MATLAB: Please help me vectorizing the following code

solving fractional order ode using l1 method

n=2:nt;
  sum1(n)=f(t(n),alpha)+(var).*bj(n).*u(1);
    k=1:n-1;var_bj=(bj(k+1)-bj(k)).*(var);
    for n=2:nt
     sum2=0;
      for k=1:n-1
          sum2=sum2+var_bj.*u(n-k);
      end
      sumout2(n)=sum2;
      u(n)=(sum1(n)-sumout2(n))/(var-beta);
end

Best Answer

For a vectorization, move the index vector from the for loop into the command. For the innermost loop:
 sum2 = 0;
 for k = 1:n-1
   sum2 = sum2 + var_bj .* u(n-k);
 end
becomes (I guess that var_bj is a scalar):
sum2 = sum(u(n - (1:n-1))) * var_bj;
This can be simplified:
sum2 = sum(u(1:n)) * var_bj;
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