multiFunData-class: 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

# S4 method for ANY
multiFunData(...)

Arguments

...

A list of funData objects or several funData objects passed as one argument, each. See Details.

Methods (by generic)

multiFunData: Constructor for multivariate functional data objects.

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).

Examples

Run this code

### 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

### 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
# Use the plot function to get an impression of the data
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)"))