[R] Odp: ^ operator

[Petr PIKAL]

Hi

r-help-bounces at r-project.org napsal dne 16.11.2009 13:55:30:

> 
> On 16-Nov-09 11:40:29, Petr PIKAL wrote:
> > Hi
> > AFAIK, this is issue of the preference of operators. 
> > 
> > r-help-bounces at r-project.org napsal dne 16.11.2009 11:24:59:
> > 
> 
> Not in this case (see below), though of course in general "-" takes
> precedence over "^", so, for example, in the expression
> 
>   -2^(1/3)
> 
> the "-" is applied first, giving (-2); and then "^" is applied
> next, giving (-2)^(1/3). There is a work-round (see below).

Are you sure?

I get

> -2^(1/3)
[1] -1.259921

> (-2)^(1/3)
[1] NaN

> 2^(1/3)
[1] 1.259921

So ^ is applied first and then the result is negated.


See ?Syntax.

I agree with what you write below, though.

Regards
Petr




> 
> >> Hi,
> >> I want to apply ^ operator to a vector but it is applied to
> >> some of the elements correctly and to some others, it generates
> >> NaN. Why is it not able to calculate -6.108576e-05^(1/3) even
> >> though it exists?
> 
> It only exists (in the real domain) if "^" takes precedence over "-"
> which (in R) it does not!
> 
> >>  tmp
> >> [1] -6.108576e-05  4.208762e-05  3.547092e-05  7.171101e-04 
> > -1.600269e-03
> >> > tmp^(1/3)
> >> [1]        NaN 0.03478442 0.03285672 0.08950802        NaN
> > 
> > This computes (-a)^(1/3) which is not possible in real numbers.
> 
> In this example, that is not accurate. "tmp" has already been
> defined, and contains numbers which are already stored as negative
> numbers, so "-" is no longer on the scene as an operator, before
> "^" is applied; the issue of precedence of "-" over "^" is no
> longer present. The NaN arises from x^(1/3) where x is negative.
> 
> > You have to use as.complex(tmp)^(1/3) to get a result.
> > 
> >> > -6.108576e-05^(1/3)
> >> [1] -0.03938341
> 
> This is not the result I get:
> 
>   as.complex(tmp)^(1/3)
> # [1] 0.01969171+0.03410703i 0.03478442+0.00000000i
> # [3] 0.03285672+0.00000000i 0.08950802+0.00000000i
> # [5] 0.05848363+0.10129662i
> 
> > this is actually
> > -(6.108576e-05^(1/3))
> > 
> > Regards
> > Petr
> 
> It is possible to work round the problem without using as.complex
> which can introduce complications -- see above, and also:
> 
>   x <- (-1)
>   x^(1/3)
>   # [1] NaN
>   as.complex(x)^(1/3)
>   # [1] 0.5+0.8660254i
> 
>   as.complex(-1)^(1/2)
>   # [1] 0+1i
> 
> which you would not want if you are working throughout in real
> numbers (you would want the result "-1" instead). Although, in the
> mathematics of complex numbers, (-1)^(1/3) has three values, one
> of which is -1, R only returns a single value.
> 
> However, you would have to define a new operator, called say "%^%":
> 
>   "%^%"<-function(X,x){sign(X)*(abs(X)^x)}
> 
>   tmp <- c(-6.108576e-05, 4.208762e-05, 3.547092e-05,
>             7.171101e-04, -1.600269e-03)
>   tmp%^%(1/3)
>   # [1] -0.03938341  0.03478442  0.03285672  0.08950802 -0.11696726
> 
> The definition of "%^%" forces "^" to take precedence over "-",
> by in effect removing "-" from the scene until "^" has done its
> work. But, if you hope to rely on this, note that if you apply
> to 'tmp' any function in which the ordinary "^" will be used on
> a negative number, you will still have the same problem.
> 
> Note: Trying to redefine "^" will not work, since invoking the
> result initiates an infinite recursion:
> 
>   "^"<- function(X,x){sign(X)*(abs(X)^x)}
>   ## (This definition will be accepted by R)
>   tmp%^%(1/3)
>   # Error: evaluation nested too deeply: infinite recursion /
>   #   options(expressions=)?
> 
> It's not a clean situatio, but I hope the above helps!
> Ted.
> 
> --------------------------------------------------------------------
> E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk>
> Fax-to-email: +44 (0)870 094 0861
> Date: 16-Nov-09                                       Time: 12:55:25
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