| tLCM {xegaGeGene} | R Documentation |
Computes the largest least common multiple of all prime factors
of the integers in the interval 1:m for k-bit integers.
Description
For 64 bit numbers, numerically stable up to m==42.
The modulo rule in grammatical evolution assigns to the choices
of substitutions for a non-terminal slightly (biased) probabilities.
For an integer coding, the least common multiple of all rule choices
from no choice (1) to the maximal number of substitutions of a non-terminal
removes this bias completely. However, whenever the prime factors of the
least common multiple contain a prime different from 2,
the bias cannot be removed completely for a binary gene coding.
However, each additional bit used for coding approximately halves the bias.
Usage
tLCM(k)
Arguments
k |
Number of bits. |
Details
This could be done with the help of
the function mLCM of the R-package numbers.
We implement this by enumerating the vector of prime factors
in 1:42.
Value
A list of three elements:
-
$k: The number of bits. -
$m: Maximal number of substitutions for a non-terminal symbol in a grammar. -
$mLCM: Least common multiple of the prime factors of all rule choices from 1 to$m.
See Also
Other Diagnostics:
CodonChoiceBiasesDeprecated(),
CodonChoiceBiases(),
CodonPrecision()
Examples
tLCM(8)
tLCM(16)
tLCM(32)