uncertain alternatives and similar packages
Based on the "Math" category.
Alternatively, view uncertain alternatives based on common mentions on social networks and blogs.
-
vector
An efficient implementation of Int-indexed arrays (both mutable and immutable), with a powerful loop optimisation framework . -
hgeometry
HGeometry is a library for computing with geometric objects in Haskell. It defines basic geometric types and primitives, and it implements some geometric data structures and algorithms. -
dimensional
Dimensional library variant built on Data Kinds, Closed Type Families, TypeNats (GHC 7.8+). -
numhask
A haskell numeric prelude, providing a clean structure for numbers and operations that combine them. -
poly
Fast polynomial arithmetic in Haskell (dense and sparse, univariate and multivariate, usual and Laurent) -
eigen
Haskel binding for Eigen library. Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms.
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README
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
Copyright (c) Justin Le 2016