procoteW {lazy.procrustes}

R Documentation

Expanded Orthogonal Procrustes Rotation

Description

Expanded Orthogonal Procrustes Rotation

Usage

procoteW(
  A,
  C,
  estm = 0,
  estW = 0,
  minW = 0.001,
  T = NULL,
  W = NULL,
  m = NULL,
  maxiter = 200,
  eps = 1e-06,
  print = 2
)

Arguments

A	The input matrix to be rotated
C	The target matrix
estm	= 1 to estimate m
estW	= 1 to estimate scalar W = 2 to estimate diagonal W
minW	minimum value of the elements of W
T	Initial value of T or NULL
W	Initial value of W or NULL
m	Initial value of m or NULL
maxiter	max # of iterations
eps	convergence criterion for rmse
print	= 1 to print result

Details

This program finds those A, m, W and orthonormal T which minimize
RSS = tr( ( C - Chat )' ( C - Chat ) )
where Chat = A %*% W %*% T + matrix(1,nv) %*% t(m), W is a diagonal Matrix, T is an orthonormal rotation matrix,
m is the column mean vector.

Note that when estW=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=A %*% W %*% T + matrix(1,nv,1)%*%t(m), T, W, , C the updated target matrix, rmse=sqrt(RSS)

Examples

 seed <- 1701; n <- 20; nr <- 2; pmiss <- 0; errstd <- 0.05
 set.seed(seed)
 resg <- gendataWmm( 1, n, nr, genm=1, genW=2, pmiss=pmiss, errstd=errstd)
 A <- resg$A
 C <- resg$C; Tg <- resg$T; mg <- resg$m; Wg <- resg$W
 res <- procoteW( A, C, estm=1, estW=2, print=1 )
 T <- res$T; m <- res$m; W <- res$W
 Print( Tg-T, mg-m, Wg-W, fmt="7.3")

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