module Statistics.Covariance
(
empiricalCovariance,
module Statistics.Covariance.LedoitWolf,
module Statistics.Covariance.RaoBlackwellLedoitWolf,
module Statistics.Covariance.OracleApproximatingShrinkage,
module Statistics.Covariance.GraphicalLasso,
DoCenter (..),
scale,
rescaleSWith,
rescalePWith,
)
where
import qualified Data.Vector.Storable as VS
import qualified Numeric.LinearAlgebra as L
import qualified Numeric.LinearAlgebra.Devel as L
import Statistics.Covariance.GraphicalLasso
import Statistics.Covariance.LedoitWolf
import Statistics.Covariance.OracleApproximatingShrinkage
import Statistics.Covariance.RaoBlackwellLedoitWolf
import Statistics.Covariance.Types
import qualified Statistics.Sample as S
empiricalCovariance ::
L.Matrix Double ->
L.Herm Double
empiricalCovariance :: Matrix Double -> Herm Double
empiricalCovariance = (Vector Double, Herm Double) -> Herm Double
forall a b. (a, b) -> b
snd ((Vector Double, Herm Double) -> Herm Double)
-> (Matrix Double -> (Vector Double, Herm Double))
-> Matrix Double
-> Herm Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Matrix Double -> (Vector Double, Herm Double)
L.meanCov
scaleWith ::
L.Vector Double ->
L.Vector Double ->
L.Matrix Double ->
L.Matrix Double
scaleWith :: Vector Double -> Vector Double -> Matrix Double -> Matrix Double
scaleWith Vector Double
ms Vector Double
ss = ((Int, Int) -> Double -> Double) -> Matrix Double -> Matrix Double
forall a b.
(Element a, Storable b) =>
((Int, Int) -> a -> b) -> Matrix a -> Matrix b
L.mapMatrixWithIndex (\(Int
_, Int
j) Double
x -> (Double
x Double -> Double -> Double
forall a. Num a => a -> a -> a
- Vector Double
ms Vector Double -> Int -> Double
forall a. Storable a => Vector a -> Int -> a
VS.! Int
j) Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/ (Vector Double
ss Vector Double -> Int -> Double
forall a. Storable a => Vector a -> Int -> a
VS.! Int
j))
scale ::
L.Matrix Double ->
(L.Vector Double, L.Vector Double, L.Matrix Double)
scale :: Matrix Double -> (Vector Double, Vector Double, Matrix Double)
scale Matrix Double
xs = (Vector Double
ms, Vector Double
ss, Vector Double -> Vector Double -> Matrix Double -> Matrix Double
scaleWith Vector Double
ms Vector Double
ss Matrix Double
xs)
where
msVs :: [(Double, Double)]
msVs = (Vector Double -> (Double, Double))
-> [Vector Double] -> [(Double, Double)]
forall a b. (a -> b) -> [a] -> [b]
map Vector Double -> (Double, Double)
forall (v :: * -> *).
Vector v Double =>
v Double -> (Double, Double)
S.meanVariance ([Vector Double] -> [(Double, Double)])
-> [Vector Double] -> [(Double, Double)]
forall a b. (a -> b) -> a -> b
$ Matrix Double -> [Vector Double]
forall t. Element t => Matrix t -> [Vector t]
L.toColumns Matrix Double
xs
ms :: Vector Double
ms = [Double] -> Vector Double
forall a. Storable a => [a] -> Vector a
L.fromList ([Double] -> Vector Double) -> [Double] -> Vector Double
forall a b. (a -> b) -> a -> b
$ ((Double, Double) -> Double) -> [(Double, Double)] -> [Double]
forall a b. (a -> b) -> [a] -> [b]
map (Double, Double) -> Double
forall a b. (a, b) -> a
fst [(Double, Double)]
msVs
ss :: Vector Double
ss = [Double] -> Vector Double
forall a. Storable a => [a] -> Vector a
L.fromList ([Double] -> Vector Double) -> [Double] -> Vector Double
forall a b. (a -> b) -> a -> b
$ ((Double, Double) -> Double) -> [(Double, Double)] -> [Double]
forall a b. (a -> b) -> [a] -> [b]
map (Double -> Double
forall a. Floating a => a -> a
sqrt (Double -> Double)
-> ((Double, Double) -> Double) -> (Double, Double) -> Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (Double, Double) -> Double
forall a b. (a, b) -> b
snd) [(Double, Double)]
msVs
rescaleSWith ::
L.Vector Double ->
L.Matrix Double ->
L.Matrix Double
rescaleSWith :: Vector Double -> Matrix Double -> Matrix Double
rescaleSWith Vector Double
ss = ((Int, Int) -> Double -> Double) -> Matrix Double -> Matrix Double
forall a b.
(Element a, Storable b) =>
((Int, Int) -> a -> b) -> Matrix a -> Matrix b
L.mapMatrixWithIndex (\(Int
i, Int
j) Double
x -> Double
x Double -> Double -> Double
forall a. Num a => a -> a -> a
* (Vector Double
ss Vector Double -> Int -> Double
forall a. Storable a => Vector a -> Int -> a
VS.! Int
i) Double -> Double -> Double
forall a. Num a => a -> a -> a
* (Vector Double
ss Vector Double -> Int -> Double
forall a. Storable a => Vector a -> Int -> a
VS.! Int
j))
rescalePWith ::
L.Vector Double ->
L.Matrix Double ->
L.Matrix Double
rescalePWith :: Vector Double -> Matrix Double -> Matrix Double
rescalePWith Vector Double
ss = Vector Double -> Matrix Double -> Matrix Double
rescaleSWith ((Double -> Double) -> Vector Double -> Vector Double
forall a b.
(Storable a, Storable b) =>
(a -> b) -> Vector a -> Vector b
VS.map Double -> Double
forall a. Fractional a => a -> a
recip Vector Double
ss)