multiFunData-class: A class for multivariate functional data

In ClaraHapp/funData: An S4 Class for Functional Data

A class for multivariate functional data

Description

The multiFunData class represents multivariate functional data on (potentially) different domains, i.e. a multivariate functional data object is a vector of (univariate) functional data objects, just as a vector in \mathrm{IR}^n is a vector of n scalars. In this implementation, a multiFunData object is represented as a list of univariate funData objects, see Details.

Usage

multiFunData(...)

## S4 method for signature 'ANY'
multiFunData(...)

## S4 method for signature 'multiFunData'
names(x)

## S4 replacement method for signature 'multiFunData'
names(x) <- value

## S4 method for signature 'multiFunData'
str(object, ...)

## S4 method for signature 'multiFunData'
summary(object, ...)

Arguments

...	A list of funData objects or several funData objects passed as one argument, each. See Details.
x	The multiFunData object.
value	The names to be given to the multiFunData curves.
object	A multiFunData object.

Details

A multiFunData object is represented as a list of univariate funData objects, each having a argvals and X slot, representing the x-values and the observed y-values (see the funData class). When constructing a multiFunData object, the elements can be supplied as a list of funData objects or can be passed directly as arguments to the constructor function.

Most functions implemented for the funData class are also implemented for multiFunData objects. In most cases, they simply apply the corresponding univariate method to each element of the multivariate object and return it as a vector (if the result of the univariate function is scalar, such as dimSupp) or as a multiFunData object (if the result of the univariate function is a funData object, such as extractObs).

The norm of a multivariate functional data f = (f_1 , \ldots, f_p) is defined as

||| f ||| := \left(\sum_{j=1}^p || f_j ||^2 \right) ^{1/2}.

A funData object can be coerced to a multiFunData object with one element using as.multiFunData(funDataObject).

Methods (by generic)

• multiFunData(ANY): Constructor for multivariate functional data objects.

• names(multiFunData): Get the names of the multiFunData object.

• names(multiFunData) <- value: Set the names of the multiFunData object.

• str(multiFunData): A str method for multiFunData objects, giving a compact overview of the structure.

• summary(multiFunData): A summary method for multiFunData objects.

Functions

• multiFunData(): Constructor for multivariate functional data objects

See Also

funData

Examples

### Creating a multifunData object with 2 observations on the same domain
# Univariate elements
x <- 1:5
f1 <- funData(x, rbind(x, x+1))
f2 <- funData(x,rbind(x^2, sin(x)))
# Basic
m1 <- new("multiFunData", list(f1,f2))
# Using the constructor, passing the elements as list
m2 <- multiFunData(list(f1,f2))
# Using the constructor, passing the elements directly
m3 <- multiFunData(f1,f2)
# Test if all the same
all.equal(m1,m2)
all.equal(m1,m3)
# Display multiFunData object in the console
m3
# Summarize
summary(m3)

### Creating a multifunData object with 2 observations on different domains (both 1D)
# A new element
y <- 1:3
g1 <- funData(y, rbind(3*y, y+4))
# Create the multiFunData object
m4 <- multiFunData(f1,g1)
# Display multiFunData object in the console
m4

### Creating a multifunData object with 2 observations on different domains (1D and 2D)
# A new element
y <- 1:3; z <- 1:4
g2 <- funData(list(y,z), array(rnorm(24), dim = c(2,3,4)))
# Create the multiFunData object
m5 <- multiFunData(f1,g2)
# Display multiFunData object in the console
m5

### A more realistic object
# element 1
x <- seq(0,2*pi, 0.01)
f1 <- funData(x, outer(seq(0.75, 1.25, length.out = 6), sin(x)))
# element 2
y <- seq(-1,1, 0.01); z <- seq(-0.5, 0.5, 0.01)
X2 <- array(NA, c(6, length(y), length(z)))
for(i in 1:6) X2[i,,] <- outer(y, z, function(x,y){sin(i*pi*y)*cos(i*pi*z)})
f2 <- funData(list(y,z), X2)
# MultiFunData Object
m6 <- multiFunData(f1,f2)
# Display multiFunData object in the console for basic information
m6
# Summarize
summary(m6)
# Use the plot function to get an impression of the data
## Not run: plot(m6) # m6 has 2D element, must specify one observation for plotting
plot(m6, obs = 1, main = c("1st element (obs 1)", "2nd element (obs 1)"))
plot(m6, obs = 6, main = c("1st element (obs 6)", "2nd element (obs 6)"))

ClaraHapp/funData documentation built on Feb. 20, 2024, 6:07 p.m.