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Re: Comparing 2 arrays [message #55677 is a reply to message #55546]

Mon, 27 August 2007 10:40

James Kuyper
Messages: 425
Registered: March 2000

Senior Member

Conor wrote:
> On Aug 26, 12:43 pm, David Fanning <n...@dfanning.com> wrote:
>> Jean H. writes:
>>> to get back to a previous discussion we had a few month ago about being
>>> "sufficiently close to zero", shouldn't it be (data1.A - data2.B) LT
>>> epsilon * data1.A , with epsilon=(machar()).eps?
>>
>> Humm, I don't recall that discussion. But I can see how
>> this number might meet the criteria of "sufficiently close".
>> On the other hand, I can also envision situations where
>> the number could be orders of magnitude larger and still
>> work for a particular application. I'm probably mistaken,
>> but it seems to me "sufficiently close" is an arbitrary
>> value that must be picked empirically to match the data
>> and what you are trying to do with it.
>>
>> Cheers,
>>
>> David
>>
>> P.S. I'm just thinking that "sufficiently close" to a
>> black hole, for example, might be a completely different
>> number than "sufficiently close" to my house.
>>
>> --
>> David Fanning, Ph.D.
>> Fanning Software Consulting, Inc.
>> Coyote's Guide to IDL Programming:http://www.dfanning.com/
>> Sepore ma de ni thui. ("Perhaps thou speakest truth.")
>
> Hmm... I think Jean might be on to something. After all, the error in
> question hear is the rounding error of the computer, and that rounding
> error is always an error on the last 'bit' of a floating point
> number. So for instance if you had two floating point numbers:
>
> 1.1123453e15
> and
> 1.1123454e15
>
> These might be the same number (to within the rounding error) but the
> difference between them is about 6.7e07. That's assuming of course
> that I'm properly understanding floating point representation (I'm an
> astronomer, not a computer engineer).

The direct effect of a single roundoff error shouldn't be more than 1
bit in the last position. However, it is often the case that two
different numbers that should mathematically be the same, have been
brought together through a long series of operations. A roundoff error
in the first operation could be magnified or reduced by the next
operation, in addition to that operation creating round-off errors of
its own. In general, you must either analyze the propogation of error
through the calculations, or at least measure the typical error sizes
empirically, as David suggested.

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[Message index]

		Re: Comparing 2 arrays By: David Fanning on Mon, 27 August 2007 08:06
		Re: Comparing 2 arrays By: Conor on Mon, 27 August 2007 06:48
		Re: Comparing 2 arrays By: David Fanning on Sun, 26 August 2007 09:43
		Re: Comparing 2 arrays By: Jean H. on Sun, 26 August 2007 08:40
		Re: Comparing 2 arrays By: David Fanning on Sun, 26 August 2007 07:32
		Re: Comparing 2 arrays By: airy.jiang on Sun, 26 August 2007 02:39
		Re: Comparing 2 arrays By: teich on Sat, 25 August 2007 22:25
		Re: Comparing 2 arrays By: David Fanning on Sat, 25 August 2007 21:47
		Re: Comparing 2 arrays By: David Fanning on Sat, 25 August 2007 21:45
		Re: Comparing 2 arrays By: David Fanning on Tue, 28 August 2007 08:15
		Re: Comparing 2 arrays By: James Kuyper on Mon, 27 August 2007 10:40
		Re: Comparing 2 arrays By: Paul Van Delst[1] on Mon, 27 August 2007 10:52

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