Nothing
if(!require("GNE"))stop("this test requires package GNE.")
limphiFB <- function(x, ab)
( sqrt(x^2*ab[1]^2 + x^2*ab[2]^2) - x*(ab[1]+ab[2]) )/x
x <- seq(-.1, .1, .001)
n <- 10
plot(x, limphiFB(x, c(1,1)), type="l", ylim=c(-5, 2),
main="limits of phiFB(ta, tb)/t as t-> 0", xlab="t", ylab="phiFB(ta, tb)/t")
for(i in 1:n)
lines(x, limphiFB(x, c(1/i,1/(i-1))), col=grey( (i+5)/(n+15) ) )
for(i in 1:n)
lines(x, limphiFB(x, c(0,1/(i-1))), col=grey( (i+5)/(n+5) ) )
for(i in 1:n)
lines(x, limphiFB(x, c(1,1/(i-1))), col=grey( (i+5)/(n+5) ) )
somevals <- sapply(1:n, function(i) limphiFB(x, c(3,1/(i+1))))
apply(somevals, 2, range, na.rm=TRUE)
limphigraFB <- function(x, ab)
sign(x)*ab[1]/sqrt(sum(ab^2)) - x*sum(ab)
x <- seq(.001, .1, .001)
n <- 10
plot(x, limphigraFB(x, c(1,1)), type="l", ylim=c(-1, 1), xlim=range(-x, x),
main="limits of GrAphiFB(ta, tb) as t-> 0", xlab="t", ylab="GrAphiFB(ta, tb)")
lines(-x, limphigraFB(-x, c(1,1)))
for(i in 1:n)
{
lines(x, limphigraFB(x, c(1/i,1/(i-1))), col=grey( (i+5)/(n+15) ) )
lines(-x, limphigraFB(-x, c(1/i,1/(i-1))), col=grey( (i+5)/(n+15) ) )
}
for(i in 1:n)
{
lines(x, limphigraFB(x, c(1,1/(i-1))), col=grey( (i+5)/(n+15) ) )
lines(-x, limphigraFB(-x, c(1,1/(i-1))), col=grey( (i+5)/(n+15) ) )
}
for(i in 1:n)
{
lines(x, limphigraFB(x, c(10,1/(i-1))), col=grey( (i+5)/(n+15) ) )
lines(-x, limphigraFB(-x, c(10,1/(i-1))), col=grey( (i+5)/(n+15) ) )
}
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