Evaluates a monotone function
Evaluates a monotone function
monfn(argvals, Wfdobj, basislist=vector("list", JMAX), returnMatrix=FALSE)
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. |
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.
A numerical vector or matrix containing the values the warping function h.
## 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) Wfd0 <- fd(matrix(0,wbasis$nbasis,1),wbasis) WfdPar <- fdPar(Wfd0, 1, 1e-4) fdObj <- smooth.basis(tbreaks, xval, WfdPar)$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")
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