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Redirecting arithmetic functions from LAPACK/BLAS?

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Andrew
Andrew on 28 Jun 2021
Edited: Jan on 3 Jul 2021
I have a specific line of code:
P2_r = 1 + 0.5*abs(U_O(:,:,ctr) - 0.5) + 0.5*abs(cand - 0.5) - 0.5*abs(U_O(:,:,ctr) - cand);
where U_0 is an array that varries in size from 10's of elements to 100,000+ elements depending on the progression of the parent's code. cand is a single element of U_0, and ctr is simply controlling the 3rd dimension. Now, when U_0 hits a size of approximately 130,000+ elements the computation time of the line of code jumps by 2 to 3 orders of magnitude. This becomes a bottleneck because P2_r is at the core of an optimization routine.
I've read that MATLAB will call LAPACK/BLAS when it is determined the overhead is worth it. If MATLAB is truly calling a different math library, is it possible to control the criteria it uses to determine the switching point? Or redirect LAPACK/BLAS calls back to MATLAB's default algorithms? multiply() and abs() are built-in functions, so I do not have access to the source code.
Thanks for your help!
EDIT:
The above figure depicts the jump in computation time observed for arrays of varrying dimensions (columns) around 130,000+ elements. The specific line of code is the bottleneck of a larger rountine that computes the following quantity known as discrepancy:
I have also attached a profile of the discrepancy routine that shows P2_r as consuming the largest fraction of computation time
  2 Comments
Andrew
Andrew on 28 Jun 2021
The speed gets slower by a factor of 100 to 1000. By size I mean total number of elements in the array. For instance, a 2D array of 10 rows and 6 columns would be 60 elements

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Accepted Answer

Jan
Jan on 28 Jun 2021
Edited: Jan on 3 Jul 2021
The question is not clear yet. Can you post some input, e.g. produced by RAND(), which reproduce the timings you are observing?
P2_r = 1 + 0.5 * abs(U_O(:,:,ctr) - 0.5) ...
+ 0.5 * abs(cand - 0.5) ...
- 0.5 * abs(U_O(:,:,ctr) - cand);
If this line is really the bottleneck, reduce the number of arithmetic operations by moving the scalar parts to the front:
P2_r = 1 + 0.5 * abs(cand - 0.5) ...
+ 0.5 * (abs(U_O(:,:,ctr) - 0.5) - abs(U_O(:,:,ctr) - cand));
With some guessing:
cand = 17;
ctr = 12;
U_O = rand(130000, 10, 20);
tic;
for k = 1:1e2
P2_r = 1 + 0.5 * abs(U_O(:,:,ctr) - 0.5) ...
+ 0.5 * abs(cand - 0.5) ...
- 0.5 * abs(U_O(:,:,ctr) - cand);
end
toc
tic;
for k = 1:1e2
P2_r = 1 + 0.5 * abs(cand - 0.5) ...
+ 0.5 * (abs(U_O(:,:,ctr) - 0.5) - abs(U_O(:,:,ctr) - cand));
end
toc
At least some percent computing time. But I do not see a large jump in computing time.
Maybe you oberserve an exhausted RAM, such that the much slower virtual RAM is used? Or the limit of the 2nd level cache size?
  3 Comments
Andrew
Andrew on 29 Jun 2021
Thanks for the tips! my general intention is overall computational efficiency, so any code improvements are always welcomed!

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More Answers (1)

Cleve Moler
Cleve Moler on 2 Jul 2021
It might help to use the transposes of your arrays or interchange the order ot your loops. MATLAB stores 2-d arrays by coluumns, For example:
A = reshape(1:25,5,5)
A =
1 6 11 16 21
2 7 12 17 22
3 8 13 18 23
4 9 14 19 24
5 10 15 20 25
If the array is very large, it would be faster to do
sum(A,1)
ans =
15 40 65 90 115
than
sum(A,2)
ans =
55
60
65
70
75
-- Cleve

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