QCApro: implicantMatrix – R documentation

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implicantMatrix

Create Implicant Matrices

Description

This function creates implicant matrices. An implicant matrix consists of all truth table minterms and their subsets, including the empty set.

Usage

implicantMatrix(noflevels, raw = FALSE, arrange = FALSE)

Arguments

`noflevels`	The number of levels for each exogenous factor.
`raw`	Logical, return implicant matrix with indicator for elimination.
`arrange`	Logical, arrange for easier visual inspection.

Details

An implicant matrix consists of all minterms and their subsets, including the empty set (Dusa 2007, 2010; Thiem and Dusa 2015). The number of implicants q is given by q = ∏_{j = 1}^{k}{(p_{j} + 1)}, where p_{j} is the number of levels for factor j and k is the total number of exogenous factors.

If raw = TRUE, the indicator for elimination (-1) is used.

Value

A matrix with ∏_{j = 1}^{k}{(p_{j} + 1)} rows and k columns.

Contributors

Dusa, Adrian	: programming
Thiem, Alrik	: development, documentation, testing

Author(s)

Alrik Thiem (Personal Website; ResearchGate Website)

References

Dusa, Adrian. 2007. Enhancing Quine-McCluskey. COMPASSS: Working Paper 2007-49. URL: http://www.compasss.org/wpseries/Dusa2007b.pdf.

Dusa, Adrian. 2010. “A Mathematical Approach to the Boolean Minimization Problem.” Quality & Quantity 44 (1):99-113. DOI: 10.1007/s11135-008-9183-x.

Dusa, Adrian, and Alrik Thiem. 2015. “Enhancing the Minimization of Boolean and Multivalue Output Functions with eQMC.” Journal of Mathematical Sociology 39 (2):92-108. DOI: 10.1080/0022250X.2014.897949.

Examples

# three exogenous factors with two levels each;
# first row is empty set
implicantMatrix(noflevels = rep(2, 3))

# two exogenous factors with three levels each
implicantMatrix(noflevels = rep(3, 2))

# arranged differently
implicantMatrix(noflevels = rep(3, 2), arrange = TRUE)

# with internal indicator for eliminated values
implicantMatrix(noflevels = rep(3, 2), raw = TRUE)

QCApro

Advanced Functionality for Performing and Evaluating Qualitative Comparative Analysis

v1.1-2

GPL-3

Authors

Alrik Thiem [aut, cre, cph], Michael Baumgartner [ctb], Adrian Dusa [ctb], Reto Spoehel [ctb]

Initial release

2018-01-10