Introduction to Mata

Let's see it work

To enter Mata, type mata at Stata’s dot prompt. To exit, type end at Mata’s colon prompt:

. mata

                             
 mata (type end to exit) 
      

: sqrt(-4)

  .

 

: sqrt(-4+0i)

  2i

 

: end

 

Mata supports real and complex numbers, binary and text strings (up to 2,147,483,647 characters long), and, for serious programming problems, even pointers! Mata also supports object–oriented programming, or class programming, with classes, methods, inheritance, constructors and destructors, and more.

Mata uses LAPACK routines from the Intel^® Math Kernel Library (MKL) for its advanced matrix features, such as Cholesky decomposition, LU decomposition, QR decomposition, SV decomposition, eigenvalues and eigenvectors, and solvers and inverters.

Mata supports matrices that are views onto, not copies of, the data. Say you have loaded a dataset of 200,000 observations and 150 variables, and you need a matrix of 80 of those variables in 180,000 of the observations. Rather than requiring 110 megabytes, Mata needs only 640 bytes.

Matrix languages evaluate matrix expressions, such as b=invsym(X'X)*X'y, and Mata is no exception. Because of Mata’s design, however, it is fast enough to work at the element level. Here is Mata’s polynomial solver:

numeric rowvector polysolve(numeric vector y, numeric vector x)
{
     numeric rowvector  res, c, empty
     real scalar        i, j, n

     if (cols(y) != cols(x) | rows(y) != rows(x)) _error(3200)
     if ((n=length(x)) == 0) _error(3200)
     res = (iscomplex(y) | iscomplex(x) ? 0i : 0)
     for (j=1; j<=n; j++) {
         c = (1)
         for (i=1; i<=n; i++) {
             if (i != j) {
                 c = polymult(c, (-x[i],1) :/ (x[j]-x[i]))
             }
         }
         res = polyadd(res, y[j] :* c)
     }
     while (res[cols(res)]==0) res = res[|1,1 \ 1,cols(res)-1|]
     return(res)
}

Much of Mata is written in Mata.