fda (version 2.4.0)

monfn: Evaluates a monotone function

Description

Evaluates a monotone function

Usage

monfn(argvals, Wfdobj, basislist=vector("list", JMAX), returnMatrix=FALSE)

Arguments

argvals

A numerical vector at which function and derivative are evaluated.

Wfdobj

A functional data object.

basislist

A list containing values of basis functions.

returnMatrix

logical: If TRUE, a two-dimensional is returned using a special class from the Matrix package.

Value

• A numerical vector or matrix containing the values the warping function h.

Details

This function evaluates a strictly monotone function of the form $$h(x) = [D^{-1} exp(Wfdobj)](x),$$ where $D^{-1}$ means taking the indefinite integral. The interval over which the integration takes places is defined in the basis object in Wfdobj.

See Also

landmarkreg

Examples

## basically this example resembles part of landmarkreg.R that uses monfn.R to
## estimate the warping function.

## Specify the curve subject to be registered
n=21
tbreaks = seq(0, 2*pi, len=n)
xval <- sin(tbreaks)
rangeval <- range(tbreaks)

## Establish a B-spline basis for the curve
wbasis <- create.bspline.basis(rangeval=rangeval, breaks=tbreaks)
WfdPar <- fdPar(wbasis, 1, 1e-4)
fdObj <- smooth.basis(tbreaks, xval, WfdPar)$fd

## Set the mean landmark times. Note that the objective of the warping
## function is to transform the curve such that the landmarks of the curve
## occur at the designated mean landmark times.

## Specify the mean landmark times: tbreak[8]=2.2 and tbreaks[13]=3.76
meanmarks <- c(rangeval[1], tbreaks[8], tbreaks[13], rangeval[2])
## Specify landmark locations of the curve: tbreaks[6] and tbreaks[16]
cmarks <- c(rangeval[1], tbreaks[6], tbreaks[16], rangeval[2])

## Establish a B-basis object for the warping function
Wfd = smooth.morph(x=meanmarks, y=cmarks, WfdPar=WfdPar)$Wfdobj

## Estimate the warping function
h = monfn(tbreaks, Wfd)

## scale using a linear equation h such that h(0)=0 and h(END)=END
b <- (rangeval[2]-rangeval[1])/ (h[n]-h[1])
a <- rangeval[1] - b*h[1]
h <- a + b*h
plot(tbreaks, h, xlab="Time", ylab="Transformed time", type="b")