Find series of maxima of array (and matrix) within blocks of size n

I have a simple problem, and it's, perhaps, less simple extension:

1. I have an array A=[1 2 5 1 0 0 5 0 1 2 4 0 5 3 2 0 1 0 0 5] (all positive). How do I produce a vector B, which contains the maxima of, say, blocks of n=5 within A?

Namely, I want to produce B=[5 5 5 5].

2. I have a matrix: A=[1 2 5 1 0 0 5 0 1 2 4 0 5 3 2 0 1 0 0 5; 1 2 5 1 0 0 7 0 1 2 4 0 7 3 2 0 1 0 0 5; 1 2 5 1 0 0 5 0 1 2 4 0 5 3 2 0 1 0 0 5;] . Now, I want to get the matrix: C=[5 5 5 5; 5 7 7 5; 5 5 5 5] .

Can these two tasks be achomplished with a single procedure, without using loops?

Thanks!

Answer 1

[Ted Shultz]

You could use rehsape and max:

[reshape(max(reshape(A',5,[])), [], size(A,1))]'

Test:

A=[1 2 5 1 0 0 5 0 1 2 4 0 5 3 2 0 1 0 0 5] 
[reshape(max(reshape(A',5,[])), [], size(A,1))]'

A=[1 2 5 1 0 0 5 0 1 2 4 0 5 3 2 0 1 0 0 5; 1 2 5 1 0 0 7 0 1 2 4 0 7 3 2 0 1 0 0 5; 1 2 5 1 0 0 5 0 1 2 4 0 5 3 2 0 1 0 0 5;] 

[reshape(max(reshape(A',5,[])), [], size(A,1))]'

ans =

5 5 5 5

ans =

5 5 5 5

5 7 7 5

5 5 5 5

[Erez]

Thanks a lot!

Answer 2

[Bruno Luong]

maxfun =  @(A) squeeze(max(reshape(A,size(A,1),5,[]),[],2));

A = [1 2 5 1 0 0 5 0 1 2 4 0 5 3 2 0 1 0 0 5]
B = maxfun(A)

A = [1 2 5 1 0 0 5 0 1 2 4 0 5 3 2 0 1 0 0 5; 1 2 5 1 0 0 7 0 1 2 4 0 7 3 2 0 1 0 0 5; 1 2 5 1 0 0 5 0 1 2 4 0 5 3 2 0 1 0 0 5]
C = maxfun(A)

[Erez]

Awsome solution! I can't formally accept two solutions on this website, so I'll "accept" the first (arbitrarily). But this solution of yours works just as great. Thanks!