Provides tools to manipulate numbers with inherent experimental/measurement uncertainty, and propagates them through functions based on principles from statistics.
Documentation maintained at https://mstksg.github.io/uncertain.
import Numeric.Uncertain7.13 +/- 0.05
91800 +/- 100
12.5 `withVar` 0.36
exact 7.9512
81.42 `withPrecision` 4
7 :: Uncert Double
9.18 :: Uncert Double
fromSamples [12.5, 12.7, 12.6, 12.6, 12.5]Can be descontructed/analyzed with :+/- (pattern synonym/pseudo-constructor
matching on the mean and standard deviation), uMean, uStd, uVar, etc.
ghci> let x = 1.52 +/- 0.07
ghci> let y = 781.4 +/- 0.3
ghci> let z = 1.53e-1 `withPrecision` 3
ghci> cosh x
2.4 +/- 0.2
ghci> exp x / z * sin (y ** z)
10.9 +/- 0.9
ghci> pi + 3 * logBase x y
52 +/- 5Propagates uncertainty using second-order multivariate Taylor expansions of functions, computed using the ad library.
ghci> liftUF (\[x,y,z] -> x*y+z)
[ 12.2 +/- 0.5
, 56 +/- 2
, 0.12 +/- 0.08
]
680 +/- 40Can propagate uncertainty on complex functions take from potentially correlated samples.
ghci> import Numeric.Uncertain.Correlated
ghci> evalCorr $ do
x <- sampleUncert $ 12.5 +/- 0.8
y <- sampleUncert $ 15.9 +/- 0.5
z <- sampleUncert $ 1.52 +/- 0.07
let k = y ** x
resolveUncert $ (x+z) * logBase z k
1200 +/- 200Correlated module functionality can be used in ghci or IO or ST, for
"interactive" exploration.
ghci> x <- sampleUncert $ 12.5 +/- 0.8
ghci> y <- sampleUncert $ 15.9 +/- 0.5
ghci> z <- sampleUncert $ 1.52 +/- 0.07
ghci> let k = y**x
ghci> resolveUncert $ (x+z) * logBase z k
1200 +/- 200Provides a module for propagating uncertainty using Monte Carlo simulations
ghci> import qualified Numeric.Uncertain.MonteCarlo as MC
ghci> import System.Random.MWC
ghci> let x = 1.52 +/- 0.07
ghci> let y = 781.4 +/- 0.3
ghci> let z = 1.53e-1 `withPrecision` 3
ghci> g <- create
ghci> cosh x
2.4 +/- 0.2
ghci> MC.liftU cosh x g
2.4 +/- 0.2
ghci> exp x / z * sin (y ** z)
10.9 +/- 0.9
ghci> MC.liftU3 (\a b c -> exp a / c * sin (b**c)) x y z g
10.8 +/- 1.0
ghci> pi + 3 * logBase x y
52 +/- 5
ghci> MC.liftU2 (\a b -> pi + 3 * logBase a b) x y g
51 +/- 5Note that this is very different from other libraries with similar data types (like from intervals and rounding); these do not attempt to maintain intervals or simply digit precisions; they instead are intended to model actual experimental and measurement data with their uncertainties, and apply functions to the data with the uncertainties and properly propagating the errors with sound statistical principles.
For a clear example, take
> (52 +/- 6) + (39 +/- 4)
91. +/- 7.In a library like intervals, this would result in 91 +/- 10 (that is, a
lower bound of 46 + 35 and an upper bound of 58 + 43). However, with
experimental data, errors in two independent samples tend to "cancel out", and
result in an overall aggregate uncertainty in the sum of approximately 7.
Copyright (c) Justin Le 2016
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