# orthobasis: Orthonormal basis for orthonormal transform In ade4: Analysis of Ecological Data: Exploratory and Euclidean Methods in Environmental Sciences

 orthobasis R Documentation

## 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 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

### 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

### Note

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

### Author(s)

Sébastien Ollier sebastien.ollier@u-psud.fr
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.

`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)
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)
}

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(mafragh\$neig)
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)```

ade4 documentation built on Nov. 2, 2022, 1:07 a.m.