How do I divide matrix elements by column sums in MATLAB?

Question

Is there an easy way to divide each matrix element by the column sum? For example:

input:

1  4

4  10

output:

1/5  4/14

4/5  10/14

Answer 1

Here's a list of the different ways to do this ...

• ... using BSXFUN:

  B = bsxfun(@rdivide,A,sum(A));
  

• ... using REPMAT:

  B = A./repmat(sum(A),size(A,1),1);
  

• ... using an outer product (as suggested by Amro):

  B = A./(ones(size(A,1),1)*sum(A));
  

• ... and using a for loop (as suggested by mtrw):

  B = A;
  columnSums = sum(B);
  for i = 1:numel(columnSums)
    B(:,i) = B(:,i)./columnSums(i);
  end
  

Answer 2

Couldn't resist trying a list comprehension. If this matrix was represented in a row-major list of lists, try this:

>>> A = [[1,4],[4,10]]
>>> [[float(i)/j for i,j in zip(a,map(sum,zip(*A)))] for a in A]
[[0.20000000000000001, 0.2857142857142857], [0.80000000000000004, 0.7142857142857143]]

Yes, I know that this is not super-efficient, as we compute the column sums once per row. Saving this in a variable named colsums looks like:

>>> colsums = map(sum,zip(*A))
>>> [[float(i)/j for i,j in zip(a,colsums)] for a in A]
[[0.20000000000000001, 0.2857142857142857], [0.80000000000000004, 0.7142857142857143]]

Note that zip(*A) gives transpose(A).