MATLAB: Speeding up solve() function in a for loop

for loopsolvespeed

I am trying to write a bit of code to solve for a system of 4 equations inside a rather large while loop, this leads to the solve() function being performed multiple times and drastically slows down the run time. Is there a way to preallocate the symbolically solved variables (so as to only input the new number) or is there a way to have matlab solve the system with matrices.
The code:
for d_t = 0:100
    burn_back = d_t*5e-3;
    x_5 = 0.0710;
    x_3 = 0.4397;
    y_5 = 0.5487;
    y_3 = 0.3358;
syms alpha beta x_intct y_intct;
    
    [alpha,beta,x_intct,y_intct] = solve(...
        x_intct == x_3 + burn_back*cos(alpha),...
        x_intct == x_5 + burn_back*cos(beta),...
        y_intct == y_3 + burn_back*sin(alpha),...
        y_intct == y_5 + burn_back*sin(beta),...
        [alpha beta x_intct y_intct]);
    alpha = double(alpha);
    beta = double(beta);
    x_intct = double(x_intct);
    y_intct = double(y_intct);
end
Any help would be greatly apreciated.

Best Answer

If a solution exists, it has the analytical form,
x_intct=(x_3+x_5)/2;
y_intct=(y_3+y_5)/2;
alpha=atan2((y_intct-y_3)/burn_back, (x_intct-x_3)/burn_back);
beta=alpha+pi;
Instead of looping, you could just vectorize the above.
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