Copyright	David Johnson (c) 2019-2026
License	BSD3
Maintainer	David Johnson <code@dmj.io>
Stability	Experimental
Portability	GHC
Safe Haskell	None
Language	Haskell2010

ArrayFire.Statistics

Description

Statistics API. Example of finding the top k elements along with their indices from an Array

>>> let (vals,indexes) = topk ( vector @Double 10 [1..] ) 3 TopKDefault
>>> vals

ArrayFire Array
[3 1 1 1]
   10.0000
    9.0000
    8.0000

>>> indexes

ArrayFire Array
[3 1 1 1]
         9
         8
         7

Synopsis

mean :: (AFType a, Fractional a) => Array a -> Int -> Array a
meanWeighted :: (AFType a, Fractional a) => Array a -> Array a -> Int -> Array a
var :: (AFType a, Fractional a) => Array a -> VarianceType -> Int -> Array a
data VarianceType
- = Population
- | Sample
varWeighted :: (AFType a, Fractional a) => Array a -> Array a -> Int -> Array a
stdev :: (AFType a, Fractional a) => Array a -> Int -> Array a
cov :: (AFType a, Fractional a) => Array a -> Array a -> Bool -> Array a
median :: (AFType a, Fractional a) => Array a -> Int -> Array a
meanAll :: AFResult a => Array a -> Scalar a
meanAllWeighted :: AFResult a => Array a -> Array a -> Scalar a
varAll :: AFResult a => Array a -> VarianceType -> Scalar a
varAllWeighted :: AFResult a => Array a -> Array a -> Scalar a
stdevAll :: AFResult a => Array a -> Scalar a
medianAll :: AFResult a => Array a -> Scalar a
corrCoef :: AFResult a => Array a -> Array a -> Scalar a
topk :: AFType a => Array a -> Int -> TopK -> (Array a, Array Word32)
meanVar :: (AFType a, Fractional a) => Array a -> VarBias -> Int -> (Array a, Array a)
meanVarWeighted :: (AFType a, Fractional a) => Array a -> Array a -> VarBias -> Int -> (Array a, Array a)

Documentation

mean Source #

Arguments

:: (AFType a, Fractional a)
=> Array a	Input `Array`
-> Int	The dimension along which the mean is extracted
-> Array a	Will contain the mean of the input `Array` along dimension dim

Calculates mean of Array along user-specified dimension.

>>> mean (vector @Double 10 [1..]) 0
ArrayFire Array
  [1 1 1 1]
     5.5000

meanWeighted Source #

Arguments

:: (AFType a, Fractional a)
=> Array a	Input `Array`
-> Array a	Weights `Array`
-> Int	The dimension along which the mean is extracted
-> Array a	Will contain the mean of the input `Array` along dimension dim

Calculates meanWeighted of Array along user-specified dimension.

>>> meanWeighted (vector @Double 10 [1..10]) (vector @Double 10 [1..10]) 0
ArrayFire Array
  [1 1 1 1]
     7.0000

var Source #

Arguments

:: (AFType a, Fractional a)
=> Array a	Input `Array`
-> VarianceType	boolean denoting Population variance (false) or Sample Variance (true)
-> Int	The dimension along which the variance is extracted
-> Array a	will contain the variance of the input array along dimension dim

Calculates variance of Array along user-specified dimension.

>>> var (vector @Double 8 [1..8]) Population 0
ArrayFire Array
  [1 1 1 1]
     5.2500

data VarianceType Source #

Data type used to express variance type in the var function

Constructors

Population
Sample

Instances

Instances details

Enum VarianceType Source #
Instance details Defined in ArrayFire.Statistics Methods succ :: VarianceType -> VarianceType # pred :: VarianceType -> VarianceType # toEnum :: Int -> VarianceType # fromEnum :: VarianceType -> Int # enumFrom :: VarianceType -> [VarianceType] # enumFromThen :: VarianceType -> VarianceType -> [VarianceType] # enumFromTo :: VarianceType -> VarianceType -> [VarianceType] # enumFromThenTo :: VarianceType -> VarianceType -> VarianceType -> [VarianceType] #
Show VarianceType Source #
Instance details Defined in ArrayFire.Statistics Methods showsPrec :: Int -> VarianceType -> ShowS # show :: VarianceType -> String # showList :: [VarianceType] -> ShowS #
Eq VarianceType Source #
Instance details Defined in ArrayFire.Statistics Methods (==) :: VarianceType -> VarianceType -> Bool # (/=) :: VarianceType -> VarianceType -> Bool #

varWeighted Source #

Arguments

:: (AFType a, Fractional a)
=> Array a	Input `Array`
-> Array a	Weights `Array` used to scale input in before getting variance
-> Int	The dimension along which the variance is extracted
-> Array a	Contains the variance of the input array along dimension dim

Calculates varWeighted of Array along user-specified dimension.

>>> varWeighted (vector @Double 10 [1..]) (vector @Double 10 [1..]) 0
ArrayFire Array
  [1 1 1 1]
     1.9091

stdev Source #

Arguments

:: (AFType a, Fractional a)
=> Array a	Input `Array`
-> Int	The dimension along which the standard deviation is extracted
-> Array a	Contains the standard deviation of the input array along dimension dim

Calculates stdev of Array along user-specified dimension.

>>> stdev (vector @Double 10 (cycle [1,-1])) 0
ArrayFire Array
  [1 1 1 1]
     1.0000

cov Source #

Arguments

:: (AFType a, Fractional a)
=> Array a	First input `Array`
-> Array a	Second input `Array`
-> Bool	A boolean specifying if biased estimate should be taken (default: `False`)
-> Array a	Contains will the covariance of the input `Array`s

Calculates covariance of two Arrays with a bias specifier.

>>> cov (vector @Double 10 (repeat 1)) (vector @Double 10 (repeat 1)) False
ArrayFire Array
  [1 1 1 1]
     0.0000

median Source #

Arguments

:: (AFType a, Fractional a)
=> Array a	Input `Array`
-> Int	Dimension along which to calculate `median`
-> Array a	Array containing `median`

Calculates median of Array along user-specified dimension.

>>> median (vector @Double 10 [1..]) 0
ArrayFire Array
  [1 1 1 1]
     5.5000

meanAll Source #

Arguments

:: AFResult a
=> Array a	Input `Array`
-> Scalar a	Mean of all elements

Calculates mean of all elements in an Array

>>> meanAll $ matrix @Double (2,2) [[1,2],[4,5]]
3.0

meanAllWeighted Source #

Arguments

:: AFResult a
=> Array a	Input `Array`
-> Array a	`Array` of weights
-> Scalar a	Weighted mean

Calculates weighted mean of all elements in an Array

>>> meanAllWeighted (matrix @Double (2,2) [[1,2],[3,4]]) (matrix @Double (2,2) [[1,2],[3,4]])
2.8181818181818183

varAll Source #

Arguments

:: AFResult a
=> Array a	Input `Array`
-> VarianceType	`Population` variance (÷N) or `Sample` variance (÷N-1)
-> Scalar a	Variance of all elements

Calculates variance of all elements in an Array

>>> varAll (vector @Double 10 (repeat 10)) Population
0.0

varAllWeighted Source #

Arguments

:: AFResult a
=> Array a	Input `Array`
-> Array a	`Array` of weights
-> Scalar a	Weighted variance of all elements

Calculates weighted variance of all elements in an Array

>>> varAllWeighted ( vector @Double 10 [1..] ) ( vector @Double 10 [1..] )
6.011479591836735

stdevAll Source #

Arguments

:: AFResult a
=> Array a	Input `Array`
-> Scalar a	Standard deviation of all elements

Calculates standard deviation of all elements in an Array

>>> stdevAll (vector @Double 10 (repeat 10))
0.0

medianAll Source #

Arguments

:: AFResult a
=> Array a	Input `Array`
-> Scalar a	Median of all elements

Calculates median of all elements in an Array

>>> medianAll (vector @Double 10 (repeat 10))
10.0

corrCoef Source #

Arguments

:: AFResult a
=> Array a	First input `Array`
-> Array a	Second input `Array`
-> Scalar a	Correlation coefficient

This algorithm returns Pearson product-moment correlation coefficient. https://en.wikipedia.org/wiki/Pearson_correlation_coefficient

>>> corrCoef ( vector @Int 10 [1..] ) ( vector @Int 10 [10,9..] )
-1.0

topk Source #

Arguments

:: AFType a
=> Array a	First input `Array`, with at least k elements along dim
-> Int	The number of elements to be retrieved along the dim dimension
-> TopK	If descending, the highest values are returned. Otherwise, the lowest values are returned
-> (Array a, Array Word32)	Returns The values of the top k elements along the dim dimension along with the indices of the top k elements along the dim dimension

This function returns the top k values along a given dimension of the input array.

>>> let (vals,indexes) = topk ( vector @Double 10 [1..] ) 3 TopKDefault
>>> indexes

ArrayFire Array
[3 1 1 1]
         9
         8
         7

>>> vals
ArrayFire Array
[3 1 1 1]
   10.0000
    9.0000
    8.0000

The indices along with their values are returned. If the input is a multi-dimensional array, the indices will be the index of the value in that dimension. Order of duplicate values are not preserved. This function is optimized for small values of k. This function performs the operation across all dimensions of the input array. This function is optimized for small values of k. The order of the returned keys may not be in the same order as the appear in the input array

meanVar Source #

Arguments

:: (AFType a, Fractional a)
=> Array a	Input `Array`
-> VarBias	Variance bias correction: `VariancePopulation` (÷N) or `VarianceSample` (÷N-1)
-> Int	Dimension along which to compute
-> (Array a, Array a)	(mean, variance)

Simultaneously compute the mean and variance of an Array along a dimension.

More efficient than calling mean and var separately.

>>> let (m, v) = meanVar (vector @Double 4 [1,2,3,4]) VariancePopulation 0
>>> m
ArrayFire Array
[1 1 1 1]
   2.5000
>>> v
ArrayFire Array
[1 1 1 1]
   1.2500

meanVarWeighted Source #

Arguments

:: (AFType a, Fractional a)
=> Array a	Input `Array`
-> Array a	Weights `Array`
-> VarBias	Variance bias correction
-> Int	Dimension along which to compute
-> (Array a, Array a)	(mean, variance)

Simultaneously compute the weighted mean and variance of an Array along a dimension.

>>> let (m, v) = meanVarWeighted (vector @Double 4 [1,2,3,4]) (vector @Double 4 [1,1,1,1]) VariancePopulation 0
>>> m
ArrayFire Array
[1 1 1 1]
   2.5000