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

## Description

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

## Usage

 ```1 2 3 4 5``` ```eigenvals(x, ...) ## S3 method for class 'cca' eigenvals(x, constrained = FALSE, ...) ## S3 method for class 'eigenvals' summary(object, ...) ```

## Arguments

 `x` An object from which to extract eigenvalues. `object` An `eigenvals` result object. `constrained` Return only constrained eigenvalues. `...` 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`, `capscale`, `pcnm`) which correspond to imaginary axes of Euclidean mapping of non-Euclidean distances (Gower 1985). In these cases, the sum of absolute values of eigenvalues is used in calculating the proportions explained, and real axes (corresponding to positive eigenvalues) will only explain a part of total variation (Mardia et al. 1979, Gower 1985).

## Value

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

Jari Oksanen.

## References

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

Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979). Chapter 14 of Multivariate Analysis, London: Academic Press.

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

## Examples

 ```1 2 3 4 5 6``` ```data(varespec) data(varechem) mod <- cca(varespec ~ Al + P + K, varechem) ev <- eigenvals(mod) ev summary(ev) ```

### Example output

```Loading required package: permute
This is vegan 2.4-3
CCA1      CCA2      CCA3       CA1       CA2       CA3       CA4       CA5
0.3615566 0.1699600 0.1126167 0.3500372 0.2200788 0.1850741 0.1551179 0.1351054
CA6       CA7       CA8       CA9      CA10      CA11      CA12      CA13
0.1002670 0.0772991 0.0536938 0.0365603 0.0350887 0.0282291 0.0170651 0.0122474
CA14      CA15      CA16      CA17      CA18      CA19      CA20
0.0101910 0.0094701 0.0055090 0.0030529 0.0025118 0.0019485 0.0005178
Importance of components:
CCA1    CCA2    CCA3    CA1    CA2     CA3     CA4
Eigenvalue            0.3616 0.16996 0.11262 0.3500 0.2201 0.18507 0.15512
Proportion Explained  0.1736 0.08159 0.05406 0.1680 0.1056 0.08884 0.07446
Cumulative Proportion 0.1736 0.25514 0.30920 0.4772 0.5829 0.67172 0.74618
CA5     CA6     CA7     CA8     CA9    CA10    CA11
Eigenvalue            0.13511 0.10027 0.07730 0.05369 0.03656 0.03509 0.02823
Proportion Explained  0.06485 0.04813 0.03711 0.02577 0.01755 0.01684 0.01355
Cumulative Proportion 0.81104 0.85917 0.89627 0.92205 0.93960 0.95644 0.96999
CA12    CA13    CA14    CA15     CA16     CA17
Eigenvalue            0.01707 0.01225 0.01019 0.00947 0.005509 0.003053
Proportion Explained  0.00819 0.00588 0.00489 0.00455 0.002640 0.001470
Cumulative Proportion 0.97818 0.98406 0.98895 0.99350 0.996140 0.997610
CA18     CA19      CA20
Eigenvalue            0.002512 0.001948 0.0005178
Proportion Explained  0.001210 0.000940 0.0002500
Cumulative Proportion 0.998820 0.999750 1.0000000
```

vegan documentation built on May 2, 2019, 5:51 p.m.