Houses, windows and DOHR's

Abstract

Anyone who buys a house can appreciate the complexity of a mortgage. Mortgage analysis requires not only significant computations, but also vast quantities of input and output. The interface between APL and Windows can provide a link between the input and the calculations; however, display of the output remains a problem. Mortgage data are inherently multi-dimensional, resulting in high-rank arrays. The dimensions involve individual mortgages or bond classes, and various prepayment and default scenarios, time periods, and cash flows.Although higher rank arrays can be difficult to visualize and interpret, a matrix can be displayed quite easily as an HTML table with row and column headers identifying the data. In a GUI, it can be displayed as a grid object. A rank-3 array can be displayed as a series of HTML tables each linked from a table of contents at the beginning of the document; as a GUI, it can be displayed as a tab control, each tab containing a grid object.APL has many functions to handle high-rank arrays, e.g. dyadic transpose, indexing, and the reduction operator. Descriptive Objects of High Rank (DOHR's) are nested arrays containing built-in captions, named axes, and named indexes. Certain fundamental operations can be performed on these objects to produce easily readable output. These include selection, summary, orientation and annexation. These fundamental operations are based on upon the following APL concepts: reduction--the removal of an axis, compression--the removal of one or more indexes, transpose--the rearrangement of axes, and catenation/lamination--combining objects along an axis. Most functions that apply to DOHR's can be built upon these fundamental operations.