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# how to index a matrix by using a index matrix that has same size?

Asked by Piment on 30 Mar 2013

I have a m by n data matrix and a m by n index matrix which rearranges the order of the n elements in each row of the data matrix. How can I get an indexed data matrix without using loop? Thanks.

## 1 Comment

Ahmed A. Selman on 30 Mar 2013

But matrices already are indexed arrays or vectors... right?

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Answer by Walter Roberson on 30 Mar 2013
Edited by Walter Roberson on 30 Mar 2013

Use sub2ind()

Cedric Wannaz on 30 Mar 2013

typo: sub2ind

To illustrate Walter's answer, if M is the matrix of data and I the matrix of column indices, you can do

``` rId = (1:size(M,1)).' * ones(1,size(M,2)) ;    % Matrix of row indices.
M_reordered = M(sub2ind(size(M), rId, I)) ;```
Walter Roberson on 30 Mar 2013

Oops, yes, I was concentrating on not putting an "s" in and so left out the "2" :(

Cedric Wannaz on 30 Mar 2013

I thought that you had forgotten the "s" and I ended up realizing that it was a "2" ;-)

Answer by Anand on 30 Mar 2013

If A is your original matrix and idx is the matrix of indices, you can use logical indexing: A(idx).

Here's an example:

```>> A = rand(3)
```
```A =
```
```      0.8147    0.9134    0.2785
0.9058    0.6324    0.5469
0.1270    0.0975    0.9575```
```>> idx = [9 8 7;6 5 4;3 2 1]
```
```idx =
```
```       9     8     7
6     5     4
3     2     1```
```>> A(idx)
```
```ans =
```
```      0.9575    0.5469    0.2785
0.0975    0.6324    0.9134
0.1270    0.9058    0.8147```

## 1 Comment

Cedric Wannaz on 30 Mar 2013

This is linear indexing actually; the idx matrix that you defined is essentially what we get after calling sub2ind() with a third arg that is a matrix of column indices for each row (different from linear index).

Answer by Piment on 30 Mar 2013
Edited by Piment on 30 Mar 2013

to be more specific, it's something like(it's actually 300 by 5500 in my case):

A =

```    0.9649    0.4854    0.9157
0.1576    0.8003    0.7922
0.9706    0.1419    0.9595
0.9572    0.4218    0.6557```

idx =

```     1     3     2
3     1     2
2     1     3
3     2     1```