# help speeding up an incrementing loop

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tamir elazari on 26 Dec 2019
Edited: Vladimir Sovkov on 28 Dec 2019
hi,
i'm trying to calculate some correlation factors using nested loop.
the equation im implementing is:
my parameters are:
H - 200*256 matrix
P - 200*370,000 matrix
AES_key_opt = 256
raw = 256*370,000 (calculated matrix)
now, i know i'm dealing with alot of data, but my question is if it possible to speed up somehow the relevant lines from the profiler?
relevant code part:
% calculates the pearson correlation mat "raw" size "AES_key_opt","l_trc"
for i = 1:AES_key_opt
% claculate H' and P' for every "i" and "j"
H_avg = H_C_sum(i)/n_trc;
P_avg = P_C_sum(j)/n_trc;
% numerator calculation
numerator=0;
for k = 1:n_trc
numerator = numerator + (H(k,i) - H_avg)*(P(k,j) - P_avg);
end
% denumerator calculation
denom_H = 0;
denom_P = 0;
for k = 1:n_trc
denom_H = denom_H + (H(k,i) - H_avg)^2;
denom_P = denom_P + (P(k,j) - P_avg)^2;
end
denominator = sqrt((denom_H*denom_P));
% pearson correlation mat calculation
raw(i,j) = numerator/denominator;
end
end
profiler:
I would be thankful for any help or tips
thanks

Walter Roberson on 26 Dec 2019
You have defined that you must use nested loops. That is what is loosing you most of your efficiency when you could be vectorizing.
You can make minor tweaks like extracting the (:,i) slice near the top of the for i loop and indexing that at k instead of indexing the array at (k,i) inside the triple loop, but I am not convinced that it would help in any meaningful way.

Walter Roberson on 26 Dec 2019
Though as Vladimir points out, pre-allocating raw() is recommended.
Image Analyst on 26 Dec 2019
Because he said "i'm trying to calculate some correlation factors using nested loop." I don't think that implied a definite requirement. It was just the way he first decided to tackle the problem. I think he's open to other, faster approaches.
Walter Roberson on 26 Dec 2019
The bar variables can be found by using mean()
Your denominators are closely related to the standard deviation. You do have sqrt() of the product of two terms, but because the terms are independent, you can separate the terms, sqrt(A) * sqrt(B), and the calculations being done individually then would be N * std(A,1) -- notice the second parameter of 1 to get the proper division (or you could use std() but change what you multiply by.)

Vladimir Sovkov on 26 Dec 2019
At the first glance, you can replace
numerator=0;
for k = 1:n_trc
numerator = numerator + (H(k,i) - H_avg)*(P(k,j) - P_avg);
end
by
numerator = (H(1:n_trc,i) - H_avg)'*(P(1:n_trc,j) - P_avg);
as well as
denom_H = 0;
denom_P = 0;
for k = 1:n_trc
denom_H = denom_H + (H(k,i) - H_avg)^2;
denom_P = denom_P + (P(k,j) - P_avg)^2;
end
by
denom_H = (H(1:n_trc,i) - H_avg)'*(H(1:n_trc,i) - H_avg);
denom_P = (P(1:n_trc,j) - P_avg)'*(P(1:n_trc,j) - P_avg);
You can use ":" instead of "1:n_trc" if the corresponding array sizes exactly equal to n_trc.
You should also preallocate "raw" before the loop in order to avoid its sequential resizing: raw=zeros(...,...).
H_avg and P_avg are also recommended to compute before the loop as vectors, otherwise you compute the same values several times repeatedly.
Probably, fufther optimization is also possible.
Not all variables have clear sense (H_C_sum, P_C_sum, etc).

tamir elazari on 26 Dec 2019
sorry if i wasnt clear, as english is not my native language.
by writing "nested loops" i just metioned the approach i took, i didnt mean it must be done with it.
Vladimir Sovkov on 26 Dec 2019
If no loops are necessary, I think that the matrix of Pearson statistics can be computed by a single line of code:
raw=normalize(H)'*normalize(P);
Vladimir Sovkov on 28 Dec 2019
raw=normalize(H)'*normalize(P)/size(H,1);