library(HMDHFDplus) # on CRAN
library(DecompHoriuchi) # on github

# define your HMD username and password as objects, us, and pw
mlt <- readHMDweb("USA","mltper_1x1",username=us,password = pw)
flt <- readHMDweb("USA","fltper_1x1",username=us,password = pw)

mxm1 <- mlt$mx[mlt$Year == 1950]
mxm2 <- mlt$mx[mlt$Year == 2000]
mxf1 <- flt$mx[flt$Year == 1950]
mxf2 <- flt$mx[flt$Year == 2000]

# translate into initial conditions versus change.
minit <- mxm1
finit <- mxf1
mchg <- mxm2 - mxm1
fchg <- mxf2 - mxf1

# cheap e0 function of initial conditions and change
mye0 <- function(mxinit, mxchg){
	mx <- mxinit + mxchg
	sum(exp(-cumsum(mx)))
}

# need the same thing but that takes a single vector of rates.
mye0vec <- function(mxvec){
# clearly the vecs need to be of the same length
	mxinit <- mxvec[1:(length(mxvec)/2)]
	mxchg <- mxvec[(length(mxvec)/2+1):length(mxvec)]
	mye0(mxinit, mxchg)
}

# now decompose:
males   <- c(minit,mchg)
females <- c(finit,fchg)

results <- DecompContinuousOrig(mye0vec, females, males, 20)

initial <- results[1:111]
change <- results[112:222]

# take a quick look.
barplot(rbind(initial,change),space=0,border=NA)