Script too Long to Run

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I've just finish creating the script on one of the Optimisation Method. The problem that I currently have is the script took around 20 minutes
I've also preallocate changing vectors, but that hasn't made any difference. Not sure what I can do to resolve this?
clear
clc
format long
syms X1 X2 X3 X4 real;
%Preallocating changing vectors
x1=zeros(10000,1);
x2=zeros(10000,1);
x3=zeros(10000,1);
x4=zeros(10000,1);
error=zeros(10000,1);
A=[1 0 -1 3; 0 2 1 0; -1 1 6 -1; 3 0 -1 10];
b=[0; -2; -1; -1];
X=[X1; X2; X3; X4];
f=@(X1, X2, X3, X4) (1/2)*X'*A*X + b'*X;
x1(1)=0; x2(1)=1; x3(1)=0; x4(1)=0;
g=A*X+b;
alpha=0.1;
tol=10^(-6)
k=1;
gl = subs(g, [X1, X2, X3, X4], [x1(k), x2(k), x3(k), x4(k)]);
while norm(gl)>tol
gl = subs(g, [X1, X2, X3, X4], [x1(k), x2(k), x3(k), x4(k)]);
alpha=gl'*gl./(gl'*A*gl);
x1(k+1)=x1(k)-alpha*gl(1);
x2(k+1)=x2(k)-alpha*gl(2);
x3(k+1)=x3(k)-alpha*gl(3);
x4(k+1)=x4(k)-alpha*gl(4);
error(k)=norm(gl);
k=k+1;
end
  2 Comments
Stephen23
Stephen23 on 27 Mar 2022
"Not sure what I can do to resolve this?"
Don't use the symbolic toolbox. Numeric operations are much faster.
Charles Thomas
Charles Thomas on 27 Mar 2022
Thank you very much! Just removed "syms", and made some few changes before running the loop. Never realise that is the cause of the immeasurable run time for my script, but I really appreciate your help.

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Accepted Answer

Sulaymon Eshkabilov
Sulaymon Eshkabilov on 28 Mar 2022
Here is a little simplified version of your code:
clc
format long
n=1e4;
x1=zeros(n,1);
x2=x1;
x3=x1;
x4=x1;
error=x1;
A=[1 0 -1 3; 0 2 1 0; -1 1 6 -1; 3 0 -1 10];
b=[0; -2; -1; -1];
x1(1)=0; x2(1)=1; x3(1)=0; x4(1)=0;
g=@(y1,y2, y3, y4)(A*([y1; y2; y3; y4])+b);
alpha=0.1;
tol=1e-6;
k=1;
gl =g(x1(k), x2(k), x3(k), x4(k));
while norm(gl)>tol
gl = g(x1(k), x2(k), x3(k), x4(k));
alpha=gl'*gl./(gl'*A*gl);
x1(k+1)=x1(k)-alpha*gl(1);
x2(k+1)=x2(k)-alpha*gl(2);
x3(k+1)=x3(k)-alpha*gl(3);
x4(k+1)=x4(k)-alpha*gl(4);
error(k)=norm(gl);
k=k+1;
end

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