A collection of functions to perform Hadamard conjugation. Hadamard matrix H with a vector v using fast Hadamard multiplication.
Usage
hadamard(x)
fhm(v)
h4st(obj, levels = c("a", "c", "g", "t"))
h2st(obj, eps = 0.001)Arguments
- x
a vector of length \(2^n\), where n is an integer.
- v
a vector of length \(2^n\), where n is an integer.
- obj
a data.frame or character matrix, typical a sequence alignment.
- levels
levels of the sequences.
- eps
Threshold value for splits.
Details
h2st and h4st perform Hadamard conjugation for 2-state
(binary, RY-coded) or 4-state (DNA/RNA) data. write.nexus.splits
writes splits returned from h2st or
distanceHadamard to a nexus file, which can be
processed by Spectronet or SplitsTree.
References
Hendy, M.D. (1989). The relationship between simple evolutionary tree models and observable sequence data. Systematic Zoology, 38 310--321.
Hendy, M. D. and Penny, D. (1993). Spectral Analysis of Phylogenetic Data. Journal of Classification, 10, 5--24.
Hendy, M. D. (2005). Hadamard conjugation: an analytical tool for phylogenetics. In O. Gascuel, editor, Mathematics of evolution and phylogeny, Oxford University Press, Oxford
Waddell P. J. (1995). Statistical methods of phylogenetic analysis: Including hadamard conjugation, LogDet transforms, and maximum likelihood. PhD thesis.
Author
Klaus Schliep klaus.schliep@gmail.com
Examples
H <- hadamard(3)
v <- 1:8
H %*% v
#> [,1]
#> [1,] 36
#> [2,] -4
#> [3,] -8
#> [4,] 0
#> [5,] -16
#> [6,] 0
#> [7,] 0
#> [8,] 0
fhm(v)
#> [1] 36 -4 -8 0 -16 0 0 0
data(yeast)
# RY-coding
dat_ry <- acgt2ry(yeast)
#> Warning: Found unknown characters (not supplied in levels). Deleted sites with unknown states.
fit2 <- h2st(dat_ry)
lento(fit2)
# write.nexus.splits(fit2, file = "test.nxs")
# read this file into Spectronet or SplitsTree to show the network
fit4 <- h4st(yeast)
old.par <- par(no.readonly = TRUE)
par(mfrow=c(3,1))
lento(fit4[[1]], main="Transversion")
lento(fit4[[2]], main="Transition 1")
lento(fit4[[3]], main="Transition 2")
par(old.par)