# Copyright © 2016 by Justin Bedő
#
# Permission to use, copy, modify, and/or distribute this software for any
# purpose with or without fee is hereby granted, provided that the above
# copyright notice and this permission notice appear in all copies.
#
# THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
# WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
# MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
# ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
# WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
# ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
# OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
pmt <- function(a, b, two.sided=T, signed=F) {
if(any(a == 0) | any(b == 0))
stop("cannot handle 0 counts")
if(length(a) != length(b))
stop("vectors must be same length")
ce <- function(mu){
pt1 <- mapply(function(xa, mu, rho) logsumexp(cumsum(log(((1 + rho) * (xa - (0:(xa-1)))/(2 * mu))))), a, mu, rho)
pt2 <- mapply(function(xb, mu, rho) logsumexp(cumsum(log((2*mu*rho) / ((1 + rho)*(xb + (1:100)))))), b, mu, rho)
rho + rho * (exp(pt1) - exp(pt2))
}
logsumexp <- function(x) {
x <- sort(x, decreasing=T)
log1p(sum(exp(x[-1] - x[1]))) + x[1]
}
Ra <- sum(a)
Rb <- sum(b)
chi <- a/b
rho <- rep(Ra/Rb, length(a))
msk <- a/Ra > b/Rb
rho[msk] <- 1/rho[msk]
tmp <- a[msk]
a[msk] <- b[msk]
b[msk] <- tmp
chi[msk] <- 1/chi[msk]
lb <- (rho - chi + sqrt(((rho - chi)^2 + 4 * chi * rho * (1 + rho)))) / (4 * rho) * b * 0.75
ub <- (1 + chi) * (1 + rho) / (2 * rho + 1) * b * 1.25
while(max(ub - lb) > 1e-6){
mu <- (ub + lb) / 2
scmu <- ce(mu) >= 0
ub <- ub * scmu + mu * (1 - scmu)
lb <- lb * (1 - scmu) + mu * scmu
}
t1 <- mapply(function(xa, mu, rho) { i <- 0:xa; logsumexp(i * log(2 * mu) - lfactorial(i) - i * log(1 + rho))}, a, mu, rho)
t2 <- mapply(function(xb, mu, rho) { j <- xb:(xb*100); logsumexp(j * log(2 * mu * rho) - lfactorial(j) - j * log(1 + rho))}, b, mu, rho)
ps <- (2*mu-t1-t2)
ps <- ps - log1p(ps)
ps <- ps / log(10)
if(!two.sided) ps[msk] <- NA
else if(signed) ps <- ps * (1-2*msk)
ps
}
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