Extened Orthogonal Procrustes Rotation

Description

Extened Orthogonal Procrustes Rotation

Usage

procote(A, C, estm = 0, estd = 0, maxiter = 200, eps = 1e-06, print = 2)

Arguments

Details

This program finds those A, m, d and orthonormal T which minimize

RSS = tr( ( C - Chat )' ( C - Chat ) )

where Chat = d * A \%*\% T + matrix(1,nv) \%*\% t(m),
d is a scalar, T is an orthonormal rotation matrix,
and m is the column mean vector.

Note that when estd=0 and estm=0 , and the target matrix does not have missing elements,
this is equivalent to the usual orthogonal Procrustes rotation.

Value

A list of:
B=d * A %*% T + matrix(1,nv,1)%*%t(m),
T, m, d, Cm the updated target matrix, rmse=sqrt(RSS)

Examples

 set.seed(1701)
 nv <- 10; nr <- 2
 pmiss <- 0.3

 A <- matrix(rnorm(nv*nr),nv,nr)
 dum <- matrix(rnorm(nv*nr),nv,nr)
 T <- eigen(t(dum)%*%dum)[[2]]
 m <- matrix(rnorm(nr),nr,1)
 d <- 10*runif(1)
 C <- d*A%*%T + matrix(rep(1,nv),nv,1)%*%t(m)

 res <- procote( A, C, estm=0, estd=0, print=1 )
 res2 <- procote( A, C, estm=1, estd=1, print=1 )

 # missing elements in the target
 dum <- matrix(runif(nv*nr),nv,nr)
 C[which(dum < pmiss)] <- NA

 res3 <- procote( A, C, estm=0, estd=0, print=1 )
 res4 <- procote( A, C, estm=1, estd=1, print=1 )