indexing nearest number problem

Hi all, I'm hoping for some help on this problem.

I have a matrix A 384x320. every point represents a depth. I also have a vector b 1x50, which is depths from 0-500.

I want to find the index of b, that corresponds to the nearest depth within matrix A.

For example: A[1,1] = 256 b [1:10:500]

So the corresponding nearest index on b that is closest to 256 of A, would be index 26 (or b 251).

I've tried a few loops, but nothing working...this is the closest I can come, but not correct.

for i=1:384 for j=1:320 x=nearest(b<=A(i,j)); end end

Thank you in advance for your time! Corinne

Answer 1

[Jan]

Get the index for a single element of A:

A = rand(384, 320);
b = rand(1, 50);
[absDiff, Index] = min(abs(A(1, 1) - b));

Get the index for all elements at once: EDITED: Get MIN over 2nd dimension - thanks Matt Fig!

[absDiff, Index] = min(abs(bsxfun(@minus, A(:), b)), [], 2);
Index = reshape(Index, size(A));

If b is equidistant the calculation can be made much more efficient by scaling the values of A and a simple ROUND.

[Corinne]

Thanks Jan! works great!

I took the first part and ran it in a loop to go through all the elements. I know not the fastest way, but a little easier to understand at first.

When I run through all the elements above, Index only ends up being 1x50...

[Matt Fig]

If I am not mistaken, Jan simply made a dimensional error.

[absDiff, Index] = min(abs(bsxfun(@minus, A(:), b)),[],2);

Index = reshape(Index, size(A));

[Corinne]

Thanks Matt. That fixed the problem.

Answer 2

[Teja Muppirala]

For this problem, I suspect HISTC may be a better (faster and more memory efficient) alternative to BSXFUN.

A = rand(384,320);
b = sort(rand(1,50));

tic
[~,Index1] = histc(A,[-Inf interp1(1:numel(b),b,0.5 + (1:numel(b)-1)) Inf]);
toc

tic
[absDiff, Index2] = min(abs(bsxfun(@minus,A(:),b)),[],2);
Index2 = reshape(Index2,size(A));
toc

isequal(Index1,Index2)

For larger data, BSXFUN will give poor performance or run out of memory, like this:

A = rand(1000,1000);
b = sort(rand(1,10000));

tic
[~,Index1] = histc(A,[-Inf interp1(1:numel(b),b,0.5 + (1:numel(b)-1)) Inf]);
toc

tic
[absDiff, Index2] = min(abs(bsxfun(@minus,A(:),b)),[],2);
Index2 = reshape(Index2,size(A));
toc

[Jan]

What about: interp1(b, 1:numel(b), A, 'nearest');

But unfortunately Matlab's INTERP1 is not implemented efficiently, in opposite to HISTC.