Converting a matlab matrix to a vector

Question

I want to get a vector of elements of a Matlab matrix at predefined locations. For example, I have the following

>> i = [1,2,3];
>> j = [1,3,4];
>> A = [1,2,3,4; 5,6,7,8; 9,10,11,12; 13,14,15,16]

A =

     1     2     3     4
     5     6     7     8
     9    10    11    12
    13    14    15    16

I want a vector that will give me the values of A at the locations correspongin to i,j. I tried

A(i,j)

ans =

     1     3     4
     5     7     8
     9    11    12

but this is not what I wanted. I want to get the following

>> [A(i(1),j(1)); A(i(2),j(2));A(i(3),j(3))]

ans =

     1
     7
    12

What is the matlab syntax for that? Please, avoid suggesting for loops or anything that is not in a vectorized form, as I need this to be done fast. Hopefully there will be some built-in function.

Answer 1

For now I'm using this:

>> diag(A(i,j))

ans =

     1
     7
    12

Answer 2

A(sub2ind(size(A),i,j))

If you really crave speed, you might try making your own copy of sub2ind.m that strips out all the input-checking that that function does.

Answer 3

to get it in the fastest way, use linear indexing:

A((j-1)*size(A,1)+i)

remember that MATLAB uses a column-major order.

Answer 4

To understand how to do this, it is best to understand how matlab stores its arrays. In the matrix:

i = [1,2,3];
j = [1,3,4];
A = [1,2,3,4; 5,6,7,8; 9,10,11,12; 13,14,15,16]

matlab stores the elements going DOWN the columns. So they actually reside in memory in the order:

{1 5 9 13 2 6 10 14 3 7 11 15 4 8 12 16}

You can actually index a 2-d array using a SINGLE index. This is why the sub2ind trick works. Since the elements that you want to get are the 1st, 10th and 15th elements, as stored in a column-wise ordering,

singleIndex = [1 10 15];
A(singleIndex)
ans =
     1     7    12

To confirm that sub2ind gave that index list, try it...

ind = sub2ind([4 4],i,j)
ind =
     1    10    15