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03c_estim_directmiss.R
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# initalizations
source('00_system.R')
args <- commandArgs(trailingOnly = TRUE)
loadstring <- as.character(args[1])
print(loadstring)
# estimation
tt <- sum(.Internal(gc(FALSE, TRUE, TRUE))[13:14]) # memory report
elapsed_time <- system.time({
# get the data and simulationspecs
load(file = paste0(CommonPath, '/fields/', loadstring))
delta <- get_range_help(this_field@truetheta) / 2
memory_values <- get_memory_values(this_field)
# Covariance function taperfunction chosen only on true smoothness
Covariance <- function( h, theta, delta, ... ) {
if (this_field@truetheta[3] <= 0.5)
return(cov.sph_1( h, c(delta, theta), ...))
if (this_field@truetheta[3] <= 1.5)
return(cov.wend1_1( h, c(delta, theta), ...))
return(cov.wend2_1( h, c(delta, theta), ...))
}
options(spam.nearestdistnnz = c(memory_values[1] / 2, 1)) # pseudo - optimized
if(this_field@gaussian){
# Estimate betas
distmat <- nearest.dist((this_field@locs), delta = delta, upper = NULL)
Sigma_oracle <- Covariance(h = distmat, theta = this_field@truetheta[c(2, 4)], delta = delta)
Rstruct <- chol(Sigma_oracle, memory = list(nnzR = memory_values[2] / 2))
z <- this_field@fulldata
X <- cbind(rep(1, length(this_field@fulldata)), cos(this_field@locs))
n <- length(z)
colnames(X) <- NULL
xsigma <- t(solve(Sigma_oracle, X))
right_side <- xsigma %*% as.matrix(z, ncol = 1)
beta0_init <- solve(xsigma %*% X, right_side)
z_nomean <- z - ( X %*% beta0_init )
neg2loglikelihood <- function(theta) {
Sigma <- Covariance(h = distmat, theta = theta, delta = delta)
cholS <- chol(Sigma, Rstruct = Rstruct)
logdet <- sum(log(diag(cholS)))
return(n * log(2 * pi) + 2 * logdet + sum(z_nomean * backsolve(cholS,
forwardsolve(cholS, z_nomean, transpose = TRUE, upper.tri = TRUE),
n)))
}
theta_lower <- c(1e-8, 1e-8)
theta_upper <- c(Inf, 1)
theta_0 <- c(0.9*var(z_nomean), 0.1*var(z_nomean))
cl <- makeCluster(ifelse(ncores > length(theta_0)*2 +1, length(theta_0)*2 + 1, 1 + floor(ncores/3)),
useXDR = F)
setDefaultCluster(cl = cl)
clusterExport(cl, c('lib.loc'))
clusterEvalQ(cl, .libPaths(new = lib.loc))
clusterEvalQ(cl, library('spam', lib.loc = lib.loc))
clusterEvalQ(cl, library('spam64', lib.loc = lib.loc))
clusterExport(cl, c('neg2loglikelihood', 'z_nomean', 'distmat', 'Rstruct', 'n', 'Covariance',
'this_field', 'delta', 'cov.sph_1', 'cov.wend1_1', 'cov.wend2_1'))
output <- optimParallel::optimParallel(fn = neg2loglikelihood,
method = 'L-BFGS-B',
lower = theta_lower,
upper = theta_upper,
par = theta_0,
parallel = list(forward = FALSE,
loginfo = TRUE),
control = list(factr = 1e8, # approx. 1e-8
trace = TRUE, maxit = 1000))
stopCluster(cl)
} else {
distmat <- nearest.dist(this_field@locs, delta = delta, upper = NULL)
Sigma_oracle <- Covariance(h = distmat, theta = this_field@truetheta[c(2, 4)], delta = delta)
Rstruct <- chol(Sigma_oracle, memory = list(nnzR = memory_values[2] / 2))
z <- this_field@fulldata
X <- cbind(rep(1, length(this_field@fulldata)), cos(this_field@locs))
n <- length(z)
colnames(X) <- NULL
neg2logliksasbetas <- function(theta){
Sigma <- Covariance(h = distmat,
theta = c(theta[1:2]),
delta = delta)
corr_matrixd <- Sigma/Sigma[1, 1] # assuming second-order stationarity
cholS <- chol(corr_matrixd, Rstruct = Rstruct)
logdet <- 2 * sum(log(diag(cholS)))
stdata <- (z - X %*% matrix(theta[5:7], nrow = 3)) / sqrt(theta[1])
skew <- theta[3]
kurt <- theta[4]
Z <- sinh(kurt * asinh(stdata) - skew)
C <- sqrt(1+Z^2)
return( - 2 * (n * log(kurt) - (n/2) * log(2 * pi * (theta[1])) - 0.5 * logdet +
sum( log(C) - 0.5 * log(1 + stdata^2)) - 0.5 * sum(Z * backsolve(cholS,
forwardsolve(cholS, Z, transpose = TRUE, upper.tri = TRUE),
n)) )
)
}
theta_lower <- c(1e-8, 1e-8, -5, 1e-8, -20, - 20, -20)
theta_upper <- c(Inf, 1, 5, 5, 20, 20, 20)
theta_0 <- c(0.9 * var(this_field@fulldata), 0.1 * var(this_field@fulldata), 0, 1, mean(this_field@fulldata), 0, 0)
cl <- makeCluster(ifelse(ncores > length(theta_0)*2 +1, length(theta_0)*2 + 1, 1 + floor(ncores/3)),
useXDR = F)
setDefaultCluster(cl = cl)
clusterExport(cl, c('lib.loc'))
clusterEvalQ(cl, .libPaths(new = lib.loc))
clusterEvalQ(cl, library('spam', lib.loc = lib.loc))
clusterEvalQ(cl, library('spam64', lib.loc = lib.loc))
clusterExport(cl, c('neg2logliksasbetas', 'z', 'distmat', 'Rstruct', 'n', 'X', 'this_field', 'cov.mat2', 'Covariance',
'delta', 'cov.sph_1', 'cov.wend1_1', 'cov.wend2_1'))
output <- optimParallel::optimParallel(fn = neg2logliksasbetas,
method = 'L-BFGS-B',
lower = theta_lower,
upper = theta_upper,
par = theta_0,
parallel = list(forward = FALSE,
loginfo = TRUE),
control = list(factr = 1e8, # approx. 1e-8
trace = TRUE, maxit = 1000))
stopCluster(cl)
}
})[3]
ifelse(this_field@gaussian, betas_hat <- beta0_init,
betas_hat <- output$par[5:7])
memory_used <- sum(.Internal(gc(FALSE, FALSE, TRUE))[13:14]) - tt
this_estimates <- new('directmiss_estimate',
specsnr = this_field@specsnr,
fielditer = this_field@fielditer,
delta = delta,
time = elapsed_time,
optimout = output,
betas_hat = betas_hat,
memory_used = memory_used,
loadstring = loadstring)
save(this_estimates, file =paste0(CommonPath, '/estimates/estimates.directmiss.', this_field@specsnr, '.iter', this_field@fielditer, '.RData'))