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#This file is part of the source code for
#SPGS: an R package for identifying statistical patterns in genomic sequences.
#Copyright (C) 2015 Universidad de Chile and INRIA-Chile
#
#This program is free software; you can redistribute it and/or modify
#it under the terms of the GNU General Public License as published by
#the Free Software Foundation; either version 2 of the License, or
#(at your option) any later version.
#
#This program is distributed in the hope that it will be useful,
#but WITHOUT ANY WARRANTY; without even the implied warranty of
#MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
#GNU General Public License for more details.
#
#A copy of Version 2 of the GNU Public License is available in the
#share/licenses/gpl-2 file in the R installation directory or from
#http://www.R-project.org/Licenses/GPL-2.
agct.test <- function(x, alg=c("exact", "simulate", "lower", "Lower", "upper"),
n)
{
#Check arguments
dname <- deparse(substitute(x))
if (is.character(x) || inherits(x, "SeqFastadna"))
{ #extract relative frequencies of nucleic acids from DNA sequence
probs <- table(x)
x <- c(probs/sum(probs)) #probability-normalise vector
}
else
x <- c(x) #convert to vector, leaving names in tact
probs <- ISPX2vec(x) #prepare correctly ordered probability vector
alg <- match.arg(alg)
if (alg=="simulate")
{
if (missing(n)) stop("n has not been specified")
if (!is.numeric(n) || length(n)!=1 || n<=0 || n!=floor(n))
stop("n must be a positive integer")
} #if
#Compute test statistic and perform test
xstar <- 0.25+0.5*(probs[1]-probs[3])
if (xstar<0) xstar <- 0
if (xstar>0.5) xstar <- 0.5
ystar <- 0.25+0.5*(probs[2]-probs[4])
if (ystar<0) ystar <- 0
if (ystar>0.5) ystar <- 0.5
offset <- probs-c(xstar, ystar, 0.5-xstar, 0.5-ystar)
stat <- c(etaV=sqrt(sum(offset*offset)))
#Compute p-value using the specified method
p.value <- switch(alg,
exact=agctTestPValue(stat),
simulate=agctTestPValueFromMonteCarlo(stat, n),
lower=agctTestPValueLowerBound(stat),
Lower=agctTestPValueLowerBoundTight(stat),
upper=agctTestPValueUpperBound(stat)
) #switch
names(p.value) <- "p-value"
#Return result
method <- "Test of relative purine/pyrimidine frequency equivalence based on Euclidean distance\n"
method2 <- switch(alg,
exact="",
simulate=sprintf(" with simulated p-value (based on %d replicates)", n),
lower=" with lower bound computed for p-value",
Lower=" with alternative, tighter lower bound computed for p-value",
upper=" with upper bound computed for p-value"
) #switch
method <- sprintf("%s%s", method, method2)
rval <- list(statistic=stat, p.value=p.value, method=method,
data.name=dname, estimate=probs,
stat.desc= "etaV = Euclidean distance from relative frequency vector to closest point in\nthetaV ={(x,y,1/2-x,1/2-y) : 0 <= x,y <= 1/2}",
null="A+G != C+T",
alternative="A+G = C+T")
class(rval) <- "htest.ext"
rval
} #function
pagcttest <- function(stat)
#The cumulative distribution function of etaV based on uniform distribution
#over the 3-simplex.
{
if (missing(stat)) stop("stat has not been specified")
if (!is.vector(stat, "numeric") || length(stat)==0)
stop("stat must be a non-empty numeric vector")
sapply(stat, agctTestPValue)
} #function
agctTestPValue <- function(epsilon)
{
if (epsilon<0) return(0)
if (epsilon>sqrt(3/8)) return(1)
#Declare function for computing area of trapezoids in the corners of the simplex
intCurvedCornerTrapezoids <- function(epsilon, x)
{
epsilon*(epsilon*(asin(x)+x*sqrt(1-x*x))/2 - epsilon*x*x/sqrt(2) + x*x*x*epsilon*epsilon-epsilon*epsilon*x)/sqrt(2)
} #function
if (epsilon<=0.5)
{
triPrismVol <- 3*epsilon*(1-epsilon)
shrinkingTriangleVol <- 0
curvedVol <- 12*(intCurvedCornerTrapezoids(epsilon, 1/sqrt(3)) - intCurvedCornerTrapezoids(epsilon, 0))
}
else
{
triPrismVol <- 0.75
shrinkingTriangleVol <- 0.25 - 2*(0.5-sqrt(2*epsilon*epsilon-.5))^3
curvedVol <- 12*(intCurvedCornerTrapezoids(epsilon, 1/sqrt(3)) - intCurvedCornerTrapezoids(epsilon, sqrt(1-0.25/(epsilon*epsilon))))
} #if
triPrismVol+shrinkingTriangleVol +curvedVol
} #function
agctTestPValueFromMonteCarlo <- function(epsilon, n)
{
if (missing(epsilon)) stop("epsilon has not been specified")
if (!is.numeric(epsilon) || length(epsilon)!=1) stop("epsilon must be a single numerical value")
if (epsilon<=0) return(0)
if (epsilon>=1) return(1)
if (missing(n)) stop("n has not been specified")
if (!is.numeric(n) || length(n)!=1 || n<=0 || n!=floor(n))
stop("n must be a positive integer")
rexp <- rexp(4*n, 1)
pr <- .C(c_ProbabilityNormalise,
as.double(rexp),
as.integer(n),
as.integer(1),
as.integer(4),
res=double(4*n)
)$res
dim(pr) <- c(n,4)
xstar <- 0.25+0.5*(pr[,1]-pr[,3])
xstar[xstar<0] <- 0
xstar[xstar>0.5] <- 0.5
ystar <- 0.25+0.5*(pr[,2]-pr[,4])
ystar[ystar<0] <- 0
ystar[ystar>0.5] <- 0.5
offset <- pr-cbind(xstar, ystar, 0.5-xstar, 0.5-ystar)
stat <- sqrt(rowSums(offset*offset))
return(sum(stat<=epsilon)/n)
} #function
agctTestPValueLowerBound <- function(epsilon)
{
3*epsilon*(1-epsilon)
} #function
agctTestPValueLowerBoundTight <- function(epsilon)
{
l <- sqrt(2/3)*epsilon
# 3*l-4*l^3 + 3*(epsilon-l)*(1-l-epsilon)
3*l-4*l^3 + 3*(epsilon*(1-epsilon)-l*(1-l))
} #function
agctTestPValueUpperBound <- function(epsilon)
{
3*epsilon-4*epsilon^3
} #function
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