QCA (version 1.0-2)

createMatrix: Create the prod(k) matrix

Description

The prod(k + 1) matrix is the generalisation of the $3^k$ matrix, for any combination of binary and multi-value crisp sets, where $k$ is a vector with the number of levels for each causal condition. For example, the truth table consists of all combinations of the presence and absence of conditions (coded binary 1/0). There are $2^k$ such combinations and createMatrix() should be among the fastest to create this matrix, optimising ideas inspired from the base R function expand.grid(). The prod(k + 1) matrix has exactly the same structure as the $3^k$ matrix, given that, for instance, $3^3$ = 3*3*3, which is simply the same as prod(rep(3, 3)). It is easy to observe that $3^k$ is just a special case of prod(rep(3, k)). For multi-values, the structure $3^k$ cannot hold, as each causal combination can have different number of levels. This issue is easily solved by using createMatrix() instead.

Usage

createMatrix(noflevels, logical = FALSE)

Arguments

noflevels

A vector containing the number of levels for each variable in the dataset

logical

Logical, return the matrix in logical values (only binary-value crisp data)

References

A. Dusa. A Mathematical Approach to the Boolean Minimization Problem. Quality & Quantity, 44(1), pp.99-113, 2010. A. Dusa. Enhancing Quine-McCluskey. WP 2007-49, COMPASSS, 2007. URL: http://www.compasss. org/files/WPfiles/Dusa2007a.pdf. C. C. Ragin. The Comparative Method: Moving beyond Qualitative and Quantitative Strategies. University of California Press, Berkeley, 1987.

See Also

allExpressions truthTable

Examples

# create a binary 2^k matrix based on 3 conditions, essentially the truth table
noflevels <- rep(2, 3)
createMatrix(noflevels)

# its 3^k matrix, where all the prime implicants are, where "-1" means a minimised literal
createMatrix(noflevels + 1) - 1

# this is essentially the same structure as the more familiar
# (N.B. there is also a "raw" argument)
allExpressions(noflevels)

# or even more familiar, with all possible PIs arranged
allExpressions(noflevels, arrange = TRUE)

# create a truth table matrix based on 3 conditions where the second has three levels
# the matrix has 2*3*2 = prod(c(2, 3, 2)) = 12 rows
noflevels <- c(2, 3, 2)
createMatrix(noflevels)

# its prod(k) matrix, the generalised version of the 3^k matrix
# which has prod(noflevels + 1) rows
createMatrix(noflevels + 1) - 1