How can I join columns of an array without overlapping elements?

So, I have a tri-diagonal (10x10) and would like to join some columns without overlapping the elements, that means columns 1,4, 7 and 10 can be joined without overlapping as well columns 2,5,8. All I have to do is put this elements together and all the other elements turn to 0. This is what I get, any suggestion? X is a random tri-diagonal matrix and Y the matrix with the joined columns.

clear all
x = [1 1 0 0 0 0 0 0 0 0; 2 3 4 0 0 0 0 0 0 0; 0 1 1 1 0 0 0 0 0 0; 0 0 1 1 1 0 0 0 0 0; ...
    0 0 0 1 1 1 0 0 0 0; 0 0 0 0 2 4 3 0 0 0; 0 0 0 0 0 4 5 1 0 0; 0 0 0 0 0 0 1 1 1 0; ...
    0 0 0 0 0 0 0 1 1 1; 0 0 0 0 0 0 0 0 1 1];
[nelem,ielem] = size (x);
y=zeros(nelem,nelem);
lin = 1;
col = 1;
j = 2;
if (x(lin,col) == 0 && x(lin,j) ~= 0 || (x(lin,col) ~= 0 && x(lin,j) == 0) || (x(lin,col)) == (x(lin,j)))
    if(x(lin,col))~=0
        y(lin,col)=x(lin,col);
        
    elseif (x(lin,j))~=0
        y(lin,col)= x(lin,j);
    else
        y(lin,col)=x(lin,col);
    end
end
%COLUNAS 1 e 2
% for i = 2:nelem
i = 2;
while (i < nelem && j < nelem)
    while (((x(i,col)==0)&&(x(i,j)~= 0))||((x(i,col)~=0)&&(x(i,j)==0))||((x(i,col)==0)&&(x(i,j)==0))&&j<nelem)
        if (x(i,col)) ~= 0
            y(i,col) = x(i,col);
        else
            y(i,col) = x(i,j);
        end
        if (i<nelem)
            i=i+1;
        elseif (i == nelem)
            i = 1;
            col = col +1;
            j = j+1;
        end
    end
    if (i < nelem && j < nelem)
        y(:,col) = x(:,col);
        i = 1;
        j = j+1;
    end
end
while(((x(i,col)) == 0 && (x(i,j)) ~= 0 || (x(i,col)) ~= 0 && (x(i,j)) == 0 ||(x(i,col)) == (x(i,j))) && i<nelem)
    if (x(i,col) ==(x(i,j)))
        y(i,col) = (x(i,col));
    end
    if((x(i,col))~=0 && (x(i,j)) == 0)
        y(i,col)=x(i,col);            
    elseif ((x(i,col))==0 && (x(i,j)) ~= 0)
        y(i,col)=x(i,j);
    end
    i=i+1;
end
if (x(i,col) ==(x(i,j)))
    y(i,col) = (x(i,col));
end
if((x(i,col))~=0 && (x(i,j)) == 0)
    y(i,col)=x(i,col);            
elseif ((x(i,col))==0 && (x(i,j)) ~= 0)
    y(i,col)=x(i,j);
end

[Chunru]

Given

x = [1 1 0 0 0 0 0 0 0 0; 
     2 3 4 0 0 0 0 0 0 0;
     0 1 1 1 0 0 0 0 0 0; 
     0 0 1 1 1 0 0 0 0 0;
     0 0 0 1 1 1 0 0 0 0; 
     0 0 0 0 2 4 3 0 0 0; 
     0 0 0 0 0 4 5 1 0 0; 
     0 0 0 0 0 0 1 1 1 0;
     0 0 0 0 0 0 0 1 1 1; 
     0 0 0 0 0 0 0 0 1 1];

What is the desired outputt?

[Emanoel Santos]

x = [1 1 0 0 0 0 0 0 0 0;

2 3 4 0 0 0 0 0 0 0;

1 1 1 0 0 0 0 0 0 0;

1 1 1 0 0 0 0 0 0 0;

1 1 1 0 0 0 0 0 0 0;

3 2 4 0 0 0 0 0 0 0;

5 1 4 0 0 0 0 0 0 0;

1 1 1 0 0 0 0 0 0 0;

1 1 1 0 0 0 0 0 0 0;

1 0 1 0 0 0 0 0 0 0]

The first column is the reuslt of colum 1, 4, 7 and 10.

The second, 2,5 and 8.

Thank you.

[Chunru]

Your above description is not clear. I could not understand: "The first column is the reuslt of colum 1, 4, 7 and 10. The second, 2,5 and 8."

Are you trying to get the tri-diagonal elements?

[Emanoel Santos]

Really sorry, english isn't my native language. Exactly, I'm trying to get only the tri-diagonal elements, and put on the same column, without overlapping the elements (only possible if 1 element is equal to 0 and the other one is not), if the 2 elements are equals to 0, we can join them on the same column.

The first column of x is:

1

2

0

0

0

0

0

0

0

0

the 4th column is:

0

0

1

1

1

0

0

0

0

0

the result I expect is for the column 1 and column 4 is:

1

2

1

1

1

0

0

0

0

0

basically, I would like to do this to the columns N1:{1,4,7,10} N2:{2,5,8} and N3{3,6,9}, and the rest elements = 0, to obtain this output:

x = [1 1 0 0 0 0 0 0 0 0;

2 3 4 0 0 0 0 0 0 0;

1 1 1 0 0 0 0 0 0 0;

1 1 1 0 0 0 0 0 0 0;

1 1 1 0 0 0 0 0 0 0;

3 2 4 0 0 0 0 0 0 0;

5 1 4 0 0 0 0 0 0 0;

1 1 1 0 0 0 0 0 0 0;

1 1 1 0 0 0 0 0 0 0;

1 0 1 0 0 0 0 0 0 0]

[Emanoel Santos]

for example, the columns bellow:

[Chunru]

See the updated answer.

Answer 1

[Chunru]

Not sure if this is what you intend to do:

x = [1 1 0 0 0 0 0 0 0 0; 
     2 3 4 0 0 0 0 0 0 0;
     0 1 1 1 0 0 0 0 0 0; 
     0 0 1 1 1 0 0 0 0 0;
     0 0 0 1 1 1 0 0 0 0; 
     0 0 0 0 2 4 3 0 0 0; 
     0 0 0 0 0 4 5 1 0 0; 
     0 0 0 0 0 0 1 1 1 0;
     0 0 0 0 0 0 0 1 1 1; 
     0 0 0 0 0 0 0 0 1 1];
y = zeros(size(x));
y(:, 1) = sum(x(:, [1 4 7 10]), 2);
y(:, 2) = sum(x(:, [2 5 8]), 2);
y(:, 3) = sum(x(:, [3 6 9]), 2);
y

y = 10×10

1 1 0 0 0 0 0 0 0 0 2 3 4 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 3 2 4 0 0 0 0 0 0 0 5 1 4 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0

[Emanoel Santos]

Really really thank you!