Using reshape to manipulate a large matrix

I have a 10000x10000 matrix of data that I'm trying to scale down. You goal is to make it a 400x400 matrix by taking every cell in 25x25 cell chunk and averaging them into one value. I'm trying to use the reshape function to do this, but I dont know how to scale down the matrix by any factor other than 2, the code for that is below. Any advice on hw I can do to adapt or rewrite this is appreciated.

[x,y] = size(matrix);
x1 = x/2;
y1 = y/2;
R = reshape(reSizedData,2 , x1, 2, y1);
S = sum(sum(R, 1), 3) * 0.5;
Y = reshape(S, x1, y1);

Answer 1

[per isakson]

"I dont know how to scale down the matrix by any factor other than 2" What's wrong with your code?

I think your code works just fine with scale down by 25

%%
M = 1:1:1e8;
M = reshape( M, 1e4, 1e4 );
%%
tic
[x,y] = size( M );
x1 = x/25;
y1 = y/25;
R = reshape( M, 25, x1, 25, y1 );
S = sum( sum(R,1), 3 );
Y1 = reshape( S, x1, y1 );
toc
%%
Y2 = nan( 4e2, 4e2 );
tic
for rr = 1 : 1 : 4e2
    for cc = 1 : 1 : 4e2
        chunk = M( (rr-1)*25+1:rr*25, (cc-1)*25+1:cc*25 );     
        Y2(rr,cc) = sum(chunk(:));  
    end
end
toc
%%
imagesc(M)
figure
imagesc(Y1)
figure
imagesc(Y2)

Your result and the for-loop result are identical!

>> all(all(Y1==Y2))
ans =
  logical
   1
>> 

And I think your code works just fine with "any" scale down factor

%%
M = 1:1:1e8;
M = reshape( M, 1e4, 1e4 );
D = 2e2; % 1e4/D must be a whole number
%%
tic
[x,y] = size( M );
x1 = x/D;
y1 = y/D;
R = reshape( M, D, x1, D, y1 );
S = sum( sum(R,1), 3 );
Y1 = reshape( S, x1, y1 );
toc
%%
M = 1:1:1e8;
M = reshape( M, 1e4, 1e4 );
Y2 = nan( 1e4/D, 1e4/D );
tic
for rr = 1 : 1 : 1e4/D
    for cc = 1 : 1 : 1e4/D
        chunk = M( (rr-1)*D+1:rr*D, (cc-1)*D+1:cc*D );     
        Y2(rr,cc) = sum(chunk(:));  
    end
end
toc
%%
imagesc(M)
figure
imagesc(Y1)
figure
imagesc(Y2)
%%
all(all(Y1==Y2))

Or what have I missed?