GAUSS Programming

Creating and Editing a GAUSS Program

File I/O and Data Transformation

GAUSS Built-In Functions

• Data Generating Functions:
  ones, zeros, eye, seqa, seqm, rndu, rndn
• Data Conversion Functions:
  reshape, selif, delif, vec, vech, xpnd, submat, diag, diagrv
• Basic Matrix Functions:
  • Matrix Description:
    rows, cols, maxc, minc, meanc, median, stdc
  • Matrix Operations:
    sumc, cumsumc, prodc, cumprodc, sortc, sorthc, sortind
  • Matrix Computation:
    det, inv, invpd, solpd, vcx, corrx, cond, rank, eig,eigh
• Probability and Statistical Functions:
  pdfn, cdfn, cdftc, cdffc, cdfchic, dstat, ols
• Calculus Functions:
  gradp, hessp, intsimp, linsolve, eqsolve, sqpsolve

Controlling Execution Flow

• If Statement
  if; then; else; elseif; endif;
• For Loop
  for i (start,stop,step); ... endfor;
• Do Loop
  do while ... endo;
  do until ... endo;

Example: 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? (Program).

Writing Your Own Functions

• Single Line Function
  fn fn_name(args) = code_for_function;
• Procedure
  proc [[(nrets)=]] proc_name(arg_list);
  local list of local variables;
  ... statements in the body of procedure;
  retp(ret_list);
  endp;

Example: Write a single-line GAUSS function to convert a quarterly time series into the annual series by taking the average of every four data points. How you extend the single-line version of time series conversion function to a multi-line procedure so that it can handle the conversion of more than one time series? (Program).

Library and Package

• Publication Quality Graphics (PQG) Library
• Commercial Packages: CML, CO, FANPAC, etc.

Example: Using GAUSS to present and solve the following functions:

1. f(x) = ln(x) - x²
   Hint: The maximal of f(x) is found at x = Ö½ or 0.707. (Program).

2. g(x) = (x₁² + x₂ - 11)² + (x₁ + x₂² -7)²
   Hint: There are four minima: (3, 2), (3.5844, -1.8481), (-3.7793, -3.2832), (-2.8051, 3.1313). (Program).