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#############################################################
#
# varComprob.compositeMM function
# Author: Claudio Agostinelli and Victor J. Yohai
# E-mail: claudio@unive.it
# Date: June, 28, 2014
# Version: 0.1
#
# Copyright (C) 2014 Claudio Agostinelli
# and Victor J. Yohai
#
#############################################################
varComprob.compositeMM <- function(y, x, V, S=NULL, beta=NULL, gamma=NULL, scales=NULL, control=varComprob.control()) {
# y: matrix. dim(y)=c(p,n)
# x: array. dim(x)=c(p,n,k)
# V: array. dim(V)=c(p,p,R)
# beta: vector or NULL. length(beta)=k
# gamma: vector or NULL. length(gamma)=R
# scales: vector or NULL. length(scales)=p*(p-1)/2
if (control$psi=="rocke")
stop("Rocke rho function is not yet available for composite methods")
## SET STORAGE MODE OF y, x and V
storage.mode(y) <- "double"
storage.mode(x) <- "double"
storage.mode(V) <- "double"
xdim <- dim(x)
p <- xdim[1]
n <- xdim[2]
k <- xdim[3]
Vdim <- dim(V)
R <- Vdim[3]
JL <- p*(p-1)/2
## About initial values
if (is.null(beta))
beta <- S$beta
if (is.null(gamma))
gamma <- S$gamma
if (is.null(scales))
scales <- S$scales
if(is.null(beta) | is.null(gamma) | is.null(scales))
stop('Initial values for beta and gamma and values for scales must be supplied')
v <- qchisq(seq(0.0001,0.9999,length=5000), 2)
s0 <- doSstep(m=v, scale=1, bb=control$bb, cc=control$tuning.chi, psi=control$psi, tol=control$rel.tol.scale, verbose=(control$trace.lev>2))
##BEGIN# Iterations
iter <- 0
dbeta <- control$rel.tol.beta+1
dgamma <- control$rel.tol.gamma+1
while ((max(dbeta) > control$rel.tol.beta | dgamma > control$rel.tol.gamma) & iter < control$max.it) {
iter <- iter+1
## SIGMA
Sigma <- Vprod(V=V, gamma=gamma)
## RESIDUALS
if (k==0) {
rr <- y
beta <- beta1 <- vector(mode="numeric", length=0)
control$cov <- FALSE
} else
rr <- vcrobresid(y=y, x=x, beta=beta)
## SQUARED MAHALANOBIS DISTANCES
RR <- rssr(resid=rr, Sigma=Sigma)
## WEIGHTS
W <- vcrobweightspw(RR=RR, scale=scales, cc=control$tuning.psi, psi=control$psi)
## BETAS
if (k > 0) {
XX <- xssx(x=x, Sigma=Sigma)
XY <- xssy(x=x, y=y, Sigma=Sigma)
beta1 <- drop(doBetastep(Wdot=W, XX=XX, XY=XY))
dbeta <- max(abs(beta-beta1))
} else
dbeta <- 0
Mmax <- doGammaCompositeMMGoal(x=gamma, resid=rr, scales=scales, V=V, Mmax=NA, controllo=control)+10
if (is.na(Mmax))
stop("The Sigma matrix is singular and we do not know how to fix it")
gamma1 <- drop(doGammaCompositeMMstep(gamma=gamma, resid=rr, scales=scales, V=V, Mmax, control=control))
dgamma <- max(abs(gamma1-gamma))
if (iter > control$max.it/2) {
beta <- (beta1+beta)/2
gamma <- (gamma1+gamma)/2
} else {
beta <- beta1
gamma <- gamma1
}
if (control$trace.lev>1) {
cat('Iterations: ', iter, '\n')
cat('beta: ', beta, '\n')
cat('gamma: ', gamma, '\n')
M <- doGammaCompositeMMGoal(x=gamma, resid=rr, scales=scales, V=V, Mmax=Mmax, controllo=control)
cat('M: ', M, '\n')
cat('diff max(abs(beta_i - beta_i+1)): ', dbeta, '\n')
cat('diff max(abs(gamma_i - gamma_i+1)): ', dgamma, '\n')
}
}
##END# Iterations
##BEGIN# Eta0
Sigma <- Vprod(V=V, gamma=gamma)
RSR <- rsr(resid=rr, Sigma=Sigma)
eta0 <- doSstep(m=RSR/s0, scale=1, bb=control$bb, cc=control$tuning.chi, psi=control$psi, tol=control$rel.tol.scale, verbose=(control$trace.lev>2))
##END# Eta0
##BEGIN# VCOV
if (control$cov) {
vcov <- VCOV.CompositeMM(beta=beta, gamma=gamma, scales=scales, y=y, x=x, V=V, control=control)
vcov.beta <- vcov[1:k,1:k]
vcov.gamma <- vcov[(k+1):(k+R),(k+1):(k+R)]
} else {
vcov.beta <- matrix(NA, k, k)
vcov.gamma <- matrix(NA, R, R)
}
##END# VCOV
result <- list()
result$call <- match.call()
result$beta <- drop(beta)
result$vcov.beta <- vcov.beta
result$eta <- drop(gamma*eta0)
result$vcov.eta <- vcov.gamma*eta0^2
result$gamma <- drop(gamma)
result$vcov.gamma <- vcov.gamma
result$eta0 <- eta0
result$resid <- rr
result$weights <- W
result$scales <- scales
result$scale0 <- s0
result$min <- doGammaCompositeMMGoal(x=gamma, resid=rr, scales=scales, V=V, Mmax=NA, controllo=control)
result$iterations <- iter
result$control <- control
result$control$method <- "compositeMM"
class(result) <- 'varComprob.compositeMM'
return(result)
}
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