How To apply vectorization on for loop in Matlab?

Question

Can anyone tell me how vectorize the following:

a = randi([6 10],5);; 
c = unique(a);
d = [1:5]; % some comparison Values length should be equal to length(c)

Mat = zeros(size(a));
for i = 1:length(c)
  Mat(a==c(i)) = d(i);
end

Result:

     3     1     5     3     3
     3     5     4     2     3
     5     1     3     3     3
     2     2     2     3     3
     3     5     5     3     4

Here 6 is replaced by 1, 7 is replaced by 2, etc.

This is of course just an example; my real Mat is more like 2000×2000.

I started formulating an answer with the old version of your question; the new version seems a lot simpler actually :) Ah well, I think it's enough to get you going. — Rody Oldenhuis
– Rody Oldenhuis, Commented Feb 12, 2014 at 8:57
Well, it was indeed so simple, that I just planted another answer. — Rody Oldenhuis
– Rody Oldenhuis, Commented Feb 12, 2014 at 9:08

Rody Oldenhuis · Accepted Answer · 2014-02-12 09:07:32Z

2

NOTE: read my other answer first

To answer the question in your latest edit:

[~, inds] = histc(a(:), c);
Mat = reshape(d(inds), size(a));

Doing a similar test for 600×100 data:

a = randi(500,[600 100]); 
c = unique(a);
d = randi(20, size(c));

tic
Mat = zeros(size(a));
for ii = 1:length(c)
  Mat(a==c(ii)) = d(ii);
end
toc


tic
[~, inds] = histc(a(:), c);
Mat2 = reshape(d(inds), size(a));
toc

isequal(Mat,Mat2)

Gives the following:

Elapsed time is 0.166673 seconds.  %// your method
Elapsed time is 0.006669 seconds.  %// my method
ans =                              %// yes they're equal
    1

The speeds again differ by a factor of ~250.

answered Feb 12, 2014 at 9:07

Rody Oldenhuis

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1 Comment

Adiel Over a year ago

+1 great! I didn't know about the second output of histc, it seems to be usefull.

Rody Oldenhuis · Accepted Answer · 2014-02-12 09:09:31Z

0

NOTE: this is an answer to the original question; the second edit changed the question completely, so the answer below no longer applies. The edit greatly simplifies the problem, so this answer is still a good place to start.

Basically, all unique values of a will be replaced by corresponding values in b. That implies the matrix to analyze is b, and the only difficulty lies in the fact that the condition b < d must hold for corresponding indices in b.

To do this, you can simply bin all elements of a in groups defined by c and determine what group each element in b belongs to. That information can be used to find the proper indices in d.

In other words:

NewMat = b;
[~, inds] = histc(a(:), c);
NewMat(NewMat(:) > d(inds)) = 0;

A small test to compare the performance and validate the equality of the two methods:

a = randi(1000, 74,100);
b = randi(1000, 74,100);

c = unique(a);
d = randi(1000, size(c)); % some comparison Values

%// Your method
tic
NewMat = zeros(size(a));
for i = 1:length(c)
  Mat = zeros(size(a));
  Mat(a==c(i)) = b(a==c(i));
  Mat(Mat > d(i)) =0;
  NewMat = NewMat + Mat;
end
NewMat1 = NewMat;
toc

%// My method
tic
[~,inds] = histc(a(:), c);
b(b(:) > d(inds)) = 0;
NewMat2 = b;
toc

%// validate solution
isequal(NewMat1, NewMat2)

Results:

%// 74 × 100
Elapsed time is 0.151808 seconds.   %// your method 
Elapsed time is 0.001007 seconds.   %// my method
ans =                               %// yes, they're equal
     1

So a factor of ~150 performance increase. Using not 74×100 but 740×1000 gives

%// 740 × 1000
Elapsed time is 27.587543 seconds.  %// your method
Elapsed time is 0.111467 seconds.   %// my method
ans =                               %// yes, they're equal
     1

or a factor of ~250 difference. So apparently, your method also scaled worse than the histc approach.

edited Feb 12, 2014 at 9:09

answered Feb 12, 2014 at 8:56

Rody Oldenhuis

38.1k7 gold badges53 silver badges98 bronze badges

2 Comments

Rody Oldenhuis Over a year ago

@user2851655: also see my other answer, which answers your question as it currently is.

Rody Oldenhuis Over a year ago

@user2851655: you're welcome; I enjoy these kinds of puzzles, so it was my pleasure really :)

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