hadamard: Hadamard Matrices and Fast Hadamard Multiplication

In KlausVigo/phangorn: Phylogenetic Reconstruction and Analysis

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)

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.

Value

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

Author(s)

Klaus Schliep [e-mail]

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)

KlausVigo/phangorn documentation built on Nov. 5, 2024, 11 a.m.