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st: Re: Linear indexing of matrices in Mata


From   "Joseph Coveney" <jcoveney@bigplanet.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Re: Linear indexing of matrices in Mata
Date   Sun, 22 Jul 2012 12:13:14 +0900

Joerg Luedicke wrote (excerpted):

. . . So my first question
would be: is my impression correct that there is no linear indexing
for matrices in Mata?

If yes, the second question would be how to best circumvent this?
Consider the following problem: suppose we have two matrices, m1 and
m2 with the same dimensions. Now we want to check a certain condition
in m1 and if true, record the position index. Then we want to select
elements in m2 that are corresponding to the recorded positions. For
example, if we type in R

*--R code--
m1=matrix(c(1,2,3,4), nrow = 2)
m2=matrix(c(5,6,7,8), nrow = 2)
index=which(m1>2)
m2[index]
*-------------

then m1 looks like

     [,1] [,2]
[1,]    1    3
[2,]    2    4

and m2 looks like

     [,1] [,2]
[1,]    5    7
[2,]    6    8

Then, with the which() function we create a vector of integers that
denote the position in the matrix m1 - for which the element is
greater than 2 - by a single number. In this example, these are matrix
positions 3 and 4 (coinciding with the values in that matrix).
Finally, we can use the indices to index elements, as -m2[index]-
yields

[1] 7 8

i.e., the elements of m2 with the linear indices 3 and 4.

So, the basic problem is how to refer to elements of a matrix, based
on a selection of elements in another matrix. The above example
demonstrates how this could be done in R. Any ideas about solutions in
Mata?

--------------------------------------------------------------------------------

I'll try to address your three questions in turn.

I'm not aware of linear indexing for matrixes in Mata.  Others more 
knowledgeable than I could ever hope to be might be able to point to such 
a feature, though.

You would circumvent this by using Mata's -select()- function.

One solution in Mata would be:

    select(vec(m2)', vec(m1 :> 2)')

There are undoubtedly other, more elegant, solutions.  This one is illustrated
below using your two matrices.  It assumes that the corresponding R code returns
only row vectors.  I've incorporated the statement into a rudimentary function
for convenience, but you'd want to add some conformability- and type-checking
for production use.

Joseph Coveney

. version 11.2

. 
. clear *

. set more off

. 
. mata:
------------------------------------------------- mata (type end to exit) ------
: mata set matastrict on

: 
: real rowvector index_which(real matrix Target, real matrix Selector)
>     return(select(vec(Target)', vec(Selector)'))

: 
: M1 = (1, 3 \ 2, 4)

: M2 = (5, 7 \ 6, 8)

: 
: index_which(M2, (M1 :> 2))
       1   2
    +---------+
  1 |  7   8  |
    +---------+

: 
: end
--------------------------------------------------------------------------------
. 
. exit

end of do-file



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