phangorn (version 2.11.1)

hadamard: Hadamard Matrices and Fast Hadamard Multiplication

Description

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)

Value

hadamard returns a Hadamard matrix. fhm returns the fast Hadamard multiplication.

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.

Author

Klaus Schliep

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.

See Also

distanceHadamard, lento, plot.networx

Examples

H <- hadamard(3)
v <- 1:8
H %*% v
fhm(v)

data(yeast)

# RY-coding
dat_ry <- acgt2ry(yeast)
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)