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#############################################################
#
# varComprob.S function
# Author: Claudio Agostinelli and Victor J. Yohai
# E-mail: claudio@unive.it
# Date: June, 24, 2014
# Version: 0.1
#
# Copyright (C) 2014 Claudio Agostinelli
# and Victor J. Yohai
#
#############################################################
varComprob.S <- function(y, x, V, beta=NULL, gamma=NULL, eta0=NULL, scale=10, 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
# eta0: scalar or NULL.
# scale: scalar or NULL.
## 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
initbeta <- beta
initgamma <- gamma
initeta0 <- eta0
initscale <- scale
Sigma <- Vprod(V=V, gamma=gamma) ## V0 is added automatically in Vprod
v <- qchisq(seq(0.0001,0.9999,length=5000), nrow(Sigma))
if (control$psi!="rocke")
s0 <- doSstep(m=v, scale=1, bb=control$bb, cc=control$tuning.chi, psi=control$psi, tol=control$rel.tol.scale, verbose=(control$trace.lev>2))
else
s0 <- doSsteprocke(m=v, scale=1, bb=control$bb, p=p, arp=control$arp.chi, 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
dscale <- control$rel.tol.scale+1
while ((dbeta > control$rel.tol.beta | dgamma > control$rel.tol.gamma | dscale > control$rel.tol.scale) & iter < control$max.it) {
iter <- iter+1
Sigma <- Vprod(V=V, gamma=gamma) ## V0 is added automatically in Vprod
Sigmastar <- Sigma/det(Sigma)^(1/nrow(Sigma))
Sigmastarinv <- solve(Sigmastar)
if (k==0) {
rr <- y
beta <- beta1 <- vector(mode="numeric", length=0)
control$cov <- FALSE
} else
rr <- vcrobresid(y=y, x=x, beta=beta)
RR <- rep(0, n)
for (i in 1:n)
RR[i] <- drop(rr[,i]%*%Sigmastarinv%*%rr[,i])
if (control$psi!="rocke") {
scale1 <- doSstep(m=RR, scale=scale, bb=control$bb, cc=control$tuning.chi, psi=control$psi, tol=control$rel.tol.scale/1000, verbose=(control$trace.lev>2))
W <- vcrobweights(m=RR, scale=scale1, cc=control$tuning.chi, psi=control$psi)
} else {
scale1 <- doSsteprocke(m=RR, scale=scale, bb=control$bb, p=p, arp=control$arp.chi, tol=control$rel.tol.scale/1000, verbose=(control$trace.lev>2))
W <- vcrobweightsrocke(m=RR, scale=scale1, p=p, arp=control$arp.chi)
}
Wdot <- scale*W/drop(W%*%RR)
if (k > 0) {
XX <- matrix(0, nrow=k, ncol=k)
XY <- matrix(0, nrow=k, ncol=1)
for (i in 1:n) {
XX <- XX + Wdot[i]*t(x[,i,])%*%Sigmastarinv%*%x[,i,]
XY <- XY + Wdot[i]*t(x[,i,])%*%Sigmastarinv%*%y[,i]
}
beta1 <- drop(solve(XX)%*%XY)
dbeta <- max(abs(beta-beta1))
} else
dbeta <- 0
gamma1 <- drop(doGammaClassicSstep(gamma=gamma, resid=rr, scale=scale, V=V, control=control))
dscale <- max(abs(scale-scale1))
dgamma <- max(abs(gamma1-gamma))
if (iter > control$max.it/2) {
beta <- (beta1+beta)/2
scale <- (scale1+scale)/2
gamma <- (gamma1+gamma)/2
} else {
beta <- beta1
scale <- scale1
gamma <- gamma1
}
if (control$trace.lev>1) {
cat('Iterations: ', iter, '\n')
cat('Summary of the weights\n')
print(summary(c(W)))
cat('beta: ', beta, '\n')
cat('gamma: ', gamma, '\n')
cat('scale: ', scale, '\n')
cat('diff max(abs(beta_i - beta_i+1)): ', dbeta, '\n')
cat('diff max(abs(gamma_i - gamma_i+1)): ', dgamma, '\n')
cat('diff max(abs(scale_i - scale_i+1)): ', dscale, '\n')
}
}
##END# Iterations
##BEGIN# Eta0
Sigma <- Vprod(V=V, gamma=gamma)
Sigmainv <- solve(Sigma)
RSR <- rep(0, ncol(rr))
for (i in 1:ncol(rr))
RSR[i] <- drop(rr[,i]%*%Sigmainv%*%rr[,i])
if (control$psi!="rocke")
eta0 <- doSstep(m=RSR/s0, scale=1, bb=control$bb, cc=control$tuning.chi, psi=control$psi, tol=control$rel.tol.scale, verbose=(control$trace.lev>2))
else
eta0 <- doSsteprocke(m=RSR/s0, scale=1, bb=control$bb, p=p, arp=control$arp.chi, tol=control$rel.tol.scale, verbose=(control$trace.lev>2))
##END# Eta0
##BEGIN# VCOV
if (control$cov) {
vcov <- VCOV.ClassicS(beta=beta, gamma=gamma, scale=scale, 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$dotweights <- Wdot
result$Sigma <- eta0*Vprod(V=V, gamma=gamma)
result$scale <- result$min <- scale
result$scale0 <- s0
result$initial.values <- list()
result$initial.values$beta <- initbeta
result$initial.values$gamma <- initgamma
result$initial.values$eta0 <- initeta0
result$initial.values$scale <- initscale
result$iterations <- iter
result$control <- control
result$control$method <- "S"
class(result) <- 'varComprob.S'
return(result)
}
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