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+# 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=F) {
+ 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)
+
+ (2*mu-t1-t2) / log(10)
+}