# Random.Start: Generate a Random Orthogonal Rotation In GPArotation: GPA Factor Rotation

## Description

Random orthogonal rotation to use as Tmat matrix to start GPForth or GPFoblq.

## Usage

 ```1 2``` ``` Random.Start(k) ```

## Arguments

 `k` An integer indicating the dimension of the square matrix.

## Details

The random start function produces an orthogonal matrix with columns of length one based on the QR decompostion.

## Value

An orthogonal matrix.

## Author(s)

Coen A. Bernaards and Robert I. Jennrich with some R modifications by Paul Gilbert

`GPForth`, `GPFoblq`, `oblimin`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ``` Global.min <- function(A,method,B=10){ fv <- rep(0,B) seeds <- sample(1e+7, B) for(i in 1:B){ cat(i," ") set.seed(seeds[i]) gpout <- GPFoblq(A=A, Random.Start(ncol(A)), method=method) dtab <- dim(gpout\$Table) fv[i] <- gpout\$Table[dtab[1],2] cat(fv[i], "\n") } cat("Min is ",min(fv),"\n") set.seed(seeds[order(fv)[1]]) ans <- GPFoblq(A=A, Random.Start(ncol(A)), method=method) ans } data("Thurstone", package="GPArotation") Global.min(box26,"simplimax",10) ```