R Under development (unstable) (2024-10-16 r87241 ucrt) -- "Unsuffered Consequences"
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> if(!require("GNE"))stop("this test requires package GNE.")
Loading required package: GNE
Loading required package: alabama
Loading required package: numDeriv
Loading required package: nleqslv
Loading required package: BB
Loading required package: SQUAREM
> 
> 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)
           [,1]       [,2]       [,3]       [,4]       [,5]       [,6]
[1,] -6.5413813 -6.3517950 -6.2603986 -6.2066593 -6.1712927 -6.1462566
[2,] -0.4586187 -0.3148716 -0.2396014 -0.1933407 -0.1620406 -0.1394577
          [,7]       [,8]       [,9]     [,10]
[1,] -6.127603 -6.1131680 -6.1016662 -6.092286
[2,] -0.122397 -0.1090542 -0.0983338 -0.089532
> 	
> 	
> 	
> 
> 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) ) )
+ }
> 
> proc.time()
   user  system elapsed 
   0.48    0.18    0.65