If only one positive elem per row (rest are 0), then fill both sides of positive element

Hi, I have a square matrix of non-negative elements. In each row, at least one element is positive.

For rows where there is only one positive element (the rest are 0) I need to put 1e-4 next to that element, both sides. In A below, the second and last row have only 1 positive (note last row has only one side to add)

A=...

[0.9 0.1 0 0;
0 0.8 0 0;
0 0.1 0.7 0.1;
0 0 0 0.9]

Ouput should be:

B=...
[0.9 0.1 0 0;
1E-4 0.8 1E-4 0;
0 0.1 0.7 0.1;
0 0 1E-4 0.9]

The dimension of the matrix is fixed, so I can get rows that need to be changed (if result is 3 in this case) with

sum(A==0,2)

But this doesn't tell me the position of the positive element (I could use something like find(A) ) , nor fill both sides (loop free if possible)

Answer 1

[Guillaume]

A = [0.9 0.1   0   0
     0   0.8   0   0
     0   0.1 0.7 0.1
     0   0   0   0.9];

Apadded = [zeros(size(A, 1), 1) A zeros(size(A, 1), 1)]; %pad to avoid dealing with edges
lonelyrows = find(sum(A ~= 0, 2) == 1);
[~, singlecols] =  find(Apadded(lonelyrows, :));
Apadded(sub2ind(size(Apadded), [lonelyrows lonelyrows], [singlecols-1 singlecols+1])) = 1e-4;
Afilled = Apadded(:, 2:end-1)

Answer 2

[Sean de Wolski]

And just for fun:

A=...
[0.9 0.1 0 0;
0 0.8 0 0;
0 0.1 0.7 0.1;
0 0 0 0.9];

B = A;
sgn = sign(A)==1;

B(logical(conv2(double(bsxfun(@and,sum(sgn,2)==1,sgn)),[1 0 1],'same'))) = 1e-4

[John D'Errico]

Fun, and pretty too.

Answer 3

[dpb]

Find the locations needing to be worked around. Pick one dimension first as you've done; I'll stick with the rows...

>> irow=find(sum(A>0,2)==1)
irow =
   2
   4
>> [~,icol]=ind2sub(size(A(irow,:)),find(A(irow,:)>0))
icol =
   2
   4
>>

These are now indices in the original array since didn't reduce the number of columns by subselecting the rows.

[Dave]

Thanks dpb, those are the locations, how do I fill next to them with 1E-4?

[dpb]

Ran out of time...methinks bsxfun the irow,icol array of indices with padded array as Guillame did would also work...