correlation of an array

i've an array in which i've stored different matrices. i want to calculate the correlation between the matrices stored in an array

like:

 A=[ 12 23 12 34    21 32 43 65   65 76  1 23     43 21 54 98 ]
     21 43  2 13    76 87 34 22   89 67 45 88     55 77 54 65
     32 45 56 78    89 87 84 54   22 33 43 54     78 98 97 65      
     67 54 33 44    88 77 66 54   21 15 16 48     90 80 21 66

like if i've array=[A;B;C;D]

i want the correlation between A and B

           correlation between A and C

           correlation between A and D

           correlation between B and C

           correlation between B and D

           correlation between C and D

help me in doing so

[Tobias]

Isn't that basicly the xcorr function? I have not worked with that before, but did you check Cross-correlation?

[Raman]

xcorr2 is fine but how make a loop on it so that it can calculate all the above combination which mentioned above....

 for k1=1:length(A)
  A1=A(k1)
  for k2=k1:length(A)
     A2=A(k2)
     correlation=xcorr2(k1,k2);
     fprintf('%d',correlation);
   end
end

the above code calculates the correlation in only one matrix i'e correlation between one pixel and the second pixel in the same matrix... i want to calculate correlation between the different matrix as the combination i've given above...

Answer 1

[Image Analyst]

Extract the 4 submatrices and correlate all the permutations.

A = fullMatrix(:, 1:4);
B = fullMatrix(:, 5:8);
C = fullMatrix(:, 9:12);
D = fullMatrix(:, 13:16);

% Now correlate:
AB = xcorr2(A, B);
AC = xcorr2(A, C);
AD = xcorr2(A, D);
BC = xcorr2(B, C);
BD = xcorr2(B, D);
CD = xcorr2(C, D);

There is no need for complicated loops when you have this few matrices, and just a few simple lines of code will do it for you.

[Raman]

this is ok sir but what if i've a loop and each time m storing a different values in matrix then the above code works how?

can u tell me how can i do so?

like i've an array

        B1=[12 34 56]  here 12 34 and 56 are block number of an image
        L=length(B1);
        for b=1:L
            blockNumber1 = B1(b);
            fprintf('\n block %d\n',B1(b));
            blockrows =16; blockcols = 16;
            [blockcol, blockrow] = ind2sub( [blockcols, blockrows], blockNumber1);
            colstart = (blockcol-1) * blockSizeC + 1;
            rowstart = (blockrow - 1) * blockSizeR + 1;
            oneBlock1=grayImage(rowstart : rowstart + blockSizeR - 1, colstart : colstart + blockSizeC - 1);
            %fprintf('\n oneblock------------------------1\n');
            disp(oneBlock1);
         end

here i want to store each matrix in array and want to find the correlation between these matrices as i told u earlier...

the above 3 blocks(block 12, block 34 and block 56) has its corresponding intensity matrix i want to calculate the correlation between these matrices i.e

             correlation between block 12 matrix and block 34 matrix

             correlation between block 12 matrix and block 56 matrix

             correlation between block 34 matrix and block 56 matrix

can u tell me plz sir how it can be done?

[Image Analyst]

Why do you want a for loop? It's just more complicated that way.

[Raman]

this is in my project...m just giving u a hint that my codes is something like this...here i've got three different matrices corresponding to oneBlock1.. now u tell me how to do this in order to find the correlation between these matrices...

[Image Analyst]

I think you're on your way. You just need to get rowstart and colstart correct for each block, and have two loops one over 1 to L and the other from there to L

for k1 = 1 : L
  for k2 = k1+1 : L
    % Get blocks k1 and k2 and call xcorr2()
  end
end

[angel]

one more thing sir the code i've given u, in that oneBlock1 is giving me a matrix right?

i want to store it in a array can u help me in storing this as i m confused...

            for b=1:L
            blockNumber1 = B1(b);
            fprintf('\n block %d\n',B1(b));
            blockrows =16; blockcols = 16;
            [blockcol, blockrow] = ind2sub( [blockcols, blockrows], blockNumber1);
            colstart = (blockcol-1) * blockSizeC + 1;
            rowstart = (blockrow - 1) * blockSizeR + 1;

 oneBlock1=grayImage(rowstart : rowstart + blockSizeR - 1, colstart : colstart + blockSizeC - 1);

the following line of code i wrote for storing matrices in array is it correct or not?

 [oneBlock2]=oneBlock1;

if not correct it for me sir....

[Image Analyst]

oneBlock1 will be a matrix of the same type as grayImage. You don't need brackets around oneBlock2.

[Raman]

ok then what should i do to store oneBlock in an array so that i can calculate the correlation between the matrices...

12 34 56 78
56 78 89 21
66 43 22 32
23 43 76 89

the code i wrote caculates

 correlation between 12 and 56
 correlation between 12 and 66
 correlation between 12 and 23
 correlation between 56 and 66
 correlation between 56 and 23
 correlation between 66 and 23

this i dont want...

i want it to calculate correlation like this if

 12 37 56 78            34 99 11 21
 56 78 89 21            10 40 89 90
 66 43 22 32            45 43 22 55
 23 43 76 89            56 44 23 22

i want to calculate

 correlation between 12 and 34
 correlation between 37 and 99
 correlation between 56 and 11
 correlation between 78 and 21
 correlation between 56 and 10 
 correlation between 78 and 40
 and so on......

i.e correlation between first element of matrice 1 and matrix 2, then second element of matrix 1 and matrix 2 and so on..... how can i acheive this sir?

help me to do so...

[Image Analyst]

I don't understand - those look like pixel values, not ID numbers of blocks. I thought you just had 16 blocks and each block was a 4 by 4 array. You wouldn't compute correlation of single pixel values - you do it with 2D arrays. But frankly I don't know what you're after since you didn't give us the whole picture, the larger context, so I don't know if your approach is even correct to do what you think you want to do, or not.