Setup of the mean and covariance vectors for the Gaussian Diffusion process

Description

vectorsetup evaluates the vectors mp (mean of the process) and the two covariance factors up and vp (i.e. covariance of the process is given by up*vp) in the interval [t0, Tfin] with timestep deltat

Usage

vectorsetup(obj)

Arguments

Value

Values are returned as a matrix (mp,up,vp)

Author(s)

A. Buonocore, M.F. Carfora

Examples

##---- Should be DIRECTLY executable !! ----
##-- ==>  Define data, use random,
##--	or do  help(data=index)  for the standard data sets.

## Continuing the Wiener() example:


####       INITIALIZATION OF VECTORS

tempi <- numeric(N+1)
mp <- numeric(N+1)
up <- numeric(N+1)
vp <- numeric(N+1)

# dummy vector
app <- numeric(N)

####    EVALUATION OF MEAN AND COVARIANCE OF THE PROCESS

tempi <- seq(t0, by=deltat, length=N+1)

dum <- vectorsetup(param)
mp <- dum[,1]
up <- dum[,2]
vp <- dum[,3]

## plot of S and m

splot <- S(tempi)
mp1 <- mp - sqrt(2*sigma2)
mp2 <- mp + sqrt(2*sigma2)
matplot(tempi, cbind(mp,mp1,mp2,splot),type="l",lty=c(1,2,2,1),lwd=1,
        main="mean of the process vs. threshold",xlab="time(ms)",ylab="")
legend("bottomright",c("mean","threshold"),
       lty=c(1,1),col=c("black","blue"))

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(GaDiFPT)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/GaDiFPT/vectorsetup.Rd_%03d_medium.png", width=480, height=480)
> ### Name: vectorsetup
> ### Title: Setup of the mean and covariance vectors for the Gaussian
> ###   Diffusion process
> ### Aliases: vectorsetup mp up vp
> 
> ### ** Examples
> 
> ##---- Should be DIRECTLY executable !! ----
> ##-- ==>  Define data, use random,
> ##--	or do  help(data=index)  for the standard data sets.
> 
> ## Continuing the Wiener() example:
> ## Don't show: 
> library(GaDiFPT)
> 
> Wiener <- diffusion(c("mu","sigma2"))
> 
> # user-provided parameters and functions
> mu <- 0.0
> sigma2 <- 1.0
> Scost <- 10
> Sslope <- 0
> Stype <- "constant"
> 
> t0 <- 0.0
> x0 <- 0.0
> Tfin <- 4000    
> deltat <- 0.5
> N <- floor((Tfin - t0)/deltat)  
> M <- 1000
> quadflag <- 1
> RStudioflag <- TRUE
> 
> param <- inputlist(mu,sigma2,Stype,t0,x0,Tfin,deltat,M,quadflag,RStudioflag)
> 
> aaa <- function(t) {
+   aaa <- 0.0 + 0.0*t
+ }
> 
> bbb <- function(t) {
+   bbb <- mu + 0.0*t
+ }
> 
> SSS <- function(t) {
+   SSS <- Scost + Sslope*t
+ }
> 
> SSSp <- function(t) {
+   SSSp <- Sslope
+ }
> ## End(Don't show)
> 
> ####       INITIALIZATION OF VECTORS
> 
> tempi <- numeric(N+1)
> mp <- numeric(N+1)
> up <- numeric(N+1)
> vp <- numeric(N+1)
> 
> # dummy vector
> app <- numeric(N)
> 
> ####    EVALUATION OF MEAN AND COVARIANCE OF THE PROCESS
> 
> tempi <- seq(t0, by=deltat, length=N+1)
> 
> dum <- vectorsetup(param)
> mp <- dum[,1]
> up <- dum[,2]
> vp <- dum[,3]
> 
> ## plot of S and m
> 
> splot <- S(tempi)
> mp1 <- mp - sqrt(2*sigma2)
> mp2 <- mp + sqrt(2*sigma2)
> matplot(tempi, cbind(mp,mp1,mp2,splot),type="l",lty=c(1,2,2,1),lwd=1,
+         main="mean of the process vs. threshold",xlab="time(ms)",ylab="")
> legend("bottomright",c("mean","threshold"),
+        lty=c(1,1),col=c("black","blue"))
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>