# Falgorithm.Rd: Flury and Gautschi algorithms In FGalgorithm: Flury and Gautschi algorithms

## Description

Find the orthogonal matrix B_0 such that minimize Φ(B).

## Usage

 `1` ```FGalgorithm(eF, eG, p, n , A) ```

## Arguments

 `eF,eG` small positive constants controlling error terms. `p` dimensionality. `n ` a numeric vector containing the positive integers. `A` a list of length k of positive definite symmetric matrices.

## Value

Orthogonal matrix B_0 such that minimize Φ with respect to the group of orthogonal matrices B.

## References

Flury, B. N., & Gautschi, W. (1986). An algorithm for simultaneous orthogonal transformation of several positive definite symmetric matrices to nearly diagonal form. SIAM Journal on Scientific and Statistical Computing, 7(1), 169-184.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ``` n<-numeric(3) n[[1]]<-50 n[[2]]<-50 n[[3]]<-50 A<-vector("list",length=3) A[[1]]<-var(iris[51:100,1:4]) A[[2]]<-var(iris[101:150,1:4]) A[[3]]<-var(iris[1:50,1:4]) B0<-FGalgorithm(1e-5,1e-5,4,n,A) B0 ```

### Example output

```          [,1]       [,2]        [,3]       [,4]
[1,] 0.7366533 -0.6470732  0.16396782  0.1084104
[2,] 0.2467858  0.4655193  0.83460794 -0.1606802
[3,] 0.6047478  0.5002357 -0.52210632 -0.3338402
[4,] 0.1752676  0.3381603 -0.06284209  0.9224856
```

FGalgorithm documentation built on May 29, 2017, 2:25 p.m.