Subset of an array with a moving window

I have the following code for computing structure functions. I have provided examples of "ULs" and "UTs" merely for simplicity.

ULs = rand(1,145); % called in from function
UTs = rand(1,145); % called in from function
nrmax = 145;       % called in from function, I just happen to be using 145

for nr = 1:nrmax
    Nts = numel(ULs);          % number of elements
    Umat_L = nan(Nts-nr,nr+1); % must be NaN, so zeros() won't work
    Umat_T = nan(Nts-nr,nr+1); % must be NaN, so zeros() won't work  
    
    for i = 1:(Nts-nr)            % this is
        Umat_L(i,:)=ULs(i:i+nr);  % the for loop
        Umat_T(i,:)=UTs(i:i+nr);  % I want to remove
    end
end

The nested loop thus takes subsets ULs(1:1+nr), then ULs(2:2+nr), ULs(17:17+nr), etc. Is it possible to replicate this subsetting process without using a loop?

It would improve my code run time if I could remove the nested "for i = 1:(Nts-nr)". However, as I see it, there is no way around this because of the nature of the moving window. I tried the following substitution, but it didn't work.

i = (1:Nts-nr);
inr = i + nr;
Umat_L(i,:) = ULs(i:inr);
Umat_T(i,:) = UTs(i:inr);

[Rik]

Many moving window operations can be replaced by movmean and other mov* functions, or by convolutions. The image processing toolbox also contains several useful functions.

Is this code representative of the result you actually want, or is there a further step in calculation?

[Alex Nickerson]

Well, as can be seen in the code, there is no moving mean. I don't have access to the Image Processing Toolbox. I just need to be able to get these variable subsets of the code. I will add some details to the original question to further clarify.

Answer 1

[Rik]

The code below relies on implicit expansion to create an index array, which replicates the results from the inner for-loop. Since your code overwrites the results every iteration, you can also have a substantial speed increase by only doing the last one.

nrmax = 145;       % called in from function, I just happen to be using 145
ULs = rand(1,nrmax); % called in from function
UTs = rand(1,nrmax); % called in from function

%tic,toc is only an approximate, use timeit for real performance testing
tic,[Umat_L1,Umat_T1]=fun_original(nrmax,ULs,UTs);toc

Elapsed time is 1.689398 seconds.

tic,[Umat_L2,Umat_T2]=fun_unlooped(nrmax,ULs,UTs);toc

Elapsed time is 0.994556 seconds.

if ~isequal(Umat_L1,Umat_L2) || ~isequal(Umat_T1,Umat_T2)
    error('results don''t match')
else
    disp('everything OK')
end

everything OK

function [Umat_L,Umat_T]=fun_original(nrmax,ULs,UTs)
for slowdown=1:100
for nr = 1:nrmax
    Nts = numel(ULs);          % number of elements
    Umat_L = nan(Nts-nr,nr+1); % must be NaN, so zeros() won't work
    Umat_T = nan(Nts-nr,nr+1); % must be NaN, so zeros() won't work  
    
    for i = 1:(Nts-nr)            % this is
        Umat_L(i,:)=ULs(i:i+nr);  % the for loop
        Umat_T(i,:)=UTs(i:i+nr);  % I want to remove
    end
end
end
end
function [Umat_L,Umat_T]=fun_unlooped(nrmax,ULs,UTs)
for slowdown=1:100
for nr = 1:nrmax
    Nts = numel(ULs);          % number of elements
    
    ind=( 0:nr ) + ( 1:(Nts-nr) ).';
    Umat_L=ULs(ind);
    Umat_T=UTs(ind);
end
end
end

[Alex Nickerson]

I have more lines of code that go far beyond the nested loop... I just didn't include them here to save space. This code did exactly what I needed, @Rik, and it cut my code run time (the sample on which I tested it) in half. Thank you for your help.