encodeSmoothFunctionOrder12: Encodes a smooth function into a sequence of states

In snandi/Registration: Contains functions for registration algorithms, simulation and testing

Description

Encodes a smooth function by its first and second derivatives. At each point on the abscissa the function is encoded into a two dimensional point. These points are represented as sequence of states

Usage

encodeSmoothFunctionOrder12(smoothFunc, abscissa)

Arguments

smoothFunc	A smooth function, already converted into an fda::fd object.
abscissa	A vector representing the x-axis or abscissa

Details

To use this function for a vector use the function createSmoothFD to convert to a fd object. For a smooth function f(x), the eight possible states are as follows:

• A=(1,1): (f'>0, f''>0)

• B=(1,0): (f'>0, f''≤q 0)

• C=(0,1): (f' ≤q 0, f''> 0)

• D=(0,0): (f'≤q 0, f''≤q 0)

Value

A string of states representing the encoded form of the smooth function, example "AADDCCCB"

Author(s)

Subhrangshu Nandi, PhD Statistics; [e-mail] or [e-mail]

Examples

 data( growth, package = 'fda')
 Mat1 <- growth[['hgtm']]
 Arguments <- growth[['age']]
 Mean <- rowMeans( Mat1 )
 MeanFD <- createSmoothFD( 
     curvesToSmooth = Mean,
     abscissa       = Arguments,
     lambdas        = exp( -5:5 ),
     basisBreakFreq = 3,
     basisOrder     = 4,
     pbasis         = NULL )
 MeanStates <- encodeSmoothFunctionOrder12( smoothFunc = (MeanFD$curvesSmooth)$fd, abscissa = Arguments )

snandi/Registration documentation built on May 30, 2019, 5:04 a.m.