ade4 (version 1.2-2)

orthobasis: Orthonormal basis for orthonormal transform

Description

These functions returns object of class 'orthobasis' that contains data frame with n rows and n-1 columns. Each data frame defines an orthonormal basis for the uniform weights.

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.listw returns the eigen vectors of the general link matrix M associated to a listw object. orthobasis.haar returns wavelet haar basis.

Usage

orthobasis.neig(neig)
orthobasis.line(n)
orthobasis.circ(n)
orthobasis.mat(mat, cnw=TRUE)
orthobasis.listw(listw)
orthobasis.haar(n)
print.orthobasis(x,...)

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

listw

is a 'listw' object

cnw

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

x

is an object of class orthobasis

...

: further arguments passed to or from other methods

Value

• All the functions excepted print.ortobasis return an object of class orthobasis containing a data frame. This data frame defines an orthonormal basis with n-1 vectors of length n. Various attributes are associated to it :
• names
  : names of the vectors
• row.names
  : row names of the data frame
• class
  : class
• values
  : row weights (uniform weights)
• weights
  : numeric values to class vectors according to their quadratic forms (Moran ones)
• call
  : call

References

Misiti, M., Misiti, Y., Oppenheim, G. and Poggi, J.M. (1993) Analyse de signaux classiques par d�composition en ondelettes. Revue de Statistique Appliqu�e, 41, 5--32.

Cornillon, P.A. (1998) Prise en compte de proximit�s en analyse factorielle et comparative. Th�se, Ecole Nationale Sup�rieure 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
par(mfrow = c(4,4))
w <- gridrowcol(8,8)
 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)
}

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"))

# a spatial orthobasis
data(mafragh)
w <- orthobasis.neig(mafragh$neig)
par(mfrow = c(4,2))
for (k in 1:8)
    s.value(mafragh$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)