Re: [Haskell-cafe] Uncertainty analysis library?

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 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 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 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@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

_______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

-- Edward Amsden Student Computer Science Rochester Institute of Technology www.edwardamsden.com