update to 5.5.0

Author: JamesRamsay5

man/monfn.Rd

@@ -1,68 +1,88 @@
-\name{monfn}
-\alias{monfn}
-\title{Evaluates a monotone function}
-\description{Evaluates a monotone function}
-\usage{
-  monfn(argvals, Wfdobj, basislist=vector("list", JMAX), returnMatrix=FALSE)
-}
-\arguments{
-  \item{argvals}{A numerical vector at which function and derivative are
-                 evaluated.}
-  \item{Wfdobj}{A functional data object.}
-  \item{basislist}{A list containing values of basis functions.}
-  \item{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
-  \deqn{h(x) = [D^{-1} exp(Wfdobj)](x),}
-  where \eqn{D^{-1}} means taking the indefinite integral. The interval over
-  which the integration takes places is defined in the basis object in Wfdobj.
-}
-\seealso{
-  \code{\link{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)
-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)$Wfdobj
-
-## Estimate the warping function
-h = monfn(tbreaks, Wfd)
-
-## scale using a linear equation h such that h(0)=0 and h(END)=END
-b <- (rangeval[2]-rangeval[1])/ (h[n]-h[1])
-a <- rangeval[1] - b*h[1]
-h <- a + b*h
-plot(tbreaks, h, xlab="Time", ylab="Transformed time", type="b")
-}
-
+\name{monfn}
+\alias{monfn}
+\title{Evaluate the a monotone function}
+\description{Evaluate a monotone function defined as the indefinite integral of
+$exp(W(t))$ where $W$ is a function defined by a basis expansion.  Function $W$
+is the logarithm of the derivative of the monotone function.}
+\usage{
+  monfn(argvals, Wfdobj, basislist=vector("list", JMAX), returnMatrix=FALSE)
+}
+\arguments{
+  \item{argvals}{A numerical vector at which function and derivative are
+                 evaluated.}
+  \item{Wfdobj}{A functional data object.}
+  \item{basislist}{A list containing values of basis functions.}
+  \item{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
+  \deqn{h(x) = [D^{-1} exp(Wfdobj)](x),}
+  where \eqn{D^{-1}} means taking the indefinite integral. The interval over
+  which the integration takes places is defined in the basis object in Wfdobj.
+}
+\references{
+  Ramsay, James O., Hooker, G. and Graves, S. (2009), \emph{Functional
+    Data Analysis with R and Matlab}, Springer, New York.
+    
+  Ramsay, James O., and Silverman, 
+  Bernard W. (2005), \emph{Functional
+    Data Analysis, 2nd ed.}, Springer, New York.
+
+  Ramsay, James O., and Silverman, 
+  Bernard W. (2002), \emph{Applied
+    Functional Data Analysis}, Springer, New York.
+}
+\author{
+  J. O. Ramsay
+}
+\seealso{
+  \code{\link{mongrad}},
+  \code{\link{landmarkreg}},
+  \code{\link{smooth.morph}},
+  \code{\link{smooth.morph2}}
+}
+\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)
+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")
+}
+