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] 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.
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.
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E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk>
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Date: 16-Nov-09 Time: 12:55:25
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