Description Usage Arguments Details Value See Also Examples
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.
1 |
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
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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 | # 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) )
# do the second order pda
pdaList = pda.fd(xfdlist, bwtlist)
# plot the results
eigres = eigen.pda(pdaList)
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