how to Expanand any matrix

If Have 3x3 Matrix example

a = [-1  2  0;
      2  1 -1;
      1, 0, 1]

if my expansion factor is 5 i need to make eack element as 5x5 matrix with -1 replaced by all zero matris of 5x5,0 with identitiy matrix and 1 with identity right shift the column by one times and so on.

How can i do this?

[Andrei Bobrov]

Please show off your expanded matrix in your case for matrix a.

Answer 1

[the cyclist]

I am not certain I interpreted your question correctly, especially the "righth shift the column by ones times". But I believe that the algorithm below does what you want, or can be easily changed to do so.

a = [-1  2  0;
      2  1 -1;
      1, 0, 1];
  
expandFac = 5;

[m,n] = size(a);

A = zeros(expandFac*m,expandFac*n);

for mi = 1:m
for ni = 1:n
    rowZero = expandFac*(mi - 1);
    colZero = expandFac*(ni - 1);
    switch a(mi,ni)
        case -1
            insertedMatrix = zeros(expandFac);
        otherwise
            insertedMatrix = diag(ones(1,expandFac-a(mi,ni)),a(mi,ni));
    end
    A(rowZero+1:rowZero+expandFac,colZero+1:colZero+expandFac) = insertedMatrix;
end
end

The key conceptual elements of this algorithm are

• Preallocating the 15x15 array
• For each element of a, finding the appropriating location to insert its corresponding 5x5 array. (That's what rowZero and colZero are doing)
• For each element of a, figure what 5x5 to insert. (That's what the switch statement is doing.)
• Use the diag command to create the identity and "shifted identity" arrays.

Answer 2

[Andrei Bobrov]

out = cell2mat(arrayfun(@(x,y)diag(ones(5-x,1),x)*y ,abs(a),a>=0,'un',0));

or

z = cell(size(a));
k = zeros(5);
for ii = 1:numel(z)
    if a(ii) >= 0
        z{ii} = diag(ones(5-a(ii),1),a(ii));
    else
        z{ii} = k;
    end
end
out = cell2mat(z);

[the cyclist]

I like how you handled the special case of a == -1 in your one-liner. I should have thought of that in my solution.