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Re: machine precision [message #66503 is a reply to message #66502]

Mon, 18 May 2009 06:33

jameskuyper
Messages: 79
Registered: October 2007

Member

Wox wrote:
> Hi all,
>
> When checking whether two foating point variables are equal, one has
> to do this:
>
> pres = (machar()).eps
> bequal = abs(f1-f2) lt pres
>
> This can go wrong however, as illustrated by the example below. Do I
> need to do error propagation on this? This means that every time f1
> and f2 are calculated differently, I have to calculate a different
> uncertainty?

Yes.

> ... This seems like a lot of work, not to mention the machine
> precision in calculation the propagation of uncertainty... Is there a
> more general rule of thumb I can use?
>
> vec1=[1.,2,3,4,5]
> vec2=vec1
> pres=(machar()).eps
> norm1=sqrt(total(vec1^2,1,/pres))
> norm2=sqrt(total(vec2^2,1,/pres))
> f1=total(vec1*vec2,/pres) ; inner product
> f2=norm1*norm2 ; product of the norms
> ; f1 and f2 must be equal so

At a minimum, you should use pres*(f1^2+f2^2)^0.5 instead of pres for
the following comparison. eps gives you the relative precision, not the
absolute precision; it needs to be scaled by the numbers you're working
with.

> if abs(f1-f2) ge pres then print,'wrong wrong wrong...'

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[Message index]

		Re: machine precision By: Wout De Nolf on Wed, 20 May 2009 06:08
		Re: machine precision By: Carsten Lechte on Wed, 20 May 2009 03:44
		Re: machine precision By: jameskuyper on Wed, 20 May 2009 03:28
		Re: machine precision By: Carsten Lechte on Wed, 20 May 2009 01:46
		Re: machine precision By: David Fanning on Tue, 19 May 2009 20:01
		Re: machine precision By: jameskuyper on Tue, 19 May 2009 18:41
		Re: machine precision By: Kenneth P. Bowman on Tue, 19 May 2009 11:15
		Re: machine precision By: jeffnettles4870 on Tue, 19 May 2009 08:16
		Re: machine precision By: jameskuyper on Mon, 18 May 2009 18:44
		Re: machine precision By: Wout De Nolf on Mon, 18 May 2009 07:02
		Re: machine precision By: Wout De Nolf on Mon, 18 May 2009 06:55
		Re: machine precision By: jameskuyper on Mon, 18 May 2009 06:33
		Re: machine precision By: David Fanning on Mon, 18 May 2009 06:30
		Re: machine precision By: Wout De Nolf on Mon, 18 May 2009 06:04
		Re: machine precision By: David Fanning on Mon, 18 May 2009 04:53

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