Dismiss
InnovationQ will be updated on Sunday, Oct. 22, from 10am ET - noon. You may experience brief service interruptions during that time.
Browse Prior Art Database

Vectorized Sparse Matrix Triple Product

IP.com Disclosure Number: IPCOM000039463D
Original Publication Date: 1987-Jun-01
Included in the Prior Art Database: 2005-Feb-01
Document File: 2 page(s) / 44K

Publishing Venue

IBM

Related People

Chang, CS: AUTHOR [+4]

Abstract

The disclosed software programs utilize a vector processing environment to efficiently obtain the result of a triple matrix product. The algorithms will operate on any stored program digital computer using floating point arithmetic. To be effective, however, their use should be directed toward systems with a vector processing capability. Given a triple product matrix of the form AL-1 AT, where A is a sparse topological containing only the values 1, -1, or zero, and L-1is a full upper triangular matrix of floating point numbers, a straight- forward evaluation of AL-1 AT will require elements from L-1to be used in a non-sequential manner. This fact prohibits efficient evaluation of the triple matrix product in a vector processing environment.

This text was extracted from a PDF file.
At least one non-text object (such as an image or picture) has been suppressed.
This is the abbreviated version, containing approximately 53% of the total text.

Page 1 of 2

Vectorized Sparse Matrix Triple Product

The disclosed software programs utilize a vector processing environment to efficiently obtain the result of a triple matrix product. The algorithms will operate on any stored program digital computer using floating point arithmetic. To be effective, however, their use should be directed toward systems with a vector processing capability. Given a triple product matrix of the form AL-1 AT, where A is a sparse topological containing only the values 1, -1, or zero, and L-1is a full upper triangular matrix of floating point numbers, a straight- forward evaluation of AL-1 AT will require elements from L-1to be used in a non-sequential manner. This fact prohibits efficient evaluation of the triple matrix product in a vector processing environment. When, however, the terms are evaluated in the following manner, vectorization of most of the operations can be achieved. Working down a column of AT (see Figs. 1 and 2), use the entry (0, 1, -1) to select a full column from L-1 . Add or subtract this column from an "answer" column, and continue until the column in AT has been completed. This completes an "answer" column and terminates the first half of the multiplication. Next, proceed across each row in A and select elements from the "answer" column and either add or subtract them depending on the sign of the elements in A. Once one row of A has been completed, one element of the triple product matrix has been evaluated. Scanning all ro...