ade4 (version 1.7-19)

orthobasis: Orthonormal basis for orthonormal transform

Description

These functions returns object of class 'orthobasis' that contains data frame defining an orthonormal basis.

orthobasic.neig returns the eigen vectors of the matrix N-M where M is the symmetric n by n matrix of the between-sites neighbouring graph and N is the diagonal matrix of neighbour numbers.
orthobasis.line returns the analytical solution for the linear neighbouring graph.
orthobasic.circ returns the analytical solution for the circular neighbouring graph.
orthobsic.mat returns the eigen vectors of the general link matrix M.
orthobasis.haar returns wavelet haar basis.

Usage

orthobasis.neig(neig)
orthobasis.line(n)
orthobasis.circ(n)
orthobasis.mat(mat, cnw=TRUE)
orthobasis.haar(n)
# S3 method for orthobasis
print(x,..., nr = 6, nc = 4)
# S3 method for orthobasis
plot(x,...)
# S3 method for orthobasis
summary(object,...)
is.orthobasis(x)

Value

All the functions return an object of class orthobasis containing a data frame. This data frame defines an orthonormal basis with various attributes:

names

names of the vectors

row.names

row names of the data frame

class

class

values

optional associated eigenvalues

weights

weights for the rows

call

: call

Arguments

neig

is an object of class neig

n

is an integer that defines length of vectors

mat

is a n by n phylogenetic or spatial link matrix

cnw

if TRUE, the matrix of the neighbouring graph is modified to give Constant Neighbouring Weights

x, object

is an object of class orthobasis

nr, nc

the number of rows and columns to be printed

...

: further arguments passed to or from other methods

Author

Sébastien Ollier
Daniel Chessel

References

Misiti, M., Misiti, Y., Oppenheim, G. and Poggi, J.M. (1993) Analyse de signaux classiques par décomposition en ondelettes. Revue de Statistique Appliquée, 41, 5--32.

Cornillon, P.A. (1998) Prise en compte de proximités en analyse factorielle et comparative. Thèse, Ecole Nationale Supérieure Agronomique, Montpellier.

See Also

gridrowcol that defines an orthobasis for square grid, phylog that defines an orthobasis for phylogenetic tree, orthogram and mld

Examples

# a 2D spatial orthobasis
w <- gridrowcol(8, 8)
if(adegraphicsLoaded()) {
  g1 <- s.value(w$xy, w$orthobasis[, 1:16], pleg.drawKey = FALSE, pgri.text.cex = 0, 
    ylim = c(0, 10), porigin.include = FALSE, paxes.draw = FALSE)
  g2 <- s1d.barchart(attr(w$orthobasis, "values"), p1d.horizontal = FALSE, 
    labels = names(attr(w$orthobasis, "values")), plabels.cex = 0.7)

} else {
  par(mfrow = c(4, 4))
  for(k in 1:16)
    s.value(w$xy, w$orthobasis[, k], cleg = 0, csi = 2, incl = FALSE,
      addax = FALSE, sub = k, csub = 4, ylim = c(0, 10), cgri = 0)
  par(mfrow = c(1, 1))
  barplot(attr(w$orthobasis, "values"))
}


# Haar 1D orthobasis
w <- orthobasis.haar(32)
par(mfrow = c(8, 4))
par(mar = c(0.1, 0.1, 0.1, 0.1))
 for (k in 1:31) {
    plot(w[, k], type = "S", xlab = "", ylab = "", xaxt = "n",
     yaxt = "n", xaxs = "i", yaxs = "i", ylim = c(-4.5, 4.5))
    points(w[, k], type = "p", pch = 20, cex = 1.5)
}

# a 1D orthobasis
w <- orthobasis.line(n = 33)
par(mfrow = c(8, 4))
par(mar = c(0.1, 0.1, 0.1, 0.1))
 for (k in 1:32) {
    plot(w[, k], type = "l", xlab = "", ylab = "", xaxt = "n",
     yaxt = "n", xaxs = "i", yaxs = "i", ylim = c(-1.5, 1.5))
    points(w[, k], type = "p", pch = 20, cex = 1.5)
}

if(adegraphicsLoaded()) {
  s1d.barchart(attr(w, "values"), p1d.horizontal = FALSE, labels = names(attr(w, "values")), 
    plab.cex = 0.7)
} else {
  par(mfrow = c(1, 1))
  barplot(attr(w, "values"))
}

w <- orthobasis.circ(n = 26)
#par(mfrow = c(5, 5))
#par(mar = c(0.1, 0.1, 0.1, 0.1))
# for (k in 1:25) 
#    dotcircle(w[, k], xlim = c(-1.5, 1.5), cleg = 0)

par(mfrow = c(1, 1))
#barplot(attr(w, "values"))

if (FALSE) {
# a spatial orthobasis
data(mafragh)
w <- orthobasis.neig(mafragh$neig)
if(adegraphicsLoaded()) {
  s.value(mafragh$xy, w[, 1:8], plegend.drawKey = FALSE)
  s1d.barchart(attr(w, "values"), p1d.horizontal = FALSE)
} else {
  par(mfrow = c(4, 2))
  for(k in 1:8)
    s.value(mafragh$xy, w[, k], cleg = 0, sub = as.character(k), csub = 3)
  par(mfrow = c(1, 1))
  barplot(attr(w, "values"))
}

# a phylogenetic orthobasis
data(njplot)
phy <- newick2phylog(njplot$tre)
wA <- phy$Ascores
wW <- phy$Wscores
table.phylog(phylog = phy, wA, clabel.row = 0, clabel.col  = 0.5)
table.phylog(phylog = phy, wW, clabel.row = 0, clabel.col  = 0.5)

}