How do I convert a 2X2 matrix to 4X4 matrix in MATLAB?

Question

I need some help in converting a 2X2 matrix to a 4X4 matrix in the following manner:

A = [2 6;
     8 4]

should become:

B =         


        

Answer 1

Here's a method based on simple indexing that works for an arbitrary matrix. We want each element to be expanded to an MxN submatrix:

A(repmat(1:end,[M 1]),repmat(1:end,[N 1]))

Example:

>> A=reshape(1:6,[2,3])

A =

     1     3     5
     2     4     6

>> A(repmat(1:end,[3 1]),repmat(1:end,[4 1]))

ans =

     1     1     1     1     3     3     3     3     5     5     5     5
     1     1     1     1     3     3     3     3     5     5     5     5
     1     1     1     1     3     3     3     3     5     5     5     5
     2     2     2     2     4     4     4     4     6     6     6     6
     2     2     2     2     4     4     4     4     6     6     6     6
     2     2     2     2     4     4     4     4     6     6     6     6

To see how the method works, let's take a closer look at the indexing. We start with a simple row vector of consecutive numbers

>> m=3; 1:m

ans =

     1     2     3

Next, we extend it to a matrix, by repeating it M times in the first dimension

>> M=4; I=repmat(1:m,[M 1])

I =

     1     2     3
     1     2     3
     1     2     3
     1     2     3

If we use a matrix to index an array, then the matrix elements are used consecutively in the standard Matlab order:

>> I(:)

ans =

     1
     1
     1
     1
     2
     2
     2
     2
     3
     3
     3
     3

Finally, when indexing an array, the 'end' keyword evaluates to the size of the array in the corresponding dimension. As a result, in the example the following are equivalent:

>> A(repmat(1:end,[3 1]),repmat(1:end,[4 1]))
>> A(repmat(1:2,[3 1]),repmat(1:3,[4 1]))
>> A(repmat([1 2],[3 1]),repmat([1 2 3],[4 1]))
>> A([1 2;1 2;1 2],[1 2 3;1 2 3;1 2 3;1 2 3])
>> A([1 1 1 2 2 2],[1 1 1 1 2 2 2 2 3 3 3 3])