# uncertain

Manipulating numbers with inherent experimental/measurement uncertainty https://github.com/mstksg/uncertain

 LTS Haskell 15.14: 0.3.1.0 Stackage Nightly 2020-05-30: 0.3.1.0 Latest on Hackage: 0.3.1.0

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Maintained by

#### Module documentation for 0.3.1.0

This version can be pinned in stack with:[email protected]:25752a3ef8e66968ab75dc8ec3c741bcfdb39a46ee2a97de2503fa46e31a478f,1797

# Uncertain

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.

## Usage

import Numeric.Uncertain

### Create numbers

7.13 +/- 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.

### Manipulate with error propagation

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 +/- 5

Propagates uncertainty using second-order multivariate Taylor expansions of functions, computed using the ad library.

#### Arbitrary numeric functions

ghci> liftUF (\[x,y,z] -> x*y+z)
[ 12.2 +/- 0.5
, 56 +/- 2
, 0.12 +/- 0.08
]
680 +/- 40

## Correlated samples

Can 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 +/- 200

### “Interactive” Exploratory Mode

Correlated 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 +/- 200

## Monte Carlo-based propagation of uncertainty

Provides 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 +/- 5

## Comparisons

Note 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

# Version 0.3.1.0

https://github.com/mstksg/uncertain/releases/tag/v0.3.1.0

• Added support for GHC 8.0 by providing pattern synonym type signatures in the proper format.
• (:+/-) pattern synonym now exported as a “constructor” with Uncert
• Generalized the type signatures for liftCX functions to work for all a. Restriction to Fractional now occurs only at exit points of the CVar abstraction.
• Removed the redundant constraint on Functor m for the MonteCarlo module’s liftUX functions.

# Version 0.3.0.0

https://github.com/mstksg/uncertain/releases/tag/v0.3.0.0

• (Breaking change) Moved the top-level modules from Data to Numeric, to better reflect the nature of the library and to align with the convention of other similar libraries.

# Version 0.2.0.0

https://github.com/mstksg/uncertain/releases/tag/v0.2.0.0

• Initial release, re-written from the unreleased 0.1.0.0 by re-implementing error propagation with the ad library.
Depends on 8 packages(full list with versions):