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Improved Test Coverage via Orthogonal Matrices

IP.com Disclosure Number: IPCOM000113368D
Original Publication Date: 1994-Aug-01
Included in the Prior Art Database: 2005-Mar-27
Document File: 4 page(s) / 86K

Publishing Venue

IBM

Related People

Barrett, KL: AUTHOR [+4]

Abstract

This disclosure presents a method of generating a quality sample of IVGEN testcases from the vast domain of potential testcases using the properties of an orthogonal matrix.

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Improved Test Coverage via Orthogonal Matrices

      This disclosure presents a method of generating a quality
sample of IVGEN testcases from the vast domain of potential testcases
using the properties of an orthogonal matrix.

      IVGEN creates custom testcases by varying event (or function)
arguments over specific, valid intervals.  Thus, events with large
intervals per argument and with large numbers of arguments require a
large number of testcases to cover all possible combinations.

      The properties of an orthogonal matrix are the following: each
column of a binary orthogonal matrix has an equal number of 1's and
0's; two consecutive columns have an equal distribution of the 4
binary values which can be represented by the two columns (namely,
00, 01, 10 and 11); any number of consecutive columns have an equal
distribution of the binary values that can be represented by the
columns.

Fig. 1 gives examples of 8x7 and 16x15 orthogonal matrices.
 1 1 1 0 0 1 0           1 1 1 1 0 0 0 1 0 0 1 1 0 1 0
 0 1 1 1 0 0 1           0 1 1 1 1 0 0 0 1 0 0 1 1 0 1
 1 0 1 1 1 0 0           1 0 1 1 1 1 0 0 0 1 0 0 1 1 0
 0 1 0 1 1 1 0           0 1 0 1 1 1 1 0 0 0 1 0 0 1 1
 0 0 1 0 1 1 1           1 0 1 0 1 1 1 1 0 0 0 1 0 0 1
 1 0 0 1 0 1 1           1 1 0 1 0 1 1 1 1 0 0 0 1 0 0
 1 1 0 0 1 0 1           0 1 1 0 1 0 1 1 1 1 0 0 0 1 0
 0 0 0 0 0 0 0           0 0 1 1 0 1 0 1 1 1 1 0 0 0 1
                         1 0 0 1 1 0 1 0 1 1 1 1 0 0 0
                         0 1 0 0 1 1 0 1 0 1 1 1 1 0 0
                         0 0 1 0 0 1 1 0 1 0 1 1 1 1 0
                         0 0 0 1 0 0 1 1 0 1 0 1 1 1 1
                         1 0 0 0 1 0 0 1 1 0 1 0 1 1 1
                         1 1 0 0 0 1 0 0 1 1 0 1 0 1 1
                         1 1 1 0 0 0 1 0 0 1 1 0 1 0 1
                         0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

        Fig. 1.  8x7 and 16x15 Orthogonal Matrices

      The purpose of this technique is to generate a small quantity
of quality random testcases.  It is time-consuming and costly to
exhaustively create testcases which use all combinations of event
arguments.  It is generally sufficient to create enough testcases to
test each value of an argument at least once.  The distribution
properties of an orthogonal matrix satisfy this requirement.
Furthermore, by using orthogonal matrices, testcases are created
programmatically and efficiently.  Fig. 2 shows a general schematic
of the orthogonal matrix concept.
                         -----  Function  ----
                        |      Arguments     |
                        |              ...