MATLAB: Problem with for loop within a loop of a loop

for loopMATLAB

The following code calculates the excess pore water pressure u after consolidation, and generates a m x n matrix, where the thickness of the soil layer i divided into m equal parts and u is calculated for n time steps.
In this simplified exampel, beta is a constant, but I want to impliment specifik values of beta for different equal sized depths indicated by m.
So say I have a beta-vector containing 5 values and a soil layer divided into m=50 equal parts. beta(1) will run from m(1):m(10), beta(2) will run from m(11):m(20) and so forth.
Does anyone have a suggestion on how to impliment the beta-vector?
beta=0.2; n= 10; m= 5
u_1=[60 54 41 29 19 15]';
u(:,1)=u_1;
for j=(1:n)
  for i=(2:m) 
    u(i,j+1)=u(i,j)+beta*(u(i-1,j)+u(i+1,j)-2*u(i,j));
    for i=(m+1) % As we look at a half-closed layer
      u(i,j+1)=u(i,j)+beta(end)*(2*u(i-1,j)-2*u(i,j))
    end
  end
end
(Ultimatly I will end up with lenght(beta)=30, m= 300 and n=>130 and even with beta as a constant it takes some time to run.)
Much appriciated!

Best Answer

Probably, the biggest source of slow down is the lack of preallocation of u. As a result, it grows one column at a time, necessating reallocation and copying on each j step.
u = zeros(m+1, n+1);  %preallocation
u(:, 1) = u1;
for j = 1:n   %why the () ?
    for i = 2:m   %so u(1, j) is 0 for all but j = 1? 
        u(i,j+1)=u(i,j)+beta*(u(i-1,j)+u(i+1,j)-2*u(i,j));
    end
    u(m+1,j+1)=u(m+1,j)+beta*(2*u(m,j)-2*u(m+1,j));  %not sure why there was a beta(end) here.
end
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