{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE GADTs #-}
module Numeric.LAPACK.Matrix.Class (
SquareShape(toSquare, takeDiagonal, mapSquareSize, identityFrom),
MapSize(mapHeight, mapWidth),
trace,
Complex(conjugate, fromReal, toComplex),
adjoint,
) where
import qualified Numeric.LAPACK.Matrix.Array.Basic as OmniMatrix
import qualified Numeric.LAPACK.Matrix.Array as ArrMatrix
import qualified Numeric.LAPACK.Matrix.Type as Matrix
import qualified Numeric.LAPACK.Matrix.Banded.Basic as Banded
import qualified Numeric.LAPACK.Matrix.Layout.Private as Layout
import qualified Numeric.LAPACK.Matrix.Extent.Private as Extent
import qualified Numeric.LAPACK.Matrix.Permutation as Permutation
import qualified Numeric.LAPACK.Permutation.Private as Perm
import qualified Numeric.LAPACK.Permutation as PermPub
import qualified Numeric.LAPACK.Vector as Vector
import qualified Numeric.LAPACK.Scalar as Scalar
import Numeric.LAPACK.Matrix.Type (Matrix)
import Numeric.LAPACK.Vector (Vector)
import Numeric.LAPACK.Scalar (RealOf, ComplexOf)
import qualified Numeric.Netlib.Class as Class
import qualified Data.Array.Comfort.Shape as Shape
class Complex typ where
conjugate ::
(Matrix typ xl xu lower upper meas vert horiz height width ~ matrix,
Extent.Measure meas, Extent.C vert, Extent.C horiz,
Shape.C height, Shape.C width, Class.Floating a) =>
matrix a -> matrix a
fromReal ::
(Matrix typ xl xu lower upper meas vert horiz height width ~ matrix,
Extent.Measure meas, Extent.C vert, Extent.C horiz,
Shape.C height, Shape.C width, Class.Floating a) =>
matrix (RealOf a) -> matrix a
toComplex ::
(Matrix typ xl xu lower upper meas vert horiz height width ~ matrix,
Extent.Measure meas, Extent.C vert, Extent.C horiz,
Shape.C height, Shape.C width, Class.Floating a) =>
matrix a -> matrix (ComplexOf a)
instance Complex (ArrMatrix.Array pack property) where
conjugate :: matrix a -> matrix a
conjugate (ArrMatrix.Array a) = OmniArray pack property lower upper meas vert horiz height width a
-> Matrix
(Array pack property)
()
()
lower
upper
meas
vert
horiz
height
width
a
forall pack prop lower upper meas vert horiz height width a.
OmniArray pack prop lower upper meas vert horiz height width a
-> Matrix
(Array pack prop) () () lower upper meas vert horiz height width a
ArrMatrix.Array (OmniArray pack property lower upper meas vert horiz height width a
-> Matrix
(Array pack property)
()
()
lower
upper
meas
vert
horiz
height
width
a)
-> OmniArray
pack property lower upper meas vert horiz height width a
-> Matrix
(Array pack property)
()
()
lower
upper
meas
vert
horiz
height
width
a
forall a b. (a -> b) -> a -> b
$ OmniArray pack property lower upper meas vert horiz height width a
-> OmniArray
pack property lower upper meas vert horiz height width a
forall sh a. (C sh, Floating a) => Vector sh a -> Vector sh a
Vector.conjugate OmniArray pack property lower upper meas vert horiz height width a
a
fromReal :: matrix (RealOf a) -> matrix a
fromReal (ArrMatrix.Array a) = OmniArray pack property lower upper meas vert horiz height width a
-> Matrix
(Array pack property)
()
()
lower
upper
meas
vert
horiz
height
width
a
forall pack prop lower upper meas vert horiz height width a.
OmniArray pack prop lower upper meas vert horiz height width a
-> Matrix
(Array pack prop) () () lower upper meas vert horiz height width a
ArrMatrix.Array (OmniArray pack property lower upper meas vert horiz height width a
-> Matrix
(Array pack property)
()
()
lower
upper
meas
vert
horiz
height
width
a)
-> OmniArray
pack property lower upper meas vert horiz height width a
-> Matrix
(Array pack property)
()
()
lower
upper
meas
vert
horiz
height
width
a
forall a b. (a -> b) -> a -> b
$ Vector
(Omni pack property lower upper meas vert horiz height width)
(RealOf a)
-> OmniArray
pack property lower upper meas vert horiz height width a
forall sh a.
(C sh, Floating a) =>
Vector sh (RealOf a) -> Vector sh a
Vector.fromReal Vector
(Omni pack property lower upper meas vert horiz height width)
(RealOf a)
a
toComplex :: matrix a -> matrix (ComplexOf a)
toComplex (ArrMatrix.Array a) = OmniArray
pack
property
lower
upper
meas
vert
horiz
height
width
(ComplexOf a)
-> Matrix
(Array pack property)
()
()
lower
upper
meas
vert
horiz
height
width
(ComplexOf a)
forall pack prop lower upper meas vert horiz height width a.
OmniArray pack prop lower upper meas vert horiz height width a
-> Matrix
(Array pack prop) () () lower upper meas vert horiz height width a
ArrMatrix.Array (OmniArray
pack
property
lower
upper
meas
vert
horiz
height
width
(ComplexOf a)
-> Matrix
(Array pack property)
()
()
lower
upper
meas
vert
horiz
height
width
(ComplexOf a))
-> OmniArray
pack
property
lower
upper
meas
vert
horiz
height
width
(ComplexOf a)
-> Matrix
(Array pack property)
()
()
lower
upper
meas
vert
horiz
height
width
(ComplexOf a)
forall a b. (a -> b) -> a -> b
$ Vector
(Omni pack property lower upper meas vert horiz height width) a
-> OmniArray
pack
property
lower
upper
meas
vert
horiz
height
width
(ComplexOf a)
forall sh a.
(C sh, Floating a) =>
Vector sh a -> Vector sh (ComplexOf a)
Vector.toComplex Vector
(Omni pack property lower upper meas vert horiz height width) a
a
instance Complex Matrix.Scale where
conjugate :: matrix a -> matrix a
conjugate (Matrix.Scale sh m) = height -> a -> Quadratic Scale () () Empty Empty height a
forall sh a. sh -> a -> Quadratic Scale () () Empty Empty sh a
Matrix.Scale height
sh (a -> Quadratic Scale () () Empty Empty height a)
-> a -> Quadratic Scale () () Empty Empty height a
forall a b. (a -> b) -> a -> b
$ a -> a
forall a. Floating a => a -> a
Scalar.conjugate a
m
fromReal :: matrix (RealOf a) -> matrix a
fromReal (Matrix.Scale sh m) = height -> a -> Quadratic Scale () () Empty Empty height a
forall sh a. sh -> a -> Quadratic Scale () () Empty Empty sh a
Matrix.Scale height
sh (a -> Quadratic Scale () () Empty Empty height a)
-> a -> Quadratic Scale () () Empty Empty height a
forall a b. (a -> b) -> a -> b
$ RealOf a -> a
forall a. Floating a => RealOf a -> a
Scalar.fromReal RealOf a
m
toComplex :: matrix a -> matrix (ComplexOf a)
toComplex (Matrix.Scale sh m) = height
-> ComplexOf a
-> Quadratic Scale () () Empty Empty height (ComplexOf a)
forall sh a. sh -> a -> Quadratic Scale () () Empty Empty sh a
Matrix.Scale height
sh (ComplexOf a
-> Quadratic Scale () () Empty Empty height (ComplexOf a))
-> ComplexOf a
-> Quadratic Scale () () Empty Empty height (ComplexOf a)
forall a b. (a -> b) -> a -> b
$ a -> ComplexOf a
forall a. Floating a => a -> ComplexOf a
Scalar.toComplex a
m
instance Complex Matrix.Permutation where
conjugate :: matrix a -> matrix a
conjugate = matrix a -> matrix a
forall a. a -> a
id
fromReal :: matrix (RealOf a) -> matrix a
fromReal (Matrix.Permutation p) = Permutation height
-> Quadratic Permutation () () lower upper height a
forall sh lower upper a.
Permutation sh -> Quadratic Permutation () () lower upper sh a
Matrix.Permutation Permutation height
p
toComplex :: matrix a -> matrix (ComplexOf a)
toComplex (Matrix.Permutation p) = Permutation height
-> Quadratic Permutation () () lower upper height (ComplexOf a)
forall sh lower upper a.
Permutation sh -> Quadratic Permutation () () lower upper sh a
Matrix.Permutation Permutation height
p
adjoint ::
(Matrix.Transpose typ, Complex typ) =>
(Extent.Measure meas, Extent.C vert, Extent.C horiz) =>
(Shape.C height, Shape.C width, Class.Floating a) =>
Matrix typ xl xu lower upper meas vert horiz height width a ->
Matrix typ xu xl upper lower meas horiz vert width height a
adjoint :: Matrix typ xl xu lower upper meas vert horiz height width a
-> Matrix typ xu xl upper lower meas horiz vert width height a
adjoint = Matrix typ xu xl upper lower meas horiz vert width height a
-> Matrix typ xu xl upper lower meas horiz vert width height a
forall typ xl xu lower upper meas vert horiz height width
(matrix :: * -> *) a.
(Complex typ,
Matrix typ xl xu lower upper meas vert horiz height width ~ matrix,
Measure meas, C vert, C horiz, C height, C width, Floating a) =>
matrix a -> matrix a
conjugate (Matrix typ xu xl upper lower meas horiz vert width height a
-> Matrix typ xu xl upper lower meas horiz vert width height a)
-> (Matrix typ xl xu lower upper meas vert horiz height width a
-> Matrix typ xu xl upper lower meas horiz vert width height a)
-> Matrix typ xl xu lower upper meas vert horiz height width a
-> Matrix typ xu xl upper lower meas horiz vert width height a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Matrix typ xl xu lower upper meas vert horiz height width a
-> Matrix typ xu xl upper lower meas horiz vert width height a
forall typ meas vert horiz width height a xl xu lower upper.
(Transpose typ, Measure meas, C vert, C horiz, C width, C height,
Floating a) =>
Matrix typ xl xu lower upper meas vert horiz height width a
-> Matrix typ xu xl upper lower meas horiz vert width height a
Matrix.transpose
class (Matrix.Box typ) => SquareShape typ where
toSquare ::
(Shape.C sh, Class.Floating a) =>
Matrix.Quadratic typ xl xu lower upper sh a -> ArrMatrix.Square sh a
takeDiagonal ::
(Shape.C sh, Class.Floating a) =>
Matrix.Quadratic typ xl xu lower upper sh a -> Vector sh a
mapSquareSize ::
(Shape.C shA, Shape.C shB) =>
(shA -> shB) ->
Matrix.Quadratic typ xl xu lower upper shA a ->
Matrix.Quadratic typ xl xu lower upper shB a
identityFrom ::
(Shape.C sh, Class.Floating a) =>
Matrix.Quadratic typ xl xu lower upper sh a ->
Matrix.Quadratic typ xl xu lower upper sh a
instance SquareShape (ArrMatrix.Array pack property) where
toSquare :: Quadratic (Array pack property) xl xu lower upper sh a
-> Square sh a
toSquare a :: Quadratic (Array pack property) xl xu lower upper sh a
a@(ArrMatrix.Array _) = ArrayMatrix pack property lower upper Shape Small Small sh sh a
-> Square sh a
forall meas vert horiz height width a pack property lower upper.
(Measure meas, C vert, C horiz, C height, C width, Floating a) =>
ArrayMatrix
pack property lower upper meas vert horiz height width a
-> Full meas vert horiz height width a
OmniMatrix.toFull Quadratic (Array pack property) xl xu lower upper sh a
ArrayMatrix pack property lower upper Shape Small Small sh sh a
a
takeDiagonal :: Quadratic (Array pack property) xl xu lower upper sh a
-> Vector sh a
takeDiagonal a :: Quadratic (Array pack property) xl xu lower upper sh a
a@(ArrMatrix.Array _) = Quadratic pack property lower upper sh a -> Vector sh a
forall sh a pack property lower upper.
(C sh, Floating a) =>
Quadratic pack property lower upper sh a -> Vector sh a
OmniMatrix.takeDiagonal Quadratic (Array pack property) xl xu lower upper sh a
Quadratic pack property lower upper sh a
a
mapSquareSize :: (shA -> shB)
-> Quadratic (Array pack property) xl xu lower upper shA a
-> Quadratic (Array pack property) xl xu lower upper shB a
mapSquareSize shA -> shB
f a :: Quadratic (Array pack property) xl xu lower upper shA a
a@(ArrMatrix.Array _) = (shA -> shB)
-> Quadratic pack property lower upper shA a
-> Quadratic pack property lower upper shB a
forall shA shB pack property lower upper a.
(C shA, C shB) =>
(shA -> shB)
-> Quadratic pack property lower upper shA a
-> Quadratic pack property lower upper shB a
OmniMatrix.mapSquareSize shA -> shB
f Quadratic (Array pack property) xl xu lower upper shA a
Quadratic pack property lower upper shA a
a
identityFrom :: Quadratic (Array pack property) xl xu lower upper sh a
-> Quadratic (Array pack property) xl xu lower upper sh a
identityFrom a :: Quadratic (Array pack property) xl xu lower upper sh a
a@(ArrMatrix.Array _) = Quadratic pack property lower upper sh a
-> Quadratic pack property lower upper sh a
forall sh a pack property lower upper.
(C sh, Floating a) =>
Quadratic pack property lower upper sh a
-> Quadratic pack property lower upper sh a
OmniMatrix.identityFrom Quadratic (Array pack property) xl xu lower upper sh a
Quadratic pack property lower upper sh a
a
instance SquareShape Matrix.Scale where
toSquare :: Quadratic Scale xl xu lower upper sh a -> Square sh a
toSquare (Matrix.Scale sh a) =
PlainArray
Unpacked Arbitrary Filled Filled Shape Small Small sh sh a
-> Square sh a
forall pack prop lower upper meas vert horiz height width a.
FromPlain pack prop lower upper meas vert horiz height width =>
PlainArray pack prop lower upper meas vert horiz height width a
-> ArrayMatrix pack prop lower upper meas vert horiz height width a
ArrMatrix.lift0 (PlainArray
Unpacked Arbitrary Filled Filled Shape Small Small sh sh a
-> Square sh a)
-> PlainArray
Unpacked Arbitrary Filled Filled Shape Small Small sh sh a
-> Square sh a
forall a b. (a -> b) -> a -> b
$ Banded U0 U0 Shape Small Small sh sh a
-> Full Shape Small Small sh sh a
forall sub super meas vert horiz height width a.
(Natural sub, Natural super, Measure meas, C vert, C horiz,
C height, C width, Floating a) =>
Banded sub super meas vert horiz height width a
-> Full meas vert horiz height width a
Banded.toFull (Banded U0 U0 Shape Small Small sh sh a
-> Full Shape Small Small sh sh a)
-> Banded U0 U0 Shape Small Small sh sh a
-> Full Shape Small Small sh sh a
forall a b. (a -> b) -> a -> b
$
Order -> Vector sh a -> Banded U0 U0 Shape Small Small sh sh a
forall sh a.
(C sh, Floating a) =>
Order -> Vector sh a -> Diagonal sh a
Banded.diagonal Order
Layout.RowMajor (Vector sh a -> Banded U0 U0 Shape Small Small sh sh a)
-> Vector sh a -> Banded U0 U0 Shape Small Small sh sh a
forall a b. (a -> b) -> a -> b
$ sh -> a -> Vector sh a
forall sh a. (C sh, Floating a) => sh -> a -> Vector sh a
Vector.constant sh
sh a
a
takeDiagonal :: Quadratic Scale xl xu lower upper sh a -> Vector sh a
takeDiagonal (Matrix.Scale sh a) = sh -> a -> Vector sh a
forall sh a. (C sh, Floating a) => sh -> a -> Vector sh a
Vector.constant sh
sh a
a
mapSquareSize :: (shA -> shB)
-> Quadratic Scale xl xu lower upper shA a
-> Quadratic Scale xl xu lower upper shB a
mapSquareSize shA -> shB
f (Matrix.Scale sh a) =
shB -> a -> Quadratic Scale () () Empty Empty shB a
forall sh a. sh -> a -> Quadratic Scale () () Empty Empty sh a
Matrix.Scale (String -> (shA -> shB) -> shA -> shB
forall sha shb.
(C sha, C shb) =>
String -> (sha -> shb) -> sha -> shb
Layout.mapChecked String
"Scale.mapSquareSize" shA -> shB
f shA
sh) a
a
identityFrom :: Quadratic Scale xl xu lower upper sh a
-> Quadratic Scale xl xu lower upper sh a
identityFrom (Matrix.Scale sh _a) = sh -> a -> Quadratic Scale () () Empty Empty sh a
forall sh a. sh -> a -> Quadratic Scale () () Empty Empty sh a
Matrix.Scale sh
sh a
forall a. Floating a => a
Scalar.one
instance SquareShape Matrix.Permutation where
toSquare :: Quadratic Permutation xl xu lower upper sh a -> Square sh a
toSquare (Matrix.Permutation perm) = Permutation sh -> Square sh a
forall sh a. (C sh, Floating a) => Permutation sh -> Square sh a
PermPub.toMatrix Permutation sh
perm
takeDiagonal :: Quadratic Permutation xl xu lower upper sh a -> Vector sh a
takeDiagonal a :: Quadratic Permutation xl xu lower upper sh a
a@(Matrix.Permutation _) =
Permutation sh -> Vector sh a
forall sh a. (C sh, Floating a) => Permutation sh -> Vector sh a
Perm.takeDiagonal (Permutation sh -> Vector sh a)
-> (FlexPermutation lower upper sh a -> Permutation sh)
-> FlexPermutation lower upper sh a
-> Vector sh a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. FlexPermutation lower upper sh a -> Permutation sh
forall sh lower upper a.
C sh =>
FlexPermutation lower upper sh a -> Permutation sh
Permutation.toPermutation (FlexPermutation lower upper sh a -> Vector sh a)
-> FlexPermutation lower upper sh a -> Vector sh a
forall a b. (a -> b) -> a -> b
$ Quadratic Permutation xl xu lower upper sh a
FlexPermutation lower upper sh a
a
mapSquareSize :: (shA -> shB)
-> Quadratic Permutation xl xu lower upper shA a
-> Quadratic Permutation xl xu lower upper shB a
mapSquareSize shA -> shB
f (Matrix.Permutation perm) =
Permutation shB -> Quadratic Permutation () () lower upper shB a
forall sh lower upper a.
Permutation sh -> Quadratic Permutation () () lower upper sh a
Matrix.Permutation (Permutation shB -> Quadratic Permutation () () lower upper shB a)
-> Permutation shB -> Quadratic Permutation () () lower upper shB a
forall a b. (a -> b) -> a -> b
$ (shA -> shB) -> Permutation shA -> Permutation shB
forall shA shB.
(C shA, C shB) =>
(shA -> shB) -> Permutation shA -> Permutation shB
Perm.mapSize shA -> shB
f Permutation shA
perm
identityFrom :: Quadratic Permutation xl xu lower upper sh a
-> Quadratic Permutation xl xu lower upper sh a
identityFrom (Matrix.Permutation perm) =
Permutation sh -> Quadratic Permutation () () lower upper sh a
forall sh lower upper a.
Permutation sh -> Quadratic Permutation () () lower upper sh a
Matrix.Permutation (Permutation sh -> Quadratic Permutation () () lower upper sh a)
-> Permutation sh -> Quadratic Permutation () () lower upper sh a
forall a b. (a -> b) -> a -> b
$ sh -> Permutation sh
forall sh. C sh => sh -> Permutation sh
Perm.identity (sh -> Permutation sh) -> sh -> Permutation sh
forall a b. (a -> b) -> a -> b
$ Permutation sh -> sh
forall sh. Permutation sh -> sh
Perm.size Permutation sh
perm
trace ::
(SquareShape typ, Shape.C sh, Class.Floating a) =>
Matrix.Quadratic typ xl xu lower upper sh a -> a
trace :: Quadratic typ xl xu lower upper sh a -> a
trace = Vector sh a -> a
forall sh a. (C sh, Floating a) => Vector sh a -> a
Vector.sum (Vector sh a -> a)
-> (Quadratic typ xl xu lower upper sh a -> Vector sh a)
-> Quadratic typ xl xu lower upper sh a
-> a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Quadratic typ xl xu lower upper sh a -> Vector sh a
forall typ sh a xl xu lower upper.
(SquareShape typ, C sh, Floating a) =>
Quadratic typ xl xu lower upper sh a -> Vector sh a
takeDiagonal
class (Matrix.Box typ) => MapSize typ where
mapHeight ::
(Extent.C vert, Extent.C horiz,
Shape.C heightA, Shape.C heightB, Shape.C width) =>
(heightA -> heightB) ->
Matrix typ extraLower extraUpper lower upper
Extent.Size vert horiz heightA width a ->
Matrix typ extraLower extraUpper lower upper
Extent.Size vert horiz heightB width a
mapWidth ::
(Extent.C vert, Extent.C horiz,
Shape.C height, Shape.C widthA, Shape.C widthB) =>
(widthA -> widthB) ->
Matrix typ extraLower extraUpper lower upper
Extent.Size vert horiz height widthA a ->
Matrix typ extraLower extraUpper lower upper
Extent.Size vert horiz height widthB a
instance MapSize (ArrMatrix.Array pack property) where
mapHeight :: (heightA -> heightB)
-> Matrix
(Array pack property)
extraLower
extraUpper
lower
upper
Size
vert
horiz
heightA
width
a
-> Matrix
(Array pack property)
extraLower
extraUpper
lower
upper
Size
vert
horiz
heightB
width
a
mapHeight heightA -> heightB
f a :: Matrix
(Array pack property)
extraLower
extraUpper
lower
upper
Size
vert
horiz
heightA
width
a
a@(ArrMatrix.Array _) = (heightA -> heightB)
-> Matrix
(Array pack property)
extraLower
extraUpper
lower
upper
Size
vert
horiz
heightA
width
a
-> Matrix
(Array pack property)
extraLower
extraUpper
lower
upper
Size
vert
horiz
heightB
width
a
forall pack property lower upper vert horiz
(matrix :: * -> * -> * -> *) heightA heightB width a.
(ArrayMatrix pack property lower upper Size vert horiz ~ matrix,
C vert, C horiz, C heightA, C heightB, C width) =>
(heightA -> heightB)
-> matrix heightA width a -> matrix heightB width a
OmniMatrix.mapHeight heightA -> heightB
f Matrix
(Array pack property)
extraLower
extraUpper
lower
upper
Size
vert
horiz
heightA
width
a
a
mapWidth :: (widthA -> widthB)
-> Matrix
(Array pack property)
extraLower
extraUpper
lower
upper
Size
vert
horiz
height
widthA
a
-> Matrix
(Array pack property)
extraLower
extraUpper
lower
upper
Size
vert
horiz
height
widthB
a
mapWidth widthA -> widthB
f a :: Matrix
(Array pack property)
extraLower
extraUpper
lower
upper
Size
vert
horiz
height
widthA
a
a@(ArrMatrix.Array _) = (widthA -> widthB)
-> Matrix
(Array pack property)
extraLower
extraUpper
lower
upper
Size
vert
horiz
height
widthA
a
-> Matrix
(Array pack property)
extraLower
extraUpper
lower
upper
Size
vert
horiz
height
widthB
a
forall pack property lower upper vert horiz
(matrix :: * -> * -> * -> *) widthA widthB height a.
(ArrayMatrix pack property lower upper Size vert horiz ~ matrix,
C vert, C horiz, C widthA, C widthB, C height) =>
(widthA -> widthB)
-> matrix height widthA a -> matrix height widthB a
OmniMatrix.mapWidth widthA -> widthB
f Matrix
(Array pack property)
extraLower
extraUpper
lower
upper
Size
vert
horiz
height
widthA
a
a