Flury and Gautschi algorithms

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Description

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

Usage

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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.

Author(s)

Dariush Najarzadeh

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

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  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

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