{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
module Numeric.LAPACK.Matrix.BandedHermitian (
BandedHermitian,
Transposition(..),
Hermitian.Semidefinite,
Hermitian.assureFullRank,
Hermitian.assureAnyRank,
Hermitian.relaxSemidefinite,
Hermitian.relaxIndefinite,
Hermitian.assurePositiveDefiniteness,
Hermitian.relaxDefiniteness,
size,
fromList,
identity,
diagonal,
takeDiagonal,
toHermitian,
toBanded,
forceOrder,
takeTopLeft,
takeBottomRight,
negate,
multiplyVector,
multiplyFull,
gramian,
sumRank1,
eigenvalues,
eigensystem,
) where
import qualified Numeric.LAPACK.Matrix.BandedHermitian.Eigen as Eigen
import qualified Numeric.LAPACK.Matrix.BandedHermitian.Basic as Basic
import qualified Numeric.LAPACK.Matrix.Array.Hermitian as Hermitian
import qualified Numeric.LAPACK.Matrix.Array.Banded as Banded
import qualified Numeric.LAPACK.Matrix.Array.Private as ArrMatrix
import qualified Numeric.LAPACK.Matrix.Shape.Omni as Omni
import qualified Numeric.LAPACK.Matrix.Shape as MatrixShape
import qualified Numeric.LAPACK.Matrix.Extent as Extent
import qualified Numeric.LAPACK.Vector as Vector
import qualified Numeric.LAPACK.Shape as ExtShape
import Numeric.LAPACK.Matrix.Array.Banded (Square)
import Numeric.LAPACK.Matrix.Array.Mosaic (FlexHermitian)
import Numeric.LAPACK.Matrix.Array.Private (Full)
import Numeric.LAPACK.Matrix.Layout.Private (Order, UnaryProxy, natFromProxy)
import Numeric.LAPACK.Matrix.Modifier (Transposition(NonTransposed, Transposed))
import Numeric.LAPACK.Vector (Vector)
import Numeric.LAPACK.Scalar (RealOf)
import qualified Numeric.Netlib.Class as Class
import qualified Type.Data.Num.Unary.Literal as TypeNum
import qualified Type.Data.Num.Unary.Proof as Proof
import qualified Type.Data.Num.Unary as Unary
import qualified Type.Data.Bool as TBool
import Type.Data.Num.Unary ((:+:))
import qualified Data.Array.Comfort.Shape as Shape
import Data.Array.Comfort.Shape ((::+))
import Data.Tuple.HT (mapPair, mapFst)
import Prelude hiding (negate)
type BandedHermitian offDiag sh = Banded.Hermitian offDiag sh
type Diagonal size = BandedHermitian TypeNum.U0 size
size :: BandedHermitian offDiag sh a -> sh
size = Omni.height . ArrMatrix.shape
fromList ::
(Unary.Natural offDiag, Shape.C size, Class.Floating a) =>
UnaryProxy offDiag -> Order -> size -> [a] ->
BandedHermitian offDiag size a
fromList numOff order size_ =
ArrMatrix.fromVector . Basic.fromList numOff order size_
identity ::
(Shape.C sh, Class.Floating a) =>
sh -> Banded.HermitianPosDef TypeNum.U0 sh a
identity = ArrMatrix.lift0 . Basic.identity
diagonal ::
(Shape.C sh, Class.Floating a) => Vector sh (RealOf a) -> Diagonal sh a
diagonal = ArrMatrix.lift0 . Basic.diagonal
takeDiagonal ::
(TBool.C neg, TBool.C zero, TBool.C pos) =>
(Unary.Natural offDiag, Shape.C size, Class.Floating a) =>
Banded.FlexHermitian neg zero pos offDiag size a ->
Vector size (RealOf a)
takeDiagonal = Basic.takeDiagonal . ArrMatrix.toVector
toHermitian ::
(TBool.C neg, TBool.C zero, TBool.C pos) =>
(Unary.Natural offDiag, Shape.C size, Class.Floating a) =>
Banded.FlexHermitian neg zero pos offDiag size a ->
FlexHermitian neg zero pos size a
toHermitian = ArrMatrix.lift1 Basic.toHermitian
toBanded ::
(TBool.C neg, TBool.C zero, TBool.C pos,
Unary.Natural offDiag, Shape.C size, Class.Floating a) =>
Banded.FlexHermitian neg zero pos offDiag size a ->
Square offDiag offDiag size a
toBanded = ArrMatrix.lift1 Basic.toBanded
forceOrder ::
(TBool.C neg, TBool.C zero, TBool.C pos,
Unary.Natural offDiag, Shape.C size, Class.Floating a) =>
Order ->
Banded.FlexHermitian neg zero pos offDiag size a ->
Banded.FlexHermitian neg zero pos offDiag size a
forceOrder = ArrMatrix.lift1 . Basic.forceOrder
takeTopLeft ::
(TBool.C neg, TBool.C zero, TBool.C pos,
Unary.Natural offDiag, Shape.C sh0, Shape.C sh1, Class.Floating a) =>
Banded.FlexHermitian neg zero pos offDiag (sh0 ::+ sh1) a ->
Banded.FlexHermitian neg zero pos offDiag sh0 a
takeTopLeft = ArrMatrix.lift1 Basic.takeTopLeft
takeBottomRight ::
(TBool.C neg, TBool.C zero, TBool.C pos,
Unary.Natural offDiag, Shape.C sh0, Shape.C sh1, Class.Floating a) =>
Banded.FlexHermitian neg zero pos offDiag (sh0 ::+ sh1) a ->
Banded.FlexHermitian neg zero pos offDiag sh1 a
takeBottomRight = ArrMatrix.lift1 Basic.takeBottomRight
negate ::
(TBool.C neg, TBool.C zero, TBool.C pos,
Unary.Natural offDiag, Shape.C sh, Class.Floating a) =>
Banded.FlexHermitian neg zero pos offDiag sh a ->
Banded.FlexHermitian pos zero neg offDiag sh a
negate = ArrMatrix.lift1 Vector.negate
multiplyVector ::
(TBool.C neg, TBool.C zero, TBool.C pos,
Unary.Natural offDiag, Shape.C size, Eq size, Class.Floating a) =>
Transposition ->
Banded.FlexHermitian neg zero pos offDiag size a ->
Vector size a -> Vector size a
multiplyVector transposed =
Basic.multiplyVector transposed . ArrMatrix.toVector
gramian ::
(Shape.C size, Eq size, Class.Floating a,
Unary.Natural sub, Unary.Natural super) =>
Square sub super size a ->
Banded.HermitianPosSemidef (sub :+: super) size a
gramian a =
case mapPair (natFromProxy,natFromProxy) $
MatrixShape.bandedOffDiagonals $ ArrMatrix.shape a of
(sub,super) ->
case Proof.addNat sub super of
Proof.Nat -> ArrMatrix.lift1 Basic.gramian a
multiplyFull ::
(TBool.C neg, TBool.C zero, TBool.C pos,
Unary.Natural offDiag, Extent.Measure meas, Extent.C vert, Extent.C horiz,
Shape.C height, Eq height, Shape.C width, Class.Floating a) =>
Transposition ->
Banded.FlexHermitian neg zero pos offDiag height a ->
Full meas vert horiz height width a ->
Full meas vert horiz height width a
multiplyFull = ArrMatrix.lift2 . Basic.multiplyFull
sumRank1 ::
(Unary.Natural k, Shape.Indexed sh, Class.Floating a) =>
Order -> sh ->
[(RealOf a, (Shape.Index sh, Basic.StaticVector (Unary.Succ k) a))] ->
Banded.HermitianPosSemidef k sh a
sumRank1 order sh = ArrMatrix.lift0 . Basic.sumRank1 order sh
eigenvalues ::
(TBool.C neg, TBool.C zero, TBool.C pos, Unary.Natural offDiag) =>
(ExtShape.Permutable sh, Class.Floating a) =>
Banded.FlexHermitian neg zero pos offDiag sh a -> Vector sh (RealOf a)
eigenvalues = Eigen.values . ArrMatrix.toVector
eigensystem ::
(TBool.C neg, TBool.C zero, TBool.C pos, Unary.Natural offDiag) =>
(ExtShape.Permutable sh, Class.Floating a) =>
Banded.FlexHermitian neg zero pos offDiag sh a ->
(ArrMatrix.Square sh a, Vector sh (RealOf a))
eigensystem = mapFst ArrMatrix.lift0 . Eigen.decompose . ArrMatrix.toVector