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st: Submatrix extraction in Mata


From   "Jann Ben" <ben.jann@soz.gess.ethz.ch>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Submatrix extraction in Mata
Date   Mon, 5 Sep 2005 16:27:06 +0200

I lied. Here's another Mata issue.

In nonparametric statistics such as, e.g., kernel 
density estimation, it is often the case that certain 
computations have to be repeated many times based on, 
say, an observation window sliding over the data. This 
makes nonparametric statistics slow.

I am currently working on kernel density estimation 
for bounded variables. The Mata programs I wrote for 
these purposes work fine and are relatively fast 
(compared to the official -_KDE- which is used by 
Stata's -kdensity- command). However, compared to say, 
-regress-, they are slow.

I think that the programs could be made more efficient 
if there was fast way to select the relevant portion of 
the data (i.e. the data within the current observation 
window) beforehand each computation (especially if large
datasets or complicated estimation functions are used).

Consider a u=unifom(500000,1) vector and suppose you 
want to save as a new vector all elements of u within 
[.5,.8]. The fastest way I could come up with to do 
this is

	. mata:
	------ mata (type end to exit) ---------------------
	: real colvector submat(real colvector I)
	> {
	>         real scalar i, j
	>
	>         j = 0
	>         for (i=1; i<=rows(I); i++) {
	>                 if (I[i]==1) I[++j] = i
	>         }
	>         I = I[|1 \ j|]
	>         return(I)
	> }
	
	: end
	----------------------------------------------------
	r; t=0.03 16:18:57
	
	. mata: u = uniform(500000,1)
	r; t=0.02 16:18:57
	
	. mata: u2 = u[submat((u:>=.5:&u:<=.8))]
	r; t=0.43 16:18:57

which, however, is still slow (compared, e.g., to creating 
a random vector). 

Does any one have an idea how this could be sped up? Can 
this be made any faster at all using Mata commands, or 
would special C-programmed functions be needed?

Thanks,
ben


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