Matrix Filtering

I have an nxn matrix of 0's and 1's, eg:

 1 0 0 0 0 0
 1 1 0 0 0 0
 1 1 0 0 0 0
 1 0 0 1 0 0
 0 0 0 1 1 0
 0 0 0 0 1 1

I wish to zero any values to the right of a 1 in a preceding column, and additionally if the 1 on the diagonal is removed, then all the subsequent values in that column become 0, and do not affect any other colums, such that I would end up with the following:

 1 0 0 0 0 0
 1 0 0 0 0 0
 1 0 0 0 0 0 
 1 0 0 0 0 0
 0 0 0 0 1 0
 0 0 0 0 1 0

Preferably not using a loop!

Note the 1 at (4,1) causes the 1s in the 4 column to be 0ed, and the 1 at (5,5) is not removed, because the 1 at (5,4) has been 0ed.

Any ideas?

Thanks...

[Matt Fig]

I think you mean the 1 at (4,4), not (4,1). Also, why would this one at (4,4) be zeroed when it doesn't follow a 1??

Answer 1

[Matt Fig]

Say your array is called B

B([false(size(B,1),1),diff(B,[],2)==0] & B) = 0;

Oops, I didn't see the diagonal condition. Hmm...

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EDIT

idx = [false(size(B,1),1),diff(B,[],2)==0] & B & eye(size(B));
B(logical(cumsum(idx))) = 0;
B([false(size(B,1),1),diff(B,[],2)==0] & B) = 0;

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EDIT 2 After more clarification...

In that case, I think a loop may be your best bet... Perhaps someone else will come up with another way.

for ii = 1:size(A,1)
   idx = find(A(ii,1:n-1),1);
   if ~isempty(idx)
       if idx<ii && A(ii,ii)
           A(ii:m,ii) = 0;
       end
      A(ii,idx+1:n) = 0;
   end
end

[Sally]

I probably changed the question as you were answering, sorry!!

[Sally]

Close, but I end up with:

B =

1 0 0 0 0 0

1 0 0 0 0 0

1 0 0 0 0 0

1 0 0 1 0 0

0 0 0 1 0 0

0 0 0 0 0 0

[Matt Fig]

You did change the question as I was answering...

Why would (4,4) be removed when it doesn't follow a 1??

[Sally]

:) Sorry!

(4,4) follows the 1 @ (4,1) so gets removed - I'm using row,column

[Sally]

Oh... I see where you're coming from... not just the preceding column having a 1... imagine the 1's to the left sweeping right across the matrix and wiping out any other 1's.

As each element on the diagonal is hit, if it becomes a 0, this then sends a wave of 0's down the matrix, removing any 1's further down the particular column...

[Sally]

Thanks... I thought I was being hopeful without a loop!!

Answer 2

[Andrei Bobrov]

for our case

[m,n]=size(A);
II = mat2cell(A,m,ones(1,n));
I3 = nchoosek(1:n,2);
jj = I3(arrayfun(@(x)all(xor(II{I3(x,1)},II{I3(x,2)})),1:size(I3,1)),:);
I4 = zeros(size(A));
I4(:,jj) = A(:,jj);