MATA Programming

Stata Interface

• Getting Data from Stata to MATA
  st_nobs(), st_nvar(), st_data(), st_matrix(), st_view()
• Getting Data from MATA to Stata
  st_addvar(), st_store()
• Executing Stata Commands
  stata()

Using MATA Built-In Functions

• Data Generating Functions
  e(), I(), J(), runiform(), rnormal()
• Data Conversion Functions
  rowshape(), colshape(), diag(), diagonal()
  vec(), vech(), lowertriangle(), makesymmetric()
• Basic Matrix Functions
  • Matrix Description
    rows(), cols(), length()
    mean(), variance(), correlation()
  • Matrix Operations
    rowsum(), colsum(), sum(), sort()
    rowmin(), colmin(), min(), rowmax(), colmax(), max()
  • Matrix Computation
    det(), trace(), cond(), rank(), cross()
    cholesky(), lud(), grd(), svd()
    cholsolve(), lusolve(), qrsolve(), svsolve()
    invsym(), cholinv(), luinv()
• Probability Functions
  normal(), normalden(), chi2(), chi2tail(), F(), Fden(), Ftail()
• Calculus Functions
  deriv(), eigensystem(), optimize()

Controlling Execution Flow

• If Statement
  if (exp) ... else ...
• For Loop
  for (exp1; exp2; exp3) ...
• While Loop
  while (exp) ...
• Do-While Loop
  do ... while (exp)

  where exp, exp1, exp2, exp3 must evaluate to real scalars. Statements in ... may be in multiple lines written as

  {

  ...

  }

Example 1

Do you know the accuracy of your computer's numerical calculation? This example addresses this important problem. Suppose e is a known small positive number, and the 5x4 matrix X is defined as follows:

1  1  1  1
e  0  0  0
0  e  0  0
0  0  e  0
0  0  0  e

Verify that the eigenvalues of X'X are 4+e², e², e², and e². How small of the value of e your computer will allow so that X'X can be inverted?

Writing Your Own Functions

• Untyped Function
  For example, a simple function converting temperature degree from Fahrenheit to Centigrade is:
  function ftoc(f) return((f-32)*5/9)

• Typed Function
  It is recommended that a MATA function is typed in terms of two characteristics: its element type (transmorphic, numeric, real, complex, pointer, string) and their corresponding organization type (scalar, vector, rowvector, colvector, matrix). Therefore, the same temperature convertion function is now written as:

  real scalar ftoc(real scalar f) {
      real scalar c
      c=(f-32)*5/9
      return(c)
  }
  

• Creating Stata Command (.ado file)
  See: help m1_ado

Object Code and Library

• Saving MATA Function (Compiled Object Code)
  See: help mata mosave
• Creating MATA Function Library
  See: help mata mlib

Example 2

Write a MATA function to convert one or more quarterly time series into the annual series by taking the average of every four data points.