Error: using fmincon: FMINCON requires all values returned by functions to be of data type double.

I am using symbolic toolbox and fmincon for minimization. But when I am using d, r_g and G_g as symbolic variable I am getting an error. This is the error I am getting "FMINCON requires all values returned by functions to be of data type double."

[q] = optimizeParameters();% Call optimizeParameters to define the objective function q
options = optimset('PlotFcns', @optimplotfval);% Set optimization options
d0 = [-0.5, 24, 3e6];
lb = [-1, 24, 2e6];
ub = [0, 32, 6e6];
q(d0(1),d0(2),d0(3))

ans = 

NaN

%[solution, fval] = fmincon(@(x) q(x(1), x(2), x(3)), d0, [], [], [], [], lb, ub, [], options);

function q = optimizeParameters()
    
    syms d r_g G_g%symbolic variables   
    theta = pi/4;
    p = 2*pi;
    Vs = 250;
    k = p / Vs;
    c = Vs / sin(theta);
    w5 = 0.001;
    n = 3;
    dl = -6;
    d1 = dl + 2 * n * d - d;
    q = @(d, r_g, G_g) calculateObjective(theta, p, d, r_g, G_g, Vs, k, c, w5, n, dl, d1);
end

function answer = calculateObjective(theta, p, d, r_g, G_g, Vs, k, c, w5, n, dl, d1);
    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);
    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;
    B_s= k*g_b_s*d;    
    C_A_s= cos(A_s);
    S_A_s= sin(A_s);
    C_B_s= cos(B_s);
    S_B_s= sin(B_s);
    n_g= 0.17;
    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*d;
    B_g= k*g_b_g*d;

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

    C_B_g= cos(B_g);
    S_B_g= sin(B_g);

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+(1-theta_s)*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];


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+(1-theta_g)*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];


A1= (Gg_inv*Gs_inv)*(Gg_inv*Gs_inv)*Gg_inv;

A_s0= k*g_a_s*dl;
B_s0= k*g_b_s*dl;

    C_A_s0= cos(A_s0);
    S_A_s0= sin(A_s0);
    C_B_s0= cos(B_s0);
    S_B_s0= sin(B_s0);

D= [-(a_s/c)^2*C_A_s0, 1i*(a_s/c)^2*S_A_s0, -theta_s*g_b_s*C_B_s0, 1i*theta_s*g_b_s*S_B_s0;...
    -1i*(a_s/c)^2*g_a_s*S_A_s0, (a_s/c)^2*g_a_s*C_A_s0, 1i*theta_s*S_B_s0, -theta_s*C_B_s0;...
    -r_s*a_s^2*(theta_s-1)*C_A_s0, 1i*r_s*a_s^2*(theta_s-1)*S_A_s0, -r_s*c^2*theta_s^2*g_b_s*C_B_s0, 1i*r_s*c^2*theta_s^2*g_b_s*S_B_s0;...
    1i*r_s*a_s^2*theta_s*g_a_s*S_A_s0, -r_s*a_s^2*theta_s*g_a_s*C_A_s0, -1i*r_s*c^2*theta_s*(theta_s-1)*S_B_s0, r_s*c^2*theta_s*(theta_s-1)*C_B_s0];

D1= D(1,1);
D2= D(1,2);
D3= D(1,3);
D4= D(1,4);
D5= D(2,1);
D6= D(2,2);
D7= D(2,3);
D8= D(2,4);
D9= D(3,1);
D10= D(3,2);
D11= D(3,3);
D12= D(3,4);
D13= D(4,1);
D14= D(4,2);
D15= D(4,3);
D16= D(4,4);

a_bar= ((D10-D9)*(D8-D7)+(D5-D6)*(D12-D11))/((D2-D1)*(D8-D7)+(D4-D3)*(D5-D6));
b_bar= ((D9-D10)*(D4-D3)+(D2-D1)*(D12-D11))/((D2-D1)*(D8-D7)+(D4-D3)*(D5-D6));
c_bar= ((D14-D13)*(D8-D7)+(D16-D15)*(D5-D6))/((D2-D1)*(D8-D7)+(D4-D3)*(D5-D6));
d_bar= ((D13-D14)*(D4-D3)-(D16-D15)*(D1-D2))/((D2-D1)*(D8-D7)+(D4-D3)*(D5-D6));

A_s1= k*g_a_s*d1;
B_s1= k*g_b_s*d1;

    C_A_s1= cos(A_s1);
    S_A_s1= sin(A_s1);

    C_B_s1= cos(B_s1);
    S_B_s1= sin(B_s1);


D_l= [-(a_s/c)^2*C_A_s1, 1i*(a_s/c)^2*S_A_s1, -theta_s*g_b_s*C_B_s1, 1i*theta_s*g_b_s*S_B_s1;...
    -1i*(a_s/c)^2*g_a_s*S_A_s1, (a_s/c)^2*g_a_s*C_A_s1, 1i*theta_s*S_B_s1, -theta_s*C_B_s1;...
    -r_s*a_s^2*(theta_s-1)*C_A_s1, 1i*r_s*a_s^2*(theta_s-1)*S_A_s1, -r_s*c^2*theta_s^2*g_b_s*C_B_s1, 1i*r_s*c^2*theta_s^2*g_b_s*S_B_s1;...
    1i*r_s*a_s^2*theta_s*g_a_s*S_A_s1, -r_s*a_s^2*theta_s*g_a_s*C_A_s1, -1i*r_s*c^2*theta_s*(theta_s-1)*S_B_s1, r_s*c^2*theta_s*(theta_s-1)*C_B_s1];


B= A1*D_l;
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);


w_in= (D_l(2,4)-D_l(2,3))*c*w5;
mag_w_in= abs(w_in);

u_in= (D_l(1,4)-D_l(1,3))*c*w5;
mag_u_in= abs(u_in);

Input= sqrt(mag_u_in^2+mag_w_in^2);

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*c3*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;-w5;w5]);

u_out1= c*abs(Y2(1,1));
w_out1= c*abs(Y2(2,1));
Output= sqrt(u_out1^2+w_out1^2);
answer= Output/Input;
end

Answer 1

[Torsten]

As you can see above, your function returns a symbolic NaN, but it must return a numerical defined value.

To change the output to numeric, use

function q = optimizeParameters()    
    %syms d r_g G_g%symbolic variables   
    theta = pi/4;
    p = 2*pi;
    Vs = 250;
    k = p / Vs;
    c = Vs / sin(theta);
    w5 = 0.001;
    n = 3;
    dl = -6;
    d1 = @(d)dl + 2 * n * d - d;
    q = @(d, r_g, G_g) calculateObjective(theta, p, d, r_g, G_g, Vs, k, c, w5, n, dl, d1(d));
end

To avoid NaN output, debug "calculateObjective".