GAMS and HotGAMS

GAMS, the Guide to Available Mathematical Software, is a cross-index and virtual repository of mathematical and statistical software useful in science and engineering [2]. The majority of software indexed by GAMS represents subprograms for mathematical problems which commonly occur in computational science and engineering, such as solution of systems of linear algebraic equations, computing matrix eigenvalues, solving nonlinear systems of differential equations, finding minima of nonlinear functions of several variables, evaluating the special functions of applied mathematics, and performing nonlinear regression. All cataloged problem-solving software modules, of which there are over 10,000, are assigned one or more problem classifications from the GAMS 736-node tree-structured taxonomy of mathematical and statistical problems. Users can browse through modules in any given problem class. To find an appropriate class, one can utilize the taxonomy as a decision tree, or enter keywords which are then mapped to problem classes. Search filters can be declared which allow users to specify preferences such as computing precision or programming language. In addition, users can browse through all modules in a given package, all modules with a given name, or all modules with user-supplied keywords in their abstracts.

Classification systems have long been used to give structure to large bodies of information. A well-formulated system can improve understanding of the information as well as ease access to it, thus making the information more useful. To be effective, a software classification system must have the following properties:

• Problem-orientation

  It must classify the problems which can be solved by computer software. Other orientations, such as classification by algorithm or classification by software package, are of less interest to end users.

• Variable-level tree structure

  A tree structure is the most natural for a classification system. Allowing arbitrary levels of refinement permits the system to adapt to both mature and young subject areas. In young subject areas little software is available, and hence little refinement is necessary. In mature areas where much software is available, increased refinement is necessary to distinguish among the choices.

The concept of filters helps users narrow down the number of desired software modules. Partitioning more than 10000 problem-solving software modules using a 736-node taxonomy necessarily leads to classes populated by a large number of modules. Differentiating among modules in a single class can then be quite tedious. Filters allow the user to specify additional preferences in a number of areas: language (e.g., Fortran, C), precision (e.g., single, double, multiple), access (e.g., free, proprietary), package, and repository. When presenting the user with modules in a given class, GAMS screen out those that do not satisfy the current set of filters.

Two interfaces to GAMS are available: an HTTP gateway and a Java-powered Web client. The native gams (command-line) and xgams (X11) client programs are still available for downloading from math.nist.gov but are obsolete and are being phased out. Although Web browsers provide a universal client interface, implementing sophisticated user actions is often awkward and sometimes impossible. For example, the xgams client requested information from the GAMS server about existing query filters and their possible values on startup. xgams could then present these to the user on demand, without any additional server interaction. By setting these filters, the user provided a profile that xgams used to qualify each subsequent query. Because implementing a persistent user profile in the context of HTTP would be at best awkward and inefficient, GAMS filters have not been implemented in the HTTP gateway.

The functionality that was lost in moving from the xgams client to a Web interface via the HTTP gateway has been regained through the use of Java, and additional functionality has been added. HotGAMS is a Java-powered GAMS client . Taking advantage of Java allows us to improve interactivity in conducting searches and exploring the problem hierarchy. Currently two version of HotGAMS are operational. They both require a Java enabled browser. They differ essentially in how they present the main interaction window, and in where the referenced URLs (e.g., for documentation, subroutine sources, etc.) are displayed in the browser. The HotGAMS version appears on its own Web page and displays referenced URLs on the ``next'' page. HotGAMS in a Frame is a compact HotGAMS that appears within a Netscape Frame, with referenced URLs displayed in a separate frame in the same window. The frame version allows the user to select a sequence of URLs while keeping the HotGAMS applet visible and operational. With either version of HotGAMS, you may specify preferences (i.e., filters) in advance about the software you're interested in, such as the source language or numerical precision. You may also refine your selections after the fact to reduce the set of apparently appropriate modules to the truly relevant ones.

The HotGAMS applet itself consists of a set of tab cards across the top which provide ways of selecting or manipulating a set of software modules which are listed in the lower half of the applet. Clicking the tab selects the associated card. The following describes the functioning of the various cards.

• Help Card. The Help Card displays a welcome message and a set of buttons linking you to various documents about the Gams project and to the help text.
• Classes Card. This card shows the Gams Problem Classification Hierarchy. A Class corresponds to a general class of mathematical problems. Clicking the mouse on a class opens it, revealing a set of software modules or the class's subclasses, or both. Clicking the class again will close it, hiding its parts. The subclasses represent more specific problems. Thus the hierarchy can be used as a decision tree, to find the most specific class that describes the problem you want to solve. The modules set represents the set of modules which solve problems of this class. Opening the set gets the modules and displays them in the Modules panel at lower half of the applet, where you may then examine and/or download them.
• Packages Card This card shows all software Packages known to the Gams server. A package is a collection, commercial or otherwise, of related software modules. Clicking a package opens it to reveal a module set (as in the Classes card) and a set of documents relating to the package.
• Search Card. The search card allows you to search for Classes, Packages or Modules that match a given name. There is also an apropos function to find problem classes. This search results in a list of phrases in the index which match the given keyword, along with the class or classes appropriate to those phrases. Open the class corresponding to the phrase closest to your intended meaning to view that class in the Classes card. Other suggested keywords may also be shown; opening them performs a recursive apropos. The Digest button displays the search information indexed by class, instead of by keyword.
• Preferences Card. The preferences card allows you to specify preferences in using HotGAMS. It provides a couple of switches to control the display, and it provides a set of global filters to restrict the set of modules shown.
• Refine Card. This card allows you to refine a set of modules, once they have been selected from one of the other cards. Currently, the user interface is much the same as for the filters in the Preferences card, but the only attribute values shown are those in the currently selected set of modules (those passing global preferences, if any). This can be useful when a search has generated a list of too many modules; It shows you what attributes differentiate the modules, and by selecting desirable properties you may reduce the set to a more manageable size. In further research, we intend to explore including additional problem-dependent `facets' which will further distinguish modules from one another. An example would be the type of boundary conditions on a differential equation solver.

The next step for systems such as GAMS is to provide expert-level advice on software selection. We are particularly interested in the situation where many similar, but not identical, pieces of software appear to meet the user's criteria. We are focusing on extensions to the filtering mechanism that support both simple knowledge representations and effective user interactions [1]. This issue of refining the search will be the subject of further research, with HotGAMS serving as the testbed.