[ Home | GAUSS | GAUSS Engine | GAUSS Apps | 3rd Party Apps | Keywords Index ] Symbolic Tools/Symbolic Tools GE for GAUSS and the GAUSS EngineIntroduction The concept behind Symbolic Tools is to augment the numeric and graphicalcapabilities of the GAUSS Mathematical & Statistical System (TM) and GAUSS Engine (TM) with additional types of mathematical functionality based on symbolic computations. These include:
The computational work is carried out by the Maple kernel using the Open Maple API. Maple is a symbolic mathematics package developed at the University of Waterloo. Symbolic Tools provides for an interface between GAUSS and the Maple Kernel. This interface permits code to be evaluated symbolically in Maple, and the results returned to GAUSS , or to create a GAUSS proc based on Maple's symbolic results. One of the main uses of Symbolic Tools is to enable GAUSS to undertake Automatic Differentiation. Optimization packages, such as Aptech's Maximum Likelihood, Constrained Maximum Likelihood, Optimization, and Nonlinear Equations GAUSS Applications, can use procedures that return the gradient and/or Hessian, instead of doing forward differencing. Thus, as a trivial example, if the function being optimized were Ln(b), then the analytic gradient would be 1/b, and the analytic Hessian -1/b. Symbolic Tools can create compiled procs for the analytic gradient or Hessian of a likelihood, on the fly. The time savings are impressive. Using Monte Carlo simulation of a Tobit model with 2000 observations and 11 parameters, the AD gradient took 10% of the time required for forward differences using gradp - ie. approximately a 10 fold speed improvement. Similar results were also obtained for the Hessian, with the additional advantage that the AD methodology generated much more precise estimates of the gradients and Hessian. Examples:
Requirements
Symbolic Tools is a registered trademarks of Econotron Software, Inc. GAUSS and GAUSS Engine is a trademark of Aptech Systems, Inc. Copyright 1983-2003. All Rights Reserved World-wide. Maple is a registered trademark of Waterloo Maple, Inc. |