How we count number of matrices with respect to some condition?

I have 1000 rows

for i=1:1000
B=A(i,:);
C=reshape(B,4,4);
D=bsxfun(@minus,C,max(C(:)))
end

Now I have 1000 D matrices , How can I check that

1- How many of D matrices are Null matrix (having all the entries are zero);

2- How many of D matrices have all the 4 distinct column;

3-How many of D matrices have 3 distinct column;

4- How many of D matrices have 2 distinct column;

5- How many of D matrices have 0 on its diagonal ;

6-How many of D matrices have non-zero entry on its diagonal.

Thanking for anticipation

[Guillaume]

Now I have 1000 D matrices

Well, actually, you have only one D matrix that you overwrite 999 times, leaving only the one created at step i = 1000.

D=bsxfun(@minus,C,max(C(:)))

That's a very convoluted way of doing

D = C - max(C(:));

Now if you were to get rid of the loop and operate on the whole A at once which would be a lot faster, and indeed create your 1000 matrices, then yes bsxfun could be useful:

D = permute(reshape(A.', 4, 4, []), [2 1 3]); %creates a 4x4x1000 matrix
D = bsxfun(@minus, D, max(max(D, [], 1), [], 2)));

[Ammy]

I have a lots of matrices in which some matrices are null matrices, How can I get total number of null matrices.

Answer 1

[KSSV]

1- How many of D matrices are Null matrix (having all the entries are zero);

Try using nnz()...nnz gives you number of non-zero sin the matrix.

2- How many of D matrices have all the 4 distinct column;

Try using unique. Read about it. You can use unique along rows and columns.

3-How many of D matrices have 3 distinct column;

Read abiut unique

4- How many of D matrices have 2 distinct column;

Read about unique

5- How many of D matrices have 0 on its diagonal ;

Read about diag. This gives you diagonal elements. And then you can use nnz.

6-How many of D matrices have non-zero entry on its diagonal.

Read about diag and nnz.

[Ammy]

nnz counts the number of entries in a matrix, but I want to count number of matrices having all the entries 0.

[Steven Lord]

The nnz function counts the Number of NonZero elements in the array. It ignores zero elements.

When all elements are non-zero, nnz is the same as numel which returns the NUMber of ELements.

A = magic(4)
nnzA = nnz(A)
nA = numel(A)

When some elements are non-zero and some are zero, nnz and numel return different values.

B = eye(4)
nnzB = nnz(B)
nB = numel(B)

When all elements are zero, nnz should return ...

C = zeros(4)
nncZ = nnz(C)
nC = numel(C)