[Haskell-cafe] Uncertainty analysis library?
Edward Amsden
eca7215 at cs.rit.edu
Mon Mar 21 00:59:15 CET 2011
I'm actually a CS undergrad in a physics lab class. I have permission
from my professor to use computer programs for analysis of lab data. I
need to do calculations on data with uncertainty, but uncertainty
analysis on many formulae in physics is rather tedious. I was hoping
for something with instances for Num, Fractional, Floating, etc. that
would allow me to combine two uncertain values and get a new value
with uncertainty. I've been working on writing one myself and I don't
find the concept hard, but it's a lot of effort that I don't want to
duplicate if it's been done already.
On Sun, Mar 20, 2011 at 5:46 PM, Tom Nielsen <tanielsen at gmail.com> wrote:
> Interval arithmetic is of course not the same as uncertainty, although
> computer scientists like to pretend that is the case. (and uncertainty
> estimates do not have the be "rough".)
>
> In general the propagation of errors depends on whether the errors are
> independent or not. The rules are given in Taylor: An introduction to
> Error analysis (1997). Interval artihmetic corresponds to the worst
> case of non-independent and non-random errors. In the case of
> independent of random errors, you get:
>
> data Approximately a = a :+/-: a
>
> instance Num a => Num (Approximately a) where
> (m1 :+/-: err1) + (m2 :+/-: err2) = (m1+m2) :+/-: (sqrt(err1^2+err2^2)
> (m1 :+/-: err1) - (m2 :+/-: err2) = (m1-m2) :+/-: (sqrt(err1^2+err2^2)
> (m1 :+/-: err1) * (m2 :+/-: err2) = (m1*m2) :+/-:
> (sqrt((err1/m1)^2+(err2/m2)^2)
>
> the general rule is
>
> if y = f xs where xs :: [Approximately a], i.e f :: [Approximately a]
> -> Approximately a
>
> the error term= sqrt $ sum $ map (^2) $ map (\(ym :+/-: yerr) ->
> partial-derivative-of-yerr-with-respect-to-partial-ym * yerr) xs
>
> You can verify these things by running your calculation through soem
> sort of randomness monad (monte-carlo or random-fu packages) Anyways,
> I ended up not going down this route this because probabilistic data
> analysis gives you the correct error estimate without propagating
> error terms.
>
> Tom
>
> PS if you're a scientist and your accuracy estimate is on the same
> order as your rounding error, your are doing pretty well :-) At least
> in my field...
>
> On Sun, Mar 20, 2011 at 8:38 PM, Edward Kmett <ekmett at gmail.com> wrote:
>> I have a package for interval arithmetic in hackage
>> http://hackage.haskell.org/package/intervals-0.2.0
>> However it does not currently properly adjust the floating point rounding
>> mode so containment isn't perfect.
>> However, we are actively working on fixing up the Haskell MPFR bindings,
>> which will let us reliably set rounding modes, cleaning up the interval
>> arithmetic library to be just a little bit more pedantic. Due to the way GHC
>> interacts with GMP this is a disturbingly difficult process.
>> I have an unreleased library for working with Taylor models that builds on
>> top of that and my automatic differentiation library, but without working
>> MPFR bindings, it isn't sufficiently accurate for me to comfortably release.
>> -Edward
>>
>> On Sun, Mar 20, 2011 at 4:27 PM, Edward Amsden <eca7215 at cs.rit.edu> wrote:
>>>
>>> Hi cafe,
>>>
>>> I'm looking for a library that provides an instance of Num,
>>> Fractional, Floating, etc, but carries uncertainty values through
>>> calculations. A scan of hackage didn't turn anything up. Does anyone
>>> know of a library like this?
>>>
>>> Thanks!
>>>
>>> --
>>> Edward Amsden
>>> Student
>>> Computer Science
>>> Rochester Institute of Technology
>>> www.edwardamsden.com
>>>
>>> _______________________________________________
>>> Haskell-Cafe mailing list
>>> Haskell-Cafe at haskell.org
>>> http://www.haskell.org/mailman/listinfo/haskell-cafe
>>
>>
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>
--
Edward Amsden
Student
Computer Science
Rochester Institute of Technology
www.edwardamsden.com
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