MATLAB: Speed-up the given code

for loopMATLABperformance

The following code is taking a most of the time in my script and I have to run the script many times Is there a way to reduce the time for its execution.
t=0:200000;
lambda=[1,2,3;4,5,6;7,8,9;10,11,12];
for trans=1:size(lambda,1)
  uh_fun{trans}=expconv(lambda(trans,:));
end
uh=zeros(length(t),1);
for i=1:length(uh_fun)
  temp_uh_fun=uh_fun{i};
  f_gamma=zeros(length(t),1);
  for j=1:length(temp_uh_fun)
      f_gamma=f_gamma+temp_uh_fun{j}(t)';   % this line take a lot of time
  end
  uh=uh+p(i)*f_gamma;  % p is an array of scalars
end
I have added expconv function for reference. I need some suggestions to improve the performance. I have also attached a pdf which contains profiler analysis of anonymous function in expconv.

Best Answer

This might be a variant of the xy-problem that @Stephen points out. http://xyproblem.info/
Solve X: you want to add the values for a function for all P, C, lambda values. Attempt with using function handles, called Solution Y.
Solve Y: you make a lot of function handles for all P, C, lambda sets. But this is too slow. You want a solution to make Solution Y faster, not seeing a faster solution for X.
%This is just an EXAMPLE. Check to make sure you get the right results
C = rand(1000, 1);
P = rand(1000, 1);
lambda = rand(1000, 1);
t = 1:10000;
%Solution Y approach  : use handles
Ysum = zeros(1, length(t));
for i = 1:length(C)
  fh = @(t) P(i)*exp(-lambda(i)*t) + C(i);
  Ysum = Ysum + fh(t);
end
t2 = toc
%Solution X approach  : use vectorized math
tic
Ysum = sum(bsxfun(@times, exp(-lambda*t), P) + C, 1);
t1 = toc  % ~5 times faster
I notice you like using repmat and find. Note that use of repmat is slower than bsxfun. Also, if possible, avoid using find if dealing with logical indexing. For instance:
function uh_fun=expconv(lambda)
      k=length(lambda);
  %     Lambda=repmat(lambda,k,1);
  %     temp_den=Lambda'-Lambda;   
      temp_den = lambda' - lambda; %faster
  %     ind=find(temp_den==0);
      ind = temp_den == 0; %stick with logical indexing
      if sum(ind(:)) > k % length(ind)>k %corrected this
          error('atleast two of the pdfs to be convolved are identical')
      else
  %         temp_den(temp_den==0)=1; 
          temp_den(ind) = 1; %no need to re-find temp_den == 0;
          den=prod(temp_den);
          nume=prod(lambda);
          C=nume./den;
          for i=1:k
              uh_fun{i}=@(t)exp(-lambda(i)*t)*C(i); %Do you reallly have to make all these handles?
          end
      end
  end
If this is still too slow, then you could try using parfor or mex functions.
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