Using For loop to plot graphs of functions

I'm trying to write a matlab (for loop) code to produce the graphs: Q as a function of A, F as a function of A, Z as a function of A from the known functions f1, f2 and f3 Z = f1 (A, F, Q) F = f2 (A, Q, Z) A = f3 (Z, Q). I made several attempts that were unsuccessful:

clear
syms w e d n A Z F Q;
w=pi;
e=0.5;
d=10;
n=1;
eqn1 = Z+A.*w./(1-Q.*(1+e))*cos(F)==0;
eqn2 = cos(F+2.*Q.*n.*pi)+Z.*((e-Q.*(1+e))./A.*w)==0;
eqn3 = A-1/(2.*w.*abs(sin(Q.*n.*pi))).*(((1-e).*Z).^2+(d.*w+2.*(1+e).*(1-Q).*Q.*n.*pi.*Z).^2).^0.5==0;
equations = [eqn1 eqn2 eqn3];
vars = [A Z F Q];
range = [0 10;-40 40;0 6;NaN NaN];
for A=0:0.5:10;
    for i=1:5
    temp=vpasolve(equations, vars, range, 'random', true);
    sol(i,1)=temp.Z;
    sol(i,2)=temp.F;
    sol(i,3)=temp.Q;
    end
figure (1);
subplot(2,2,1)
plot(A,sol(i,1));
xlabel('A');
ylabel('Z');
subplot(2,2,2)
plot(A,sol(i,2));
xlabel('A');
ylabel('F');
subplot(2,2,3)
plot(A,sol(i,2));
xlabel('A');
ylabel('Q');
end

Error using getEqnsVars (line 50) Expecting two arguments: a vector of equations and a vector of variables.

Error in sym/vpasolve (line 95) [eqns,vars] = getEqnsVars(varargin{1:N});

Error in Sucesso (line 15) temp=vpasolve(equations, vars, range, 'random', true);

I do not know how to solve this error, because in the three equations eqn1 eqn2 eqn3 A is a variable that in the loop assumes the constant values in the interval (0, 10) so in each loop step a system of three equations with three variables (Z, Q, F) supposed to be solved.

If someone can help me I would thank you a lot.

[Stephen23]

See also:

https://www.mathworks.com/matlabcentral/answers/404871-for-loop-to-plot-graphs-of-functions

Answer 1

[Anurag Ojha]

Hey

The error you are encountering is due to the fact that the vpasolve function expects the equations and variables to be symbolic expressions, not symbolic variables. To fix this, you need to substitute the symbolic variables with their corresponding values in each iteration of the loop.

You can refer to following code, I have taken certain assumtions, kindly modify as per your use case:

syms w e d n A Z F Q;
w = pi;
e = 0.5;
d = 10;
n = 1;
A_values = 0:0.5:10;
num_A_values = length(A_values);
sol = nan(num_A_values, 3);  % Initialize with NaN to handle cases with no solution

for i = 1:num_A_values
    A = A_values(i);
    eqn1 = Z + A * w / (1 - Q * (1 + e)) * cos(F) == 0;
    eqn2 = cos(F + 2 * Q * n * pi) + Z * ((e - Q * (1 + e)) / (A * w)) == 0;
    eqn3 = A - 1 / (2 * w * abs(sin(Q * n * pi))) * (((1 - e) * Z)^2 + (d * w + 2 * (1 + e) * (1 - Q) * Q * n * pi * Z)^2)^0.5 == 0;
    equations = [eqn1, eqn2, eqn3];
    vars = [Z, F, Q];
    range = [-40 40; 0 6; -1 1];  % Q is typically between -1 and 1 based on its typical physical range

    % Solve the equations for the current value of A
    try
        temp = vpasolve(equations, vars, range);

        % Handle the case where vpasolve might return multiple solutions or empty
        if ~isempty(temp)
            if isstruct(temp)
                if isfield(temp, 'Z') && isfield(temp, 'F') && isfield(temp, 'Q')
                    sol(i, 1) = double(temp.Z);
                    sol(i, 2) = double(temp.F);
                    sol(i, 3) = double(temp.Q);
                end
            elseif iscell(temp) && ~isempty(temp{1})
                temp = temp{1};  % Extract the first solution
                if isfield(temp, 'Z') && isfield(temp, 'F') && isfield(temp, 'Q')
                    sol(i, 1) = double(temp.Z);
                    sol(i, 2) = double(temp.F);
                    sol(i, 3) = double(temp.Q);
                end
            end
        end
    catch
        % Handle any unexpected errors by skipping to the next iteration
        continue;
    end
end

figure;
subplot(2, 2, 1)
plot(A_values, sol(:, 1), 'o-');
xlabel('A');
ylabel('Z');
title('Z vs A');

subplot(2, 2, 2)
plot(A_values, sol(:, 2), 'o-');
xlabel('A');
ylabel('F');
title('F vs A');

subplot(2, 2, 3)
plot(A_values, sol(:, 3), 'o-');
xlabel('A');
ylabel('Q');
title('Q vs A');

sgtitle('Solutions of the System of Equations');