# How to clump/consolidate values together using the mean function

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William Gray on 15 Jan 2021
Commented: Alan Stevens on 18 Jan 2021
Hi everyone,
So to explain the title a little more, say I have a 8x8 matrix all of different values, how would I make another 8x8 matrix but just with 4 values in each quadrant?
I have written the following code in an attempt to do this
cw = 4; %cell width
a = [1:8];
b=[1:8]';
c=a.*b;
lp = [1 5]; %length position
mat=ones(8,8); %temporary matrix
for i = 1:numel(lp)
for j = 1:numel(lp)
mat(lp(i):lp(i)+cw-1,lp(i):lp(i)+cw-1)=mean(c(lp(i):lp(i)+cw-1,lp(i):lp(i)+cw-1),"all");
end
end
it partially achieves the desired outcome, calcualting the upper left quadrant as 6.25 and the lower right value as 42.25 but you can see the other quadrants remain as the pre-defined 1.
I'm sure there is an easier way to do this, I probably just don't know the name for what I'm trying to do, but any help would be really appreciated.
Thank you all

Alan Stevens on 15 Jan 2021
Edited: Alan Stevens on 15 Jan 2021
Here's one way
cw = 4; %cell width
a = 1:8;
b = (1:8)';
c = a.*b;
mat=ones(8,8); %temporary matrix
avfn = @(m) mean(m,'ALL');
p = 1:cw; q = cw+1:2*cw;
mat(p,p) = avfn(c(p,p));
mat(p,q) = avfn(c(p,q));
mat(q,p) = avfn(c(q,p));
mat(q,q) = avfn(c(q,q));
William Gray on 18 Jan 2021
Hi Alan
Thank you for the answer, this works great for 4 quadrants. However, say the grid was bigger, 16x16 for example, and so you wanted 16 values instead of 4, is there a more systematic way to calculate this? posibly using a for loop or something of that nature?
Alan Stevens on 18 Jan 2021
I think the following does it, though you should check it carefully:
n = 16; % n x n matrix
cw = 4; %cell width
a = 1:n;
b = (1:n)';
c = a.*b;
nc = n/cw; % nc x nc cells (Assumes nc is integer)
mat=ones(n); %temporary matrix
avfn = @(m) mean(m,'ALL');
s = 1;
for i = 1:nc
f = s-1+cw;
p(i,:) = s:f;
s = f+1;
end
for i = 1:nc
for j = 1:nc
mat(p(i,:),p(j,:)) = avfn(c(p(i,:),p(j,:)));
end
end