Vectorize 3 for loops

Hello,

I have to do a large calculation and right now I use 3 for loops to do it....but I wonder if I could use vectorization to make it faster.

my code:

PermPolynom = allVL1(dim,2,'==',inf);
lenghtPermPolynom = size(PermPolDiag,1);

     for n = 1:lenght_X2
         for k = 1:lenght_X1      
             for l = 1:lengthPermPolynom
                 DiagVek(k,n) = DiagVek(k,n)-(prod((X2(n,:) X1(k,:)).^                                                                  PermPolynom(l,:)));
             end
         end
     end

X1 and X2 are matrices with different number of rows but same number of columns (every row stands for a multidimensional vector of length dim).

For example:

X1 = [0 2 3 2 3;  2 3 4 1 3; 3 4 5 4 3;.....;4 5 2 1 2] -> dim = 5

PermPolynom gives me all possible Permutations for a vector of length dim so that the sum of all entries in the vector is 2.

example for dim 3 and sum = 1:

[0 0 1; 0 1 0; 1 0 0]

The goal is to calculate for every entry in X1 and X2 the multidimensional polynomial.

I tried to vectorize it like it is said in a help of matlab:

i = 0;
for t = 0:.01:10
    i = i + 1;
    y(i) = sin(t);
end

A vectorized version of the same code is

t = 0:.01:10;
y = sin(t);

but that doesn't work...I think because of the different length of X1 and X2.

Is there a way to get rid of the loops?

Thanks Tim

[Jan]

The expression is not complete:

DiagVek(k,n)-(prod((X2(n,:) ??? X1(k,:)).^ PermPolynom(l,:)));

What does appear instead of the ???

[Tim]

a minus...strange that it doesn't appear...

Answer 1

[Daniel Shub]

Loops are no longer painfully slow in MATLAB and haven't been for quite some time. A better question would be how can I speed up my code. For this we need more than just the code, we also need details about the dataset (how big is it). Have you run your code through mlint and the profiler?

It doesn't look like you have preallocated DiagVek. While there have been improvements in MATLAB's dynamic memory allocation, preallocation still tends to be very important.

[Tim]

Good to know that loops aren't so slow. :)

The vecors X1 and X2 are 5000x(three to fifteen) matrices and preallocated every vector or matric in my code. I already used mlint. It told my that there are 3 matrices that change size in every loop and that I should preallocate them but in these cases this is not possible because I need them in different sizes every iteration. There is nothing more that mlint tells me.

I didn't use profiler yet.

The thing is that the code above is only the first matrice I have to calculate and the whole code is much longer. It is probably to much to ask to look through all the 90 lines of code I wrote ^^

I just thought that replacing the loops could help a bit because I have several calculations which look the same as above :)

Thank you for your quick answer and your help.

Tim

[Daniel Shub]

That mlint warning is key and despite needing the matrix to be a different size every iteration, suggests you are doing something wrong. You should take a look at cell arrays and/or consider simply overwriting the matrix on every iteration instead of saving all the different size matrices.