RBFpack produces a model of a multi-dimensional surface from numerical scattered data arranged in columns. The first n columns represent inputs (independent variables) while the next m columns represent the output (dependent variables). The multi-dimensional surface model produced by RBFpack can be evaluated at points other than the data points to predict outputs for new inputs or it can be searched for maxima.

Below we graphically illustrate the fundamental situation addressed by RBFpack. This particular example involves n independent variables and m dependent variables. RBRpack can support any number of independent and dependent variables.

This is a typical situation in Engineering applications. It is less well appreciated, but none the less true that these relationships exist in many other fields including: Quantitative Analysis, Simulation, Data Mining, Neural Nets, etc. We discuss applications in each of these areas.

• Control - Consider the independent variables to represent the state of an engine and its environment (including temperature, air humidity, current running speed, etc.). The dependent output variables could represent control variables that could be adjusted to economize on fuel or to minimize pollutant output. They might represent fuel/air mixture, fuel flow rate, etc.
   
• Plant Optimization - The independent variables might represent the state of a chemical plant (including amount of input raw materials, temperature, mixing rate, etc.) and the output could represent the output of the m products from this chemical plant. One could use the RBF fit to the data to adjust the plant parameters to optimize the output.

• Insurance - A database of current policy holders includes the coverage purchased and the amount paid out (the independent variables might be the amount of purchased coverage in various areas as well as additional information on the insured person's status). The output variables could be the amount paid out and the profit (this could be negative) each person generated for the company. The RBF surface produced by RBFpack could be used to predict profit on various coverages and to adjust policies to guarantee a given profit.
   
• Sales by Mail - A database of mailings is kept by a company. The success rates for various products are known as well as individual numerical characteristics such as gross income, zip-code, debt, etc. This information could be used to build a surface that would predict success rates for a new mailing list.

• Speed-up simulator -- Most simulators fit the model above. There are inputs and outputs. In order to compute the outputs it may be necessary to solve ODE's and PDE's or to perform some Monte Carlo experiments. One can use RBFpack to produce a model of a given simulation scenario by recording the inputs and outputs for several runs and then fitting the data. This can mean that future simulation runs can be by-passed and the RBF surface can be evaluated instead. This could result in large savings in computer time since one simulation run can be very costly.

• Derivative Pricing - The price of a derivative is dependent on (for a simple model) five numerical quantities including strike price, time to expiration, risk-free interest rate, volatility, price of underlying security. The model in this case has one output (the price of the derivative) and five inputs as described above. The RBF surface constructed by RBFpack could be used to compute the price of a new derivative as well as predicting the rate of increase in the derivative as the underlying security increases in value.

• The model described above is actually the precise situation which Neural Nets address. The data pairs represent the training data. Thus one can use RBFpack to build sophisticated Neural Nets.

• Recently, there has been some interest in solving Partial Differential Equations using RBF surfaces. RBFpack can facilitate this solution process.

RBFpack is available as a DLL and in C source code formats. The DLL version is specially designed for the Windows 95 operating system. The DLL can be used by C programs, by Fortran programs (MS PowerStation Fortran and Digital Visual Fortran), by MATLAB 5, and by any Windows application capable of referencing a DLL. The RBFpack User's Guide describes the C interface and gives examples using C and MATLAB. Contact The MathWorks, Inc. for more information about MATLAB.

The Windows 95 DLL version of RBFpack is available for $1495.

A single user development C source code license for RBFpack only is priced at $1995. The C source code license for RBFpack and LSGRG2 is $6995. The C source code can be compiled and run on Windows and Unix systems.

Our Premier Partners program provides licensing terms and service specially designed to meet the needs of commercial software development organizations.

We offer discounts to universities.

Contact Windward Technologies for information about RBFpack and other WTI products.

View the RBFpack User's Guide. The User's Guide contains examples in C and MATLAB.

Back to the MAXTHIS home page.