Clear Filters
Clear Filters

Reduce dimensionality using indices

3 views (last 30 days)
Hi all.
I have what I tink should be a fairly simple question but I just can't work it out. In one of my scripts I have a three-dimensional array A like this:
A(:,:,1) =
2 4 8
5 6 3
10 3 6
A(:,:,2) =
7 6 3
9 2 9
10 2 3
A(:,:,3) =
9 4 7
3 2 5
10 3 4
I also have a 2D matrix d which looks sth like this:
d =
1 2 3
1 1 3
2 1 1
Now, what I want to reduce A to two dimensions using the third dimension elements indicated by d. The result should be:
AA =
2 6 7
5 6 5
10 3 6
Surely there's a clever way to do this without loops? I fiddled around with a combination of meshgrid and d but that got ugly really quickly...
EDIT : I should have made clear that this is just an example and I don't necessarily know the dimensions of A. It will always be true that
size(A,1) == size(d,1)
size(A,2) == size(d,2)
but A may be 5x5x13.
Thanks so much for your help.

Accepted Answer

Jos (10584)
Jos (10584) on 28 May 2014
Convert sub indices into linear indices:
% some data
A = ceil(10*rand(3,4,3)) % A has an arbitrary size
d = ceil(size(A,3)*rand(size(A,1),size(A,2))) % d is the subindex in the 3rd dimension
% engine
Nrc = size(d) ;
[r,c] = ndgrid(1:Nrc(1), 1:Nrc(2)) ; %r,c, specify the subindices in the 1st and 2nd dimension
ix = sub2ind(size(A),r, c, d) % convert to linear indices
B = A(ix) % retrieve from A
% check
x = 2 ; y = 3 ;
A(x,y,d(x,y)) == B(x,y)

More Answers (3)

George Papazafeiropoulos
George Papazafeiropoulos on 28 May 2014
This is an alternative solution which does not contain external functions, thanks to Jos!
% initial data
A=ceil(10*rand(3,4,3))
d=ceil(size(A,3)*rand(size(A,1),size(A,2)))
% engine
dim1=size(A,1);
dim2=size(A,2);
linind=(1:dim1*dim2)';
linind=reshape(linind,dim1,dim2);
modind=linind+(d-1)*dim1*dim2;
AA=A(modind);
% check
x=2;
y=1;
A(x,y,d(x,y)) == AA(x,y)
Thanks Jos!

George Papazafeiropoulos
George Papazafeiropoulos on 28 May 2014
After specifying A...
d=[1 2 3;
1 1 3;
2 1 1];
B=zeros(3,3,3);
B(:,:,1)=(d==1);
B(:,:,2)=2*(d==2);
B(:,:,3)=3*(d==3);
AA=sum(A.*B,3)
  1 Comment
fromLondon
fromLondon on 28 May 2014
Hi.
Thanks for the quick reply. I like the solution but I should have made clear that I don't necessarily know the size of A. I will change the question accordingly. My bad.

Sign in to comment.


fromLondon
fromLondon on 28 May 2014
Perfect. Thank you both! :-)

Categories

Find more on Cell Arrays in Help Center and File Exchange

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!