Selecting certain zero elements from a matrix in MATLAB - arrays

Question

Suppose I have this matrix:
M =
90 0 40 0
0 0 10 60
55 15 0 10
0 15 5 0
I would like to find all zeroes such that once I select a zero from row i and column j, no more zeroes from row i and column j should be selected. In this example, scanning from left to right and top to bottom, the rows and columns I should get are:
Row Column
1 2
2 1
3 3
4 4
What MATLAB code will produce this for me?

Answer 1

Luis Mendo's answer is correct given the OP's original question of selecting the first zero of each row. However, with our discussion seen in the comments, this requirement has now changed. The understanding (at least from what I gathered from the snippets of code and the requirements) is that once you select a zero at row i and column j, no more zeroes from all of row i and all of column j should be selected. As for loops are usually frowned upon in MATLAB, I saw no other choice but to do this with loops.
My approach was the following:
Find all zeroes in the matrix and find their row and column locations and place each into separate lists.
While we still have a zero to consider:
Place this row and column into a list
Remove all indices from the row list that contain this row in question.
Remove all indices from the column list that contain this column in question
Repeat Step #2 until our row and column location list is empty.
Without further ado, here is the code.
clear all;
close all;
M =[90,0,40,0;0,0,10,60;55,15,0,10;0,15,5,0];
%// Find row and column locations
%// find traverses columns first, so I had to
%// transpose and swap J,I so that it reports
%// row locations first.
[J,I] = find(M.' == 0);
%// List of co-ordinates that meet our criteria
rowCoords = [];
%// While there is still one zero to consider...
while (~isempty(I) && ~isempty(J))
%// Store these for processing
rowToAdd = I(1);
colToAdd = J(1);
%// Add to the list
rowCoords = [rowCoords; [rowToAdd colToAdd]];
%// Remove all row and column co-ordinates
%// that share the same row and column
rowsToRemove = I == rowToAdd | J == colToAdd;
I(rowsToRemove) = [];
J(rowsToRemove) = [];
end
As such, we finally get:
rowCoords =
1 2
2 1
3 3
4 4
It is still unclear on whether the OP wants what Luis Mendo has provided, or what I have interpreted in the comments. The OP verified that how I specified his requirements is what he actually wants but we still do not have any verification. OP: Please verify.

Answer 2

Find the first zero (if any) in each row
[ind1, ind2] = max(M.'==0);
result = [find(ind1); ind2(ind1)].';
In your example, this gives
result =
1 2
2 1
3 3
4 1
Find the first zero (if any) in each row, ignoring columns that have been previously used
M2 = M; %// make a copy of M2. It will be overwritten
[R C] = size(M2);
cols = NaN(R,1); %// initiallize. This will store the result for each row
ind = false(R,1); %// intiallize. This will indicate rows that have a valid zero
for r = 1:R %// for each row
c = find(M2(r,:)==0,1); %// find first valid zero, if any
if ~isempty(c)
cols(r) = c; %// store result
ind(r) = true; %// this row has been found to have a valid zero
M2(:,c) = inf; %// this col can no longer be used
end
end
result = [find(ind) cols(ind)]; %// build result. Only rows with a valid zero
In your example:
result =
1 2
2 1
3 3
4 4