Is there a way to group matrix elements in matlab? - matlab

Question

I am working on a problem which requires me to group array elements and average each group. For example consider the 4 x 4 matrix M,
M = [ 1 0 0 1;
1 0 1 1;
1 1 0 1;
0 0 0 1;]
I want to group this into a 2 x 2 matrix, taking an average of the elements so we would get
M1 = [0.5 0.75;
0.5 0.5;]
does anyone know a way to do this?
Many thanks

Answer 1

You can do this using conv2, and a little indexing, like so:
>> A = conv2(M,ones(2), 'same');
>> A(1:2:end,1:2:end)/4
ans =
0.5000 0.7500
0.5000 0.5000

Answer 2

I think the way to go is to first split your matrix in parts using mat2cell, then apply your functions to each part and merge them to a new matrix:
>> M = [ 1 0 0 1;
1 0 1 1;
1 1 0 1;
0 0 0 1;]
M =
1 0 0 1
1 0 1 1
1 1 0 1
0 0 0 1
>> T=mat2cell(M, [2 2], [2 2])
T =
2×2 cell array
{2×2 double} {2×2 double}
{2×2 double} {2×2 double}
>> M1 = cellfun(#mean, cellfun(#mean, T, 'UniformOutput', false))
M1 =
0.5000 0.7500
0.5000 0.5000
>>

Answer 3

You can do something like this for any rectangle, where x and y denote the size of domains that you want to average.
function M1 = get_means(M, x, y)
[rows, cols] = size(M);
if mod(rows, x) == 0 && mod(cols, y) == 0
for i = 1:y:cols
for j = 1:x:rows
M1((j+x-1)/x, (i+y-1)/y) = sum(M(j:j+x-1,i:i+y-1),'all')/(x*y);
end
end
else
error('The matrix doesn''t have compatible dimensions.')
end
end

Answer 4

You can loop over the grouped matrices and then calculate the mean
M = [ 1 0 0 1;
1 0 1 1;
1 1 0 1;
0 0 0 1;];
n=2; % 2x2 mat
% create new matrix with means
MM = zeros(n,n);
% row counter for mean-Matrix
r=1;
% loop over matrix groups
for row=1:n:size(M,1)
c = 1; % column counter for mean-Matrix
for col=1:n:size(M,2)
MM(r,c) = mean(mean(M(row:row+n-1, col:col+n-1)));
c = c+1;
end
r = r+1;
end
Output:
MM =
0.5000 0.7500
0.5000 0.5000