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Re: Math Question [message #51107 is a reply to message #51106]

Mon, 30 October 2006 09:04

James Kuyper
Messages: 425
Registered: March 2000

Senior Member

Rob wrote:
> In general, powers of negative numbers are complex so you should start
> with that assumption in the expression:
>
> IDL> print,(dcomplex(-1.0,0.0))^2.01
> ( 0.99950656, 0.031410729)
> IDL> print,(dcomplex(-1.0,0.0))^2.0
> ( 1.0000000, -2.4492127e-016)
>
> It would be nice if IDL told you this rather than throwing a NaN at
> you.
>
> Rob
>
> On Oct 29, 11:02 am, David Fanning <n...@dfanning.com> wrote:
>> Folks,
>>
>> OK, I get the feeling that I am going to be referred to
>> my own web page with this question:
>>
>> http://www.dfanning.com/math_tips/sky_is_falling.html
>>
>> And it is certainly true that I have been watching WAY
>> too much TV lately (World Series, you know), but here is
>> my question. How does one explain the following two
>> IDL commands?
>>
>> IDL> Help, (-0.1)^2.0
>> <Expression> FLOAT = 0.0100000
>> IDL> Help, (-0.1)^2.01
>> <Expression> FLOAT = -NaN
>>
>> In general, raising a negative number to any integer
>> power seems to produce a real number, whereas raising
>> a negative number to a non-integer power causes a NAN.
>>
>> I am sure this is explained in one of those textbooks
>> covered with dust in my garage, but I thought one of
>> you math guys could rescue me from a beautiful day
>> spent covered with dust. :-)

If a and b are mutually prime integers, then mathematically, x^(a/b)
has b different values, at most two of which are real, the others are
complex. If b is odd, only one of the values is real. This is true,
whether or not 'x' is negative. However, I don't think we want to have
(-0.10)^2.01 return a list of 200 different complex values. Even when
the operands are complex number IDL only attempts to return one of the
possible values.

More imporatantly, I don't think it should return any complex values at
all. In most cases, if the operands of the ^ operator aren't already
complex, there's a pretty good chance that the code wasn't written to
handle the possiblity of complex values from the result.

Considered solely as a function whose domain and range are restricted
to real numbers, x^(a/b), should have two solutions if b is even, and 1
solution if b is odd, regardless of whether x is positive. In practice,
for computer arithmetic that's not generally implementable. When you
calculate x^y, y can, in general, only be a floating point
approximation of a/b; it is an exact representation only if b is a
power of 2. I've used implementations of the power function that
attempt to recognize when y is an approximation of a/b for small values
of b, however, I gather that IDL is implemented using C code, expwhich
probably calls pow(x,y) to implement x^y. The pow() function does not
attempt to recognise approximations to rational numbers with small
denominators. It is required by the C standard to return a domain error
if x is negative and y is a finite non-integer. IDL handles this by
returning a NaN. This strikes me as a reasonable approach.

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[Message index]

		Re: Math Question By: rkombiyil on Wed, 01 November 2006 04:51
		Re: Math Question By: Jo Klein on Tue, 31 October 2006 04:33
		Re: Math Question By: news.qwest.net on Mon, 30 October 2006 13:07
		Re: Math Question By: Jean H. on Mon, 30 October 2006 12:32
		Re: Math Question By: Jean H. on Mon, 30 October 2006 12:35
		Re: Math Question By: Jo Klein on Mon, 30 October 2006 12:17
		Re: Math Question By: Braedley on Mon, 30 October 2006 10:22
		Re: Math Question By: James Kuyper on Mon, 30 October 2006 10:15
		Re: Math Question By: David Fanning on Mon, 30 October 2006 09:19
		Re: Math Question By: James Kuyper on Mon, 30 October 2006 09:04
		Re: Math Question By: news.qwest.net on Mon, 30 October 2006 08:54
		Re: Math Question By: Foldy Lajos on Mon, 30 October 2006 07:29
		Re: Math Question By: edward.s.meinel@aero. on Mon, 30 October 2006 07:19
		Re: Math Question By: Rob Dimeo on Sun, 29 October 2006 16:15
		Re: Math Question By: Robbie on Sun, 29 October 2006 15:40
		Re: Math Question By: Robbie on Sun, 29 October 2006 15:01
		Re: Math Question By: Foldy Lajos on Sun, 29 October 2006 09:59

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