How to increase or decrease granularity of a matrix?

I want to increase or decrease the granularity of a matrix by a scalar factor, which would look like this:

Increasing Granularity

Increasing the granularity of a matrix replicates elements to scale the size of the matrix up by an integer factor.

A = [1 2
     3 4]
B = increase(A, 2)
B = [1 1 2 2
     1 1 2 2
     3 3 4 4
     3 3 4 4]

Decreasing Granularity

Decreasing the granularity of a matrix averages together elements to scale the size of the matrix down by an integer factor.

C = [1 2 3 4
     5 6 7 8
     4 1 8 3
     6 7 2 5]
D = decrease(C, 2)
D = [(1+2+5+6)/4 (3+4+7+8)/4
     (4+1+6+7)/4 (8+3+2+5)/4]
D = [3.5 5.5
     4.5 4.5]

Is there a way to accomplish these workflows in MATLAB?

Answer 1

[MathWorks Support Team]

Increasing Granularity

Increasing the granularity of a matrix can be accomplished by either of the following workflows (assuming A is the matrix from the Question):

B = repelem(A, 2, 2)

or 

B = kron(A, ones(2))

The "repelem" function is a more flexible version of the hypothetical "increase" function posed in the Question, since it allows a user to set different scale factors for each dimension of the matrix.

The documentation pages for these functions can be found here:

https://www.mathworks.com/help/releases/R2023a/matlab/ref/repelem.html

https://www.mathworks.com/help/releases/R2023a/matlab/ref/kron.html

Decreasing granularity

Decreasing the granularity of a matrix can be accomplished by the following workflow (assuming C is the matrix from the Question):

C = [1 2 3 4
     5 6 7 8
     4 1 8 3
     6 7 2 5]
[Xq,Yq] = meshgrid([1.5 3.5], [1.5 3.5]);
D = interp2(C, Xq, Yq)

The three-argument syntax of "interp2" treats the matrix "C" as lying on a grid, where the x-coordinate starts at 1 in the first column and increases rightward and the y-coordinate starts at 1 in the first row and increases downward. The call to "meshgrid" creates two matrices corresponding to the x- and y-coordinates of the interpolation query points for each of the quadrants of "C". Finally "interp2" interpolates "C" at those query points, scaling the size of the matrix down by 2. This process becomes challenging for scaling factors greater than 2, but is still possible. 

The documentation pages for these functions can be found here:

https://www.mathworks.com/help/releases/R2023a/matlab/ref/meshgrid.html

https://www.mathworks.com/help/releases/R2023a/matlab/ref/interp2.html