# How to vectorize a specific for-loop

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Paolo Binetti on 9 Dec 2016
Commented: Jan on 19 Dec 2016
I am trying to vectorize the for-loop hereafter. Would you have any hint? Thank you
for i = 1 : numel(text)-k+1 % "text" is a string
pattern(i,:) = text(i:i+k-1);
end

Jan on 9 Dec 2016
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Paolo Binetti on 9 Dec 2016
Thank you

Jan on 9 Dec 2016
Edited: Jan on 9 Dec 2016
Before you start a vectorization, care for a pre-allocation:
n = numel(str) - k + 1;
pattern = repmat(' ', n, k); % <-- added
for ii = 1:n
pattern(ii,:) = str(ii:ii+k-1); % [EDITED, was: pattern(k, :)]
end
For a string with 10'000 characters and k=6 this 8 times faster already. But you can get much faster with a loop:
n = numel(str) - k + 1;
pattern = repmat(' ', n, k);
for ii = 1:k % <-- k instead of n
pattern(:, ii) = str(ii:ii+n-1); % <-- (:, ii) instead of (ii, :)
end
Now the values are copied to a continuous block of memory, which is much faster. In addition the loop is much shorter assumed that k << n.
[EDITED] For your amusement a vectorized version:
index = bsxfun(@plus, (1:numel(str) - k + 1).', 0:k-1);
pattern = str(index);
[EDITED 2] And if we are on the way, a C-MEX for completeness:
#include "mex.h"
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
mwSize k, n, f;
mxChar *in, *out;
mwSize dims;
// Get inputs:
in = (mxChar *) mxGetData(prhs);
k = (mwSize) mxGetScalar(prhs);
// Create outputs:
n = mxGetNumberOfElements(prhs) - k + 1;
dims = n;
dims = k;
plhs = mxCreateCharArray(2, dims);
out = (mxChar *) mxGetData(plhs);
// Copy data:
f = out + n * k;
while (out < f) {
memcpy(out, in++, n * sizeof(mxChar));
out += n;
}
}
Timings for Matlab 2015b, Win64, mean of 100 iterations:
str = repmat(' ', 1, 10000);
k = 6;
Original: 0.134 sec
Pre-allocation: 0.0178 sec
Vectorized: 0.000806 sec
Continuous: 0.000348 sec
C-MEX: 0.0000529 sec
Now use the profiler to find out, if this piece of code is still the bottleneck of the program. If this piece of code takes 1% of the processing time only, accelerating it by a factor of 2 let the total program run only 0.5% faster. Therefore it is most likely a waste of time.
[EDITED 2] Conclusion:
• The continuous copying is the fastest M-version I can imagine.
• Vectorizing wastes time with creating the large index. Do not overestimate vectorization, when you do not operate on complete matrices.
• The C-MEX is 7 times faster than the continuous copy version.
• Avoiding the creation of the large redundant array would be much more efficient. Better use str(ii:ii+k-1) in the code instead of the fluffy pattern matrix.

Jan on 16 Dec 2016
A speed up of factor 2530 with the C-mex compared to the original code. I am happy about this.
Paolo Binetti on 17 Dec 2016
Thank you very much! Amazing how much you can learn from a simple question, how many ways exist to code a simple operation, and how different is the performance.
Too bad my email provider originally classed the notification of your answer as spam, so I only saw your answer late. In the meantime I had independently came up with the column-wise version, and was happy because indeed the improvement was significant and good enough. I had not tried pre-allocation, because I did not understand its influence.
I will now try adding pre-allocation, and not only in that piece of code, because I understand that it is a good thing in general. I will not try the vectorized version, since you proved it's slower. I don't know what a C-MEX, but having seen the performance, I need to find out, and thern I will try your code.
I see what you mean by "Avoiding the creation of the large redundant array would be much more efficient". But do not understand what exactly you mean by "Better use str(ii:ii+k-1) in the code instead of the fluffy pattern matrix."
Jan on 19 Dec 2016
Pre-allocation is very important in all software projects. Example:
v = [];
for k = 1:1000
v(k) = k;
end
Now in each iteration Matlab creates a new array and copied the old data. Therefore Matlab has to reserve and write sum(1:1000)*8 bytes, which is >4MB, although the results has 8kB only.
C-Mex is an interface from Matlab to C-code. C is usually much slower during the processing, but extremely tedious during writing and debugging.
If you do not use the large array "pattern" fianlly, but stay at the dynamic indexing and use str(ii:ii+k-1), the code might run faster. But this depends on what you do with the pattern array later on.

Roger Stafford on 9 Dec 2016
You might try the ‘hankel’ function:
n = numel(text);
nk = n-k+1;
pattern = hankel(text(1:nk),text(nk:n));