Matrix indexed by another matrix in matlab?

Question

I have the following matrices:

A=zeros(2,4);
D=[ 1 2;
    3 4;
    5 6;
    7 8];

v=rand(1,8);

For example:

v= [0.8147    0.9058    0.1270    0.9134    0.6324    0.0975    0.2785    0.5469]

Now when I run A(D)=v, A becomes:

A=[0.8147    0.9058    0.1270    0.9134;
   0.6324    0.0975    0.2785    0.5469]

When I change D entries to another values, I get different configurations of A, for example, if I put:

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

then A becomes:

A=[0.5469    0.2785    0.0975    0.6324;
   0.9134    0.1270    0.9058    0.8147]

Does any one know what this kind of indexing is?

It's linear indexing: mathworks.com/help/matlab/math/matrix-indexing.html#f1-85511 — Dan
– Dan, Commented May 3, 2013 at 13:15

Dan · Accepted Answer · 2013-05-03 13:54:32Z

So to make it clearer lets redefine your v as

v = 10:10:80

(i.e. v = [10 20 30 40 50 60 70 80];)

Now when

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

then

A(D)=v

    A =

    80    70    60    50
    40    30    20    10

Lets look at how this works. So firstly when you index A by D, D gets flattened so A(D) = v is the same as A(D(:)) = v (test it!) and

So for breaking it down element by element we're going A(D(1)) = v(1) which after substituting for D(1) and v(1) is A(8) = 10, hence the last element is 10. Lets look a few elements further. A(D(4)) = v(4) become A(2) = 40. but which element is A(2)? Well linear indexing counts down the rows first (column major ordering) i.e.

A(1) == A(1,1)
A(2) == A(2,1)
A(3) == A(1,2)
A(4) == A(2,2)
A(5) == A(1,3)
A(6) == A(2,3)
etc...

So A(2) is in the (2,1) position etc...

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