funData-class | R Documentation |
The funData
class represents functional data on d
-dimensional
domains. The two slots represent the domain (x-values) and the values of the
different observations (y-values).
funData(argvals, X)
## S4 method for signature 'list,array'
funData(argvals, X)
## S4 method for signature 'numeric,array'
funData(argvals, X)
## S4 method for signature 'funData'
show(object)
## S4 method for signature 'funData'
names(x)
## S4 replacement method for signature 'funData'
names(x) <- value
## S4 method for signature 'funData'
str(object, ...)
## S4 method for signature 'funData'
summary(object, ...)
argvals |
A list of numeric vectors or a single numeric vector, giving the sampling points in the domains. See Details. |
X |
An array of dimension |
object |
A |
x |
The |
value |
The names to be given to the |
... |
Other parameters passed to |
Functional data can be seen as realizations of a random process
X:
\mathcal{T} \to \mathrm{IR}
on a d
-dimensional
domain \mathcal{T}
. The data is usually sampled on a fine grid
T \subset \mathcal{T}
, which is represented in the
argvals
slot of a funData
object. All observations are assumed
to be sampled over the same grid T
, but can contain missing values
(see below). If \mathcal{T}
is one-dimensional, argvals
can be supplied either as a numeric vector, containing the x-values or as a
list, containing such a vector. If \mathcal{T}
is
higher-dimensional, argvals
must always be supplied as a list,
containing numeric vectors of the x-values in dimensions
1,\ldots,d
.
The observed values are represented in the X
slot of a funData
object, which is an array of dimension N \times M
(for
one-dimensional domains, or N \times M_1 \times \ldots \times M_d
for higher-dimensional domains). Here N
equals
the number of observations and M
denotes the number of sampling
points (for higher dimensional domains M_i
denotes the number of
sampling points in dimension i, i = 1,\ldots, d
).
Missing values in the observations are allowed and must be marked by
NA
. If missing values occur due to irregular observation points, the
data can be stored alternatively as an object of class
irregFunData
.
Generic functions for the funData
class include a print method,
plotting and basic arithmetics.
Further methods for funData
:
dimSupp
,
nObs
: Informations about the support dimensions and the number
of observations,
getArgvals
, extractObs
:
Getting/Setting slot values (instead of accessing them directly via
funData@argvals, funData@X
) and extracting single observations or
data on a subset of the domain,
integrate
,
norm
: Integrate all observations over their domain or
calculating the L^2
norm.
A funData
object can be coerced to a multiFunData
object using
as.multiFunData(funDataObject).
funData(argvals = list, X = array)
: Constructor for functional data objects with argvals
given as list.
funData(argvals = numeric, X = array)
: Constructor for functional data objects with argvals
given as vector of numerics (only valid for one-dimensional domains).
show(funData)
: Print basic information about the funData
object
in the console. The default console output for funData
objects.
names(funData)
: Get the names of the funData
object.
names(funData) <- value
: Set the names of the funData
object.
str(funData)
: A str
method for funData
objects, giving a compact overview of the structure.
summary(funData)
: A summary
method for funData
objects.
funData()
: Constructor for functional data objects, first argument (argvals) passed as list or vector of numerics
argvals
The domain \mathcal{T}
of the data. See Details.
X
The functional data samples. See Details.
irregFunData
, multiFunData
### Creating a one-dimensional funData object with 2 observations
# Basic
f1 <- new("funData", argvals = list(1:5), X = rbind(1:5,6:10))
# Using the constructor with first argument supplied as array
f2 <- funData(argvals = list(1:5), X = rbind(1:5, 6:10))
# Using the constructor with first argument supplied as numeric vector
f3 <- funData(argvals = 1:5, X = rbind(1:5, 6:10))
# Test if all the same
all.equal(f1,f2)
all.equal(f1,f3)
# Display funData object in the console
f3
# A more realistic object
argvals <- seq(0,2*pi,0.01)
object <- funData(argvals, outer(seq(0.75, 1.25, by = 0.05), sin(argvals)))
# Display / summary give basic information
object
summary(object)
# Use the plot function to get an impression of the data
plot(object)
### Higher-dimensional funData objects with 2 observations
# Basic
g1 <- new("funData", argvals = list(1:5, 1:3),
X = array(1:30, dim = c(2,5,3)))
# Using the constructor
g2 <- funData(argvals = list(1:5, 1:3),
X = array(1:30, dim = c(2,5,3)))
# Test if the same
all.equal(g1,g2)
# Display funData object in the console
g2
# Summarize information
summary(g2)
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