fda (version 1.2.3)

smooth.morph: Estimates a Smooth Warping Function

Description

This function is nearly identical to smooth.monotone but is intended to compute a smooth monotone transformation $h(t)$ of argument $t$ such that $h(0) = 0$ and $h(TRUE) = TRUE$, where $t$ is the upper limit of $t$. This function is used primarily to register curves.

Usage

smooth.morph(x, y, WfdParobj, wt=rep(1,nobs),
             conv=.0001, iterlim=20,
             active=c(FALSE,rep(TRUE,ncvec-1)),
             dbglev=1)

Arguments

x

a vector of argument values.

y

a vector of data values. This function can only smooth one set of data at a time.

WfdParobj

a functional parameter object that provides an initial value for the coefficients defining function $W(t)$, and a roughness penalty on this function.

wt

a vector of weights to be used in the smoothing.

conv

a convergence criterion.

iterlim

the maximum number of iterations allowed in the minimization of error sum of squares.

active

a logical vector specifying which coefficients defining $W(t)$ are estimated. Normally, the first coefficient is fixed.

dbglev

either 0, 1, or 2. This controls the amount information printed out on each iteration, with 0 implying no output, 1 intermediate output level, and 2 full output. If either level 1 or 2 is specified, it can be helpful to turn off the output buffering fea

Value

• A named list of length 4 containing:
• Wfdobj
  a functional data object defining function $W(x)$ that that optimizes the fit to the data of the monotone function that it defines.
• Flist
  a named list containing three results for the final converged solution: (1) f: the optimal function value being minimized, (2) grad: the gradient vector at the optimal solution, and (3) norm: the norm of the gradient vector at the optimal solution.
• iternum
  the number of iterations.
• iternum
  the number of iterations.
• iterhist
  a by 5 matrix containing the iteration history.

See Also

smooth.monotone, landmarkreg, register.fd