Loop never stops?

Why does my loop never stops after I assign k1 & k2 as symbolic variables?

n=10;
T=sym(zeros(n,n));
T(1,:)   = 410; % Top
T(end,:) = 420; % Bottom
T(:,1)   = 400; % Left
T(:,end) = 400; % Right
T_old = T; 

for k = 1:20 %time steps  
    for j = 2: (n-1)
        for i = 2: (n-1)
           %k1 = 0.02; k2=0.33;
           syms k1 k2
           T(i,j) = T_old(i,j)*(1-2*k1-2*k2)+k1*(T_old(i-1,j)+T_old(i+1,j))+k2*(T_old(i,j-1)+T_old(i,j+1));
        end
    end
     T_old = T; 
end

[KSSV]

This line

 syms k1 k2

need not to be loop, keep it at the begining. Are you sure you want k1, k2 to be symbolic?

[Amanda Liu]

Yes as I have 2 different values of k1 and of k2.

Answer 1

[Walter Roberson]

The code does finish. It just takes a long time. You are building some complicated expressions. You can improve performance by putting in an expand() call:

On my system, execution time is about 22 seconds, but on the demonstration system here it is over 55 seconds so I cannot show you the result.

tic
n = 10;
T=sym(zeros(n,n));
T(1,:)   = 410; % Top
T(end,:) = 420; % Bottom
T(:,1)   = 400; % Left
T(:,end) = 400; % Right
T_old = T; 
syms k1 k2
for k = 1:20 %time steps  
    for j = 2: (n-1)
        for i = 2: (n-1)
           T(i,j) = expand(T_old(i,j)*(1-2*k1-2*k2)+k1*(T_old(i-1,j)+T_old(i+1,j))+k2*(T_old(i,j-1)+T_old(i,j+1)));
        end
    end
     T_old = T; 
end
toc

T(1:5,1:5)

Tn = subs(T, {k1, k2}, {0.02, 0.33});
Tn(1:5,1:5)
vpa(Tn,5)

[Walter Roberson]

Numeric results look like

[400.0,  410.0,  410.0,  410.0,  410.0,  410.0,  410.0,  410.0,  410.0, 400.0]
[400.0, 346.97, 300.07, 265.17, 246.58, 246.58, 265.17, 300.07, 346.97, 400.0]
[400.0, 327.52, 263.81, 216.56, 191.43, 191.43, 216.56, 263.81, 327.52, 400.0]
[400.0, 323.92, 257.06, 207.47, 181.11, 181.11, 207.47, 257.06, 323.92, 400.0]
[400.0, 323.48, 256.23, 206.35, 179.84, 179.84, 206.35, 256.23, 323.48, 400.0]
[400.0, 323.48, 256.23, 206.36, 179.84, 179.84, 206.36, 256.23, 323.48, 400.0]
[400.0, 323.94, 257.09, 207.51, 181.15, 181.15, 207.51, 257.09, 323.94, 400.0]
[400.0, 327.67, 264.07, 216.89,  191.8,  191.8, 216.89, 264.07, 327.67, 400.0]
[400.0, 348.09, 301.89, 267.39, 248.99, 248.99, 267.39, 301.89, 348.09, 400.0]
[400.0,  420.0,  420.0,  420.0,  420.0,  420.0,  420.0,  420.0,  420.0, 400.0]

[Amanda Liu]

Thank you for replying. I will proceed with this method and get back to you soon.