How to calculate average in a large matrix?

Dear all,

I'm working with a large amount of data in a project.For each row of my matrix , I calculate the average. Here is an example that help you to understand my problem

   y1 y2 y3 y4 y5                                      
x1 2  4  4  6  7      Av1=4,6          
x2 1  2  3  4  5      Av2=3
x3 1  2  3  4  5      Av3=3
x4 1  2  4  5  6      Av4=3,6
x5 2  5  6  8  9      Av5=6
x6 4  7  8  4  9      Av6=6,4
x7 2  3  4  8  7      Av7=4,8
x8 1  2  4  6  4      Av8=3,4

I want to make my programm user friendly, that means the user enter the number of average that he wants.For instance, if the user enter the number 2 , the programm calculates the average of each 2 rows

   y1 y2 y3 y4 y5                                      
x1 2  4  4  6  7      NewAv1=Av1+Av2=3,8      
x2 1  2  3  4  5   
x3 1  2  3  4  5      NewAv2=Av3+Av4=3,3
x4 1  2  4  5  6    
x5 2  5  6  8  9      NewAv3=Av5+Av6=6,2
x6 4  7  8  4  9      
x7 2  3  4  8  7      NewAv4=Av7+Av8=4,1
x8 1  2  4  6  4

Thank you in advance

Answer 1

[Andrei Bobrov]

xy = [2  4  4  6  7     
1  2  3  4  5   
1  2  3  4  5
1  2  4  5  6    
2  5  6  8  9
4  7  8  4  9      
2  3  4  8  7
1  2  4  6  4];

k = 2;

i0 = zeros(size(xy,1),1);
i0(1:k:end) = 1;
out = accumarray(repmat(cumsum(i0),size(xy,2),1),xy(:),[],@mean);

ADD

xy2 = xy(1:floor(size(xy,1)/k)*k,:);

s = size(xy2);
i0 = zeros(s(1),1);
i0(1:k:end) = 1;
out = accumarray(repmat(cumsum(i0),s(2),1),xy2(:),[],@mean);

[afrya]

Thank you for your answer.I have another problem. For exemple if k=3, I will get Av1= 3.5333 Av2= 5.3333 Av3= 4.1000

How can I delete Av3 because it calculates only the average of the 2 last raws and not the 3 last rows. How can I do it in general for the programm ?

[Andrei Bobrov]

see ADD

[Jos (10584)]

My suggestion seems more efficient (no cumsum, for instance) ...

Answer 2

[Azzi Abdelmalek]

%Example--------------
A=rand(10)
p=3
%-----------------------
[n,m]=size(A);
q=ceil(n/p)*p
B=nan(q,m)
B(1:n,:)=A
ii2=p:p:q
ii1=[1 ii2(1:end-1)+1]
out=arrayfun(@(x) nanmean(nanmean(B(ii1(x):ii2(x),:))),1:numel(ii2))'

[afrya]

Thanks for your answer, I tried your example, however if you work with a matrix that contains a lot of values, it's not convenient

[Azzi Abdelmalek]

What is the size of your matrix?

[afrya]

the size of the matrix is: 3500*579

[Azzi Abdelmalek]

%Example--------------
A=rand(3500,379);
p=3;
%-----------------------
tic
[n,m]=size(A);
q=ceil(n/p)*p;
B=nan(q,m);
B(1:n,:)=A;
B=reshape(B',p*m,[]);
out=nanmean(B);
toc

result

Elapsed time is 0.043406 sec

Answer 3

[Jos (10584)]

Here is a trick, using clever indexing with accumarray:

% data
  A = rand(10,5) ;
  K = 3 ; % average of so many rows
% engine
  ix = repmat(floor((0:(size(A,1)-1))/K),size(A,2),1).' + 1 % indices
  AV = accumarray(ix(:), A(:),  [ix(end) 1], @mean) % averages
% check
  abs(AV(1) - mean(reshape(A(1:K,:),1,[]))) < eps

[afrya]

Thank you for your answer, .. I just have a question about your program, what does eps means?

[Jos (10584)]

see

doc eps

In many cases, like here, differences smaller than the value of eps are not important

[afrya]

Thanks