app designer error: Attempt to add "theta" to a static workspace.

Hello, i wrote a code and it works while running the script. but when i use it in an app this error shows up Attempt to add "theta" to a static workspace. can somebody help me out. thanks

The code:

%% Constants and parameters
J1 = 1; % Polarization of outer magnet 
J2 = 1; % Polarization of inner magnet
u0 = pi*4e-7; % Magnetic constant

%% Position vectors, define appropriately
r = [0.25, 0.3, 0.20 , 0.24]; % radius of magnets (outer to inner)
z = [0.05, 0.15, 0.08, 0.18]; % z cordinate of magnets (outer to inner)

%% main function g
g = @(a, b, c) computeG(a, b, c);

% Initialize F_Z
F_Z = 0;

% Compute F_Z based on the given formula
for i = 1:2
    for k = 1:2
        for j = 3:4
            for l = 3:4
                deltaZ = z(k) - z(l);
                ri2 = r(i)^2;
                rj2 = r(j)^2;
                Fijkl = r(i) * r(j) * g(deltaZ, ri2+rj2+deltaZ^2, -2 * r(i) * r(j));
                power = 1 + i + j + k + l;
                F_Z = F_Z + ((-1)^power) * Fijkl;
            end
        end
    end
end

F_Z = ((J1 * J2) / (2 * u0)) * F_Z;

%% Define the function computeG
function result = computeG(a, b, c)
    A = (a^2 - b) / c * pi + sqrt(c^2 - (a^2 - b)^2) / c *(log((-16 * c^2) / ((c^2 - (a^2 - b)^2)^1.5)) + log(c^2 / ((c^2 - (a^2 - b)^2)^1.5)));
        
    S = computeS(a, b, c);
    result = A + S;
end

%% Define the function computeS
function S = computeS(a, b, c)
    % Define constants
    epsilon = c / (c - b);
    beta = (b + c) / (b - c);
    mu = c / (b + c);
    
    
    % Calculate terms for S
    term1 = (2 * 1i * a) / (c * sqrt(b + c)) * ...
        ((b + c) * ellipticE(asin(sqrt(beta)), beta^(-1)) - c * ellipticF(asin(sqrt(beta)), beta^(-1)));
    term2 = (2 * a) / (c * sqrt(b - c) * sqrt(epsilon)) * ...
        (c / sqrt(mu) * ellipticE1(1 / beta) - c * sqrt(mu) * ellipticK(1 / beta));
    term3 = sqrt(epsilon * (1 / beta)) * ...
        ((b - a^2) * ellipticK(2 * mu) + (a^2 - b + c) * ellipticPi(2 * c / (c + b - a^2), 2 * mu));
    
    % Sum all terms
    S = term1 + term2 + term3;
end

% Elliptic integral functions using symbolic math toolbox
function val = ellipticK(m)
    syms theta;
    val = double(int(1 / sqrt(1 - m * sin(theta)^2), theta, 0, pi/2));
end

function val = ellipticF(phi, m)
    syms theta;
    val = double(int(1 / sqrt(1 - m * sin(theta)^2), theta, 0, phi));
end

function val = ellipticE(phi, m)
    syms theta;
    val = double(int(sqrt(1 - m * sin(theta)^2), theta, 0, phi));
end

function val = ellipticE1(m)
    syms theta;
    val = double(int(sqrt(1 - m * sin(theta)^2), theta, 0, pi/2));
end

function val = ellipticPi(n, m)
    syms theta;
    val = double(int(1 / (sqrt(1 - n * sin(theta)^2) * sqrt(1 - m * sin(theta)^2)), theta, 0, pi/2));
end

Answer 1

[Walter Roberson]

Replace

syms theta

with

theta = sym('theta');

Note:

If you are trying to compile this code, then you will not be able to do so: nothing about the Symbolic Toolbox can be compiled.

[Walter Roberson]

You might need to replace it with numeric computation, such as

function val = ellipticPi(n, m)
    val = integrate(@(theta) 1 / (sqrt(1 - n * sin(theta)^2) * sqrt(1 - m * sin(theta)^2)), theta, 0, pi/2);
end

[mohammadreza j]

Thanks Walter. it worked.

[mohammadreza j]

Dear Walter,

Thanks for the heads up. I've done the changes and it works perfectly. But the matter in here is how time consuming is this code. See I'm trying to change the r array in a while loop step by step to achive a specefic amount of the F_Z. I'm asking if you can suggest me how can i optimize the code to run as fast as it possible.

Thanks in advance

[Walter Roberson]

You can vectorize computeG and so on. For example

    A = (a.^2 - b) ./ c * pi + sqrt(c.^2 - (a.^2 - b).^2) ./ c *(log((-16 * c.^2) ./ ((c.^2 - (a.^2 - b).^2).^1.5)) + log(c.^2 ./ ((c.^2 - (a.^2 - b).^2).^1.5)));

Eventually you would get down to integrate() calls, which you would code using 'Arrayvalued', true

Then you would go back and vectorize the for l = 3:4 loop.

[mohammadreza j]

Thanks for instant answering Walter. Can you please explain this more cleary this "Eventually you would get down to integrate() calls, which you would code using 'Arrayvalued', true" in an example.

Thanks

[Walter Roberson]

function val = ellipticK(m)
    val = integrate(@(theta) 1 ./ sqrt(1 - m * sin(theta).^2), 0, pi/2, 'ArrayValued', true);
end