getRow: Get a Specific Row from Configuration and Implicant Matrices

Description

This function transforms the decimal representation of a row number into its corresponding combination of levels in configuration matrices or into its corresponding combination of level index values in implicant matrices.

Usage

getRow(noflevels, row.no, zerobased = FALSE)

Arguments

noflevels

A vector containing the number of levels for each condition

row.no

A vector, the desired row numbers

zerobased

Logical, the first row number is zero

Value

a matrix with the combination of levels / level index values corresponding to the desired row number(s)

Details

A configuration matrix is formed by all unique combinations of condition levels and represents an essential part of any truth table. For any number of levels, the number of configurations is given by $\prod_{j = 1}^{k}{p_j}$, where $p_j$ is the number of levels for condition $j$ and $k$ is the number of conditions.

The implicant matrix consists of all supersets of the rows of a configuration matrix, including the configurations themselves as well as the empty set. The formula for the number of implicants is $\prod_{j = 1}^{k}{p_j + 1}$.

The getRow() function transforms the decimal representation of a row number from a configuration matrix into its corresponding combination of levels or from an implicant matrix into its corresponding combination of level index values.

Examples

Run this code

# all three conditions have two levels
x <- c(2, 2, 2)

# rows from the configuration matrix
# 1 1 1
getRow(noflevels = x, row.no = 8)

# 0 0 0
getRow(noflevels = x, row.no = 0, zerobased = TRUE)

# same as above 
getRow(noflevels = x, row.no = 1)

# second condition has three levels: 0, 1 and 2
x <- c(2, 3, 2)

# 1 2 0
getRow(noflevels = x, row.no = 11)

# the empty set in the implicant matrix 
getRow(noflevels = x, 1) - 1