Stability Analysis for Principle Differential Analysis
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 |
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
limiting 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. |
# A pda analysis of the handwriting data # reduce the size to reduce the compute time for the example ni <- 281 indx <- seq(1, 1401, length=ni) fdaarray = handwrit[indx,,] fdatime <- seq(0, 2.3, len=ni) # basis for coordinates fdarange <- c(0, 2.3) breaks = seq(0,2.3,length.out=116) 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=31) fdafd2 = fd(matrix(0,31,2),fdabasis2) pdaPar = fdPar(fdafd2,1,1e-8) pdaParlist = list(pdaPar, pdaPar) bwtlist = list( list(pdaParlist,pdaParlist), list(pdaParlist,pdaParlist) )
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