repeating for loop under another for loop

Hello,

I have 100 varibles which is organized in a hierarchical way. Some of them have only 3 different values (for example, 0.1,0.5 and 1.0) and others are calculated based on those values. a1 = 0.1, a2 = 0.5, a3 = 0.1 a4 = 0.2*a1 + 0.5*a2 + 0.3*a3 , a5 = 0.5, a6 = 0.1, a7 = 0.2*a1 + 0.3*a4+ 0.4*a5 + 0.7*a6, a8 =0.3, a9 = 0.8*a7+0.2*a8, .... a100 = 0.1*a3+ 0.2*a89 + 0.1*a9 + 0.6*a99

The number of variable is about 100. What I am trying to do is to check all possible values (for those variables(selective varibles) having only three possible values of 0.1, 0.5, 1.0) and to find proper combination of variable value set. For example, I am looking for all combination of seletive variables(a1,a2, a3, a5, a6....) to satisfy a100 > 0.5.

what I first thought is setting up almost 100 times of for-loop. assuming 90 selective variables and 10 variables determined based on equations, A = [0.1, 0.5, 1.0];

    for i99=1:3
         a99 = A(i99);
         for i97=1:3
              a97 = A(i97)
                 ......
                       for i5=1:3
                           a5 = A(i5) 
                           for i3=1:3
                               a3 = A(i3)                       
                               for i2=1:3
                                   a2 = A(i2)                    
                                   for i1=1:3
                                       a1 = A(a1)(i1) 
                                   end
                                end 
                            end
                            a4 = 0.2*a1 + 0.5*a2 + 0.3*a3,
                        end             
           end end end end end.....
      a100 = 0.1*a99 + 0.2*a98 +0.7*a95 + 0.7*a40;
           if a100>0.5 
              agoodcombinatin = (a1, a2, a3, a5, .... a97,a99)
           end
end

But this is too tedious and there should be a better way to do this in matlab. I hope you can help me solve this in a better way.

Thank you.

Answer 1

[Guru]

When looking at nested for loops like yours, the first question I always ask is why are you using a for loop to begin with? To address this question, we can look at some of your innermost for loops:

for i3=1:3
  a3 = A(i3)                       
  for i2=1:3
    a2 = A(i2)                    
    for i1=1:3
      a1 = A(a1)(i1) 
    end
  end 
end

Now we can step through this in our heads and realize the following: 1) a3 is not used in a2 or a1. a2 is not used in a1 2) A little closer inspection will tell us because of this independence in their relationship, not only are the for loops unnecessary, they are in fact pointless

The following code will produce the same results as this innermost nested for loop structure:

a3 = A(3);
a2 = A(3);

a1 would simply give you an error as you are trying to say that

a1 = A(a1)(3)

which does not make sense in MATLAB.