Nothing
R/MCM.sde.R
In Sim.DiffProc: Simulation of Diffusion Processes
Defines functions
plot.MCM.sde
.plot.MCM.sde
print.MCM.sde
MCM.sde.default
MCM.sde
Documented in
MCM.sde
MCM.sde.default
plot.MCM.sde
print.MCM.sde
## Thu Apr 30 10:50:58 2020
## Original file Copyright © 2020 A.C. Guidoum, K. Boukhetala
## This file is part of the R package Sim.DiffProc
## Department of Probabilities & Statistics
## Faculty of Mathematics
## University of Science and Technology Houari Boumediene
## BP 32 El-Alia, U.S.T.H.B, Algiers
## Algeria
## 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 3 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 the GNU General Public License is available at
## http://www.r-project.org/Licenses/
## Unlimited use and distribution (see LICENCE).
###################################################################################################
#####
##### Monte-Carlo SDE's
MCM.sde <- function(model, ...) UseMethod("MCM.sde")
MCM.sde.default <- function(model,statistic,R=100,time,exact=NULL,names=NULL,
level = 0.95, parallel = c("no", "multicore", "snow"),
ncpus = getOption("ncpus",1L), cl = NULL,...)
{
if (!is.function(statistic))
stop("'statistic' must be function")
if (!is.null(exact)){
if (!is.list(exact))
stop("'exact' must be a named list")}
if (!is.null(names)){
if (!is.character(names))
stop("'names' must be an character")}
if (any(!is.numeric(R) || (R - floor(R) > 0) || R <= 0))
stop(" 'R' must be an integer ")
if (R == 1) stop("Parallel Monte-Carlo Methods is for any R > 1")
if (missing(time)) {time = as.numeric(model$T)}
if (length(time) > 1 )
stop (" 'time' must be an integer 't0 < time <= T' ")
if (any(model$T < time | model$t0 > time) )
stop( " please use 't0 < time <= T'")
if (any(level <= 0 | level >= 1) )
stop( " please use '0 < level < 1'")
if (class(model)=="bridgesde1d" | class(model)=="bridgesde2d" | class(model)=="bridgesde3d")
stop("Not available for diffusion bridges")
if (class(model)!="snssde1d" & class(model)!="snssde2d" & class(model)!="snssde3d")
stop(" 'model' is not class of 'snssdekd', k=1,2,3. ")
if (missing(parallel))
parallel <- getOption("parallel", "no")
parallel <- match.arg(parallel)
have_mc <- have_snow <- FALSE
if (parallel != "no" && ncpus > 1L) {
if (parallel == "multicore")
have_mc <- .Platform$OS.type != "windows"
else if (parallel == "snow")
have_snow <- TRUE
if (!have_mc && !have_snow)
ncpus <- 1L
loadNamespace("parallel")
}
if (class(model)=="snssde1d"){
statistic <- match.fun(statistic)
fn1d <- function(x,...) statistic(x, ...)
rand <- matrix(0,nrow=R,ncol=model$M)
run1d <- function(...) Sim.DiffProc::rsde1d(eval(model$call),at=time)
if (ncpus > 1L && (have_mc || have_snow)){
if (have_mc) {
base::RNGkind("L'Ecuyer-CMRG")
rand <- do.call("rbind",parallel::mclapply(1:R, run1d,mc.cores = ncpus,mc.set.seed = TRUE))
}else if (have_snow) {
list(...)
if (is.null(cl)){
cl <- parallel::makePSOCKcluster(rep("localhost", ncpus))
parallel::clusterEvalQ(cl, library(Sim.DiffProc))
parallel::clusterExport(cl, varlist=c("time",all.vars(model$call),
all.vars(model$drift)[which(all.vars(model$drift)!="x" & all.vars(model$drift)!="t")],
all.vars(model$diffusion)[which(all.vars(model$diffusion)!="x" & all.vars(model$diffusion)!="t")]),envir = environment())
if (base::RNGkind()[1L] == "L'Ecuyer-CMRG") parallel::clusterSetRNGStream(cl)
rand <- do.call("rbind", parallel::parLapply(cl, 1:R, run1d))
parallel::stopCluster(cl)
}else{
parallel::clusterEvalQ(cl, library(Sim.DiffProc))
parallel::clusterExport(cl, varlist=c("time",all.vars(model$call),
all.vars(model$drift)[which(all.vars(model$drift)!="x" & all.vars(model$drift)!="t")],
all.vars(model$diffusion)[which(all.vars(model$diffusion)!="x" & all.vars(model$diffusion)!="t")]),envir = environment())
if (base::RNGkind()[1L] == "L'Ecuyer-CMRG") parallel::clusterSetRNGStream(cl)
rand <- do.call("rbind", parallel::parLapply(cl, 1:R, run1d))
parallel::stopCluster(cl)
}
}}else{
for (i in 1:R){
rand[i,] = run1d()
}
}
Stat <- do.call("cbind",lapply(1:R,function(i) fn1d(rand,i,...)))
}else if (class(model)=="snssde2d"){
statistic <- match.fun(statistic)
fn2d <- function(x,...) statistic(x, ...)
rand <- matrix(0,nrow=2*R,ncol=model$M)
run2d <- function(...) t(Sim.DiffProc::rsde2d(eval(model$call),at=time))
if (ncpus > 1L && (have_mc || have_snow)){
if (have_mc) {
base::RNGkind("L'Ecuyer-CMRG")
rand <- do.call("rbind",parallel::mclapply(1:R,run2d,mc.cores = ncpus,mc.set.seed = TRUE))
}else if (have_snow) {
list(...)
if (is.null(cl)==TRUE) {
cl <- parallel::makePSOCKcluster(rep("localhost", ncpus))
parallel::clusterEvalQ(cl, library(Sim.DiffProc))
parallel::clusterExport(cl, varlist=c("time",all.vars(model$call),
all.vars(model$driftx)[which(all.vars(model$driftx)!="x" & all.vars(model$driftx)!="y" & all.vars(model$driftx)!="t")],
all.vars(model$drifty)[which(all.vars(model$drifty)!="x" & all.vars(model$drifty)!="y" & all.vars(model$drifty)!="t")],
all.vars(model$diffx)[which(all.vars(model$diffx)!="x" & all.vars(model$diffx)!="y" & all.vars(model$diffx)!="t")],
all.vars(model$diffy)[which(all.vars(model$diffy)!="x" & all.vars(model$diffy)!="y" & all.vars(model$diffy)!="t")]),envir = environment())
if (base::RNGkind()[1L] == "L'Ecuyer-CMRG") parallel::clusterSetRNGStream(cl)
rand <- do.call("rbind", parallel::parLapply(cl, 1:R, run2d))
parallel::stopCluster(cl)
}else{
parallel::clusterEvalQ(cl, library(Sim.DiffProc))
parallel::clusterExport(cl, varlist=c("time",all.vars(model$call),
all.vars(model$driftx)[which(all.vars(model$driftx)!="x" & all.vars(model$driftx)!="y" & all.vars(model$driftx)!="t")],
all.vars(model$drifty)[which(all.vars(model$drifty)!="x" & all.vars(model$drifty)!="y" & all.vars(model$drifty)!="t")],
all.vars(model$diffx)[which(all.vars(model$diffx)!="x" & all.vars(model$diffx)!="y" & all.vars(model$diffx)!="t")],
all.vars(model$diffy)[which(all.vars(model$diffy)!="x" & all.vars(model$diffy)!="y" & all.vars(model$diffy)!="t")]),envir = environment())
if (base::RNGkind()[1L] == "L'Ecuyer-CMRG") parallel::clusterSetRNGStream(cl)
rand <- do.call("rbind", parallel::parLapply(cl, 1:R, run2d))
parallel::stopCluster(cl)
}
}}else{
for (i in 1:R){
rand[c(seq(2*i-1,2*i,by=1)),]=run2d()
}
}
rand1 <- list(x=rand[seq(1,2*R,by=2),],y=rand[seq(2,2*R,by=2),])
rand2 <- lapply(1:R,function(i) data.frame(x=rand1$x[i,], y=rand1$y[i,]))
Stat <- do.call("cbind",lapply(1:R,function(i) fn2d(rand2[[i]],...)))
}else if (class(model)=="snssde3d"){
statistic <- match.fun(statistic)
fn3d <- function(x,...) statistic(x, ...)
rand <- matrix(0,nrow=3*R,ncol=model$M)
run3d <- function(...) t(Sim.DiffProc::rsde3d(eval(model$call),at=time))
if (ncpus > 1L && (have_mc || have_snow)){
if (have_mc) {
base::RNGkind("L'Ecuyer-CMRG")
rand <- do.call("rbind",parallel::mclapply(1:R,run3d,mc.cores = ncpus,mc.set.seed = TRUE))
}else if (have_snow) {
list(...)
if (is.null(cl)==TRUE) {
cl <- parallel::makePSOCKcluster(rep("localhost", ncpus))
parallel::clusterEvalQ(cl, library(Sim.DiffProc))
parallel::clusterExport(cl, varlist=c("time",all.vars(model$call),
all.vars(model$driftx)[which(all.vars(model$driftx)!="x" & all.vars(model$driftx)!="y" & all.vars(model$driftx)!="z" & all.vars(model$driftx)!="t")],
all.vars(model$drifty)[which(all.vars(model$drifty)!="x" & all.vars(model$drifty)!="y" & all.vars(model$drifty)!="z" & all.vars(model$drifty)!="t")],
all.vars(model$driftz)[which(all.vars(model$driftz)!="x" & all.vars(model$driftz)!="y" & all.vars(model$driftz)!="z" & all.vars(model$driftz)!="t")],
all.vars(model$diffx)[which(all.vars(model$diffx)!="x" & all.vars(model$diffx)!="y" & all.vars(model$diffx)!="z" & all.vars(model$diffx)!="t")],
all.vars(model$diffy)[which(all.vars(model$diffy)!="x" & all.vars(model$diffy)!="y" & all.vars(model$diffy)!="z" & all.vars(model$diffy)!="t")],
all.vars(model$diffz)[which(all.vars(model$diffz)!="x" & all.vars(model$diffz)!="y" & all.vars(model$diffz)!="z" & all.vars(model$diffz)!="t")]),envir = environment())
if (base::RNGkind()[1L] == "L'Ecuyer-CMRG") parallel::clusterSetRNGStream(cl)
rand <- do.call("rbind", parallel::parLapply(cl, 1:R, run3d))
parallel::stopCluster(cl)
}else{
parallel::clusterEvalQ(cl, library(Sim.DiffProc))
parallel::clusterExport(cl, varlist=c("time",all.vars(model$call),
all.vars(model$driftx)[which(all.vars(model$driftx)!="x" & all.vars(model$driftx)!="y" & all.vars(model$driftx)!="z" & all.vars(model$driftx)!="t")],
all.vars(model$drifty)[which(all.vars(model$drifty)!="x" & all.vars(model$drifty)!="y" & all.vars(model$drifty)!="z" & all.vars(model$drifty)!="t")],
all.vars(model$driftz)[which(all.vars(model$driftz)!="x" & all.vars(model$driftz)!="y" & all.vars(model$driftz)!="z" & all.vars(model$driftz)!="t")],
all.vars(model$diffx)[which(all.vars(model$diffx)!="x" & all.vars(model$diffx)!="y" & all.vars(model$diffx)!="z" & all.vars(model$diffx)!="t")],
all.vars(model$diffy)[which(all.vars(model$diffy)!="x" & all.vars(model$diffy)!="y" & all.vars(model$diffy)!="z" & all.vars(model$diffy)!="t")],
all.vars(model$diffz)[which(all.vars(model$diffz)!="x" & all.vars(model$diffz)!="y" & all.vars(model$diffz)!="z" & all.vars(model$diffz)!="t")]),envir = environment())
if (base::RNGkind()[1L] == "L'Ecuyer-CMRG") parallel::clusterSetRNGStream(cl)
rand <- do.call("rbind", parallel::parLapply(cl, 1:R, run3d))
parallel::stopCluster(cl)
}
}}else{
for (i in 1:R){
rand[c(seq(3*i-2,3*i,by=1)),]=run3d()
}
}
rand1 <- list(x=rand[seq(1,3*R,by=3),],y=rand[seq(2,3*R,by=3),],z=rand[seq(3,3*R,by=3),])
rand3 <- lapply(1:R,function(i) data.frame(x=rand1$x[i,], y=rand1$y[i,],z=rand1$z[i,]))
Stat <- do.call("cbind",lapply(1:R,function(i) fn3d(rand3[[i]],...)))
}
Est <- round(apply(Stat,1,mean),digits=options()$digits)
#Sdev <- round(apply(Stat,1,sd),options()$digits)
SErr <- round(apply(Stat,1,sd)/sqrt(R),digits=options()$digits)
INF <- round(Est - qnorm(1-0.5*(1-level))*SErr,digits=options()$digits)
SUP <- round(Est + qnorm(1-0.5*(1-level))*SErr,digits=options()$digits)
Conf <- paste("(",INF,",",SUP,")",sep=" ")
if (!is.null(exact)){
rmse_f <- function(error) sqrt(mean(error^2))
Exact = round(as.numeric(exact),digits=options()$digits)
Bias = round(Est - Exact,digits=options()$digits)
Rmse = round(apply(Stat-Exact,1, rmse_f ),digits=options()$digits)
TAB <- data.frame(Exact,Est,Bias,SErr,Rmse,Conf)
names(TAB) <- c("Exact","Estimate","Bias","Std.Error","RMSE",paste("CI(",100*(1 - level)/2,"%",",",100-100*(1 - level)/2,"%",")",sep=" "))
if (!is.null(names(exact)) && is.null(names)) {rownames(TAB) <- names(exact)}
else if (is.null(names(exact)) && !is.null(names)) {rownames(TAB) <- names}
else if (!is.null(names(exact)) && !is.null(names)) {rownames(TAB) <- names}
else{rownames(TAB) <- paste("mu",1:length(Est),sep="")}
}else{
TAB <- data.frame(Est,SErr,Conf)
names(TAB) <- c("Estimate","Std.Error",paste("CI(",100*(1 - level)/2,"%",",",100-100*(1 - level)/2,"%",")",sep=" "))
if (!is.null(names)) {rownames(TAB) <- names}else{rownames(TAB) <- paste("mu",1:length(Est),sep="")}
}
structure(list(MC=TAB,name=dimnames(TAB)[[1]],ech=Stat,mod=model,Fn=statistic,corrmat=model$corrmat,time=time,call=match.call(),infC=INF,supC=SUP,dim=model$dim,Class=class(model)),class="MCM.sde")
}
print.MCM.sde <- function(x, digits=NULL, ...)
{
class(x) <- "MCM.sde"
Ito = "It\xf4"
Encoding(Ito) <- "latin1"
if (is.null(x$corrmat)){
if (x$Class=="snssde1d"){
Dr <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)))), list(e = x$mod$drift))))
DD <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)))), list(e = x$mod$diffusion))))
if(x$mod$type=="ito"){
cat(Ito," Sde 1D:","\n",
" | dX(t) = ", Dr," * dt + ", DD," * dW(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
sep="")}else{
cat("Stratonovich Sde 1D:","\n",
" | dX(t) = ", Dr," * dt + ", DD," o dW(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
sep="")}
}else if (x$Class=="snssde2d"){
Drx <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)))), list(e = x$mod$driftx))))
DDx <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)))), list(e = x$mod$diffx))))
Dry <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)))), list(e = x$mod$drifty))))
DDy <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)))), list(e = x$mod$diffy))))
if(x$mod$type=="ito"){
cat(Ito," Sde 2D:","\n",
" | dX(t) = ", Drx," * dt + ", DDx," * dW1(t)","\n",
" | dY(t) = ", Dry," * dt + ", DDy," * dW2(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
sep="")}else{
cat("Stratonovich Sde 2D:","\n",
" | dX(t) = ", Drx," * dt + ", DDx," o dW1(t)","\n",
" | dY(t) = ", Dry," * dt + ", DDy," o dW2(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
sep="")}
}else if (x$Class=="snssde3d"){
Drx <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$driftx))))
DDx <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$diffx))))
Dry <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$drifty))))
DDy <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$diffy))))
Drz <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$driftz))))
DDz <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$diffz))))
if(x$mod$type=="ito"){
cat(Ito," Sde 3D:","\n",
" | dX(t) = ", Drx," * dt + ", DDx," * dW1(t)","\n",
" | dY(t) = ", Dry," * dt + ", DDy," * dW2(t)","\n",
" | dZ(t) = ", Drz," * dt + ", DDz," * dW3(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
sep="")}else{
cat("Stratonovich Sde 3D:","\n",
" | dX(t) = ", Drx," * dt + ", DDx," o dW1(t)","\n",
" | dY(t) = ", Dry," * dt + ", DDy," o dW2(t)","\n",
" | dZ(t) = ", Drz," * dt + ", DDz," o dW3(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
sep="")}
}} else {
if (x$Class=="snssde1d"){
Dr <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)))), list(e = x$mod$drift))))
DD <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)))), list(e = x$mod$diffusion))))
if(x$mod$type=="ito"){
cat(Ito," Sde 1D:","\n",
" | dX(t) = ", Dr," * dt + ", DD," * dW(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
sep="")}else{
cat("Stratonovich Sde 1D:","\n",
" | dX(t) = ", Dr," * dt + ", DD," o dW(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
sep="")}
}else if (x$Class=="snssde2d"){
Drx <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)))), list(e = x$mod$driftx))))
DDx <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)))), list(e = x$mod$diffx))))
Dry <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)))), list(e = x$mod$drifty))))
DDy <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)))), list(e = x$mod$diffy))))
if(x$mod$type=="ito"){
cat(Ito," Sde 2D:","\n",
" | dX(t) = ", Drx," * dt + ", DDx," * dB1(t)","\n",
" | dY(t) = ", Dry," * dt + ", DDy," * dB2(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
" | Correlation structure:",sep="")
prmatrix(x$mod$corrmat,rowlab = rep(" ", 2), collab = rep("", 2),digits=digits)
}else{
cat("Stratonovich Sde 2D:","\n",
" | dX(t) = ", Drx," * dt + ", DDx," o dB1(t)","\n",
" | dY(t) = ", Dry," * dt + ", DDy," o dB2(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
" | Correlation structure:",sep="")
prmatrix(x$mod$corrmat,rowlab = rep(" ", 2), collab = rep("", 2),digits=digits)
}
}else if (x$Class=="snssde3d"){
Drx <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$driftx))))
DDx <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$diffx))))
Dry <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$drifty))))
DDy <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$diffy))))
Drz <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$driftz))))
DDz <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$diffz))))
if(x$mod$type=="ito"){
cat(Ito," Sde 3D:","\n",
" | dX(t) = ", Drx," * dt + ", DDx," * dB1(t)","\n",
" | dY(t) = ", Dry," * dt + ", DDy," * dB2(t)","\n",
" | dZ(t) = ", Drz," * dt + ", DDz," * dB3(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
" | Correlation structure:",sep="")
prmatrix(x$mod$corrmat,rowlab = rep(" ", 3), collab = rep("", 3),digits=digits)
}else{
cat("Stratonovich Sde 3D:","\n",
" | dX(t) = ", Drx," * dt + ", DDx," o dB1(t)","\n",
" | dY(t) = ", Dry," * dt + ", DDy," o dB2(t)","\n",
" | dZ(t) = ", Drz," * dt + ", DDz," o dB3(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
" | Correlation structure:",sep="")
prmatrix(x$mod$corrmat,rowlab = rep(" ", 3), collab = rep("", 3),digits=digits)
}
}
}
cat("\nPMCM Based on ", dim(x$ech)[2]," Batches with ",x$mod$M, "-Realisations at time ",x$time,":","\n\n",sep="")
print(x$MC)
}
.plot.MCM.sde <- function(x,index = 1,type=c("all","hist","qqplot","boxplot","CI"),...)
{
class(x) <- "MCM.sde"
data <- x$ech
name <- x$name
if (length(index) > 1) {
index <- index[1]
warning("The first element of 'index' will be used")}
if (index > dim(data)[1] | index < 1 )
stop("Subscript out of bounds")
#if (is.null(x$call$names)) {name <- paste("t",1:dim(data)[1],"*",sep="")}else{
#name <- sapply(2:length(x$call$names),function(i) x$call$names[[i]])}
type <- match.arg(type)
if (type=="all"){par(mfrow=c(2,2))}
if (any(type == "all" | type == "hist")){
MASS::truehist(data[index,],xlab = name[index],col="gold",ylab="Density",bty="o",las=1,...)
abline(v=mean(data[index,]),lty=2,col="red3")
}
if (any(type == "all" | type == "qqplot")){
qq <- qnorm((seq_len(dim(data)[2]))/(dim(data)[2]+1))
qlab <-"Quantiles of Standard Normal"
stats::qqplot(qq,data[index,],xlab=qlab,ylab=name[index],las=1)
abline(a=mean(data[index,]),b=sqrt(var(data[index,])),lty=2,col="red3",lwd=2)
}
if (any(type == "all" | type == "boxplot")){
bx <- boxplot(data[index,],plot=FALSE,names=name[index])
graphics::bxp(bx, notch = FALSE,las=1, boxfill = "gold", frame.plot = TRUE,outline = FALSE,show.names = TRUE)
}
if (any(type == "all" | type == "CI")){
plot(mean(data[index,]),type="n" ,xaxt='n',yaxt="n",ylim=c(x$infC[index], x$supC[index]),ylab='Confidence Interval',xlab="",las=1,panel.first = grid())
axis(1, at=1, labels=name[index],lty = 2, lwd = 0.5)
axis(side=2,lwd=0.5,las=1,cex=0.5)
arrows(1,x$infC[index],1,x$supC[index],code=3,length=0.25,lwd=2,angle=90,col='red3')
points(1,mean(data[index,]),pch=21,col="red3",bg="gold",cex=1.5)
}
par(mfrow=c(1,1))
invisible(x)
}
plot.MCM.sde <- function(x,index = 1,type=c("all","hist","qqplot","boxplot","CI"),...) .plot.MCM.sde(x,index,type,...)
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Defines functions plot.MCM.sde .plot.MCM.sde print.MCM.sde MCM.sde.default MCM.sde
Documented in MCM.sde MCM.sde.default plot.MCM.sde print.MCM.sde
## Thu Apr 30 10:50:58 2020
## Original file Copyright © 2020 A.C. Guidoum, K. Boukhetala
## This file is part of the R package Sim.DiffProc
## Department of Probabilities & Statistics
## Faculty of Mathematics
## University of Science and Technology Houari Boumediene
## BP 32 El-Alia, U.S.T.H.B, Algiers
## Algeria
## 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 3 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 the GNU General Public License is available at
## http://www.r-project.org/Licenses/
## Unlimited use and distribution (see LICENCE).
###################################################################################################
#####
##### Monte-Carlo SDE's
MCM.sde <- function(model, ...) UseMethod("MCM.sde")
MCM.sde.default <- function(model,statistic,R=100,time,exact=NULL,names=NULL,
level = 0.95, parallel = c("no", "multicore", "snow"),
ncpus = getOption("ncpus",1L), cl = NULL,...)
{
if (!is.function(statistic))
stop("'statistic' must be function")
if (!is.null(exact)){
if (!is.list(exact))
stop("'exact' must be a named list")}
if (!is.null(names)){
if (!is.character(names))
stop("'names' must be an character")}
if (any(!is.numeric(R) || (R - floor(R) > 0) || R <= 0))
stop(" 'R' must be an integer ")
if (R == 1) stop("Parallel Monte-Carlo Methods is for any R > 1")
if (missing(time)) {time = as.numeric(model$T)}
if (length(time) > 1 )
stop (" 'time' must be an integer 't0 < time <= T' ")
if (any(model$T < time | model$t0 > time) )
stop( " please use 't0 < time <= T'")
if (any(level <= 0 | level >= 1) )
stop( " please use '0 < level < 1'")
if (class(model)=="bridgesde1d" | class(model)=="bridgesde2d" | class(model)=="bridgesde3d")
stop("Not available for diffusion bridges")
if (class(model)!="snssde1d" & class(model)!="snssde2d" & class(model)!="snssde3d")
stop(" 'model' is not class of 'snssdekd', k=1,2,3. ")
if (missing(parallel))
parallel <- getOption("parallel", "no")
parallel <- match.arg(parallel)
have_mc <- have_snow <- FALSE
if (parallel != "no" && ncpus > 1L) {
if (parallel == "multicore")
have_mc <- .Platform$OS.type != "windows"
else if (parallel == "snow")
have_snow <- TRUE
if (!have_mc && !have_snow)
ncpus <- 1L
loadNamespace("parallel")
}
if (class(model)=="snssde1d"){
statistic <- match.fun(statistic)
fn1d <- function(x,...) statistic(x, ...)
rand <- matrix(0,nrow=R,ncol=model$M)
run1d <- function(...) Sim.DiffProc::rsde1d(eval(model$call),at=time)
if (ncpus > 1L && (have_mc || have_snow)){
if (have_mc) {
base::RNGkind("L'Ecuyer-CMRG")
rand <- do.call("rbind",parallel::mclapply(1:R, run1d,mc.cores = ncpus,mc.set.seed = TRUE))
}else if (have_snow) {
list(...)
if (is.null(cl)){
cl <- parallel::makePSOCKcluster(rep("localhost", ncpus))
parallel::clusterEvalQ(cl, library(Sim.DiffProc))
parallel::clusterExport(cl, varlist=c("time",all.vars(model$call),
all.vars(model$drift)[which(all.vars(model$drift)!="x" & all.vars(model$drift)!="t")],
all.vars(model$diffusion)[which(all.vars(model$diffusion)!="x" & all.vars(model$diffusion)!="t")]),envir = environment())
if (base::RNGkind()[1L] == "L'Ecuyer-CMRG") parallel::clusterSetRNGStream(cl)
rand <- do.call("rbind", parallel::parLapply(cl, 1:R, run1d))
parallel::stopCluster(cl)
}else{
parallel::clusterEvalQ(cl, library(Sim.DiffProc))
parallel::clusterExport(cl, varlist=c("time",all.vars(model$call),
all.vars(model$drift)[which(all.vars(model$drift)!="x" & all.vars(model$drift)!="t")],
all.vars(model$diffusion)[which(all.vars(model$diffusion)!="x" & all.vars(model$diffusion)!="t")]),envir = environment())
if (base::RNGkind()[1L] == "L'Ecuyer-CMRG") parallel::clusterSetRNGStream(cl)
rand <- do.call("rbind", parallel::parLapply(cl, 1:R, run1d))
parallel::stopCluster(cl)
}
}}else{
for (i in 1:R){
rand[i,] = run1d()
}
}
Stat <- do.call("cbind",lapply(1:R,function(i) fn1d(rand,i,...)))
}else if (class(model)=="snssde2d"){
statistic <- match.fun(statistic)
fn2d <- function(x,...) statistic(x, ...)
rand <- matrix(0,nrow=2*R,ncol=model$M)
run2d <- function(...) t(Sim.DiffProc::rsde2d(eval(model$call),at=time))
if (ncpus > 1L && (have_mc || have_snow)){
if (have_mc) {
base::RNGkind("L'Ecuyer-CMRG")
rand <- do.call("rbind",parallel::mclapply(1:R,run2d,mc.cores = ncpus,mc.set.seed = TRUE))
}else if (have_snow) {
list(...)
if (is.null(cl)==TRUE) {
cl <- parallel::makePSOCKcluster(rep("localhost", ncpus))
parallel::clusterEvalQ(cl, library(Sim.DiffProc))
parallel::clusterExport(cl, varlist=c("time",all.vars(model$call),
all.vars(model$driftx)[which(all.vars(model$driftx)!="x" & all.vars(model$driftx)!="y" & all.vars(model$driftx)!="t")],
all.vars(model$drifty)[which(all.vars(model$drifty)!="x" & all.vars(model$drifty)!="y" & all.vars(model$drifty)!="t")],
all.vars(model$diffx)[which(all.vars(model$diffx)!="x" & all.vars(model$diffx)!="y" & all.vars(model$diffx)!="t")],
all.vars(model$diffy)[which(all.vars(model$diffy)!="x" & all.vars(model$diffy)!="y" & all.vars(model$diffy)!="t")]),envir = environment())
if (base::RNGkind()[1L] == "L'Ecuyer-CMRG") parallel::clusterSetRNGStream(cl)
rand <- do.call("rbind", parallel::parLapply(cl, 1:R, run2d))
parallel::stopCluster(cl)
}else{
parallel::clusterEvalQ(cl, library(Sim.DiffProc))
parallel::clusterExport(cl, varlist=c("time",all.vars(model$call),
all.vars(model$driftx)[which(all.vars(model$driftx)!="x" & all.vars(model$driftx)!="y" & all.vars(model$driftx)!="t")],
all.vars(model$drifty)[which(all.vars(model$drifty)!="x" & all.vars(model$drifty)!="y" & all.vars(model$drifty)!="t")],
all.vars(model$diffx)[which(all.vars(model$diffx)!="x" & all.vars(model$diffx)!="y" & all.vars(model$diffx)!="t")],
all.vars(model$diffy)[which(all.vars(model$diffy)!="x" & all.vars(model$diffy)!="y" & all.vars(model$diffy)!="t")]),envir = environment())
if (base::RNGkind()[1L] == "L'Ecuyer-CMRG") parallel::clusterSetRNGStream(cl)
rand <- do.call("rbind", parallel::parLapply(cl, 1:R, run2d))
parallel::stopCluster(cl)
}
}}else{
for (i in 1:R){
rand[c(seq(2*i-1,2*i,by=1)),]=run2d()
}
}
rand1 <- list(x=rand[seq(1,2*R,by=2),],y=rand[seq(2,2*R,by=2),])
rand2 <- lapply(1:R,function(i) data.frame(x=rand1$x[i,], y=rand1$y[i,]))
Stat <- do.call("cbind",lapply(1:R,function(i) fn2d(rand2[[i]],...)))
}else if (class(model)=="snssde3d"){
statistic <- match.fun(statistic)
fn3d <- function(x,...) statistic(x, ...)
rand <- matrix(0,nrow=3*R,ncol=model$M)
run3d <- function(...) t(Sim.DiffProc::rsde3d(eval(model$call),at=time))
if (ncpus > 1L && (have_mc || have_snow)){
if (have_mc) {
base::RNGkind("L'Ecuyer-CMRG")
rand <- do.call("rbind",parallel::mclapply(1:R,run3d,mc.cores = ncpus,mc.set.seed = TRUE))
}else if (have_snow) {
list(...)
if (is.null(cl)==TRUE) {
cl <- parallel::makePSOCKcluster(rep("localhost", ncpus))
parallel::clusterEvalQ(cl, library(Sim.DiffProc))
parallel::clusterExport(cl, varlist=c("time",all.vars(model$call),
all.vars(model$driftx)[which(all.vars(model$driftx)!="x" & all.vars(model$driftx)!="y" & all.vars(model$driftx)!="z" & all.vars(model$driftx)!="t")],
all.vars(model$drifty)[which(all.vars(model$drifty)!="x" & all.vars(model$drifty)!="y" & all.vars(model$drifty)!="z" & all.vars(model$drifty)!="t")],
all.vars(model$driftz)[which(all.vars(model$driftz)!="x" & all.vars(model$driftz)!="y" & all.vars(model$driftz)!="z" & all.vars(model$driftz)!="t")],
all.vars(model$diffx)[which(all.vars(model$diffx)!="x" & all.vars(model$diffx)!="y" & all.vars(model$diffx)!="z" & all.vars(model$diffx)!="t")],
all.vars(model$diffy)[which(all.vars(model$diffy)!="x" & all.vars(model$diffy)!="y" & all.vars(model$diffy)!="z" & all.vars(model$diffy)!="t")],
all.vars(model$diffz)[which(all.vars(model$diffz)!="x" & all.vars(model$diffz)!="y" & all.vars(model$diffz)!="z" & all.vars(model$diffz)!="t")]),envir = environment())
if (base::RNGkind()[1L] == "L'Ecuyer-CMRG") parallel::clusterSetRNGStream(cl)
rand <- do.call("rbind", parallel::parLapply(cl, 1:R, run3d))
parallel::stopCluster(cl)
}else{
parallel::clusterEvalQ(cl, library(Sim.DiffProc))
parallel::clusterExport(cl, varlist=c("time",all.vars(model$call),
all.vars(model$driftx)[which(all.vars(model$driftx)!="x" & all.vars(model$driftx)!="y" & all.vars(model$driftx)!="z" & all.vars(model$driftx)!="t")],
all.vars(model$drifty)[which(all.vars(model$drifty)!="x" & all.vars(model$drifty)!="y" & all.vars(model$drifty)!="z" & all.vars(model$drifty)!="t")],
all.vars(model$driftz)[which(all.vars(model$driftz)!="x" & all.vars(model$driftz)!="y" & all.vars(model$driftz)!="z" & all.vars(model$driftz)!="t")],
all.vars(model$diffx)[which(all.vars(model$diffx)!="x" & all.vars(model$diffx)!="y" & all.vars(model$diffx)!="z" & all.vars(model$diffx)!="t")],
all.vars(model$diffy)[which(all.vars(model$diffy)!="x" & all.vars(model$diffy)!="y" & all.vars(model$diffy)!="z" & all.vars(model$diffy)!="t")],
all.vars(model$diffz)[which(all.vars(model$diffz)!="x" & all.vars(model$diffz)!="y" & all.vars(model$diffz)!="z" & all.vars(model$diffz)!="t")]),envir = environment())
if (base::RNGkind()[1L] == "L'Ecuyer-CMRG") parallel::clusterSetRNGStream(cl)
rand <- do.call("rbind", parallel::parLapply(cl, 1:R, run3d))
parallel::stopCluster(cl)
}
}}else{
for (i in 1:R){
rand[c(seq(3*i-2,3*i,by=1)),]=run3d()
}
}
rand1 <- list(x=rand[seq(1,3*R,by=3),],y=rand[seq(2,3*R,by=3),],z=rand[seq(3,3*R,by=3),])
rand3 <- lapply(1:R,function(i) data.frame(x=rand1$x[i,], y=rand1$y[i,],z=rand1$z[i,]))
Stat <- do.call("cbind",lapply(1:R,function(i) fn3d(rand3[[i]],...)))
}
Est <- round(apply(Stat,1,mean),digits=options()$digits)
#Sdev <- round(apply(Stat,1,sd),options()$digits)
SErr <- round(apply(Stat,1,sd)/sqrt(R),digits=options()$digits)
INF <- round(Est - qnorm(1-0.5*(1-level))*SErr,digits=options()$digits)
SUP <- round(Est + qnorm(1-0.5*(1-level))*SErr,digits=options()$digits)
Conf <- paste("(",INF,",",SUP,")",sep=" ")
if (!is.null(exact)){
rmse_f <- function(error) sqrt(mean(error^2))
Exact = round(as.numeric(exact),digits=options()$digits)
Bias = round(Est - Exact,digits=options()$digits)
Rmse = round(apply(Stat-Exact,1, rmse_f ),digits=options()$digits)
TAB <- data.frame(Exact,Est,Bias,SErr,Rmse,Conf)
names(TAB) <- c("Exact","Estimate","Bias","Std.Error","RMSE",paste("CI(",100*(1 - level)/2,"%",",",100-100*(1 - level)/2,"%",")",sep=" "))
if (!is.null(names(exact)) && is.null(names)) {rownames(TAB) <- names(exact)}
else if (is.null(names(exact)) && !is.null(names)) {rownames(TAB) <- names}
else if (!is.null(names(exact)) && !is.null(names)) {rownames(TAB) <- names}
else{rownames(TAB) <- paste("mu",1:length(Est),sep="")}
}else{
TAB <- data.frame(Est,SErr,Conf)
names(TAB) <- c("Estimate","Std.Error",paste("CI(",100*(1 - level)/2,"%",",",100-100*(1 - level)/2,"%",")",sep=" "))
if (!is.null(names)) {rownames(TAB) <- names}else{rownames(TAB) <- paste("mu",1:length(Est),sep="")}
}
structure(list(MC=TAB,name=dimnames(TAB)[[1]],ech=Stat,mod=model,Fn=statistic,corrmat=model$corrmat,time=time,call=match.call(),infC=INF,supC=SUP,dim=model$dim,Class=class(model)),class="MCM.sde")
}
print.MCM.sde <- function(x, digits=NULL, ...)
{
class(x) <- "MCM.sde"
Ito = "It\xf4"
Encoding(Ito) <- "latin1"
if (is.null(x$corrmat)){
if (x$Class=="snssde1d"){
Dr <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)))), list(e = x$mod$drift))))
DD <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)))), list(e = x$mod$diffusion))))
if(x$mod$type=="ito"){
cat(Ito," Sde 1D:","\n",
" | dX(t) = ", Dr," * dt + ", DD," * dW(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
sep="")}else{
cat("Stratonovich Sde 1D:","\n",
" | dX(t) = ", Dr," * dt + ", DD," o dW(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
sep="")}
}else if (x$Class=="snssde2d"){
Drx <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)))), list(e = x$mod$driftx))))
DDx <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)))), list(e = x$mod$diffx))))
Dry <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)))), list(e = x$mod$drifty))))
DDy <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)))), list(e = x$mod$diffy))))
if(x$mod$type=="ito"){
cat(Ito," Sde 2D:","\n",
" | dX(t) = ", Drx," * dt + ", DDx," * dW1(t)","\n",
" | dY(t) = ", Dry," * dt + ", DDy," * dW2(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
sep="")}else{
cat("Stratonovich Sde 2D:","\n",
" | dX(t) = ", Drx," * dt + ", DDx," o dW1(t)","\n",
" | dY(t) = ", Dry," * dt + ", DDy," o dW2(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
sep="")}
}else if (x$Class=="snssde3d"){
Drx <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$driftx))))
DDx <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$diffx))))
Dry <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$drifty))))
DDy <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$diffy))))
Drz <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$driftz))))
DDz <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$diffz))))
if(x$mod$type=="ito"){
cat(Ito," Sde 3D:","\n",
" | dX(t) = ", Drx," * dt + ", DDx," * dW1(t)","\n",
" | dY(t) = ", Dry," * dt + ", DDy," * dW2(t)","\n",
" | dZ(t) = ", Drz," * dt + ", DDz," * dW3(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
sep="")}else{
cat("Stratonovich Sde 3D:","\n",
" | dX(t) = ", Drx," * dt + ", DDx," o dW1(t)","\n",
" | dY(t) = ", Dry," * dt + ", DDy," o dW2(t)","\n",
" | dZ(t) = ", Drz," * dt + ", DDz," o dW3(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
sep="")}
}} else {
if (x$Class=="snssde1d"){
Dr <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)))), list(e = x$mod$drift))))
DD <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)))), list(e = x$mod$diffusion))))
if(x$mod$type=="ito"){
cat(Ito," Sde 1D:","\n",
" | dX(t) = ", Dr," * dt + ", DD," * dW(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
sep="")}else{
cat("Stratonovich Sde 1D:","\n",
" | dX(t) = ", Dr," * dt + ", DD," o dW(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
sep="")}
}else if (x$Class=="snssde2d"){
Drx <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)))), list(e = x$mod$driftx))))
DDx <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)))), list(e = x$mod$diffx))))
Dry <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)))), list(e = x$mod$drifty))))
DDy <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)))), list(e = x$mod$diffy))))
if(x$mod$type=="ito"){
cat(Ito," Sde 2D:","\n",
" | dX(t) = ", Drx," * dt + ", DDx," * dB1(t)","\n",
" | dY(t) = ", Dry," * dt + ", DDy," * dB2(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
" | Correlation structure:",sep="")
prmatrix(x$mod$corrmat,rowlab = rep(" ", 2), collab = rep("", 2),digits=digits)
}else{
cat("Stratonovich Sde 2D:","\n",
" | dX(t) = ", Drx," * dt + ", DDx," o dB1(t)","\n",
" | dY(t) = ", Dry," * dt + ", DDy," o dB2(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
" | Correlation structure:",sep="")
prmatrix(x$mod$corrmat,rowlab = rep(" ", 2), collab = rep("", 2),digits=digits)
}
}else if (x$Class=="snssde3d"){
Drx <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$driftx))))
DDx <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$diffx))))
Dry <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$drifty))))
DDy <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$diffy))))
Drz <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$driftz))))
DDz <- deparse(eval(substitute(substitute(e, list(x=quote(X(t)),y=quote(Y(t)),z=quote(Z(t)))), list(e = x$mod$diffz))))
if(x$mod$type=="ito"){
cat(Ito," Sde 3D:","\n",
" | dX(t) = ", Drx," * dt + ", DDx," * dB1(t)","\n",
" | dY(t) = ", Dry," * dt + ", DDy," * dB2(t)","\n",
" | dZ(t) = ", Drz," * dt + ", DDz," * dB3(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
" | Correlation structure:",sep="")
prmatrix(x$mod$corrmat,rowlab = rep(" ", 3), collab = rep("", 3),digits=digits)
}else{
cat("Stratonovich Sde 3D:","\n",
" | dX(t) = ", Drx," * dt + ", DDx," o dB1(t)","\n",
" | dY(t) = ", Dry," * dt + ", DDy," o dB2(t)","\n",
" | dZ(t) = ", Drz," * dt + ", DDz," o dB3(t)","\n",
" | t in [",format(x$mod$t0,digits=digits),",",format(x$mod$T,digits=digits),"] with mesh equal to ",format(x$mod$Dt,digits=digits),"\n",
" | Correlation structure:",sep="")
prmatrix(x$mod$corrmat,rowlab = rep(" ", 3), collab = rep("", 3),digits=digits)
}
}
}
cat("\nPMCM Based on ", dim(x$ech)[2]," Batches with ",x$mod$M, "-Realisations at time ",x$time,":","\n\n",sep="")
print(x$MC)
}
.plot.MCM.sde <- function(x,index = 1,type=c("all","hist","qqplot","boxplot","CI"),...)
{
class(x) <- "MCM.sde"
data <- x$ech
name <- x$name
if (length(index) > 1) {
index <- index[1]
warning("The first element of 'index' will be used")}
if (index > dim(data)[1] | index < 1 )
stop("Subscript out of bounds")
#if (is.null(x$call$names)) {name <- paste("t",1:dim(data)[1],"*",sep="")}else{
#name <- sapply(2:length(x$call$names),function(i) x$call$names[[i]])}
type <- match.arg(type)
if (type=="all"){par(mfrow=c(2,2))}
if (any(type == "all" | type == "hist")){
MASS::truehist(data[index,],xlab = name[index],col="gold",ylab="Density",bty="o",las=1,...)
abline(v=mean(data[index,]),lty=2,col="red3")
}
if (any(type == "all" | type == "qqplot")){
qq <- qnorm((seq_len(dim(data)[2]))/(dim(data)[2]+1))
qlab <-"Quantiles of Standard Normal"
stats::qqplot(qq,data[index,],xlab=qlab,ylab=name[index],las=1)
abline(a=mean(data[index,]),b=sqrt(var(data[index,])),lty=2,col="red3",lwd=2)
}
if (any(type == "all" | type == "boxplot")){
bx <- boxplot(data[index,],plot=FALSE,names=name[index])
graphics::bxp(bx, notch = FALSE,las=1, boxfill = "gold", frame.plot = TRUE,outline = FALSE,show.names = TRUE)
}
if (any(type == "all" | type == "CI")){
plot(mean(data[index,]),type="n" ,xaxt='n',yaxt="n",ylim=c(x$infC[index], x$supC[index]),ylab='Confidence Interval',xlab="",las=1,panel.first = grid())
axis(1, at=1, labels=name[index],lty = 2, lwd = 0.5)
axis(side=2,lwd=0.5,las=1,cex=0.5)
arrows(1,x$infC[index],1,x$supC[index],code=3,length=0.25,lwd=2,angle=90,col='red3')
points(1,mean(data[index,]),pch=21,col="red3",bg="gold",cex=1.5)
}
par(mfrow=c(1,1))
invisible(x)
}
plot.MCM.sde <- function(x,index = 1,type=c("all","hist","qqplot","boxplot","CI"),...) .plot.MCM.sde(x,index,type,...)
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