{-# LANGUAGE ViewPatterns #-}
{-# OPTIONS_GHC -fno-warn-unused-imports    #-}
--------------------------------------------------------------------------------
-- |
-- Module      : ArrayFire.Statistics
-- Copyright   : David Johnson (c) 2019-2020
-- License     : BSD3
-- Maintainer  : David Johnson <djohnson.m@gmail.com>
-- Stability   : Experimental
-- Portability : GHC
--
-- 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
-- @
--------------------------------------------------------------------------------
module ArrayFire.Statistics where

import ArrayFire.Array
import ArrayFire.FFI
import ArrayFire.Internal.Statistics
import ArrayFire.Internal.Types

-- | Calculates 'mean' of 'Array' along user-specified dimension.
--
-- >>> mean ( vector @Int 10 [1..] ) 0
-- ArrayFire Array
--   [1 1 1 1]
--      5.5000
mean
  :: AFType 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
mean :: forall a. AFType a => Array a -> Int -> Array a
mean Array a
a Int
n =
  Array a
a Array a -> (Ptr AFArray -> AFArray -> IO AFErr) -> Array a
forall a.
Array a -> (Ptr AFArray -> AFArray -> IO AFErr) -> Array a
`op1` (\Ptr AFArray
x AFArray
y ->
    Ptr AFArray -> AFArray -> DimT -> IO AFErr
af_mean Ptr AFArray
x AFArray
y (Int -> DimT
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
n))

-- | 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
meanWeighted
  :: AFType 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
meanWeighted :: forall a. AFType a => Array a -> Array a -> Int -> Array a
meanWeighted Array a
x Array a
y (Int -> DimT
forall a b. (Integral a, Num b) => a -> b
fromIntegral -> DimT
n) =
  Array a
-> Array a
-> (Ptr AFArray -> AFArray -> AFArray -> IO AFErr)
-> Array a
forall b a.
Array b
-> Array a
-> (Ptr AFArray -> AFArray -> AFArray -> IO AFErr)
-> Array a
op2 Array a
x Array a
y ((Ptr AFArray -> AFArray -> AFArray -> IO AFErr) -> Array a)
-> (Ptr AFArray -> AFArray -> AFArray -> IO AFErr) -> Array a
forall a b. (a -> b) -> a -> b
$ \Ptr AFArray
a AFArray
b AFArray
c ->
    Ptr AFArray -> AFArray -> AFArray -> DimT -> IO AFErr
af_mean_weighted Ptr AFArray
a AFArray
b AFArray
c DimT
n

-- | Calculates /variance/ of 'Array' along user-specified dimension.
--
-- >>> var (vector @Double 8 [1..8]) False 0
-- ArrayFire Array
--   [1 1 1 1]
--      6.0000
var
  :: AFType a
  => Array a
  -- ^ Input 'Array'
  -> Bool
  -- ^ 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
var :: forall a. AFType a => Array a -> Bool -> Int -> Array a
var Array a
arr (Int -> CBool
forall a b. (Integral a, Num b) => a -> b
fromIntegral (Int -> CBool) -> (Bool -> Int) -> Bool -> CBool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Bool -> Int
forall a. Enum a => a -> Int
fromEnum -> CBool
b) Int
d =
  Array a
arr Array a -> (Ptr AFArray -> AFArray -> IO AFErr) -> Array a
forall a.
Array a -> (Ptr AFArray -> AFArray -> IO AFErr) -> Array a
`op1` (\Ptr AFArray
p AFArray
x ->
    Ptr AFArray -> AFArray -> CBool -> DimT -> IO AFErr
af_var Ptr AFArray
p AFArray
x CBool
b (Int -> DimT
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
d))

-- | Calculates 'varWeighted' of 'Array' along user-specified dimension.
--
-- >>> varWeighted ( vector @Double 10 [1..] ) ( vector @Double 10 [1..] ) 0
-- ArrayFire Array
--   [1 1 1 1]
--      6.0000
varWeighted
  :: AFType 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
varWeighted :: forall a. AFType a => Array a -> Array a -> Int -> Array a
varWeighted Array a
x Array a
y (Int -> DimT
forall a b. (Integral a, Num b) => a -> b
fromIntegral -> DimT
n) =
  Array a
-> Array a
-> (Ptr AFArray -> AFArray -> AFArray -> IO AFErr)
-> Array a
forall b a.
Array b
-> Array a
-> (Ptr AFArray -> AFArray -> AFArray -> IO AFErr)
-> Array a
op2 Array a
x Array a
y ((Ptr AFArray -> AFArray -> AFArray -> IO AFErr) -> Array a)
-> (Ptr AFArray -> AFArray -> AFArray -> IO AFErr) -> Array a
forall a b. (a -> b) -> a -> b
$ \Ptr AFArray
a AFArray
b AFArray
c ->
    Ptr AFArray -> AFArray -> AFArray -> DimT -> IO AFErr
af_var_weighted Ptr AFArray
a AFArray
b AFArray
c DimT
n

-- | Calculates 'stdev' of 'Array' along user-specified dimension.
--
-- >>> stdev (vector @Double 10 (cycle [1,-1])) 0
-- ArrayFire Array
--   [1 1 1 1]
--      1.0000
stdev
  :: AFType 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
stdev :: forall a. AFType a => Array a -> Int -> Array a
stdev Array a
a Int
n =
  Array a
a Array a -> (Ptr AFArray -> AFArray -> IO AFErr) -> Array a
forall a.
Array a -> (Ptr AFArray -> AFArray -> IO AFErr) -> Array a
`op1` (\Ptr AFArray
x AFArray
y ->
    Ptr AFArray -> AFArray -> DimT -> IO AFErr
af_stdev Ptr AFArray
x AFArray
y (Int -> DimT
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
n))

-- | Calculates /covariance/ of two 'Array's with a bias specifier.
--
-- >>> cov (vector @Double 10 (repeat 1)) (vector @Double 10 (repeat 1)) False
-- ArrayFire Array
--   [1 1 1 1]
--      0.0000
cov
  :: AFType 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
cov :: forall a. AFType a => Array a -> Array a -> Bool -> Array a
cov Array a
x Array a
y (Int -> CBool
forall a b. (Integral a, Num b) => a -> b
fromIntegral (Int -> CBool) -> (Bool -> Int) -> Bool -> CBool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Bool -> Int
forall a. Enum a => a -> Int
fromEnum -> CBool
n) =
  Array a
-> Array a
-> (Ptr AFArray -> AFArray -> AFArray -> IO AFErr)
-> Array a
forall b a.
Array b
-> Array a
-> (Ptr AFArray -> AFArray -> AFArray -> IO AFErr)
-> Array a
op2 Array a
x Array a
y ((Ptr AFArray -> AFArray -> AFArray -> IO AFErr) -> Array a)
-> (Ptr AFArray -> AFArray -> AFArray -> IO AFErr) -> Array a
forall a b. (a -> b) -> a -> b
$ \Ptr AFArray
a AFArray
b AFArray
c ->
    Ptr AFArray -> AFArray -> AFArray -> CBool -> IO AFErr
af_cov Ptr AFArray
a AFArray
b AFArray
c CBool
n

-- | Calculates 'median' of 'Array' along user-specified dimension.
--
-- >>> median ( vector @Double 10 [1..] ) 0
-- ArrayFire Array
--   [1 1 1 1]
--      5.5000
median
  :: AFType a
  => Array a
  -- ^ Input 'Array'
  -> Int
  -- ^ Dimension along which to calculate 'median'
  -> Array a
  -- ^ Array containing 'median'
median :: forall a. AFType a => Array a -> Int -> Array a
median Array a
a Int
n =
  Array a
a Array a -> (Ptr AFArray -> AFArray -> IO AFErr) -> Array a
forall a.
Array a -> (Ptr AFArray -> AFArray -> IO AFErr) -> Array a
`op1` (\Ptr AFArray
x AFArray
y ->
    Ptr AFArray -> AFArray -> DimT -> IO AFErr
af_median Ptr AFArray
x AFArray
y (Int -> DimT
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
n))

-- | Calculates 'mean' of all elements in an 'Array'
--
-- >>> meanAll $ matrix @Double (2,2) [[1,2],[4,5]]
-- (3.0,2.232709401e-314)
meanAll
  :: AFType a
  => Array a
  -- ^ Input 'Array'
  -> (Double, Double)
  -- ^ Mean result (real and imaginary part)
meanAll :: forall a. AFType a => Array a -> (Double, Double)
meanAll = (Array a
-> (Ptr Double -> Ptr Double -> AFArray -> IO AFErr)
-> (Double, Double)
forall a b arr.
(Storable a, Storable b) =>
Array arr -> (Ptr a -> Ptr b -> AFArray -> IO AFErr) -> (a, b)
`infoFromArray2` Ptr Double -> Ptr Double -> AFArray -> IO AFErr
af_mean_all)

-- | 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]])
-- (3.0,1.400743288453e-312)
meanAllWeighted
  :: AFType a
  => Array a
  -- ^ Input 'Array'
  -> Array a
  -- ^ 'Array' of weights
  -> (Double, Double)
  -- ^ Weighted mean (real and imaginary part)
meanAllWeighted :: forall a. AFType a => Array a -> Array a -> (Double, Double)
meanAllWeighted Array a
a Array a
b =
  Array a
-> Array a
-> (Ptr Double -> Ptr Double -> AFArray -> AFArray -> IO AFErr)
-> (Double, Double)
forall a b arr.
(Storable a, Storable b) =>
Array arr
-> Array arr
-> (Ptr a -> Ptr b -> AFArray -> AFArray -> IO AFErr)
-> (a, b)
infoFromArray22 Array a
a Array a
b Ptr Double -> Ptr Double -> AFArray -> AFArray -> IO AFErr
af_mean_all_weighted

-- | Calculates variance of all elements in an 'Array'
--
-- >>> varAll (vector @Double 10 (repeat 10)) False
-- (0.0,1.4013073623e-312)
varAll
  :: AFType a
  => Array a
  -- ^ Input 'Array'
  -> Bool
  -- ^ Input 'Array'
  -> (Double, Double)
  -- ^ Variance (real and imaginary part)
varAll :: forall a. AFType a => Array a -> Bool -> (Double, Double)
varAll Array a
a (Int -> CBool
forall a b. (Integral a, Num b) => a -> b
fromIntegral (Int -> CBool) -> (Bool -> Int) -> Bool -> CBool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Bool -> Int
forall a. Enum a => a -> Int
fromEnum -> CBool
b) =
  Array a
-> (Ptr Double -> Ptr Double -> AFArray -> IO AFErr)
-> (Double, Double)
forall a b arr.
(Storable a, Storable b) =>
Array arr -> (Ptr a -> Ptr b -> AFArray -> IO AFErr) -> (a, b)
infoFromArray2 Array a
a ((Ptr Double -> Ptr Double -> AFArray -> IO AFErr)
 -> (Double, Double))
-> (Ptr Double -> Ptr Double -> AFArray -> IO AFErr)
-> (Double, Double)
forall a b. (a -> b) -> a -> b
$ \Ptr Double
x Ptr Double
y AFArray
z ->
    Ptr Double -> Ptr Double -> AFArray -> CBool -> IO AFErr
af_var_all Ptr Double
x Ptr Double
y AFArray
z CBool
b

-- | Calculates weighted variance of all elements in an 'Array'
--
-- >>> varAllWeighted ( vector @Double 10 [1..] ) ( vector @Double 10 [1..] )
-- (6.0,2.1941097984e-314)
varAllWeighted
  :: AFType a
  => Array a
  -- ^ Input 'Array'
  -> Array a
  -- ^ 'Array' of weights
  -> (Double, Double)
  -- ^ Variance weighted result, (real and imaginary part)
varAllWeighted :: forall a. AFType a => Array a -> Array a -> (Double, Double)
varAllWeighted Array a
a Array a
b =
  Array a
-> Array a
-> (Ptr Double -> Ptr Double -> AFArray -> AFArray -> IO AFErr)
-> (Double, Double)
forall a b arr.
(Storable a, Storable b) =>
Array arr
-> Array arr
-> (Ptr a -> Ptr b -> AFArray -> AFArray -> IO AFErr)
-> (a, b)
infoFromArray22 Array a
a Array a
b Ptr Double -> Ptr Double -> AFArray -> AFArray -> IO AFErr
af_var_all_weighted

-- | Calculates standard deviation of all elements in an 'Array'
--
-- >>> stdevAll (vector @Double 10 (repeat 10))
-- (0.0,2.190573324e-314)
stdevAll
  :: AFType a
  => Array a
  -- ^ Input 'Array'
  -> (Double, Double)
  -- ^ Standard deviation result, (real and imaginary part)
stdevAll :: forall a. AFType a => Array a -> (Double, Double)
stdevAll = (Array a
-> (Ptr Double -> Ptr Double -> AFArray -> IO AFErr)
-> (Double, Double)
forall a b arr.
(Storable a, Storable b) =>
Array arr -> (Ptr a -> Ptr b -> AFArray -> IO AFErr) -> (a, b)
`infoFromArray2` Ptr Double -> Ptr Double -> AFArray -> IO AFErr
af_stdev_all)

-- | Calculates median of all elements in an 'Array'
--
-- >>> medianAll (vector @Double 10 (repeat 10))
-- (10.0,2.1961564713e-314)
medianAll
  :: (AFType a, Fractional a)
  => Array a
  -- ^ Input 'Array'
  -> (Double, Double)
  -- ^ Median result, real and imaginary part
medianAll :: forall a. (AFType a, Fractional a) => Array a -> (Double, Double)
medianAll = (Array a
-> (Ptr Double -> Ptr Double -> AFArray -> IO AFErr)
-> (Double, Double)
forall a b arr.
(Storable a, Storable b) =>
Array arr -> (Ptr a -> Ptr b -> AFArray -> IO AFErr) -> (a, b)
`infoFromArray2` Ptr Double -> Ptr Double -> AFArray -> IO AFErr
af_median_all)

-- | 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..] )
-- (-1.0,2.1904819737e-314)
corrCoef
  :: AFType a
  => Array a
  -- ^ First input 'Array'
  -> Array a
  -- ^ Second input 'Array'
  -> (Double, Double)
  -- ^ Correlation coefficient result, real and imaginary part
corrCoef :: forall a. AFType a => Array a -> Array a -> (Double, Double)
corrCoef Array a
a Array a
b =
  Array a
-> Array a
-> (Ptr Double -> Ptr Double -> AFArray -> AFArray -> IO AFErr)
-> (Double, Double)
forall a b arr.
(Storable a, Storable b) =>
Array arr
-> Array arr
-> (Ptr a -> Ptr b -> AFArray -> AFArray -> IO AFErr)
-> (a, b)
infoFromArray22 Array a
a Array a
b Ptr Double -> Ptr Double -> AFArray -> AFArray -> IO AFErr
af_corrcoef

-- | 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
--
topk
  :: 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 a)
  -- ^ 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
topk :: forall a. AFType a => Array a -> Int -> TopK -> (Array a, Array a)
topk Array a
a (Int -> CInt
forall a b. (Integral a, Num b) => a -> b
fromIntegral -> CInt
x) (TopK -> AFTopkFunction
fromTopK -> AFTopkFunction
f)
  = Array a
a Array a
-> (Ptr AFArray -> Ptr AFArray -> AFArray -> IO AFErr)
-> (Array a, Array a)
forall a.
Array a
-> (Ptr AFArray -> Ptr AFArray -> AFArray -> IO AFErr)
-> (Array a, Array a)
`op2p` (\Ptr AFArray
b Ptr AFArray
c AFArray
d -> Ptr AFArray
-> Ptr AFArray
-> AFArray
-> CInt
-> CInt
-> AFTopkFunction
-> IO AFErr
af_topk Ptr AFArray
b Ptr AFArray
c AFArray
d CInt
x CInt
0 AFTopkFunction
f)