How to Obtain the Indeces of the Minimum Value of Each Row in a Matrix and then Apply These Indeces to a New Matrix of the Same Size

Say I have the following matrices:

x = [3 4; 1 3; 2 5; 7 4];
y = [1 2; 3 4; 5 6; 7 8];

If I want the minimum values by row in x, I can use

[M I] = min(x,[],2)

to obtain

M = [3; 1; 2; 4]
I = [1; 1; 1; 2]

but I am not sure how to apply I to the y matrix to obtain

y = [1; 3; 5; 8]

I have found that

diag(y(I,:))

works, but it is not efficient and will not work on the matrix that I need to apply this to, which is size(47*10^6,3). I also tried to use the find command, but I was unable to get that to work either.

Answer 1

[Sean de Wolski]

Use sub2ind to build a linear index and extract with this.

The rows will be (1:size(y,1)) and the columns will be your I

doc sub2ind

Something like this (not tested)

idx = sub2ind(size(y),(1:size(y,1))',I);
ymn = y(idx)

[Shawn]

In re-writing the size of the row, you wrote a "2" instead of "1", but it works once I change that. The code I use is:

ynew = y(sub2ind(size(x),(1:size(x,1))',I))

Thanks for the help!

Answer 2

[Matt J]

   [m,n]=size(x);

    mask=sparse(1:m,  I,true,m,n);

    ymin=sum(mask.*y,2)

[Shawn]

This is pretty close to what I want, but it returns a sparse logical. Is it possible to make this return just the vector? I'm also confused by that sparse command. The documentation wasn't even helpful. What is meant by true?

[Matt J]

This is pretty close to what I want, but it returns a sparse logical.

I think you mean a sparse double, not a sparse logical

    >> whos ymin
      Name      Size            Bytes  Class     Attributes

      ymin      4x1                80  double    sparse

Is it possible to make this return just the vector?

The result you see is a perfectly valid vector, but if you want to see it in the full form that you are used to,

      >> ymin=full(ymin)

    ymin =

         1
         3
         5
         8

What is meant by true?

true() is a built in MATLAB command that returns a scalar or matrix of true logical values, see

http://www.mathworks.com/help/matlab/ref/true.html

[Shawn]

Ah, yes, I meant sparse double. mask was the sparse logical. Simplifying it down to one line, I used:

ymin=full(sum(sparse(1:size(x,1), I, true, size(x,1), size(x,2)).*y,2))

I must say that this was a really interesting and out of the box solution. I compared the 2 solutions given and found the above nearly 4x faster for random 100,000x2 matrices, which is very important to me since my matrices are very large, but I really appreciate your help and am very impressed by this method.