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AuxiliaryFunctions.r
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########################################################################################################################
# Name : AuxiliaryFunctions
#
# Author : Michael Scheuerer ([email protected])
#
# Modifications: Adding the "croping" funtion
# Modified version of wgt.md in order not to use the weights
#
# By : Emixi Valdez ([email protected])
# Date : 12 MAR 2020
#
# Description : A collection of small functions used by the other R-scripts.
########################################################################################################################
library(Hmisc)
croping <- function(Date1, Date2, na.rm=FALSE) {
# Date1: date of forecast
# Date2: date of observation
datesDate1 <- as.numeric(paste(year(Date1),
sprintf("%02d",month(Date1)),
sprintf("%02d",day(Date1)),
sprintf("%02d",hour(Date1)),"00", sep=""))
datesDate2 <- as.numeric(paste(year(Date2),
sprintf("%02d",month(Date2)),
sprintf("%02d",day(Date2)),
sprintf("%02d",hour(Date2)),"00", sep=""))
return(which( datesDate2 %in% datesDate1))
}
########################################################################################################################
# CSGD FUNCTIONS
########################################################################################################################
pctg <- function(x, mu, sigma, shift) {
return(pgamma(x-shift, scale=(sigma^2)/mu, shape=(mu/sigma)^2))
}
qctg <- function(x, mu, sigma, shift) {
pmax(0, shift + qgamma( x, scale=(sigma^2)/mu, shape=(mu/sigma)^2) )
}
gini.md <- function(x, na.rm=FALSE) {
if(na.rm & any(is.na(x))) x <- x[!is.na(x)]
n <-length(x)
return(4*sum((1:n)*sort(x, na.last=TRUE))/(n^2)-2*mean(x)*(n+1)/n)
}
wgt.md <- function(x, na.rm=FALSE) {
if(na.rm) x <- x[!is.na(x)]
x.ord <- order(as.vector(x))
x.sort <- x[x.ord]
N <- length(x.sort)
w <- rep(1/N,N)
W <- cumsum(w[x.ord])
2*sum(W[-N]*(1-W[-N])*diff(x.sort))
}
crps.climo <- function(par, obs) {
obs <- sort(obs[!is.na(obs)])
n <- length(obs)
k0 <- sum(obs==0)
shape <- (par[1]/par[2])^2
scale <- par[1]/shape
shift <- par[3]
crps <- numeric(n)
c.std <- -shift/scale
y.std <- (obs[(k0+1):n]-shift)/scale
F.k.c <- pgamma(c.std, shape=shape)
F.kp1.c <- pgamma(c.std, shape=shape+1)
F.2k.2c <- pgamma(2*c.std, shape=2*shape)
B.05.kp05 <- beta(0.5,shape+0.5)
F.k.y <- pgamma(y.std, shape=shape)
F.kp1.y <- pgamma(y.std, shape=shape+1)
crps[1:k0] <- c.std*(2*F.k.c-1) - shape*(2*F.kp1.c-1+F.k.c^2-2*F.kp1.c*F.k.c) - c.std*F.k.c^2 - (shape/pi)*B.05.kp05*(1-F.2k.2c)
crps[(k0+1):n] <- y.std*(2*F.k.y-1) - shape*(2*F.kp1.y-1+F.k.c^2-2*F.kp1.c*F.k.c) - c.std*F.k.c^2 - (shape/pi)*B.05.kp05*(1-F.2k.2c)
return( scale*mean(crps) )
}
crps.reg <- function(par, obs, enspop, ensmean, ensmeandiff, par.climo) {
miss <- is.na(obs)
mu.cl <- par.climo[1]
sigma.cl <- par.climo[2]
shift.cl <- par.climo[3]
log.arg <- par[2] + par[3]*enspop[!miss] + par[4]*ensmean[!miss]
mu <- mu.cl*log1p(expm1(par[1])*log.arg)/par[1]
sigma <- par[5]*sigma.cl*sqrt(mu/mu.cl) + par[6]*sigma.cl*ensmeandiff[!miss]
shift <- shift.cl
scale <- sigma^2/mu
shape <- (mu/sigma)^2
y <- obs[!miss]
c.std <- -shift/scale
y.std <- (y-shift)/scale
F.k.c <- pgamma(c.std, shape=shape)
F.kp1.c <- pgamma(c.std, shape=shape+1)
F.2k.2c <- pgamma(2*c.std, shape=2*shape)
B.05.kp05 <- beta(0.5,shape+0.5)
F.k.y <- pgamma(y.std, shape=shape)
F.kp1.y <- pgamma(y.std, shape=shape+1)
crps <- y.std*(2*F.k.y-1) - shape*(2*F.kp1.y-1+F.k.c^2-2*F.kp1.c*F.k.c) - c.std*F.k.c^2 - (shape/pi)*B.05.kp05*(1-F.2k.2c)
return( mean(scale*crps) )
}
crps.reg.complete <- function(par, obs, enspop, ensmean, ensmeandiff, par.climo) {
#Individual values of CRPS
miss <- is.na(obs)
mu.cl <- par.climo[1]
sigma.cl <- par.climo[2]
shift.cl <- par.climo[3]
log.arg <- par[2] + par[3]*enspop[!miss] + par[4]*ensmean[!miss]
mu <- mu.cl*log1p(expm1(par[1])*log.arg)/par[1]
sigma <- par[5]*sigma.cl*sqrt(mu/mu.cl) + par[6]*sigma.cl*ensmeandiff[!miss]
shift <- shift.cl
scale <- sigma^2/mu
shape <- (mu/sigma)^2
y <- obs[!miss]
c.std <- -shift/scale
y.std <- (y-shift)/scale
F.k.c <- pgamma(c.std, shape=shape)
F.kp1.c <- pgamma(c.std, shape=shape+1)
F.2k.2c <- pgamma(2*c.std, shape=2*shape)
B.05.kp05 <- beta(0.5,shape+0.5)
F.k.y <- pgamma(y.std, shape=shape)
F.kp1.y <- pgamma(y.std, shape=shape+1)
crps <- y.std*(2*F.k.y-1) - shape*(2*F.kp1.y-1+F.k.c^2-2*F.kp1.c*F.k.c) - c.std*F.k.c^2 - (shape/pi)*B.05.kp05*(1-F.2k.2c)
return(scale*crps)
}
crps.normal <- function(par, obs, ensmeanano, ensvar, obs.climo) {
miss <- is.na(obs)
mu <- obs.climo[!miss] + par[1]*ensmeanano[!miss]
sigma <- sqrt( par[2] + par[3]*ensvar[!miss] )
obs.stdz <- (obs[!miss]-mu)/sigma
crps <- sigma * ( obs.stdz*(2*pnorm(obs.stdz)-1) + 2*dnorm(obs.stdz) - 1/sqrt(pi) )
return( mean(crps) )
}