The following error occurred converting from sym to double: Unable to convert expression containing symbolic variables into double array. Apply 'subs' function first to substitute values for variables

clc
clear
format long
% Function Definition (Enter your Function here):
syms x1 x2 lambda k;
%Optimization function
f = (x1-1)^2 +(x2-2)^2 -4;
%Constrains :
g(1) = x1+2*x2-5;
g(2) = 4*x1 +3*x2-10;
g(3) = 6*x1+x2-7;
g(4) = -x1;
g(5) = -x2;
N = 5; %number of constraints
%tolerances
eps1 = 0.00001;
conv = 1; %initialize the convergance criteria
% Initial Guess (Choose Initial Guesses):
i = 1
x_1(i) = 0.5;
x_2(i) = 0.5;
%search direction
Search_dir = -gradient(f);
% function value and constraints at initial guess
fun_value = double(subs(f,[x1,x2], [x_1(i),x_2(i)]));

while conv > eps1
    I = [x_1(i),x_2(i)]';
    for j = 1:N
        const(j) = double(subs(g(j),[x1,x2], [x_1(i),x_2(i)]));
    end
    S = subs(Search_dir,[x1,x2], [x_1(1),x_2(1)]);
    S = S/max(abs(S(1)),abs(S(2))); %normalize in suitable manner
    if max(const) ~= 0
        %go for feasible direction
        S = S;
        
    else
        for j = 1:N
            if const(j)==0
                N = double(subs(gradient(g(j)),[x1,x2], [x_1(i),x_2(i)]));
                P = eye(2)-(N*inv(N'*N)*N');
                S1 = double(P*double(subs(gradient(f),[x1,x2], [x_1(i),x_2(i)])));
                S = S1/norm(S1);
            end
        end
    end
    %step length
    if norm(S)<= eps1
        lambda = -inv(N'*N)*N'*double(subs(gradient(f),[x1,x2], [x_1(i),x_2(i)]));
        if lambda>0
            optima = [x_1(i),x_2(i)];
            optimum = double(subs(f,[x1,x2], [x_1(i),x_2(i)]));
            break;
        end
    else
        
         x_1(i+1) = x_1(i)+ lambda*S(1);
         x_2(i+1) = x_2(i)+ lambda*S(2);
        for j = 1:N
            const(j) = vpa(subs(g(j),[x1,x2], [x_1(i)+ lambda*S(1),x_2(i)+ lambda*S(2)]));
        end

[Narayan Das Ahirwar]

i'm getting error in fifth last line that is (x_1(i+1) = x_1(i)+ lambda*S(1);), where lambda is a variable and size of S is 2*1 and it contain numeric value i.e. [1/3 ; 1]. please someone help me to solve this.

i also tried vpa, sym(S) but getting same error.

Thank you in advance for the effort and time.

Answer 1

[Walter Roberson]

The norm() test is false the first time, so you do not assign to lambda, leaving it syms

[Narayan Das Ahirwar]

how it should be? could you please?

[Walter Roberson]

        const(j) = double(subs(g(j),[x1,x2], [x_1(i),x_2(i)]));

Remove the double() call so that const remains symbolic and so would be able to store symbolic lambda. Caution: you will need to figure out what max() means for an array that contains expressions in unresolved symbolic variables.

[Walter Roberson]

You should consider using

        lambda = -inv(N'*N)*N'*double(subs(gradient(f),[x1,x2], [x_1(i),x_2(i)]));

near the beginning, after you first assign to x_1 and x_2, and not using syms lambda

By the way, I suggest you have a look at matlabFunction such as

        H = matlabFunction(x1^2 - x1*x2*cos(x1-x2) -1, 'vars', {[x1, x2]})

[Narayan Das Ahirwar]

Thank you, It works for that error.