{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE GADTs #-}
module Numeric.LAPACK.Matrix.Permutation (
   Permutation,
   size,
   identity,
   Mod.Inversion(NonInverted,Inverted),
   Perm.inversionFromTransposition,
   fromPermutation,
   toPermutation,
   toSquare,
   determinant,
   transpose,
   multiplyVector,
   multiplyFull,
   ) where

import qualified Numeric.LAPACK.Matrix.Array.Private as ArrMatrix
import qualified Numeric.LAPACK.Matrix.Type as Matrix
import qualified Numeric.LAPACK.Matrix.Shape.Omni as Omni
import qualified Numeric.LAPACK.Matrix.Layout.Private as Layout
import qualified Numeric.LAPACK.Matrix.Extent.Private as Extent
import qualified Numeric.LAPACK.Matrix.Modifier as Mod
import qualified Numeric.LAPACK.Permutation.Private as Plain
import qualified Numeric.LAPACK.Permutation as Perm
import Numeric.LAPACK.Matrix.Type (Matrix(Permutation))
import Numeric.LAPACK.Vector (Vector)

import qualified Numeric.Netlib.Class as Class

import qualified Data.Array.Comfort.Shape as Shape


type Permutation sh =
      FlexPermutation Layout.Filled Layout.Filled sh
type FlexPermutation lower upper sh =
      Matrix.Quadratic Matrix.Permutation () () lower upper sh

size :: FlexPermutation lower upper sh a -> sh
size (Permutation perm) = Perm.size perm

identity :: (Shape.C sh) => sh -> FlexPermutation lower upper sh a
identity = Permutation . Perm.identity

fromPermutation ::
   (Shape.C sh) => Perm.Permutation sh -> Permutation sh a
fromPermutation = Permutation

toPermutation ::
   (Shape.C sh) => FlexPermutation lower upper sh a -> Perm.Permutation sh
toPermutation (Permutation perm) = perm

determinant ::
   (Shape.C sh, Class.Floating a) => FlexPermutation lower upper sh a -> a
determinant (Permutation perm) = Perm.numberFromSign $ Perm.determinant perm


transpose ::
   (Shape.C sh) =>
   FlexPermutation lower upper sh a -> FlexPermutation upper lower sh a
transpose (Permutation perm) = Permutation $ Perm.transpose perm

toSquare ::
   (Omni.Strip lower, Omni.Strip upper, Shape.C sh, Class.Floating a) =>
   FlexPermutation lower upper sh a ->
   ArrMatrix.Quadratic Layout.Unpacked Omni.Arbitrary lower upper sh a
toSquare (Permutation perm) = ArrMatrix.liftUnpacked0 $ Plain.toMatrix perm

multiplyVector ::
   (Shape.C size, Eq size, Class.Floating a) =>
   Mod.Inversion -> FlexPermutation lower upper size a ->
   Vector size a -> Vector size a
multiplyVector inverted (Permutation perm) =
   ArrMatrix.unliftColumn Layout.ColumnMajor (Perm.apply inverted perm)

multiplyFull ::
   (Extent.Measure meas, Extent.C vert, Extent.C horiz,
    Shape.C height, Eq height, Shape.C width, Class.Floating a) =>
   Mod.Inversion -> FlexPermutation lower upper height a ->
   ArrMatrix.Full meas vert horiz height width a ->
   ArrMatrix.Full meas vert horiz height width a
multiplyFull inverted (Permutation perm) = Perm.apply inverted perm