prev: Preview of the Semigroup Construction

In multiplex: Algebraic Tools for the Analysis of Multiple Social Networks

Preview of the Semigroup Construction

Description

A function to preview the partial right multiplication table of the semigroup to assess the size of the complete semigroup.

Usage

prev(x)

Arguments

x	an array; usually with three dimensions of stacked matrices where the multiple relations are placed.

Details

When the input data is large, i.e. having a dozen or more elements and/or more than five dimensions, it is recommended to perform this function before the semigroup construction to get the partial right multiplication table.

That is because the amount of undefined data in such a table gives an idea of how much time may take to get the complete semigroup. However, the performance depends mainly on whether the generator matrices are sparse and/or have a relatively large number of elements for a semigroup construction of the course.

Value

'2stpT'	a partial right multiplication table at two-step.
'PcU2stpT'	the proportion of undefined elements at two-step.
ordr	the dimension of the right multiplication table so far.
Note	a conditional warning message.

Note

The warning message is given only if the percentage of undefined elements and the dimension of the input data are relatively high; however, the semigroup construction can still take a long time without the message.

Author(s)

Antonio Rivero Ostoic

See Also

semigroup, edgeT.

Examples

# create the data: two binary relations among three elements
arr <- round( replace( array(runif(18), c(3,3,2)), array(runif(18),
       c(3,3,2))>.5, 1 ) )

# preview a "semigroup" structure
prev(arr)

multiplex documentation built on Sept. 30, 2024, 5:07 p.m.