Safe Haskell	None
Language	Haskell98

Numeric.LAPACK.Matrix.Array

Synopsis

data family Matrix typ a
type ArrayMatrix shape = Matrix (Array shape)
data Array shape
type Full vert horiz height width = ArrayMatrix (Full vert horiz height width)
type General height width = ArrayMatrix (General height width)
type Tall height width = ArrayMatrix (Tall height width)
type Wide height width = ArrayMatrix (Wide height width)
type Square sh = ArrayMatrix (Square sh)
shape :: ArrayMatrix sh a -> sh
reshape :: (C sh0, C sh1) => sh1 -> ArrayMatrix sh0 a -> ArrayMatrix sh1 a
mapShape :: (C sh0, C sh1) => (sh0 -> sh1) -> ArrayMatrix sh0 a -> ArrayMatrix sh1 a
toVector :: ArrayMatrix sh a -> Array sh a
fromVector :: Array sh a -> ArrayMatrix sh a
lift0 :: Array shA a -> ArrayMatrix shA a
lift1 :: (Array shA a -> Array shB b) -> ArrayMatrix shA a -> ArrayMatrix shB b
lift2 :: (Array shA a -> Array shB b -> Array shC c) -> ArrayMatrix shA a -> ArrayMatrix shB b -> ArrayMatrix shC c
lift3 :: (Array shA a -> Array shB b -> Array shC c -> Array shD d) -> ArrayMatrix shA a -> ArrayMatrix shB b -> ArrayMatrix shC c -> ArrayMatrix shD d
unlift1 :: (ArrayMatrix shA a -> ArrayMatrix shB b) -> Array shA a -> Array shB b
unlift2 :: (ArrayMatrix shA a -> ArrayMatrix shB b -> ArrayMatrix shC c) -> Array shA a -> Array shB b -> Array shC c
unliftRow :: Order -> (General () height0 a -> General () height1 b) -> Vector height0 a -> Vector height1 b
unliftColumn :: Order -> (General height0 () a -> General height1 () b) -> Vector height0 a -> Vector height1 b
class C shape => Homogeneous shape where
- zero :: Floating a => shape -> ArrayMatrix shape a
- negate :: Floating a => ArrayMatrix shape a -> ArrayMatrix shape a
- scaleReal :: Floating a => RealOf a -> ArrayMatrix shape a -> ArrayMatrix shape a
scale :: (Scale shape, Floating a) => a -> ArrayMatrix shape a -> ArrayMatrix shape a
scaleRealReal :: (Homogeneous shape, Real a) => a -> ArrayMatrix shape a -> ArrayMatrix shape a
(.*#) :: (Scale shape, Floating a) => a -> ArrayMatrix shape a -> ArrayMatrix shape a
class C shape => ShapeOrder shape where
- forceOrder :: Floating a => Order -> ArrayMatrix shape a -> ArrayMatrix shape a
- shapeOrder :: shape -> Order
adaptOrder :: (ShapeOrder shape, Floating a) => ArrayMatrix shape a -> ArrayMatrix shape a -> ArrayMatrix shape a
class Homogeneous shape => Additive shape where
- add, sub :: Floating a => ArrayMatrix shape a -> ArrayMatrix shape a -> ArrayMatrix shape a
(#+#) :: (Additive shape, Floating a) => ArrayMatrix shape a -> ArrayMatrix shape a -> ArrayMatrix shape a
(#-#) :: (Additive shape, Floating a) => ArrayMatrix shape a -> ArrayMatrix shape a -> ArrayMatrix shape a
class C shape => Complex shape
class Box shape => MultiplyLeft shape
class Box shape => MultiplyRight shape
class (Box shape, HeightOf shape ~ WidthOf shape) => MultiplySquare shape
class (C shapeA, C shapeB) => Multiply shapeA shapeB

Documentation

data family Matrix typ a Source #

Instances

(C sh, Show sh) => Show (Matrix (Permutation sh) a) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Type Methods showsPrec :: Int -> Matrix (Permutation sh) a -> ShowS # show :: Matrix (Permutation sh) a -> String # showList :: [Matrix (Permutation sh) a] -> ShowS #
(C shape, Storable a, Show shape, Show a) => Show (Matrix (Array shape) a) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Methods showsPrec :: Int -> Matrix (Array shape) a -> ShowS # show :: Matrix (Array shape) a -> String # showList :: [Matrix (Array shape) a] -> ShowS #
(MultiplySame typ, Floating a) => Semigroup (Matrix typ a) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Type Methods (<>) :: Matrix typ a -> Matrix typ a -> Matrix typ a # sconcat :: NonEmpty (Matrix typ a) -> Matrix typ a # stimes :: Integral b => b -> Matrix typ a -> Matrix typ a #
(NFData typ, NFData a) => NFData (Matrix typ a) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Type Methods rnf :: Matrix typ a -> () #
(FormatMatrix typ, Floating a) => Display (Matrix typ a) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Type Methods display :: Matrix typ a -> Graphic #
(FormatMatrix typ, Floating a) => Format (Matrix typ a) Source #
Instance details Defined in Numeric.LAPACK.Format Methods format :: Output out => String -> Matrix typ a -> out Source #
newtype Matrix (Permutation sh) a Source #
Instance details Defined in Numeric.LAPACK.Matrix.Type newtype Matrix (Permutation sh) a = Permutation (Permutation sh)
newtype Matrix (Array shape) a Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array newtype Matrix (Array shape) a = Array (Array shape a)

type ArrayMatrix shape = Matrix (Array shape) Source #

data Array shape Source #

Instances

Complex sh => Complex (Array sh) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Methods conjugate :: Floating a => Matrix (Array sh) a -> Matrix (Array sh) a Source # fromReal :: Floating a => Matrix (Array sh) (RealOf a) -> Matrix (Array sh) a Source # toComplex :: Floating a => Matrix (Array sh) a -> Matrix (Array sh) (ComplexOf a) Source #
Box sh => Box (Array sh) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Associated Types type HeightOf (Array sh) :: Type Source # type WidthOf (Array sh) :: Type Source # Methods height :: Matrix (Array sh) a -> HeightOf (Array sh) Source # width :: Matrix (Array sh) a -> WidthOf (Array sh) Source #
FormatArray sh => FormatMatrix (Array sh) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Methods formatMatrix :: (Floating a, Output out) => String -> Matrix (Array sh) a -> out Source #
Indexed sh => Indexed (Array sh) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Indexed Methods (#!) :: Floating a => Matrix (Array sh) a -> (Index (HeightOf (Array sh)), Index (WidthOf (Array sh))) -> a Source #
Inverse shape => Inverse (Array shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Divide Methods inverse :: Floating a => Matrix (Array shape) a -> Matrix (Array shape) a Source #
Solve shape => Solve (Array shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Divide Methods solve :: (HeightOf (Array shape) ~ height, Eq height, C width, C horiz, C vert, Floating a) => Transposition -> Matrix (Array shape) a -> Full vert horiz height width a -> Full vert horiz height width a Source # solveRight :: (HeightOf (Array shape) ~ height, Eq height, C width, C horiz, C vert, Floating a) => Matrix (Array shape) a -> Full vert horiz height width a -> Full vert horiz height width a Source # solveLeft :: (WidthOf (Array shape) ~ width, Eq width, C height, C horiz, C vert, Floating a) => Full vert horiz height width a -> Matrix (Array shape) a -> Full vert horiz height width a Source #
MultiplySquare shape => MultiplySquare (Array shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Methods transposableSquare :: (HeightOf (Array shape) ~ height, Eq height, C width, C horiz, C vert, Floating a) => Transposition -> Matrix (Array shape) a -> Full vert horiz height width a -> Full vert horiz height width a squareFull :: (HeightOf (Array shape) ~ height, Eq height, C width, C horiz, C vert, Floating a) => Matrix (Array shape) a -> Full vert horiz height width a -> Full vert horiz height width a fullSquare :: (WidthOf (Array shape) ~ width, Eq width, C height, C horiz, C vert, Floating a) => Full vert horiz height width a -> Matrix (Array shape) a -> Full vert horiz height width a
MultiplyLeft shape => MultiplyLeft (Array shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Methods vectorMatrix :: Floating a => Vector (HeightOf (Array shape)) a -> Matrix (Array shape) a -> Vector (WidthOf (Array shape)) a
MultiplyRight shape => MultiplyRight (Array shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Methods matrixVector :: Floating a => Matrix (Array shape) a -> Vector (WidthOf (Array shape)) a -> Vector (HeightOf (Array shape)) a
(Box shapeA, Box shapeB, Multiply shapeA shapeB) => Multiply (Array shapeA) (Array shapeB) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Array shapeA) (Array shapeB) :: Type Methods matrixMatrix :: Floating a => Matrix (Array shapeA) a -> Matrix (Array shapeB) a -> Matrix (Multiplied (Array shapeA) (Array shapeB)) a
(C shape, Storable a, Show shape, Show a) => Show (Matrix (Array shape) a) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Methods showsPrec :: Int -> Matrix (Array shape) a -> ShowS # show :: Matrix (Array shape) a -> String # showList :: [Matrix (Array shape) a] -> ShowS #
type HeightOf (Array sh) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array type HeightOf (Array sh) = HeightOf sh
type WidthOf (Array sh) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array type WidthOf (Array sh) = WidthOf sh
newtype Matrix (Array shape) a Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array newtype Matrix (Array shape) a = Array (Array shape a)

type Full vert horiz height width = ArrayMatrix (Full vert horiz height width) Source #

type General height width = ArrayMatrix (General height width) Source #

type Tall height width = ArrayMatrix (Tall height width) Source #

type Wide height width = ArrayMatrix (Wide height width) Source #

type Square sh = ArrayMatrix (Square sh) Source #

shape :: ArrayMatrix sh a -> sh Source #

reshape :: (C sh0, C sh1) => sh1 -> ArrayMatrix sh0 a -> ArrayMatrix sh1 a Source #

mapShape :: (C sh0, C sh1) => (sh0 -> sh1) -> ArrayMatrix sh0 a -> ArrayMatrix sh1 a Source #

toVector :: ArrayMatrix sh a -> Array sh a Source #

fromVector :: Array sh a -> ArrayMatrix sh a Source #

lift0 :: Array shA a -> ArrayMatrix shA a Source #

lift1 :: (Array shA a -> Array shB b) -> ArrayMatrix shA a -> ArrayMatrix shB b Source #

lift2 :: (Array shA a -> Array shB b -> Array shC c) -> ArrayMatrix shA a -> ArrayMatrix shB b -> ArrayMatrix shC c Source #

lift3 :: (Array shA a -> Array shB b -> Array shC c -> Array shD d) -> ArrayMatrix shA a -> ArrayMatrix shB b -> ArrayMatrix shC c -> ArrayMatrix shD d Source #

unlift1 :: (ArrayMatrix shA a -> ArrayMatrix shB b) -> Array shA a -> Array shB b Source #

unlift2 :: (ArrayMatrix shA a -> ArrayMatrix shB b -> ArrayMatrix shC c) -> Array shA a -> Array shB b -> Array shC c Source #

unliftRow :: Order -> (General () height0 a -> General () height1 b) -> Vector height0 a -> Vector height1 b Source #

unliftColumn :: Order -> (General height0 () a -> General height1 () b) -> Vector height0 a -> Vector height1 b Source #

class C shape => Homogeneous shape where Source #

Minimal complete definition

Nothing

Methods

zero :: Floating a => shape -> ArrayMatrix shape a Source #

negate :: Floating a => ArrayMatrix shape a -> ArrayMatrix shape a Source #

scaleReal :: Floating a => RealOf a -> ArrayMatrix shape a -> ArrayMatrix shape a Source #

Instances

C size => Homogeneous (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Methods zero :: Floating a => Hermitian size -> ArrayMatrix (Hermitian size) a Source # negate :: Floating a => ArrayMatrix (Hermitian size) a -> ArrayMatrix (Hermitian size) a Source # scaleReal :: Floating a => RealOf a -> ArrayMatrix (Hermitian size) a -> ArrayMatrix (Hermitian size) a Source #
(Natural off, C size) => Homogeneous (BandedHermitian off size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Methods zero :: Floating a => BandedHermitian off size -> ArrayMatrix (BandedHermitian off size) a Source # negate :: Floating a => ArrayMatrix (BandedHermitian off size) a -> ArrayMatrix (BandedHermitian off size) a Source # scaleReal :: Floating a => RealOf a -> ArrayMatrix (BandedHermitian off size) a -> ArrayMatrix (BandedHermitian off size) a Source #
(Content lo, NonUnit ~ diag, Content up, C size) => Homogeneous (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Methods zero :: Floating a => Triangular lo diag up size -> ArrayMatrix (Triangular lo diag up size) a Source # negate :: Floating a => ArrayMatrix (Triangular lo diag up size) a -> ArrayMatrix (Triangular lo diag up size) a Source # scaleReal :: Floating a => RealOf a -> ArrayMatrix (Triangular lo diag up size) a -> ArrayMatrix (Triangular lo diag up size) a Source #
(C vert, C horiz, C height, C width) => Homogeneous (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Methods zero :: Floating a => Full vert horiz height width -> ArrayMatrix (Full vert horiz height width) a Source # negate :: Floating a => ArrayMatrix (Full vert horiz height width) a -> ArrayMatrix (Full vert horiz height width) a Source # scaleReal :: Floating a => RealOf a -> ArrayMatrix (Full vert horiz height width) a -> ArrayMatrix (Full vert horiz height width) a Source #
(Natural sub, Natural super, C vert, C horiz, C height, C width) => Homogeneous (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Methods zero :: Floating a => Banded sub super vert horiz height width -> ArrayMatrix (Banded sub super vert horiz height width) a Source # negate :: Floating a => ArrayMatrix (Banded sub super vert horiz height width) a -> ArrayMatrix (Banded sub super vert horiz height width) a Source # scaleReal :: Floating a => RealOf a -> ArrayMatrix (Banded sub super vert horiz height width) a -> ArrayMatrix (Banded sub super vert horiz height width) a Source #

scale :: (Scale shape, Floating a) => a -> ArrayMatrix shape a -> ArrayMatrix shape a Source #

scaleRealReal :: (Homogeneous shape, Real a) => a -> ArrayMatrix shape a -> ArrayMatrix shape a Source #

(.*#) :: (Scale shape, Floating a) => a -> ArrayMatrix shape a -> ArrayMatrix shape a infixl 7 Source #

class C shape => ShapeOrder shape where Source #

Methods

forceOrder :: Floating a => Order -> ArrayMatrix shape a -> ArrayMatrix shape a Source #

shapeOrder :: shape -> Order Source #

Instances

C size => ShapeOrder (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Methods forceOrder :: Floating a => Order -> ArrayMatrix (Hermitian size) a -> ArrayMatrix (Hermitian size) a Source # shapeOrder :: Hermitian size -> Order Source #
(Content lo, TriDiag diag, Content up, C size) => ShapeOrder (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Methods forceOrder :: Floating a => Order -> ArrayMatrix (Triangular lo diag up size) a -> ArrayMatrix (Triangular lo diag up size) a Source # shapeOrder :: Triangular lo diag up size -> Order Source #
(C vert, C horiz, C height, C width) => ShapeOrder (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Methods forceOrder :: Floating a => Order -> ArrayMatrix (Full vert horiz height width) a -> ArrayMatrix (Full vert horiz height width) a Source # shapeOrder :: Full vert horiz height width -> Order Source #

adaptOrder :: (ShapeOrder shape, Floating a) => ArrayMatrix shape a -> ArrayMatrix shape a -> ArrayMatrix shape a Source #

adaptOrder x y contains the data of y with the layout of x.

class Homogeneous shape => Additive shape where Source #

Minimal complete definition

add

Methods

add :: Floating a => ArrayMatrix shape a -> ArrayMatrix shape a -> ArrayMatrix shape a infixl 6 Source #

sub :: Floating a => ArrayMatrix shape a -> ArrayMatrix shape a -> ArrayMatrix shape a infixl 6 Source #

Instances

(C size, Eq size) => Additive (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Methods add :: Floating a => ArrayMatrix (Hermitian size) a -> ArrayMatrix (Hermitian size) a -> ArrayMatrix (Hermitian size) a Source # sub :: Floating a => ArrayMatrix (Hermitian size) a -> ArrayMatrix (Hermitian size) a -> ArrayMatrix (Hermitian size) a Source #
(Content lo, Eq lo, NonUnit ~ diag, Content up, Eq up, C size, Eq size) => Additive (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Methods add :: Floating a => ArrayMatrix (Triangular lo diag up size) a -> ArrayMatrix (Triangular lo diag up size) a -> ArrayMatrix (Triangular lo diag up size) a Source # sub :: Floating a => ArrayMatrix (Triangular lo diag up size) a -> ArrayMatrix (Triangular lo diag up size) a -> ArrayMatrix (Triangular lo diag up size) a Source #
(C vert, C horiz, C height, Eq height, C width, Eq width) => Additive (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Methods add :: Floating a => ArrayMatrix (Full vert horiz height width) a -> ArrayMatrix (Full vert horiz height width) a -> ArrayMatrix (Full vert horiz height width) a Source # sub :: Floating a => ArrayMatrix (Full vert horiz height width) a -> ArrayMatrix (Full vert horiz height width) a -> ArrayMatrix (Full vert horiz height width) a Source #

(#+#) :: (Additive shape, Floating a) => ArrayMatrix shape a -> ArrayMatrix shape a -> ArrayMatrix shape a infixl 6 Source #

(#-#) :: (Additive shape, Floating a) => ArrayMatrix shape a -> ArrayMatrix shape a -> ArrayMatrix shape a infixl 6 Source #

class C shape => Complex shape Source #

Instances

C size => Complex (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Methods conjugate :: Floating a => ArrayMatrix (Hermitian size) a -> ArrayMatrix (Hermitian size) a fromReal :: Floating a => ArrayMatrix (Hermitian size) (RealOf a) -> ArrayMatrix (Hermitian size) a toComplex :: Floating a => ArrayMatrix (Hermitian size) a -> ArrayMatrix (Hermitian size) (ComplexOf a)
(Natural off, C size) => Complex (BandedHermitian off size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Methods conjugate :: Floating a => ArrayMatrix (BandedHermitian off size) a -> ArrayMatrix (BandedHermitian off size) a fromReal :: Floating a => ArrayMatrix (BandedHermitian off size) (RealOf a) -> ArrayMatrix (BandedHermitian off size) a toComplex :: Floating a => ArrayMatrix (BandedHermitian off size) a -> ArrayMatrix (BandedHermitian off size) (ComplexOf a)
(Content lo, TriDiag diag, Content up, C size) => Complex (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Methods conjugate :: Floating a => ArrayMatrix (Triangular lo diag up size) a -> ArrayMatrix (Triangular lo diag up size) a fromReal :: Floating a => ArrayMatrix (Triangular lo diag up size) (RealOf a) -> ArrayMatrix (Triangular lo diag up size) a toComplex :: Floating a => ArrayMatrix (Triangular lo diag up size) a -> ArrayMatrix (Triangular lo diag up size) (ComplexOf a)
(C vert, C horiz, C height, C width) => Complex (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Methods conjugate :: Floating a => ArrayMatrix (Full vert horiz height width) a -> ArrayMatrix (Full vert horiz height width) a fromReal :: Floating a => ArrayMatrix (Full vert horiz height width) (RealOf a) -> ArrayMatrix (Full vert horiz height width) a toComplex :: Floating a => ArrayMatrix (Full vert horiz height width) a -> ArrayMatrix (Full vert horiz height width) (ComplexOf a)
(Natural sub, Natural super, C vert, C horiz, C height, C width) => Complex (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array Methods conjugate :: Floating a => ArrayMatrix (Banded sub super vert horiz height width) a -> ArrayMatrix (Banded sub super vert horiz height width) a fromReal :: Floating a => ArrayMatrix (Banded sub super vert horiz height width) (RealOf a) -> ArrayMatrix (Banded sub super vert horiz height width) a toComplex :: Floating a => ArrayMatrix (Banded sub super vert horiz height width) a -> ArrayMatrix (Banded sub super vert horiz height width) (ComplexOf a)

class Box shape => MultiplyLeft shape Source #

Minimal complete definition

vectorMatrix

Instances

(Eq shape, C shape) => MultiplyLeft (Hermitian shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Methods vectorMatrix :: Floating a => Vector (HeightOf (Hermitian shape)) a -> Array (Hermitian shape) a -> Vector (WidthOf (Hermitian shape)) a
(Natural offDiag, C size, Eq size) => MultiplyLeft (BandedHermitian offDiag size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Methods vectorMatrix :: Floating a => Vector (HeightOf (BandedHermitian offDiag size)) a -> Array (BandedHermitian offDiag size) a -> Vector (WidthOf (BandedHermitian offDiag size)) a
(Content lo, Content up, TriDiag diag, Eq shape, C shape) => MultiplyLeft (Triangular lo diag up shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Methods vectorMatrix :: Floating a => Vector (HeightOf (Triangular lo diag up shape)) a -> Array (Triangular lo diag up shape) a -> Vector (WidthOf (Triangular lo diag up shape)) a
(C vert, C horiz, Eq height, C width, C height) => MultiplyLeft (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Methods vectorMatrix :: Floating a => Vector (HeightOf (Full vert horiz height width)) a -> Array (Full vert horiz height width) a -> Vector (WidthOf (Full vert horiz height width)) a
(Natural sub, Natural super, C vert, C horiz, Eq height, C width, C height) => MultiplyLeft (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Methods vectorMatrix :: Floating a => Vector (HeightOf (Banded sub super vert horiz height width)) a -> Array (Banded sub super vert horiz height width) a -> Vector (WidthOf (Banded sub super vert horiz height width)) a

class Box shape => MultiplyRight shape Source #

Minimal complete definition

matrixVector

Instances

(Eq shape, C shape) => MultiplyRight (Hermitian shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Methods matrixVector :: Floating a => Array (Hermitian shape) a -> Vector (WidthOf (Hermitian shape)) a -> Vector (HeightOf (Hermitian shape)) a
(Natural offDiag, C size, Eq size) => MultiplyRight (BandedHermitian offDiag size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Methods matrixVector :: Floating a => Array (BandedHermitian offDiag size) a -> Vector (WidthOf (BandedHermitian offDiag size)) a -> Vector (HeightOf (BandedHermitian offDiag size)) a
(Content lo, Content up, TriDiag diag, Eq shape, C shape) => MultiplyRight (Triangular lo diag up shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Methods matrixVector :: Floating a => Array (Triangular lo diag up shape) a -> Vector (WidthOf (Triangular lo diag up shape)) a -> Vector (HeightOf (Triangular lo diag up shape)) a
(C vert, C horiz, Eq width, C width, C height) => MultiplyRight (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Methods matrixVector :: Floating a => Array (Full vert horiz height width) a -> Vector (WidthOf (Full vert horiz height width)) a -> Vector (HeightOf (Full vert horiz height width)) a
(Natural sub, Natural super, C vert, C horiz, Eq width, C width, C height) => MultiplyRight (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Methods matrixVector :: Floating a => Array (Banded sub super vert horiz height width) a -> Vector (WidthOf (Banded sub super vert horiz height width)) a -> Vector (HeightOf (Banded sub super vert horiz height width)) a

class (Box shape, HeightOf shape ~ WidthOf shape) => MultiplySquare shape Source #

Minimal complete definition

transposableSquare | fullSquare, squareFull

Instances

(Eq shape, C shape) => MultiplySquare (Hermitian shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Methods transposableSquare :: (HeightOf (Hermitian shape) ~ height, Eq height, C width, C horiz, C vert, Floating a) => Transposition -> Array (Hermitian shape) a -> Full vert horiz height width a -> Full vert horiz height width a squareFull :: (HeightOf (Hermitian shape) ~ height, Eq height, C width, C horiz, C vert, Floating a) => Array (Hermitian shape) a -> Full vert horiz height width a -> Full vert horiz height width a fullSquare :: (WidthOf (Hermitian shape) ~ width, Eq width, C height, C horiz, C vert, Floating a) => Full vert horiz height width a -> Array (Hermitian shape) a -> Full vert horiz height width a
(Natural offDiag, C size, Eq size) => MultiplySquare (BandedHermitian offDiag size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Methods transposableSquare :: (HeightOf (BandedHermitian offDiag size) ~ height, Eq height, C width, C horiz, C vert, Floating a) => Transposition -> Array (BandedHermitian offDiag size) a -> Full vert horiz height width a -> Full vert horiz height width a squareFull :: (HeightOf (BandedHermitian offDiag size) ~ height, Eq height, C width, C horiz, C vert, Floating a) => Array (BandedHermitian offDiag size) a -> Full vert horiz height width a -> Full vert horiz height width a fullSquare :: (WidthOf (BandedHermitian offDiag size) ~ width, Eq width, C height, C horiz, C vert, Floating a) => Full vert horiz height width a -> Array (BandedHermitian offDiag size) a -> Full vert horiz height width a
(Content lo, Content up, TriDiag diag, Eq shape, C shape) => MultiplySquare (Triangular lo diag up shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Methods transposableSquare :: (HeightOf (Triangular lo diag up shape) ~ height, Eq height, C width, C horiz, C vert, Floating a) => Transposition -> Array (Triangular lo diag up shape) a -> Full vert horiz height width a -> Full vert horiz height width a squareFull :: (HeightOf (Triangular lo diag up shape) ~ height, Eq height, C width, C horiz, C vert, Floating a) => Array (Triangular lo diag up shape) a -> Full vert horiz height width a -> Full vert horiz height width a fullSquare :: (WidthOf (Triangular lo diag up shape) ~ width, Eq width, C height, C horiz, C vert, Floating a) => Full vert horiz height width a -> Array (Triangular lo diag up shape) a -> Full vert horiz height width a
(vert ~ Small, horiz ~ Small, C height, Eq height, height ~ width) => MultiplySquare (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Methods transposableSquare :: (HeightOf (Full vert horiz height width) ~ height0, Eq height0, C width0, C horiz0, C vert0, Floating a) => Transposition -> Array (Full vert horiz height width) a -> Full0 vert0 horiz0 height0 width0 a -> Full0 vert0 horiz0 height0 width0 a squareFull :: (HeightOf (Full vert horiz height width) ~ height0, Eq height0, C width0, C horiz0, C vert0, Floating a) => Array (Full vert horiz height width) a -> Full0 vert0 horiz0 height0 width0 a -> Full0 vert0 horiz0 height0 width0 a fullSquare :: (WidthOf (Full vert horiz height width) ~ width0, Eq width0, C height0, C horiz0, C vert0, Floating a) => Full0 vert0 horiz0 height0 width0 a -> Array (Full vert horiz height width) a -> Full0 vert0 horiz0 height0 width0 a
(Natural sub, Natural super, vert ~ Small, horiz ~ Small, C height, Eq height, height ~ width) => MultiplySquare (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Methods transposableSquare :: (HeightOf (Banded sub super vert horiz height width) ~ height0, Eq height0, C width0, C horiz0, C vert0, Floating a) => Transposition -> Array (Banded sub super vert horiz height width) a -> Full vert0 horiz0 height0 width0 a -> Full vert0 horiz0 height0 width0 a squareFull :: (HeightOf (Banded sub super vert horiz height width) ~ height0, Eq height0, C width0, C horiz0, C vert0, Floating a) => Array (Banded sub super vert horiz height width) a -> Full vert0 horiz0 height0 width0 a -> Full vert0 horiz0 height0 width0 a fullSquare :: (WidthOf (Banded sub super vert horiz height width) ~ width0, Eq width0, C height0, C horiz0, C vert0, Floating a) => Full vert0 horiz0 height0 width0 a -> Array (Banded sub super vert horiz height width) a -> Full vert0 horiz0 height0 width0 a

class (C shapeA, C shapeB) => Multiply shapeA shapeB Source #

This class allows to Basic.multiply two matrices of arbitrary special features and returns the most special matrix type possible. At the first glance, this is handy. At the second glance, this has some problems. First of all, we may refine the types in future and then multiplication may return a different, more special type than before. Second, if you write code with polymorphic matrix types, then matrixMatrix may leave you with constraints like ExtentPriv.Multiply vert vert ~ vert. That constraint is always fulfilled but the compiler cannot infer that. Because of these problems you may instead consider using specialised multiply functions from the various modules for production use. Btw. MultiplyLeft, MultiplyRight and MultiplySquare are much less problematic, because the input and output are always dense vectors or dense matrices.

Minimal complete definition

matrixMatrix

Instances

(C shapeA, shapeA ~ shapeB, Eq shapeB) => Multiply (Hermitian shapeA) (Hermitian shapeB) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Associated Types type Multiplied (Hermitian shapeA) (Hermitian shapeB) :: Type Methods matrixMatrix :: Floating a => Array (Hermitian shapeA) a -> Array (Hermitian shapeB) a -> Array (Multiplied (Hermitian shapeA) (Hermitian shapeB)) a
(C vert, C horiz, C size, size ~ height, Eq height, C width) => Multiply (Hermitian size) (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Associated Types type Multiplied (Hermitian size) (Full vert horiz height width) :: Type Methods matrixMatrix :: Floating a => Array (Hermitian size) a -> Array (Full vert horiz height width) a -> Array (Multiplied (Hermitian size) (Full vert horiz height width)) a
(Natural offDiagA, Natural offDiagB, C sizeA, sizeA ~ sizeB, C sizeB, Eq sizeB) => Multiply (BandedHermitian offDiagA sizeA) (BandedHermitian offDiagB sizeB) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Associated Types type Multiplied (BandedHermitian offDiagA sizeA) (BandedHermitian offDiagB sizeB) :: Type Methods matrixMatrix :: Floating a => Array (BandedHermitian offDiagA sizeA) a -> Array (BandedHermitian offDiagB sizeB) a -> Array (Multiplied (BandedHermitian offDiagA sizeA) (BandedHermitian offDiagB sizeB)) a
(Natural offDiag, C vert, C horiz, C size, size ~ height, Eq height, C width, Eq width) => Multiply (BandedHermitian offDiag size) (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Associated Types type Multiplied (BandedHermitian offDiag size) (Full vert horiz height width) :: Type Methods matrixMatrix :: Floating a => Array (BandedHermitian offDiag size) a -> Array (Full vert horiz height width) a -> Array (Multiplied (BandedHermitian offDiag size) (Full vert horiz height width)) a
(Natural offDiag, Natural sub, Natural super, C vert, C horiz, C size, size ~ height, Eq height, C width, Eq width) => Multiply (BandedHermitian offDiag size) (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Associated Types type Multiplied (BandedHermitian offDiag size) (Banded sub super vert horiz height width) :: Type Methods matrixMatrix :: Floating a => Array (BandedHermitian offDiag size) a -> Array (Banded sub super vert horiz height width) a -> Array (Multiplied (BandedHermitian offDiag size) (Banded sub super vert horiz height width)) a
(C vert, C horiz, C size, size ~ width, Eq width, C height) => Multiply (Full vert horiz height width) (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Associated Types type Multiplied (Full vert horiz height width) (Hermitian size) :: Type Methods matrixMatrix :: Floating a => Array (Full vert horiz height width) a -> Array (Hermitian size) a -> Array (Multiplied (Full vert horiz height width) (Hermitian size)) a
(Natural offDiag, C vert, C horiz, C size, size ~ width, Eq width, C height, Eq height) => Multiply (Full vert horiz height width) (BandedHermitian offDiag size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Associated Types type Multiplied (Full vert horiz height width) (BandedHermitian offDiag size) :: Type Methods matrixMatrix :: Floating a => Array (Full vert horiz height width) a -> Array (BandedHermitian offDiag size) a -> Array (Multiplied (Full vert horiz height width) (BandedHermitian offDiag size)) a
(C sizeA, sizeA ~ sizeB, Eq sizeB, MultiplyTriangular loA upA loB upB, TriDiag diagA, TriDiag diagB) => Multiply (Triangular loA diagA upA sizeA) (Triangular loB diagB upB sizeB) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Associated Types type Multiplied (Triangular loA diagA upA sizeA) (Triangular loB diagB upB sizeB) :: Type Methods matrixMatrix :: Floating a => Array (Triangular loA diagA upA sizeA) a -> Array (Triangular loB diagB upB sizeB) a -> Array (Multiplied (Triangular loA diagA upA sizeA) (Triangular loB diagB upB sizeB)) a
(Content lo, Content up, TriDiag diag, C vert, C horiz, C size, size ~ height, Eq height, C width) => Multiply (Triangular lo diag up size) (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Associated Types type Multiplied (Triangular lo diag up size) (Full vert horiz height width) :: Type Methods matrixMatrix :: Floating a => Array (Triangular lo diag up size) a -> Array (Full vert horiz height width) a -> Array (Multiplied (Triangular lo diag up size) (Full vert horiz height width)) a
(Content lo, Content up, TriDiag diag, C vert, C horiz, C size, size ~ width, Eq width, C height) => Multiply (Full vert horiz height width) (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Associated Types type Multiplied (Full vert horiz height width) (Triangular lo diag up size) :: Type Methods matrixMatrix :: Floating a => Array (Full vert horiz height width) a -> Array (Triangular lo diag up size) a -> Array (Multiplied (Full vert horiz height width) (Triangular lo diag up size)) a
(C heightA, C widthA, C widthB, widthA ~ heightB, Eq heightB, C vertA, C horizA, C vertB, C horizB) => Multiply (Full vertA horizA heightA widthA) (Full vertB horizB heightB widthB) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Associated Types type Multiplied (Full vertA horizA heightA widthA) (Full vertB horizB heightB widthB) :: Type Methods matrixMatrix :: Floating a => Array (Full vertA horizA heightA widthA) a -> Array (Full vertB horizB heightB widthB) a -> Array (Multiplied (Full vertA horizA heightA widthA) (Full vertB horizB heightB widthB)) a
(Natural sub, Natural super, C vertA, C horizA, C vertB, C horizB, C heightA, C widthA, C widthB, widthA ~ heightB, Eq heightB) => Multiply (Full vertA horizA heightA widthA) (Banded sub super vertB horizB heightB widthB) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Associated Types type Multiplied (Full vertA horizA heightA widthA) (Banded sub super vertB horizB heightB widthB) :: Type Methods matrixMatrix :: Floating a => Array (Full vertA horizA heightA widthA) a -> Array (Banded sub super vertB horizB heightB widthB) a -> Array (Multiplied (Full vertA horizA heightA widthA) (Banded sub super vertB horizB heightB widthB)) a
(Natural offDiag, Natural sub, Natural super, C vert, C horiz, C size, size ~ width, Eq width, C height, Eq height) => Multiply (Banded sub super vert horiz height width) (BandedHermitian offDiag size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Associated Types type Multiplied (Banded sub super vert horiz height width) (BandedHermitian offDiag size) :: Type Methods matrixMatrix :: Floating a => Array (Banded sub super vert horiz height width) a -> Array (BandedHermitian offDiag size) a -> Array (Multiplied (Banded sub super vert horiz height width) (BandedHermitian offDiag size)) a
(Natural sub, Natural super, C vertA, C horizA, C vertB, C horizB, C heightA, C widthA, C widthB, widthA ~ heightB, Eq heightB) => Multiply (Banded sub super vertA horizA heightA widthA) (Full vertB horizB heightB widthB) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Associated Types type Multiplied (Banded sub super vertA horizA heightA widthA) (Full vertB horizB heightB widthB) :: Type Methods matrixMatrix :: Floating a => Array (Banded sub super vertA horizA heightA widthA) a -> Array (Full vertB horizB heightB widthB) a -> Array (Multiplied (Banded sub super vertA horizA heightA widthA) (Full vertB horizB heightB widthB)) a
(Natural subA, Natural superA, Natural subB, Natural superB, C vertA, C horizA, C vertB, C horizB, C heightA, C widthA, C widthB, widthA ~ heightB, Eq heightB) => Multiply (Banded subA superA vertA horizA heightA widthA) (Banded subB superB vertB horizB heightB widthB) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Array.Multiply Associated Types type Multiplied (Banded subA superA vertA horizA heightA widthA) (Banded subB superB vertB horizB heightB widthB) :: Type Methods matrixMatrix :: Floating a => Array (Banded subA superA vertA horizA heightA widthA) a -> Array (Banded subB superB vertB horizB heightB widthB) a -> Array (Multiplied (Banded subA superA vertA horizA heightA widthA) (Banded subB superB vertB horizB heightB widthB)) a