Arith.funData {funData}

Arithmetics for functional data objects

Description

These functions allow basic arithmetics (such as '+', '-', '*', 'sqrt') for functional data and numerics based on Arith. The operations are made pointwise for each observation. See examples below.

Usage

## S4 method for signature 'funData,funData'
Arith(e1, e2)

## S4 method for signature 'funData,numeric'
Arith(e1, e2)

## S4 method for signature 'numeric,funData'
Arith(e1, e2)

## S4 method for signature 'multiFunData,multiFunData'
Arith(e1, e2)

## S4 method for signature 'multiFunData,numeric'
Arith(e1, e2)

## S4 method for signature 'numeric,multiFunData'
Arith(e1, e2)

## S4 method for signature 'irregFunData,numeric'
Arith(e1, e2)

## S4 method for signature 'numeric,irregFunData'
Arith(e1, e2)

## S4 method for signature 'irregFunData,irregFunData'
Arith(e1, e2)

## S4 method for signature 'irregFunData,funData'
Arith(e1, e2)

## S4 method for signature 'funData,irregFunData'
Arith(e1, e2)

Arguments

e1, e2

Objects of class funData, irregFunData, multiFunData or numeric. If two functional data objects are used, they must be of the same class, have the same domain and the same number of observations. For exceptions, see Details.

Details

If two objects of a functional data class (funData, irregFunData or multiFunData) are used, they normally must be of the same class, have the same domain and the same number of observations. Exceptions are accepted if

• one object has only one observation. In this case, the arithmetic operations ('+', '-', '*', ...) are done pairwise for this single function and all functions of the other object. A typical example would be when subtracting the mean function from all observations in a funData object. This single function must be defined on the same domain as the other functions (or, in case of irregFunData, on the union of all observation grids).

• one of the two objects is of class irregFunData. Then, the other object can be of class funData, too, if it is defined on the union of all observation grids. The result is an irregFunData object which is defined on the same observation grid as the original irregFunData object.

Value

An object of the same functional data class as e1 or e2, respectively.

Warning

Note that not all combinations of operations and classes make sense, e.g. e1 ^ e2 is sensible if e1 is of class funData, irregFunData or multiFunData and e2 is numeric. The reverse is not true.

See Also

funData, irregFunData, multiFunData, Arith

Examples

oldpar <- par(no.readonly = TRUE)
par(mfrow = c(3,2), mar = rep(2.1,4))

argvals <- seq(0, 2*pi, 0.01)
object1 <- funData(argvals, outer(seq(0.75, 1.25, by = 0.05), sin(argvals)))
object2 <- funData(argvals, outer(seq(0.75, 1.25, by = 0.05), cos(argvals)))

plot(object1, main = "Object1")
plot(object2, main = "Object2")

# Only functional data objects
plot(object1 + object2, main = "Sum")
plot(object1 - object2, main = "Difference")

# Mixed
plot(4 * object1 + 5,  main = "4 * Object1 + 5") # Note y-axis!
plot(object1^2 + object2^2, main = "Pythagoras")

### Irregular
ind <- replicate(11, sort(sample(1:length(argvals), sample(5:10, 1))))
i1 <- irregFunData(
   argvals = lapply(1:11, function(i, ind, x){x[ind[[i]]]}, ind = ind, x = object1@argvals[[1]]),
   X = lapply(1:11, function(i, ind, y){y[i, ind[[i]]]}, ind = ind, y = object1@X))
i2 <- irregFunData(
   argvals = lapply(1:11, function(i, ind, x){x[ind[[i]]]}, ind = ind, x = object2@argvals[[1]]),
   X = lapply(1:11, function(i, ind, y){y[i, ind[[i]]]}, ind = ind, y = object2@X))

plot(i1, main = "Object 1 (irregular)")
plot(i2, main = "Object 2 (irregular)")

# Irregular and regular functional data objects
plot(i1 + i2, main = "Sum")
plot(i1 - object2, main = "Difference")

# Mixed
plot(4 * i1 + 5,  main = "4 * i1 + 5") # Note y-axis!
plot(i1^2 + i2^2, main = "Pythagoras")
par(oldpar)