Assuming vector v of size 1 x n and function fun that takes in a vector of length L and returns a vector of size p x 1.
Is there a MATLAB function that would take in vector v, process each sliding window of length L with function fun, and return a matrix of size p x n (or p x (n-L)).
I am aware this could be achieved with creating a matrix of windowed vectors with im2col and processing each of those, but this takes too much memory for a long vector v.
funsl=@(is) fun(v(is:is+l-1));
cell2mat(arrayfun(funsl,1:length(v)-l+1,'UniformOutput',false))
What I did here is define an anonymous function that, for a fixed v and l and a starting index parameter (is), gets the respective slice of v and applies fun to it.
Then this function is applied, via arrayfun, to all useful values for this starting index. For reasons I myself cannot quite name at the moment, each application returns a p x 1 vector, but arrayfun cannot arrange it into a proper matrix, thus the UniformOutput=false setting and the cell2mat call around it.
Edit: To test this with a function that turns 1-by-5 vectors into 4-by-1 vectors I used
l=5;v=1:12; fun=@(x) cumsum(x(2:end))';
and got this result:
ans =
2 3 4 5 6 7 8 9
5 7 9 11 13 15 17 19
9 12 15 18 21 24 27 30
14 18 22 26 30 34 38 42
Note again that in the definition of funsl v is fixed, To apply this approach to different v you could make another function that takes v (and l, if you do not want to fix this) as parameter(s), contains the two lines above and returns the result of the second one.
The same solution from this other post could apply (with some modifications):
n = 7; L = 3;
v = rand(1,n); %# 1-by-n vector
M = num2cell(v(hankel(1:L,L:n)),1); %# sliding windows of length L
fcn = @(x)[min(x);max(x);sum(x)]; %# function that takes a vector of length L
%# and returns a p-by-1 vector (p=3)
%# apply function to sliding windows, result is a p-by-(n-L+1) matrix
M = cell2mat(cellfun(fcn, M, 'UniformOutput',false));
