Subtract column from a matrix

In matlab it is easy to subtract number from column or row. I want to subtract column [n x 1] from a matrix [n x m]. Is it possible to doit without for loop? When I wrote it just with '-', there was dimension mismatch error. Thanks.

[Stephen23]

Use bsxfun . This is exactly what it is for.

Answer 1

[Image Analyst]

You could use repmat() to create an array of the same size:

out = inputArray - repmat(columnVector, [1, m]);

[Mikhail]

Yea, seems like this is the fastest way. I think this must work faster, then for loop. Thanks.

[Guillaume]

No, bsxfun is faster and this is the exact purpose of it.

[Image Analyst]

Not always.

inputArray = rand(100,100);
columnVector = rand(100, 1);
tic
out = bsxfun(@minus, inputArray, columnVector);
toc
tic;
out = inputArray - repmat(columnVector, [1, 100]);
toc

Elapsed time is 0.000508 seconds.
Elapsed time is 0.000357 seconds.

[José-Luis]

To continue with the one-upping: When it is that fast, unless you are doing it many many times, it doesn't really matter.

Just did a quick test:

ii = [10 100 200 300  400 500 1000 2000 5000 7500 10000 20000]
a = [ii' ii'];
cnt = 0;
for sz = ii

      sz
      cnt = cnt + 1;
      inputArray = rand(sz);
      columnVector = rand(sz, 1);
      tic
      bsxfun(@minus, inputArray, columnVector);
      out(1) = toc;
      tic;
      inputArray - repmat(columnVector, [1, sz]);
      out(2) = toc;
      a(cnt,:) = out;
  end

plot(ii,a);
legend({'bsxfun','repmat'});
ylabel('Elapsed time (s)')
xlabel('Array size')

That results in:

[Titus Edelhofer]

Nice comparison!

One aspect has not been mentioned yet: for larger matrices/vectors the memoryfriendliness of bsxfun compared to repmat (which blows up the memory usage significantly).

Titus

[Image Analyst]

Good point. This can be done by adding these lines into the loop:

memoryUsed = memory;
fprintf('Memory used by MATLAB = %d bytes.\n', memoryUsed.MemUsedMATLAB)

Answer 2

[Guillaume]

Use bsxfun, it will expands singleton dimensions:

n = 10; m = 20;
matrix = rand(n, m);
column = rand(n, 1);
bsxfun(@minus, matrix, column)

[Mikhail]

Thanks