How can I find and remove the nonzero duplicates in each column of a matrix

X is a n-by-n matrix of integers ranging from 0 to n. I want to find nonzero duplicate entries in each column and remove them.

[Image Analyst]

Unless there is exactly the same number of elements to remove in each column, you can't. For example, you can't "remove" 3 elements from column 1 and 8 elements from column 2. Can you give an example of input and output and how you used unique() to try to solve it?

[Matt Talebi]

The number of duplicates in each column is either 1 or none. Also the duplicate, if exists, is always the same integer as the column number. Example:

X = [ 1 2 3 4 5
      2 9 5 3 8
      7 5 4 0 1
      6 7 3 2 0
      3 1 6 7 9 ];

As can be seen in the 3rd column, 3 is a duplicate. Also in my real data set, the first row is always the column number (similar to this example). If it's not too much to ask I want Y to be:

Y = [ 1 2 5 4 5
      2 9 4 3 8
      7 5 6 0 1
      6 7 0 2 0
      3 1 0 7 9 ];

where duplicates removed by shifting one element up and adding two zeros at the end to balance the matrix (the order of numbers should be preserved). Otherwise, I think it should be still fine for me to be able to just identify columns with duplicate and then remove them manually. Thank you for your time!

Answer 1

[per isakson]

Given

• "matrix of integers"
• "the first row is always the column number"
• "the duplicate, if exists, is always the same integer as the column number"

Try this

X = [ 1 2 3 4 5
      2 9 5 3 8
      7 5 4 0 1
      6 7 3 2 0
      3 1 6 7 9 ];
Y = nan( size(X) );
for jj = 1 : size( X, 2)
    isdub = X( :, jj ) == jj;
    if  any( isdub(2:end) ) 
        col = X(:,jj);
        col( isdub ) = [];
        Y(:,jj) = cat( 1, col, zeros(sum(isdub),1) );
    else
        Y(:,jj) = X(:,jj);
    end
end

result

>> Y
Y =
     1     2     5     4     5
     2     9     4     3     8
     7     5     6     0     1
     6     7     0     2     0
     3     1     0     7     9
>>

This code trades performance for readability.

&nbsp

Requirement of comment: "modify the codes ... keep the one in the first row and only remove the other one"

Y = nan( size(X) );
for jj = 1 : size( X, 2)
    col = X(2:end,jj);
    isdub = col == jj;
    if  any( isdub ) 
        col( isdub ) = [];
        Y(:,jj) = cat( 1, jj, col, zeros(sum(isdub),1) );
    else
        Y(:,jj) = X(:,jj);
    end
end

result

>> Y
Y =
     1     2     3     4     5
     2     9     5     3     8
     7     5     4     0     1
     6     7     6     2     0
     3     1     0     7     9

[Matt Talebi]

Thanks Per, it works flawlessly! Just as a minor modification can you possibly modify the codes such that, once a duplicate detected in a column, keep the one in the first row and only remove the other one (to preserve the column numbers).

[Matt Talebi]

All good now, thanks a lot!