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Error using function handles in genetic algorithm.

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Manoj Manoj
Manoj Manoj 2024-5-13
编辑： Torsten 2024-5-14
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
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Manoj Manoj
Manoj Manoj 2024-5-14
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
Torsten 2024-5-14
编辑：Torsten 2024-5-14
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

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