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Hi I have the following matrix:

A= 1 2 3; 0 4 0; 1 0 9

I want matrix A to be:

A= 1 2 3; 1 4 9

PS - semicolon represents the end of each column and new column starts.

How can I do that in Matlab 2014a? Any help?

Thanks

George
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  • Related: http://stackoverflow.com/questions/738438/removing-zeros-from-a-matrix-not-sparse – Cecilia Jun 25 '14 at 12:57
  • For the result column, the sizes obey any constraints? e.g. same number of columns etc. –  Jun 25 '14 at 13:00

4 Answers4

2

The problem you run into with your problem statement is the fact that you don't know the shape of the "squeezed" matrix ahead of time - and in particular, you cannot know whether the number of nonzero elements is a multiple of either the rows or columns of the original matrix.

As was pointed out, there is a simple function, nonzeros, that returns the nonzero elements of the input, ordered by columns. In your case, 

A = [1 2 3;
     0 4 0;
     1 0 9];
B = nonzeros(A)

produces

1
1
2
4
3
9

What you wanted was 

1 2 3
1 4 9

which happens to be what you get when you "squeeze out" the zeros by column. This would be obtained (when the number of zeros in each column is the same) with

reshape(B, 2, 3);

I think it would be better to assume that the number of elements may not be the same in each column - then you need to create a sparse array. That is actually very easy:

S = sparse(A);

The resulting object S is a sparse array - that is, it contains only the non-zero elements. It is very efficient (both for storage and computation) when lots of elements are zero: once more than 1/3 of the elements are nonzero it quickly becomes slower / bigger. But it has the advantage of maintaining the shape of your matrix regardless of the distribution of zeros.

A more robust solution would have to check the number of nonzero elements in each column and decide what the shape of the final matrix will be:

cc = sum(A~=0);

will count the number of nonzero elements in each column of the matrix.

nmin = min(cc);
nmax = max(cc);

finds the smallest and largest number of nonzero elements in any column

[i j s] = find(A); % the i, j coordinates and value of nonzero elements of A
nc = size(A, 2); % number of columns

B = zeros(nmax, nc);
for k = 1:nc
  B(1:cc(k), k) = s(j == k);
end

Now B has all the nonzero elements: for columns with fewer nonzero elements, there will be zero padding at the end. Finally you can decide if / how much you want to trim your matrix B - if you want to have no zeros at all, you will need to trim some values from the longer columns. For example:

B = B(1:nmin, :);
Floris
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0

Simple solution:

A = [1 2 3;0 4 0;1 0 9]

A =

     1     2     3
     0     4     0
     1     0     9

A(A==0) = [];

A =

     1     1     2     4     3     9

reshape(A,2,3)

ans =

     1     2     3
     1     4     9

It's very simple though and might be slow. Do you need to perform this operation on very large/many matrices?

Benoit_11
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0

From your question it's not clear what you want (how to arrange the non-zero values, specially if the number of zeros in each column is not the same). Maybe this:

A = reshape(nonzeros(A),[],size(A,2));
Luis Mendo
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0

Matlab's logical indexing is extremely powerful. The best way to do this is create a logical array:

>> lZeros = A==0

then use this logical array to index into A and delete these zeros

>> A(lZeros) = []

Finally, reshape the array to your desired size using the built in reshape command

>> A = reshape(A, 2, 3)
Noah
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