# eigenvals: Extract Eigenvalues from an Ordination Object In vegan: Community Ecology Package

 eigenvals R Documentation

## Extract Eigenvalues from an Ordination Object

### Description

Function extracts eigenvalues from an object that has them. Many multivariate methods return such objects.

### Usage

``````eigenvals(x, ...)
## S3 method for class 'cca'
eigenvals(x, model = c("all", "unconstrained", "constrained"),
constrained = NULL, ...)
## S3 method for class 'decorana'
eigenvals(x, kind = c("additive", "axiswise", "decorana"),
...)
## S3 method for class 'eigenvals'
summary(object, ...)
``````

### Arguments

 `x` An object from which to extract eigenvalues. `object` An `eigenvals` result object. `model` Which eigenvalues to return for objects that inherit from class `"cca"` only. `constrained` Return only constrained eigenvalues. Deprecated as of vegan 2.5-0. Use `model` instead. `kind` Kind of eigenvalues returned for `decorana`. Only `"additive"` eigenvalues can be used for reporting importances of components in `summary`. `"axiswise"` gives the non-additive eigenvalues, and `"decorana"` the decorana values (see `decorana` for details). `...` Other arguments to the functions (usually ignored)

### Details

This is a generic function that has methods for `cca`, `wcmdscale`, `pcnm`, `prcomp`, `princomp`, `dudi` (of ade4), and `pca` and `pco` (of labdsv) result objects. The default method also extracts eigenvalues if the result looks like being from `eigen` or `svd`. Functions `prcomp` and `princomp` contain square roots of eigenvalues that all called standard deviations, but `eigenvals` function returns their squares. Function `svd` contains singular values, but function `eigenvals` returns their squares. For constrained ordination methods `cca`, `rda` and `capscale` the function returns the both constrained and unconstrained eigenvalues concatenated in one vector, but the partial component will be ignored. However, with argument `constrained = TRUE` only constrained eigenvalues are returned.

The `summary` of `eigenvals` result returns eigenvalues, proportion explained and cumulative proportion explained. The result object can have some negative eigenvalues (`wcmdscale`, `dbrda`, `pcnm`) which correspond to imaginary axes of Euclidean mapping of non-Euclidean distances (Gower 1985). In these case real axes (corresponding to positive eigenvalues) will "explain" proportion >1 of total variation, and negative eigenvalues bring the cumulative proportion to 1. `capscale` will only find the positive eigenvalues and only these are used in finding proportions. For `decorana` the importances and cumulative proportions are only reported for `kind = "additive"`, because other alternatives do not add up to total inertia of the input data.

### Value

An object of class `"eigenvals"`, which is a vector of eigenvalues.

The `summary` method returns an object of class `"summary.eigenvals"`, which is a matrix.

Jari Oksanen.

### References

Gower, J. C. (1985). Properties of Euclidean and non-Euclidean distance matrices. Linear Algebra and its Applications 67, 81–97.

`eigen`, `svd`, `prcomp`, `princomp`, `cca`, `rda`, `capscale`, `wcmdscale`, `cca.object`.

### Examples

``````data(varespec)
data(varechem)
mod <- cca(varespec ~ Al + P + K, varechem)
ev <- eigenvals(mod)
ev
summary(ev)

## choose which eignevalues to return
eigenvals(mod, model = "unconstrained")
``````

vegan documentation built on Sept. 11, 2024, 7:57 p.m.