spray (version 1.0-26)

pmax: Parallel maxima and minima for sprays

Description

Parallel (pairwise) maxima and minima for sprays.

Usage

maxpair_spray(S1,S2)
minpair_spray(S1,S2)
# S3 method for spray
pmax(x, ...)
# S3 method for spray
pmin(x, ...)

Value

Returns a spray object

Arguments

x,S1,S2

Spray objects

...

spray objects to be compared

Author

Robin K. S. Hankin

Details

Function maxpair_spray() finds the pairwise maximum for two sprays. Specifically, if S3 <- maxpair_spray(S1,S2), then S3[v] == max(S1[v],S2[v]) for every index vector v.

Function pmax.spray() is the method for the generic pmax(), which takes any number of arguments. If S3 <- maxpair_spray(S1,S2,...), then S3[v] == max(S1[v],S2[v],...) for every index vector v.

Function pmax.spray() operates right-associatively:

pmax(S1,S2,S3,S4) == f(S1,f(S2,f(S3,S4))) where f() is short for maxpair_spray(). So if performance is important, put the smallest spray (in terms of number of nonzero entries) last.

In these functions, a scalar is interpreted as a sort of global maximum. Thus if S3 <- pmax(S,x) we have S3[v] == max(S[v],x) for every index v. Observe that this operation is not defined if x>0, for then there would be an infinity of v for which S3[v] != 0, an impossibility (or at least counter to the principles of a sparse array). The frab package discussses this issue in vignette inst/wittgenstein.Rmd. Note also that x cannot have length \(>1\) as the elements of a spray object are stored in an arbitrary order, following disordR discipline.

Functions minpair_spray() and pmin.spray() are analogous. Note that minpair_spray(S1,S2) is algebraically equivalent to -pmax_spray(-S1,-S2); see the examples.

The value of pmax(S) is problematic. Suppose all(coeffs(S)<0); the current implementation returns pmax(S)==S but there is a case for returning the null polynomial.

Examples

S1 <- rspray(100,vals=sample(100)-50)
S2 <- rspray(100,vals=sample(100)-50)
S3 <- rspray(100,vals=sample(100)-50)


# following comparisons should all be TRUE:

jj <- pmax(S1,S2,S3)
jj ==  maxpair_spray(S1,maxpair_spray(S2,S3))
jj ==  maxpair_spray(maxpair_spray(S1,S2),S3)

pmax(S1,S2,S3)  == -pmin(-S1,-S2,-S3)
pmin(S1,S2,S3)  == -pmax(-S1,-S2,-S3)

pmax(S1,-Inf) == S1
pmin(S1, Inf) == S2


pmax(S1,-3)

if (FALSE) {
pmax(S1,3) # not defined
}