Compress down a 1000x1000 matrix into a 100x100 matrix

I have a 1000x1000 matrix that contains various values. I would like to compress it down into a 100 by 100 matrix by averaging each 10 by 10 cell's values into 1, but im not really sure how to go about doing this

Answer 1

[Ameer Hamza]

If you have image processing toolbox

M = rand(1000, 1000);
M_new = blockproc(M, [10 10], @(x) mean(x.data, 'all'))

Alternative Solution 1: (surprisingly the fastest)

M_new = conv2(M, ones(10)/100, 'valid');
M_new = M_new(1:10:end, 1:10:end);

Alternative Solution 2:

M_C = mat2cell(M, 10*ones(1,100), 10*ones(1,100));
M_new = cellfun(@(x) mean(x, 'all'), M_C);

Alternative Solution 3:

M_new = zeros(size(M)/10);
for i=1:100
    for j=1:100
        M_new(i, j) = mean(M(10*(i-1)+1:10*i,10*(j-1)+1:10*j), 'all');
    end
end

[Robert Jansen]

Amazing array of solutions. These all give the same results. The last one is surprisingly fast too. Thanks.

[larasupernovae]

thank you so much!

Answer 2

[David Hill]

count=1;
for col=1:100:1000
    for row=1:100:1000
        newMatrix(count)=mean(yourMatrix(row:row+99,col:col+99),'all');
        count=count+1;
    end
end
newMatrix=reshape(newMatrix,10,[]);

Answer 3

[Jan]

X = rand(1000, 1000);
Y = reshape(X, [10, 100, 10, 100]);
Z = reshape(sum(sum(Y, 1), 3), [100, 100]) / 100;

Or with FEX: BlockMean :

Z = BlockMean(X, 10, 10)