eigen.pda {fda} | R Documentation |
Performs a stability analysis of the result of pda.fd
, returning
the real and imaginary parts of the eigenfunctions associated with the linear
differential operator.
eigen.pda(pdaList,plotresult=TRUE,npts=501,...)
pdaList |
a list object returned by pda.fd .
|
plotresult |
should the result be plotted? Default is TRUE |
npts |
number of points to use for plotting. |
... |
other arguments for 'plot'. |
Conducts an eigen decomposition of the linear differential equation implied
by the result of pda.fd
. Imaginary eigenvalues indicate instantaneous
oscillatory behavior. Positive real eigenvalues indicate exponential increase,
negative real eigenvalues correspond to exponential decay. If the principle
differential analysis also included the estimation of a forcing function, the
limitting stable points are also tracked.
Returns a list with elements
argvals |
The evaluation points of the coefficient functions. |
eigvals |
The corresponding eigenvalues at each time. |
limvals |
The stable points of the system at each time. |
pda.fd
plot.pda.fd
pda.overlay
# A pda analysis of the handwriting data fdaarray = handwrit fdatime <- seq(0, 2.3, len=1401) # basis for coordinates fdarange <- c(0, 2.3) breaks = seq(0,2.3,length.out=501) norder = 6 fdabasis = create.bspline.basis(fdarange,norder=norder,breaks=breaks) # parameter object for coordinates fdaPar = fdPar(fdabasis,int2Lfd(4),1e-8) # coordinate functions and a list tontaining them Xfd = smooth.basis(fdatime, fdaarray[,,1], fdaPar)$fd Yfd = smooth.basis(fdatime, fdaarray[,,2], fdaPar)$fd xfdlist = list(Xfd, Yfd) # basis and parameter object for weight functions fdabasis2 = create.bspline.basis(fdarange,norder=norder,nbasis=51) pdaPar = fdPar(fdabasis2,1,1e-8) pdaParlist = list(pdaPar, pdaPar) bwtlist = list( list(pdaParlist,pdaParlist), list(pdaParlist,pdaParlist) ) # do the second order pda pdaList = pda.fd(xfdlist, bwtlist) # plot the results eigres = eigen.pda(pdaList)