NaN not expected

Dear mailing list,

Why does the following code produce numerical results for x.pos.l, but NaNs for x.neg.l?

x.pos<- function(tau.e, tau.c){
   tau.e + ((-tau.e^3 + 3*tau.e^2*tau.c -
   3*tau.e*tau.c^2 + tau.c^3)^(1/3))/(2*2^(1/3))
}
(x.pos.l<- x.pos(1, 2))

x.neg<- function(tau.c, tau.i){
   tau.i + ((tau.c^3 - 3*tau.c^2*tau.i +
   3*tau.c*tau.i^2 - tau.i^3)^(1/3))/(2*2^(1/3))
}
(x.neg.l<- x.neg(2, 3))

The expression you're taking a cube root of

tau.c^3 - 3*tau.c^2*tau.i +
   3*tau.c*tau.i^2 - tau.i^3

is negative.  You can't raise negative numbers to fractional powers in R.  (This has been discussed lots of times on the list; use Google if you don't understand why it has to be that way.)  What you should do is write a cuberoot function, something like

cuberoot<- function(x) ifelse(x<  0, -(-x)^(1/3), x^(1/3))

and use that instead.

Duncan Murdoch