orthobasis function

Orthonormal basis for orthonormal transform

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.

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

Returns

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

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.

Author(s)

Sébastien Ollier sebastien.ollier@u-psud.fr

Daniel Chessel

Note

the function orthobasis.haar uses function wavelet.filter from package waveslim.

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"))

## Not run:

# a spatial orthobasis
data(mafragh)
w <- orthobasis.neig(neig2nb(mafragh$nb))
if(adegraphicsLoaded()) {
  s.value(mafragh$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)
## End(Not run)