Multidimensional Indices of Multiple pages

Hi, I have a matrix of dimensions 5 by 7 by 50 e.g. g1 = rand(5,7,50) I have another matrix of indices for the row and column e.g. [1 3; 4 5; etc] Now I would like to index all the pages at those indices:

My attempt albeit slow:

for page = 2:50

  lg = sub2ind(size(g1), ind(:,1), ind(:,2), page.*ones(length(ind),1),1))

  g1(lg)
end

Could someone explain to me how to do the above without for loop. I think I can follow one of the link below to remove the sub2ind. Thx!

In addition to the following I did look at the doc

http://stackoverflow.com/questions/1146719/accessing-values-using-subscripts-without-using-sub2ind

http://stackoverflow.com/questions/8568548/how-to-access-multidimensional-arrays-in-matlab-with-mixed-index-format

[Sean de Wolski]

+1 well written, well researched question. Welcome to MATLAB Answers!

Answer 1

[Andrei Bobrov]

id12 = [1 3; 4 5]; 
out = g1(bsxfun(@plus,bsxfun(@minus,id12,[0 1])*[1;size(g1,1)],(0:size(g1,3)-1)*prod(size(g1(:,:,1)))));

[Wing]

thx to Geoff, Sean and andrei

[Geoff]

I really need to get my head around this bsxfun. Andrei, you seem to use it for at least 50% of your answers. It's obviously a powerful tool.

[Sean de Wolski]

@Geoff, consider these, figure out how they're working:

A = bsxfun(@times,ones(2,3),reshape(1:5,1,1,5))

B = bsxfun(@plus,1:5,(1:4).')

Then answer this one:

http://www.mathworks.com/matlabcentral/cody/problems/4-make-a-checkerboard-matrix

with bsxfun

Answer 2

[Geoff]

You could use linear indexing if you convert each row/column into a page start index, then take the page range....

g1 = rand(5,7,50);
xy = [1 3; 4 5; 2 1];

% Get the first page index for each xy pair.
start = xy(:,1) + (xy(:,2)-1) * size(g1,1);

% Generate linear index across all pages.
makerange = @(x) x:size(g1,1)*size(g1,2):numel(g1);
indices = cell2mat( arrayfun( @makerange, start, 'UniformOutput', false ) );

% Pull out the pages.  One page per row, corresponding to the rows in xy.
pages = g1(indices);

I'm a MatLab newbie, so there might be clever functions I don't know about that do some of this work for you. That effectively does what you are asking though. =)

[Wing]

thanks but it's slower so I will stick with the for loop and without sub2ind as shown in the stackoverflow link :(

[Geoff]

Bummer. I didn't think that _anything_ was slower than MatLab loops! =)

[Sean de Wolski]

@Geoff, common misperception. Since the advent of the JIT compiler for-loops are often faster than vectorized methods.

Answer 3

[Sean de Wolski]

perhaps I'm not clear but if:

A = bsxfun(@times,ones(5,7),reshape(1:50,1,1,50))  %each slice is its index

and you want to extract all slices at rows 3,4 and cols, 4,5, just use the colon operator on the 3rd dimension

A([3 4],[4 5],:)

And you are correct, sub2ind will likely be slower than a well written for-loop.

[Wing]

Not sure how this would work.

E.g.

g1 = rand(2,3,2)

g1(:,:,1) =

0.4008 0.8510 0.7962

0.9449 0.0088 0.6873

g1(:,:,2) =

0.9097 0.7171 0.0740

0.5371 0.9865 0.3725

indices = [1 3;2 1]

indices =

1 3

2 1

which means that we want to index row 1 column 3 and index row 2 and column 1.

So, getting "all"(initial post it starts from the second slice) the slices at those indices would give:

0.7962, 0.0740

0.9449, 0.5371