data2fd.old: Depricated: use 'Data2fd'
In drtagkim/mcgillfdar: Functional Data Analysis

Description Usage Arguments Details Value See Also Examples

This function converts an array y of function values plus an array argvals of argument values into a functional data object. This a function that tries to do as much for the user as possible. A basis function expansion is used to represent the curve, but no roughness penalty is used. The data are fit using the least squares fitting criterion. NOTE: Interpolation with data2fd(...) can be shockingly bad, as illustrated in one of the examples.

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data2fd(y, argvals=seq(0, 1, len = n), basisobj,
        fdnames=defaultnames,
        argnames=c("time", "reps", "values"))

`y`	an array containing sampled values of curves. If `y` is a vector, only one replicate and variable are assumed. If `y` is a matrix, rows must correspond to argument values and columns to replications or cases, and it will be assumed that there is only one variable per observation. If `y` is a three-dimensional array, the first dimension (rows) corresponds to argument values, the second (columns) to replications, and the third layers) to variables within replications. Missing values are permitted, and the number of values may vary from one replication to another. If this is the case, the number of rows must equal the maximum number of argument values, and columns of `y` having fewer values must be padded out with NA's.
`argvals`	a set of argument values. If this is a vector, the same set of argument values is used for all columns of `y`. If `argvals` is a matrix, the columns correspond to the columns of `y`, and contain the argument values for that replicate or case.
`basisobj`	either: A `basisfd` object created by function create.basis.fd(), or the value NULL, in which case a `basisfd` object is set up by the function, using the values of the next three arguments.
`fdnames`	A list of length 3, each member being a string vector containing labels for the levels of the corresponding dimension of the discrete data. The first dimension is for argument values, and is given the default name "time", the second is for replications, and is given the default name "reps", and the third is for functions, and is given the default name "values". These default names are assigned in function {tt data2fd}, which also assigns default string vectors by using the dimnames attribute of the discrete data array.
`argnames`	a character vector of length 3 containing: the name of the argument, e.g. "time" or "age" a description of the cases, e.g. "weather stations" the name of the observed function value, e.g. "temperature" These strings are used as names for the members of list `fdnames`.

This function tends to be used in rather simple applications where there is no need to control the roughness of the resulting curve with any great finesse. The roughness is essentially controlled by how many basis functions are used. In more sophisticated applications, it would be better to use the function smooth.basis

an object of the fd class containing:

`coefs`	the coefficient array
`basis`	a basis object and
`fdnames`	a list containing names for the arguments, function values and variables

Data2fd smooth.basis, smooth.basisPar, project.basis, smooth.fd, smooth.monotone, smooth.pos day.5

# Simplest possible example
b1.2 <- create.bspline.basis(norder=1, breaks=c(0, .5, 1))
# 2 bases, order 1 = degree 0 = step functions

str(fd1.2 <- data2fd(0:1, basisobj=b1.2))
plot(fd1.2)
# A step function:  0 to time=0.5, then 1 after


b2.3 <- create.bspline.basis(norder=2, breaks=c(0, .5, 1))
# 3 bases, order 2 = degree 1 =
# continuous, bounded, locally linear

str(fd2.3 <- data2fd(0:1, basisobj=b2.3))
round(fd2.3$coefs, 4)
# 0, -.25, 1
plot(fd2.3)
# Officially acceptable but crazy:
# Initial negative slope from (0,0) to (0.5, -0.25),
# then positive slope to (1,1).


b3.4 <- create.bspline.basis(norder=3, breaks=c(0, .5, 1))
# 4 bases, order 3 = degree 2 =
# continuous, bounded, locally quadratic

str(fd3.4 <- data2fd(0:1, basisobj=b3.4))
round(fd3.4$coefs, 4)
# 0, .25, -.5, 1
plot(fd3.4)
# Officially acceptable but crazy:
# Initial positive then swings negative
# between 0.4 and ~0.75 before becoming positive again
# with a steep slope running to (1,1).



#  Simple example
gaitbasis3 <- create.fourier.basis(nbasis=3)
str(gaitbasis3) # note:  'names' for 3 bases
gaitfd3 <- data2fd(gait, basisobj=gaitbasis3)
str(gaitfd3)
# Note: dimanes for 'coefs' + basis[['names']]
# + 'fdnames'

#    set up the fourier basis
daybasis <- create.fourier.basis(c(0, 365), nbasis=65)
#  Make temperature fd object
#  Temperature data are in 12 by 365 matrix tempav
#    See analyses of weather data.

#  Convert the data to a functional data object
tempfd <- data2fd(CanadianWeather$dailyAv[,,"Temperature.C"],
                  day.5, daybasis)
#  plot the temperature curves
plot(tempfd)

# Terrifying interpolation
hgtbasis <- with(growth, create.bspline.basis(range(age),
                                              breaks=age, norder=6))
girl.data2fd <- with(growth, data2fd(hgtf, age, hgtbasis))
age2 <- with(growth, sort(c(age, (age[-1]+age[-length(age)])/2)))
girlPred <- eval.fd(age2, girl.data2fd)
range(growth$hgtf)
range(growth$hgtf-girlPred[seq(1, by=2, length=31),])
# 5.5e-6 0.028 <
# The predictions are consistently too small
# but by less than 0.05 percent

matplot(age2, girlPred, type="l")
with(growth, matpoints(age, hgtf))
# girl.data2fd fits the data fine but goes berzerk
# between points