Removing zeros and then vertically collapse the matrix

Question

In MATLAB, say I have a set of square matrices, say A, with trace(A)=0 as follows:

For example,

A = [0 1 2; 3 0 4; 5 6 0] 

How can I remove the zeros and then vertically collapse the matrix to become as follow:

A_reduced = [1 2; 3 4; 5 6]

More generally, what if the zeroes can appear anywhere in the column (i.e., not necessarily at the long diagonal)? Assuming, of course, that the total number of zeros for all columns are the same.

The matrix can be quite big (hundreds x hundreds in dimension). So, an efficient way will be appreciated.

Answer 1

Case #1

Assuming that A has equal number of zeros across all rows, you can compress it horizontally (i.e. per row) with this -

At = A' %//'# transpose input array
out = reshape(At(At~=0),size(A,2)-sum(A(1,:)==0),[]).' %//'# final output

Sample code run -

>> A
A =
     0     3     0     2
     3     0     0     1
     7     0     6     0
     1     0     6     0
     0    16     0     9
>> out
out =
     3     2
     3     1
     7     6
     1     6
    16     9

Case #2

If A has equal number of zeros across all columns, you can compress it vertically (i.e. per column) with something like this -

out = reshape(A(A~=0),size(A,1)-sum(A(:,1)==0),[])  %//'# final output

Sample code run -

>> A
A =
     0     3     7     1     0
     3     0     0     0    16
     0     0     6     6     0
     2     1     0     0     9
>> out
out =
     3     3     7     1    16
     2     1     6     6     9

Answer 2

• To compress the matrix vertically (assuming every column has the same number of zeros):

  A_reduced_v = reshape(nonzeros(A), nnz(A(:,1)), []);
  

• To compress the matrix horizontally (assuming every row has the same number of zeros):

  A_reduced_h = reshape(nonzeros(A.'), nnz(A(1,:)), []).';