Making loop calculate-able

n = 450*450;
for i = 0:1:n
    for j = 0:1:n
        i = mod (i+1,n+1);
        j = mod (j + S(i+1), n+1);
        S([i+1 j+1]) = S([j+1 i+1]);
    end
end

I need to run this code for initial sequence S = {1,2,3,...,450*450}, but due to very high computation matlab is not able to do this. Is there any way to acheive this using less calculations?

[Walter Roberson]

Are you sure the loop is correct? You have for i then for j and inside that you modify i . The i value is going to be reset every time that a new for i iteration starts.

[Zeeshan Abbas]

I am not an expert but I hope so it's correct because:

for n=256 am getting what I require but when I increase 'n' to 450*450 it stucks without any error, which means the calculation is very large enough that matlab is not able to calculate.

Answer 1

[Guillaume]

Even if your code is correct, it is extremely bad practice to use the same variable names for the loop indices and for local variables within the loop. Certainly any experience coder will pause when looking at that code and start to wonder if there's a bug, as Wallter did. Make the life of the reader easier, remove the ambiguity:

n = 450*450;
for i = 0:1:n
    for j = 0:1:n
        ind1 = mod(i+1, n+1) + 1;
        ind2 = mod(j + S(ind1), n+1) + 1;
        S([ind1, ind2]) = S([ind2, ind1]);  %swap linear indices ind1 and ind2
    end
end

In the calculation of ind2 (your original 2nd j), it is unclear if you meant to use the loop index i or the i calculated on the previous line. Your code would have used the i calculated on the previous line, so i have done the same.

Note that your S needs to have n+1 elements for your code to work. Are you sure you didn't mean mod(..., n)?

edit: As for speeding it up, no it's not possible because of the dependence on S(ind1) in the calculation of ind2. And since you want to do swaps = 41,006,655,001 swaps ~= 41 billions swap, it's going to take a loooong time, but matlab will eventually get you the result. It takes about 0.3 seconds on my machine to do one i loop, so in about 18 hours you'd get your result. Do you actually need to do that many swaps?

[Zeeshan Abbas]

Dear Guillaume! Thanks for the clarification. Actually am not an expert that's why too much ambigities there. Let me explain what exactly I am trying to achieve here.

[code removed -- WDR]

I am trying to edit this to acheive another permuted sequence i.e. running the code till swapping.

I hope the query is clear?

[Zeeshan Abbas]

So, if you can change this code to make it fast or suggest any other such keyed permutaion algorithm would be much appreciated, please.

Using while loop as shown in the code is not permuting the whole sequence as 'n' is decreasing after every loop that's why I was experimenting with for loop.

[Walter Roberson]

Zeeshan Abbas :

We cannot discuss that topic due the the laws of the USA, so I have removed your explanation and code.

We can, however, discuss swapping entries just because it sounds like a fun thing to do.

[Zeeshan Abbas]

Ok please, that would be enough.

And it would be bonus if you can mention some keyed permutation algorithm names and if they have any method to check the randomess of that permuted sequences.

[Guillaume]

Since Walter removed your explanation, I have no idea what the intent of your code is. You can explain it without mentioning encryption.

As I said, as I, there's no way to speed up this code because of the depency on S in the calculation of ind2. if you remove that dependency, then the index calculation can be sped up, but you'll still have to perform 41 billion swaps which is always going to take a while. The only way to significantly speed up the code is by greatly reducing the number of swaps needed. performing 202,501 swaps takes only 0.3 seconds on my machine. But doing these 202,501 swaps another 202,501 times is 202,501 * 0.3 seconds ~= 18 hours!

[Zeeshan Abbas]

Thank you Guillaume!

I don't need any encryption. Actually I got 'S' using KSA algorithm. As the initial sequence to KSA was {1,2,3,...}, to hide this thing and to get another permutation I an trying to swap all again.

My ultimate target is to find keyed permutations and then to check the randomness of the permuted sequences using any randomness test.

If you can mention any keyed permutations and randomess tests, it will be helpful enough.

Answer 2

[Zeeshan Abbas]

What if I can make this like:

for i = 0:1:n
%     for j = 0:1:n
        ind1 = mod(i+1,n+1)+1;
        ind2 = mod(i+S(ind1), n+1) +1;
        S([ind1 , ind2]) = S([ind2 , ind1])
%     end
end

Is it correct?

[Walter Roberson]

Perhaps, but this does something different than the original code.