_bar*c4*c_bar+c6*c_bar)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (-a_bar*c2*d_bar+b_bar*c2*c_bar-b_bar*c8+c6*d_bar)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (-c2*c_bar-c4*d_bar+c8)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (a_bar*c2+b_bar*c4-c6)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7);...
    (-a_bar*c3*d_bar+a_bar*c7+b_bar*c3*c_bar-c5*c_bar)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (a_bar*c1*d_bar-b_bar*c1*c_bar+b_bar*c7-c5*d_bar)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (c1*c_bar+c3*d_bar-c7)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7), (-a_bar*c1-b_bar*c3+c5)/(a_bar*(c1*c4*d_bar-c1*c8-c2*c3*d_bar+c2*c7)+b_bar*(-c1*c4*c_bar+c2*c3*c_bar-c3*c8+c4*c7)+c_bar*(c1*c6-c2*c5)+d_bar*(c3*c6-c4*c5)+c5*c8-c6*c7)];
Y2= x2_inv*(B*[0;0;-w;w]);
u_in= (B(1,4)-B(1,3))*c*w;
mag_u_in= abs(u_in);
w_in= (B(2,4)-B(2,3))*c*w;
mag_w_in= abs(w_in);
Input= sqrt(mag_u_in^2+mag_w_in^2);
u_out= c*abs(Y2(1,1));
w_out= c*abs(Y2(2,1));
Output= sqrt(u_out^2+w_out^2);
answer = Output/Input;
end