Methods for ascertaining dimensional redundancies in mathematical functions related to electronic phenomena and for removal of redundancies are presented. Two computer programs, one to determine a complete B-matrix and the other to optimize the matrix, are discussed. Three subroutines are analyzed

Herskowitz, G. J.

English

NASA Technical Reports Server

October 1972	 B72-10656 
.
NASA TECH BRIEF 
NASA Headquarters 
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be directed to the Technology Utilization Office, NASA, Code KT, Washington, D.C. 20546. 
Analytic Procedures for Determining Dimensional

Redundancies in Electronic Devices 
The problem: 
Many modern electronic devices and their associated 
physical phenomena are extremely complex. Although 
there exists literature containing functions describing 
these phenomena, the functions require complex calcu-
lations to determine certain characteristic variables and 
constants. 
The solution: 
Analytic procedures have been developed which ascer-
tain dimensional redundancies in the mathematical func-
tions, describe the electronic phenomena and devices, and 
systematically remove them. These procedures have been 
compiled in computer program routines. Two main 
computer programs have been developed: the first deter-
mines a complete B-matrix and the second optimizes the 
matrix. 
How it's done: 
A dimensional matrix is formed by displaying the 
dimensions of the variables in a tabular arrangement, with 
the entries of the matrix determined by the exponent to 
which the dimension of the variable is raised. 
The first main program forms the complete B-matrix 
from the dimension matrix. The input consists of the 
order of the dimension matrix and its elements. A feature 
of this program is that it is possible to specify the 
variables, in a dimension matrix, which will form dimen-
sionless products. 
There are three subroutines to the main program. 
(a) The first looks for common factors in the column 
vectors of the B-matrix and removes them; 
(b) the second transposes the dimension matrix; and 
(c) the third row-reduces the matrix. 
The second main program for optimizing the B-matrix 
includes seven subroutines. The input consists of the 
complete B-matrix, obtained from the first main program, 
and the output includes all optimal B-vectors with the
sum of the absolute value of the elements and the number 
of zero elements. 
The subroutines do the following: 
(a) read in complete B-matrix; 
(b) examine whether matrices of rank N-i (where N is 
the number of columns of the complete B-matrix) 
could be obtained by deleting a finite number of rows 
from the complete B-matrix; 
(c) reduce the matrix to a canonical form, and the 
number of rows having zeroes is counted to deter-
mine the rank of a matrix; 
(d) calculate and store the associated B-vectors; 
(e) divide each element of the associated B-vectors by the 
highest common factor; 
(f) determine the sum of the absolute value of the 
elements and the number of zero elements in the 
optimal B-vectors; and 
(g) examine each associated B-vector for a common 
factor (if a common factor exists it is removed). 
These programs, written in FORTRAN IV, are listed 
and available for use. 
Note: 
Requests for further information may be directed to: 
Technology Utilization Officer 
NASA Headquarters 
Code KT 
Washington, D. C. 20546 
Reference: TSP72-10656 
Source: Gerald J. Herskowitz of
Stevens Institute of Technology
under contract to
NASA Headquarters
(HQN- 10709) 
Category 09,01 
This document was prepared under the sponsorship of the National 
Aeronautics and Space Administration. Neither the United States 
Government nor any person acting on behalf of the United States
Government assumes any liability resulting from the use of the 
information contained in this document, or warrants that such use 
will be free from privately owned rights.
https://ntrs.nasa.gov/search.jsp?R=19720000655 2020-03-17T03:41:18+00:00Z


Analytic procedures for determining dimensional redundancies in electronic devices

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