how to calculate mean of submatrices in a large matrix and print out a new matrix

Hi,

I have a matrix 4x4

M =[

11 12 13 14

21 22 23 24

31 32 33 34

41 42 43 44]

I want to calculate the mean of submatrix 2x2

M1 = [11 12

21 22]

M2 = [31 32

41 42]

...

The final result is a new matrix 2x2 containing the mean value computed from the submatrices

Thanks in advance.

Answer 1

[Stephen23]

>> M = [11,12,13,14;21,22,23,24;31,32,33,34;41,42,43,44;51,52,53,54;61,62,63,64]
M =
   11   12   13   14
   21   22   23   24
   31   32   33   34
   41   42   43   44
   51   52   53   54
   61   62   63   64

Using convolution is simple and relatively efficient:

>> A = conv2(M,ones(2,2),'valid')/4;
>> A = A(1:2:end,1:2:end)
A =
   16.500   18.500
   36.500   38.500
   56.500   58.500

Or you could rearrange the matrix before calling mean:

>> S = size(M)/2;
>> A = mean(reshape(permute(reshape(M,2,S(1),2,S(2)),[2,4,1,3]),S(1),S(2),[]),3)
A =
   16.500   18.500
   36.500   38.500
   56.500   58.500

Or split the matrix into submatrices:

>> A = cellfun(@(m)mean(m(:)),mat2cell(M,[2,2,2],[2,2]))
A =
   16.500   18.500
   36.500   38.500
   56.500   58.500

Or use blockproc (requires the image toolbox).

[Francesco]

If possible, please could you show how to do it if we have a 1000x1000 matrix and we need to convert to a new 100x100 matrix by calculating 10x10 submatrices

Thanks

[Stephen23]

>> M = randi(9,1000,1000); % fake data
>> N = 10; % size of submatrix
>> S = size(M)/N;
>> A = mean(reshape(permute(reshape(M,N,S(1),N,S(2)),[2,4,1,3]),S(1),S(2),[]),3);

and checking:

>> size(A)
ans =
   100   100
>> A(1,1)
ans =  4.2100
>> V = M(1:N,1:N); mean(V(:))
ans =  4.2100

Answer 2

[David Hill]

m=[mean(M(1:2,1:2),'all'),mean(M(1:2,3:4),'all');mean(M(3:4,1:2),'all'),mean(M(3:4,3:4),'all')];

[Francesco]

Thanks.

Is it possible to make it automatic? If I have a 1000x1000 matrix, the new matrix would be 500x500