# Evaluate the a monotone function 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. ```r 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. ## Returns 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. ## References Ramsay, James O., Hooker, G. and Graves, S. (2009), **Functional Data Analysis with R and Matlab**, Springer, New York. Ramsay, James O., and Silverman, Bernard W. (2005), **Functional Data Analysis, 2nd ed.**, Springer, New York. Ramsay, James O., and Silverman, Bernard W. (2002), **Applied Functional Data Analysis**, Springer, New York. ## Author(s) J. O. Ramsay ## See Also `mongrad`, `landmarkreg`, `smooth.morph` ## Examples ```r oldpar <- par(no.readonly=TRUE) ## 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, ylim=rangeval, 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") par(oldpar) ```

monfn function