# JacobiR: The Jacobi Algorithm in Pure R In JacobiEigen: Classical Jacobi Eigenvalue Algorithm

## Description

The Jacobi Algorithm

## Usage

 ```1 2``` ```JacobiR(x, symmetric = TRUE, only.values = FALSE, eps = if (!only.values) .Machine\$double.eps else sqrt(.Machine\$double.eps)) ```

## Arguments

 `x` a real symmetric matrix `symmetric` a logical value. Is the matrix symmetric? (Only symmetric matrices are allowed.) `only.values` A logical value: Do you want only the eigenvalues? `eps` a small positive error tolerance

## Details

Eigenvalues and optionally, eigenvectore of a real symmetric matrix using the classical Jacobi algorithm, (Jacobi, 1854)

## Value

a list of two components as for `base::eigen`

## Examples

 ```1 2 3 4``` ```V <- crossprod(matrix(rnorm(25), 5)) JacobiR(V) identical(Jacobi(V), JacobiR(V)) all.equal(Jacobi(V)\$values, base::eigen(V)\$values) ```

### Example output

```eigen decomposition (Jacobi algorithm)
\$values
 11.097223018  7.125782580  4.091586522  0.563247265  0.002640397

\$vectors
[,1]        [,2]       [,3]        [,4]        [,5]
[1,]  0.05264201 -0.96040558 -0.2053225  0.15899573  0.08609858
[2,]  0.05643221  0.06769028 -0.3136061  0.43873056 -0.83749637
[3,]  0.31412362 -0.12186404 -0.1632039 -0.84919696 -0.37243058
[4,] -0.28073510 -0.24044231  0.8427825 -0.06187231 -0.38634803
[5,]  0.90363620  0.01938562  0.3501087  0.23931612  0.05672322

 TRUE
 TRUE
```

JacobiEigen documentation built on April 17, 2021, 9:06 a.m.