MATLAB: Code optimization for nested for loop

optimization of nested-for loop

Hi, I am a newbie and I need to implement following code for 1000 beta value. I can not use nested for loop. I request to you please suggest some method to remove nested for-loop.
%% Start Session
clc;
clear all;
close all;
warning off;
tStart = tic;
ScoreTolren=-0.25;
iterations = 0;
SeqInNorm = [];
indNorm = 0;
SEqNor4Check = [];
CheckEntry =0;
ExitCondition = 0;
MaxItr =0;
step = 1/8;
IntialLoop = 0;
for beta1 = IntialLoop:step:1
    for beta2 = IntialLoop:step:1-beta1
        for beta3 = IntialLoop:step:1-beta1-beta2
            for beta4 = IntialLoop:step:1-beta1-beta2-beta3
              for beta5 = IntialLoop:step:1-beta1-beta2-beta3-beta4
                  for beta6 = IntialLoop:step:1-beta1-beta2-beta3-beta4-beta5
                      for beta7 = IntialLoop:step:1-beta1-beta2-beta3-beta4-beta5-beta6
                          for beta8 = IntialLoop:step:1-beta1-beta2-beta3-beta4-beta5-beta6-beta7
                            for beta9 = IntialLoop:step:1-beta1-beta2-beta3-beta4-beta5-beta6-beta7-beta8
                                for beta10 = IntialLoop:step:1-beta1-beta2-beta3-beta4-beta5-beta6-beta7-beta8-beta9
                                    for beta11 = IntialLoop:step:1-beta1-beta2-beta3-beta4-beta5-beta6-beta7-beta8-beta9-beta10
                                      for beta12 = IntialLoop:step:1-beta1-beta2-beta3-beta4-beta5-beta6-beta7-beta8-beta9-beta10-beta11
                                          for beta13 = IntialLoop:step:1-beta1-beta2-beta3-beta4-beta5-beta6-beta7-beta8-beta9-beta10-beta11-beta12
                                              for beta14 = IntialLoop:step:1-beta1-beta2-beta3-beta4-beta5-beta6-beta7-beta8-beta9-beta10-beta11-beta12-beta13
                                                  for beta15 = IntialLoop:step:1-beta1-beta2-beta3-beta4-beta5-beta6-beta7-beta8-beta9-beta10-beta11-beta12-beta13-beta14
                                                       beta16 = 1-beta1-beta2-beta3-beta4-beta5-beta6-beta7-beta8-beta9-beta10-beta11-beta12-beta13-beta14-beta15;
                                                      iterations = iterations+1;
                                                      b(iterations,:)= [beta1,beta2,beta3,beta4,beta5,beta6,beta7,beta8,beta9,beta10,beta11,beta12,beta13,beta14,beta15,beta16];
                                                        if iterations == 1e5 
                                                            ExitCondition = 1;
                                                            break; 
                                                        end
                                                  end
                                                  if ExitCondition == 1  
                                                     break;
                                                  end
                                              end
                                              if ExitCondition == 1  
                                                 break;
                                              end
                                          end
                                          if ExitCondition == 1  
                                             break;
                                          end
                                      end
                                      if ExitCondition == 1  
                                         break;
                                      end
                                    end
                                  if ExitCondition == 1  
                                     break;
                                  end
                                end
                                if ExitCondition == 1  
                                 break;
                                end
                            end
                            if ExitCondition == 1 
                               break;
                            end
                          end
                        if ExitCondition == 1  
                           break;
                        end
                      end
                    if ExitCondition == 1  
                       break;
                    end
                  end
                if ExitCondition == 1 
                   break;
                end
              end
            if ExitCondition == 1  
               break;
            end  
            end
        if ExitCondition == 1  
           break;
        end
        end
      if ExitCondition == 1  
         break;
      end
    end
    if ExitCondition == 1  
       break;
    end
end
%% End of iteration
elapsedTime = toc(tStart);

Best Answer

Instead of implementing the nested loop by hard coding, you can use a vector as iteration counter:
function Result = Method1
nIter  = 490314;;
i0     = 0;
n      = 16;
Result = zeros(n, nIter);
b      = [zeros(n-1, 1); 1];
step   = 1/8;
for k = 1:nIter
   Result(:, k) = b;
   
   % Increase index vector b:
   b(n) = 0;
   for ib = n-1:-1:1
      if sum(b) <= 1 - step
          b(ib) = b(ib) + step;
          break;   % Update of b has finished
      end
      b(ib) = i0;  % reset current b
   end
   b(n) = 1 - sum(b(1:15));
end
Result = Result.';
Please test and adjust this to your needs. This is about 50% slower than the code in my other answer Method2, but nicer.
Accesing the Result columnwise instead of rowwise allows a better usage of the processor cache.
By the way: This code obtains all row vectors with 16 elements, which contains elements of teh set 0:1/8:1, which have the sum of 1.0.
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