The WIND

A newsletter from //Windward Technologies, Inc.

Q2 97

INSIDE THIS ISSUE

• Computer Breezes
• Surface fitting using RBFpack
• What’s new at WTI
• HTML Documentation
• Presentations and Publications
• Products and Services
• Let us hear from you

Computer Breezes

• Microsoft to help with the $650 million overhaul of Dow Jones & Co. Telerate electronic information unit.
• Social Security records now available through the Internet pose few security threats to the individuals who request them, according to SSA officials. Others, however, are less sanguine. You can assess the security yourself by visiting www.ssa.gov
  (oops they just closed the site)
• Pulitzer for online journalism? The Pulitzer Prize Board has appointed a committee to study the possibility of starting a category for online journalism.
• WebTV Networks-- In a move it hopes will spur the merging of personal computers and televisions, Microsoft Corp. will acquire WebTV Networks, a company that sells systems that allow people to surf the Internet over their TVs.
• IRS fears the millennium. The best estimate now is the IRS has to plow through 40 million lines of computer code and 30,000 applications (which depend on two digit year designations) spread across 300 to 500 minicomputers and 100,000 microcomputers, according to Arthur Gross, an assistant IRS commissioner in charge of technology.

Surface fitting using RBFpack

RBFpack is a package (available in C and Fortran as well as a DLL) designed to fit high dimensional surfaces specified by scattered data. We have built in functions which return weighted least squares surface fits as well as support functions which differentiate and evaluate the surface. The underlying technology is based on super-position of Radial Basis Functions which has been gaining ascendancy within both the mathematical approximation community and several practitioners of Neural Network applications. As a historical note it is useful to recall that one of the original applications of radial basis functions was the fitting of geological scattered data.

We are all familiar with the idea of a two dimensional surface which we picture as a portion of a sphere or perhaps a rubber sheet stretched in space. Such a surface may be described (mathematically) by an association of coordinates and a height function h above the coordinate plane, (x, y, h(x,y)), or

(x,y) ® h(x,y)

Since we all exist in a three-dimensional world it is easy to picture applications for such surfaces. For example, an automaker would be interested in describing the shape of the latest model for a numerically controlled manufacturing process.

Less obvious are applications where instead of two independent variables there are 5, 20, or 200 independent variables. Some examples that come to mind are the variables which control a chemical plant. In this case we could have independent variables consisting of temperatures and pressures at certain points and dependent variables consisting of quantities of different outputs. Thus the modeling of the chemical plant is

(x₁, …, x_n) ® h(x₁, …, x_n)

RBFpack is designed to accept such data and produce an approximating surface so that the data can be analyzed and used to make predictions concerning future or optimal settings for running the plant.

In economic modeling there are many situations similar to the above setting. For example, the price of a call (or put) option depends on several factors including those listed in the table below:

Thus the option price, OP, depends on these variables and one can collect data of the type

  (r, s , T, K, S) ® OP

 This would yield data on a 5 dimensional surface which could be approximated by a surface produced by RBFpack and then analyzed.

In this case thousands of data points are available each day as options are bought and sold. The model discussed above does not take into account several potentially important variables such as dividends, stock splits, short term versus long term interest rates, etc. However, these variables could easily be added to the model. The above modeling technique is called phenomenological modeling since we have not resorted to First Principles as, for example, the Black-Sholes model does. Of course, one can (and many do) question the assumptions of such First Principles models.

The C version of RBFpack has been designed to take advantage of all the language benefits of C as well as to prepare for the eventual implementation in C++. Of course, we use structures to store the information in the Least Squares data set as well as structures to store the radial basis function specification. Dynamic memory allocation is used throughout the package, significantly simplifying the calling sequences. We use the fact that C allows us to pass pointers to functions to allow the user to specify a favorite radial function if desired (although the package contains several of the most familiar radial functions already). First and second partial derivatives are available and there is a ready interface to constrained curve fitting using the optimization package GRG2. This allows the user to "model" the surface by specifying physical or other constraints the surface must preserve. For example in the option pricing model it is clear that the surface, OP, should be monotone with respect to T. That is, the value of the option always increases with the expiration date. Mathematically, this means that

¶ OP/¶ T > 0.

Such constraints can be imposed on the surface while using any free parameters to minimize the sum of squares error between the approximating surface and the data. These constraints provide a very powerful means to control surface shape.

What’s New at WTI

WTI or its products can be found at the following Internet addresses:

HTML Documentation

WTI documentation is being converted to HTML format, thus standardizing on this technology and simplifying the presentation to the user. There are several advantages to the HTML format. Documentation can be viewed over the Internet, and can be downloaded and viewed on any user system, PC, Mac, or Unix, with a Web browser. Hyperlinks make it easy to navigate through the document from argument descriptions to examples to references. We are also using frames in our documents. This means that the document is viewed with a small panel on the left with the Table of Contents and a larger panel on the right with the document text. Any section of the document is just a click away. The Curvi User's Manual is available now for viewing or downloading at our Web site. Other product documents will be available soon. Take a look at the new HTML documentation and let us know what you think.

Presentations and Publications

Phil Smith will chair a session at the Center for Approximation Theory Annual Symposium held at Texas A&M on April 25-26. He will also attend the Interface ‘97 meeting in Houston, TX, May 14-17. Later in May, Phil will make a presentation highlighting RBFpack at the IMACS CONFERENCE ON RADIAL BASIS FUNCTIONS May 27-30, 1997, Pacific Grove, CA.

Tom Aird will attend the Spring meeting of the Dean’s Advisory Council, School of Science, Purdue University, in West Lafayette, Indiana, May 9-11.

WTI has agreed to develop and teach a one day course on VisSim / OptimizePRO. VisSim is a simulation package for developing continuous, discrete, multi-rate, and hybrid system models and for performing dynamic simulations. VisSim / OptimizePRO is an add-on product for VisSim developed by WTI specifically for the solution of constrained optimization problems that arise in simulation modeling. This course is designed for engineers and scientists who use VisSim to build and analyze models and want to learn how to use optimization to improve their results by increasing profit, reducing costs, or improving mechanical efficiency while adhering to a set of system constraints. It will cover the blocks that are used to setup an optimization problem (parameterUnknown, globalConstraint, and cost). Examples will be given that show how the blocks are used to build unconstrained models and constrained models. The generalized reduced gradient (GRG) algorithm will be discussed in the context of the GRG2 program used by OptimizePRO. Attendees will learn how to read the report produced by OptimizePRO. Time will be devoted to the setup and solution of attendees’ own optimization problems.

For more information concerning this course please contact:

The Wind is a quarterly newsletter written and edited by Tom Aird and Phil Smith. Please let us know what your interests are and what sort of articles you would like to see. If you would like to contribute an article to the newsletter, please contact us at: WTI@aol.com or mail the sheet on page 4 back to us.

Products and Services

• GRG2 Nonlinear optimization with bounds on variables and nonlinear constraints.
• LSGRG2 Large-scale nonlinear optimization with bounds on variables and nonlinear constraints.
• CURVI Nonlinear optimization with bounds on variables.
• BCLS Linear least squares with bounds on variables and linear constraints.
• RBFpack Multidimensional data fitting by radial basis functions.
• VisSim/OptimizePRO An add-on to VisSim a drag and drop simulation language.
• MATLAB interfaces for GRG2 and BCLS.

ON SITE CONSULTING We find that many of our clients have an explicit need to upgrade or add optimization to their products, but they do not have the time to invest in coming up to speed on the new technologies. At WTI we recognize this need and offer a site visit and consultation on your specific software needs. The cost for this service is $500 a day, plus expenses.

GUARANTEE We are so convinced in the quality of this service and our products in general that if you are not completely satisfied, we offer a 90 day money-back guarantee.

Let us hear from you!

This is a quarterly newsletter of Windward Technologies, Inc. Please let us know what your interests are and what sort of articles you would like to see. Please contact us if you would like to have your name added to our newsletter mailing list or if you would like to contribute an article to the newsletter!

Regards,

Tom Aird
TomAird@aol.com and

Phil Smith
PWSmith@aol.com