Numeric.LAPACK.Matrix.Shape

Documentation

type General height width = Full Big Big height width

type Tall height width = Full Big Small height width

type Wide height width = Full Small Big height width

type Square size = Full Small Small size size

data Full vert horiz height width

Constructors

Full

Fields

• fullOrder :: Order
• fullExtent :: Extent vert horiz height width

Instances

(C vert, C horiz, C size, size ~ height, Eq height, C width) => Multiply (Hermitian size) (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (Hermitian size) (Full vert horiz height width)

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 offDiag, C vert, C horiz, C size, size ~ height, Eq height, C width, Eq width) => Multiply (BandedHermitian offDiag size) (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (BandedHermitian offDiag size) (Full vert horiz height width)

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

(C vert, C horiz, Eq height, Eq width) => Eq (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

(==) :: Full vert horiz height width -> Full vert horiz height width -> Bool

(/=) :: Full vert horiz height width -> Full vert horiz height width -> Bool

(C vert, C horiz, Show height, Show width) => Show (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

showsPrec :: Int -> Full vert horiz height width -> ShowS

show :: Full vert horiz height width -> String

showList :: [Full vert horiz height width] -> ShowS

(C vert, C horiz, C height, C width) => C (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

size :: Full vert horiz height width -> Int

uncheckedSize :: Full vert horiz height width -> Int

(C vert, C horiz, Indexed height, Indexed width) => Indexed (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Associated Types

type Index (Full vert horiz height width)

Methods

indices :: Full vert horiz height width -> [Index (Full vert horiz height width)]

offset :: Full vert horiz height width -> Index (Full vert horiz height width) -> Int

uncheckedOffset :: Full vert horiz height width -> Index (Full vert horiz height width) -> Int

inBounds :: Full vert horiz height width -> Index (Full vert horiz height width) -> Bool

sizeOffset :: Full vert horiz height width -> (Int, Index (Full vert horiz height width) -> Int)

uncheckedSizeOffset :: Full vert horiz height width -> (Int, Index (Full vert horiz height width) -> Int)

(C vert, C horiz, InvIndexed height, InvIndexed width) => InvIndexed (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

indexFromOffset :: Full vert horiz height width -> Int -> Index (Full vert horiz height width)

uncheckedIndexFromOffset :: Full vert horiz height width -> Int -> Index (Full vert horiz height width)

(C vert, C horiz, NFData height, NFData width) => NFData (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

rnf :: Full vert horiz height width -> ()

(C vert, C horiz, C height, C width) => Box (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Associated Types

type HeightOf (Full vert horiz height width)

type WidthOf (Full vert horiz height width)

Methods

height :: Full vert horiz height width -> HeightOf (Full vert horiz height width)

width :: Full vert horiz height width -> WidthOf (Full vert horiz height width)

(C vert, C horiz, C height, C width) => FormatArray (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Format

Methods

formatArray :: (Floating a, Output out) => String -> Array (Full vert horiz height width) a -> out

(Small ~ vert, Small ~ horiz, C height, height ~ width) => SquareShape (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

toSquare :: (HeightOf (Full vert horiz height width) ~ sh, Floating a) => Array (Full vert horiz height width) a -> Square sh a

identityOrder :: (HeightOf (Full vert horiz height width) ~ sh, Floating a) => Order -> sh -> Array (Full vert horiz height width) a

takeDiagonal :: (HeightOf (Full vert horiz height width) ~ sh, Floating a) => Array (Full vert horiz height width) a -> Vector sh a

(C vert, C horiz, C height, Eq height, C width, Eq width) => Additive (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

add :: Floating a => Array (Full vert horiz height width) a -> Array (Full vert horiz height width) a -> Array (Full vert horiz height width) a

sub :: Floating a => Array (Full vert horiz height width) a -> Array (Full vert horiz height width) a -> Array (Full vert horiz height width) a

(C vert, C horiz, C height, C width) => ShapeOrder (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

forceOrder :: Floating a => Order -> Array (Full vert horiz height width) a -> Array (Full vert horiz height width) a

shapeOrder :: Full vert horiz height width -> Order

(C vert, C horiz, C height, C width) => Homogeneous (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

zero :: Floating a => Full vert horiz height width -> Array (Full vert horiz height width) a

negate :: Floating a => Array (Full vert horiz height width) a -> Array (Full vert horiz height width) a

scaleReal :: Floating a => RealOf a -> Array (Full vert horiz height width) a -> Array (Full vert horiz height width) a

(C vert, C horiz, C height, C width) => Complex (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

conjugate :: Floating a => Array (Full vert horiz height width) a -> Array (Full vert horiz height width) a

fromReal :: Floating a => Array (Full vert horiz height width) (RealOf a) -> Array (Full vert horiz height width) a

toComplex :: Floating a => Array (Full vert horiz height width) a -> Array (Full vert horiz height width) (ComplexOf a)

(Small ~ vert, Small ~ horiz, C height, height ~ width) => Power (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Methods

square :: Floating a => Array (Full vert horiz height width) a -> Array (Full vert horiz height width) a

power :: Floating a => Int -> Array (Full vert horiz height width) a -> Array (Full vert horiz height width) a

(vert ~ Small, horiz ~ Small, C height, height ~ width) => MultiplySquare (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Methods

transposableSquare :: (HeightOf (Full vert horiz height width) ~ height0, Eq height0, C width0, C vert0, C horiz0, 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 vert0, C horiz0, 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 vert0, C horiz0, Floating a) => Full0 vert0 horiz0 height0 width0 a -> Array (Full vert horiz height width) a -> Full0 vert0 horiz0 height0 width0 a

(C vert, C horiz, C width, C height) => MultiplyVector (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Methods

matrixVector :: (WidthOf (Full vert horiz height width) ~ width0, Eq width0, Floating a) => Array (Full vert horiz height width) a -> Vector width0 a -> Vector (HeightOf (Full vert horiz height width)) a

vectorMatrix :: (HeightOf (Full vert horiz height width) ~ height0, Eq height0, Floating a) => Vector height0 a -> Array (Full vert horiz height width) a -> Vector (WidthOf (Full vert horiz height width)) a

(vert ~ Small, horiz ~ Small, C height, height ~ width) => Inverse (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Divide

Methods

inverse :: Floating a => Array (Full vert horiz height width) a -> Array (Full vert horiz height width) a

(vert ~ Small, horiz ~ Small, C height, height ~ width) => Solve (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Divide

Methods

solve :: (Floating a, HeightOf (Full vert horiz height width) ~ height0, Eq height0, C vert0, C horiz0, C width0) => Transposition -> Array (Full vert horiz height width) a -> Full0 vert0 horiz0 height0 width0 a -> Full0 vert0 horiz0 height0 width0 a

solveRight :: (Floating a, HeightOf (Full vert horiz height width) ~ height0, Eq height0, C vert0, C horiz0, C width0) => Array (Full vert horiz height width) a -> Full0 vert0 horiz0 height0 width0 a -> Full0 vert0 horiz0 height0 width0 a

solveLeft :: (Floating a, HeightOf (Full vert horiz height width) ~ width0, Eq width0, C vert0, C horiz0, C height0) => Full0 vert0 horiz0 height0 width0 a -> Array (Full vert horiz height width) a -> Full0 vert0 horiz0 height0 width0 a

(vert ~ Small, horiz ~ Small, C height, height ~ width) => Determinant (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Divide

Methods

determinant :: Floating a => Array (Full vert horiz height width) a -> a

(C vert, C horiz, C size, size ~ width, Eq width, C height) => Multiply (Full vert horiz height width) (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (Full vert horiz height width) (Hermitian size)

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)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (Full vert horiz height width) (BandedHermitian offDiag size)

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

(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)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (Triangular lo diag up size) (Full vert horiz height width)

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)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (Full vert horiz height width) (Triangular lo diag up size)

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)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (Full vertA horizA heightA widthA) (Full vertB horizB heightB widthB)

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)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (Full vertA horizA heightA widthA) (Banded sub super vertB horizB heightB widthB)

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 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)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (Banded sub super vertA horizA heightA widthA) (Full vertB horizB heightB widthB)

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

type Index (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type Index (Full vert horiz height width) = (Index height, Index width)

type HeightOf (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type HeightOf (Full vert horiz height width) = height

type WidthOf (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type WidthOf (Full vert horiz height width) = width

fullHeight :: (C vert, C horiz) => Full vert horiz height width -> height

fullWidth :: (C vert, C horiz) => Full vert horiz height width -> width

data Order

Constructors

RowMajor

ColumnMajor

Instances

Eq Order

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

(==) :: Order -> Order -> Bool

(/=) :: Order -> Order -> Bool

Show Order

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

showsPrec :: Int -> Order -> ShowS

show :: Order -> String

showList :: [Order] -> ShowS

NFData Order

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

rnf :: Order -> ()

flipOrder :: Order -> Order

general :: Order -> height -> width -> General height width

square :: Order -> sh -> Square sh

wide :: (C height, C width) => Order -> height -> width -> Wide height width

tall :: (C height, C width) => Order -> height -> width -> Tall height width

data Split lower vert horiz height width

Instances

(C vert, C horiz, Eq lower, Eq height, Eq width) => Eq (Split lower vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

(==) :: Split lower vert horiz height width -> Split lower vert horiz height width -> Bool

(/=) :: Split lower vert horiz height width -> Split lower vert horiz height width -> Bool

(C vert, C horiz, Show lower, Show height, Show width) => Show (Split lower vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

showsPrec :: Int -> Split lower vert horiz height width -> ShowS

show :: Split lower vert horiz height width -> String

showList :: [Split lower vert horiz height width] -> ShowS

(Eq lower, C vert, C horiz, C height, C width) => C (Split lower vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

size :: Split lower vert horiz height width -> Int

uncheckedSize :: Split lower vert horiz height width -> Int

(Eq lower, C vert, C horiz, Indexed height, Indexed width) => Indexed (Split lower vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Associated Types

type Index (Split lower vert horiz height width)

Methods

indices :: Split lower vert horiz height width -> [Index (Split lower vert horiz height width)]

offset :: Split lower vert horiz height width -> Index (Split lower vert horiz height width) -> Int

uncheckedOffset :: Split lower vert horiz height width -> Index (Split lower vert horiz height width) -> Int

inBounds :: Split lower vert horiz height width -> Index (Split lower vert horiz height width) -> Bool

sizeOffset :: Split lower vert horiz height width -> (Int, Index (Split lower vert horiz height width) -> Int)

uncheckedSizeOffset :: Split lower vert horiz height width -> (Int, Index (Split lower vert horiz height width) -> Int)

(Eq lower, C vert, C horiz, InvIndexed height, InvIndexed width) => InvIndexed (Split lower vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

indexFromOffset :: Split lower vert horiz height width -> Int -> Index (Split lower vert horiz height width)

uncheckedIndexFromOffset :: Split lower vert horiz height width -> Int -> Index (Split lower vert horiz height width)

(NFData lower, C vert, C horiz, NFData height, NFData width) => NFData (Split lower vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

rnf :: Split lower vert horiz height width -> ()

(Eq lower, C vert, C horiz, C height, C width) => Box (Split lower vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Associated Types

type HeightOf (Split lower vert horiz height width)

type WidthOf (Split lower vert horiz height width)

Methods

height :: Split lower vert horiz height width -> HeightOf (Split lower vert horiz height width)

width :: Split lower vert horiz height width -> WidthOf (Split lower vert horiz height width)

(Eq lower, C vert, C horiz, C height, C width) => FormatArray (Split lower vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Format

Methods

formatArray :: (Floating a, Output out) => String -> Array (Split lower vert horiz height width) a -> out

type Index (Split lower vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type Index (Split lower vert horiz height width) = (Either lower Triangle, (Index height, Index width))

type HeightOf (Split lower vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type HeightOf (Split lower vert horiz height width) = height

type WidthOf (Split lower vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type WidthOf (Split lower vert horiz height width) = width

type SplitGeneral lower height width = Split lower Big Big height width

data Triangle

Constructors

Triangle

Instances

Eq Triangle

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

(==) :: Triangle -> Triangle -> Bool

(/=) :: Triangle -> Triangle -> Bool

Show Triangle

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

showsPrec :: Int -> Triangle -> ShowS

show :: Triangle -> String

showList :: [Triangle] -> ShowS

NFData Triangle

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

rnf :: Triangle -> ()

data Reflector

Constructors

Reflector

Instances

Eq Reflector

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

(==) :: Reflector -> Reflector -> Bool

(/=) :: Reflector -> Reflector -> Bool

Show Reflector

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

showsPrec :: Int -> Reflector -> ShowS

show :: Reflector -> String

showList :: [Reflector] -> ShowS

NFData Reflector

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

rnf :: Reflector -> ()

splitGeneral :: lower -> Order -> height -> width -> SplitGeneral lower height width

splitFromFull :: lower -> Full vert horiz height width -> Split lower vert horiz height width

data Hermitian size

Store the upper triangular half of a real symmetric or complex Hermitian matrix.

Constructors

Hermitian

Fields

• hermitianOrder :: Order
• hermitianSize :: size

Instances

Eq size => Eq (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

(==) :: Hermitian size -> Hermitian size -> Bool

(/=) :: Hermitian size -> Hermitian size -> Bool

Show size => Show (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

showsPrec :: Int -> Hermitian size -> ShowS

show :: Hermitian size -> String

showList :: [Hermitian size] -> ShowS

C size => C (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

size :: Hermitian size -> Int

uncheckedSize :: Hermitian size -> Int

Indexed size => Indexed (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Associated Types

type Index (Hermitian size)

Methods

indices :: Hermitian size -> [Index (Hermitian size)]

offset :: Hermitian size -> Index (Hermitian size) -> Int

uncheckedOffset :: Hermitian size -> Index (Hermitian size) -> Int

inBounds :: Hermitian size -> Index (Hermitian size) -> Bool

sizeOffset :: Hermitian size -> (Int, Index (Hermitian size) -> Int)

uncheckedSizeOffset :: Hermitian size -> (Int, Index (Hermitian size) -> Int)

InvIndexed size => InvIndexed (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

indexFromOffset :: Hermitian size -> Int -> Index (Hermitian size)

uncheckedIndexFromOffset :: Hermitian size -> Int -> Index (Hermitian size)

NFData size => NFData (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

rnf :: Hermitian size -> ()

C size => Box (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Associated Types

type HeightOf (Hermitian size)

type WidthOf (Hermitian size)

Methods

height :: Hermitian size -> HeightOf (Hermitian size)

width :: Hermitian size -> WidthOf (Hermitian size)

C size => FormatArray (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Plain.Format

Methods

formatArray :: (Floating a, Output out) => String -> Array (Hermitian size) a -> out

C size => SquareShape (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

toSquare :: (HeightOf (Hermitian size) ~ sh, Floating a) => Array (Hermitian size) a -> Square sh a

identityOrder :: (HeightOf (Hermitian size) ~ sh, Floating a) => Order -> sh -> Array (Hermitian size) a

takeDiagonal :: (HeightOf (Hermitian size) ~ sh, Floating a) => Array (Hermitian size) a -> Vector sh a

(C size, Eq size) => Additive (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

add :: Floating a => Array (Hermitian size) a -> Array (Hermitian size) a -> Array (Hermitian size) a

sub :: Floating a => Array (Hermitian size) a -> Array (Hermitian size) a -> Array (Hermitian size) a

C size => ShapeOrder (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

forceOrder :: Floating a => Order -> Array (Hermitian size) a -> Array (Hermitian size) a

shapeOrder :: Hermitian size -> Order

C size => Homogeneous (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

zero :: Floating a => Hermitian size -> Array (Hermitian size) a

negate :: Floating a => Array (Hermitian size) a -> Array (Hermitian size) a

scaleReal :: Floating a => RealOf a -> Array (Hermitian size) a -> Array (Hermitian size) a

C size => Complex (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

conjugate :: Floating a => Array (Hermitian size) a -> Array (Hermitian size) a

fromReal :: Floating a => Array (Hermitian size) (RealOf a) -> Array (Hermitian size) a

toComplex :: Floating a => Array (Hermitian size) a -> Array (Hermitian size) (ComplexOf a)

C size => Power (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Methods

square :: Floating a => Array (Hermitian size) a -> Array (Hermitian size) a

power :: Floating a => Int -> Array (Hermitian size) a -> Array (Hermitian size) a

C shape => MultiplySquare (Hermitian shape)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Methods

transposableSquare :: (HeightOf (Hermitian shape) ~ height, Eq height, C width, C vert, C horiz, 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 vert, C horiz, 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 vert, C horiz, Floating a) => Full vert horiz height width a -> Array (Hermitian shape) a -> Full vert horiz height width a

C shape => MultiplyVector (Hermitian shape)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Methods

matrixVector :: (WidthOf (Hermitian shape) ~ width, Eq width, Floating a) => Array (Hermitian shape) a -> Vector width a -> Vector (HeightOf (Hermitian shape)) a

vectorMatrix :: (HeightOf (Hermitian shape) ~ height, Eq height, Floating a) => Vector height a -> Array (Hermitian shape) a -> Vector (WidthOf (Hermitian shape)) a

C shape => Inverse (Hermitian shape)

Defined in Numeric.LAPACK.Matrix.Plain.Divide

Methods

inverse :: Floating a => Array (Hermitian shape) a -> Array (Hermitian shape) a

C shape => Solve (Hermitian shape)

Defined in Numeric.LAPACK.Matrix.Plain.Divide

Methods

solve :: (Floating a, HeightOf (Hermitian shape) ~ height, Eq height, C vert, C horiz, C width) => Transposition -> Array (Hermitian shape) a -> Full vert horiz height width a -> Full vert horiz height width a

solveRight :: (Floating a, HeightOf (Hermitian shape) ~ height, Eq height, C vert, C horiz, C width) => Array (Hermitian shape) a -> Full vert horiz height width a -> Full vert horiz height width a

solveLeft :: (Floating a, HeightOf (Hermitian shape) ~ width, Eq width, C vert, C horiz, C height) => Full vert horiz height width a -> Array (Hermitian shape) a -> Full vert horiz height width a

C shape => Determinant (Hermitian shape)

Defined in Numeric.LAPACK.Matrix.Plain.Divide

Methods

determinant :: Floating a => Array (Hermitian shape) a -> a

(C shapeA, shapeA ~ shapeB, Eq shapeB) => Multiply (Hermitian shapeA) (Hermitian shapeB)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (Hermitian shapeA) (Hermitian shapeB)

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)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (Hermitian size) (Full vert horiz height width)

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

(C vert, C horiz, C size, size ~ width, Eq width, C height) => Multiply (Full vert horiz height width) (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (Full vert horiz height width) (Hermitian size)

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

type Index (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type Index (Hermitian size) = (Index size, Index size)

type HeightOf (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type HeightOf (Hermitian size) = size

type WidthOf (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type WidthOf (Hermitian size) = size

hermitian :: Order -> size -> Hermitian size

data Triangular lo diag up size

Constructors

Triangular

Fields

• triangularDiag :: diag
• triangularUplo :: (lo, up)
• triangularOrder :: Order
• triangularSize :: size

Instances

(Eq diag, Eq lo, Eq up, Eq size) => Eq (Triangular lo diag up size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

(==) :: Triangular lo diag up size -> Triangular lo diag up size -> Bool

(/=) :: Triangular lo diag up size -> Triangular lo diag up size -> Bool

(Show diag, Show lo, Show up, Show size) => Show (Triangular lo diag up size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

showsPrec :: Int -> Triangular lo diag up size -> ShowS

show :: Triangular lo diag up size -> String

showList :: [Triangular lo diag up size] -> ShowS

(Content lo, TriDiag diag, Content up, C size) => C (Triangular lo diag up size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

size :: Triangular lo diag up size -> Int

uncheckedSize :: Triangular lo diag up size -> Int

(Content lo, TriDiag diag, Content up, Indexed size) => Indexed (Triangular lo diag up size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Associated Types

type Index (Triangular lo diag up size)

Methods

indices :: Triangular lo diag up size -> [Index (Triangular lo diag up size)]

offset :: Triangular lo diag up size -> Index (Triangular lo diag up size) -> Int

uncheckedOffset :: Triangular lo diag up size -> Index (Triangular lo diag up size) -> Int

inBounds :: Triangular lo diag up size -> Index (Triangular lo diag up size) -> Bool

sizeOffset :: Triangular lo diag up size -> (Int, Index (Triangular lo diag up size) -> Int)

uncheckedSizeOffset :: Triangular lo diag up size -> (Int, Index (Triangular lo diag up size) -> Int)

(Content lo, TriDiag diag, Content up, InvIndexed size) => InvIndexed (Triangular lo diag up size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

indexFromOffset :: Triangular lo diag up size -> Int -> Index (Triangular lo diag up size)

uncheckedIndexFromOffset :: Triangular lo diag up size -> Int -> Index (Triangular lo diag up size)

(Content lo, TriDiag diag, Content up, NFData size) => NFData (Triangular lo diag up size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

rnf :: Triangular lo diag up size -> ()

(Content lo, TriDiag diag, Content up, C size) => Box (Triangular lo diag up size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Associated Types

type HeightOf (Triangular lo diag up size)

type WidthOf (Triangular lo diag up size)

Methods

height :: Triangular lo diag up size -> HeightOf (Triangular lo diag up size)

width :: Triangular lo diag up size -> WidthOf (Triangular lo diag up size)

(Content lo, Content up, TriDiag diag, C size) => FormatArray (Triangular lo diag up size)

Defined in Numeric.LAPACK.Matrix.Plain.Format

Methods

formatArray :: (Floating a, Output out) => String -> Array (Triangular lo diag up size) a -> out

(Content lo, TriDiag diag, Content up, C size) => SquareShape (Triangular lo diag up size)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

toSquare :: (HeightOf (Triangular lo diag up size) ~ sh, Floating a) => Array (Triangular lo diag up size) a -> Square sh a

identityOrder :: (HeightOf (Triangular lo diag up size) ~ sh, Floating a) => Order -> sh -> Array (Triangular lo diag up size) a

takeDiagonal :: (HeightOf (Triangular lo diag up size) ~ sh, Floating a) => Array (Triangular lo diag up size) a -> Vector sh a

(Content lo, Eq lo, NonUnit ~ diag, Content up, Eq up, C size, Eq size) => Additive (Triangular lo diag up size)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

add :: Floating a => Array (Triangular lo diag up size) a -> Array (Triangular lo diag up size) a -> Array (Triangular lo diag up size) a

sub :: Floating a => Array (Triangular lo diag up size) a -> Array (Triangular lo diag up size) a -> Array (Triangular lo diag up size) a

(Content lo, TriDiag diag, Content up, C size) => ShapeOrder (Triangular lo diag up size)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

forceOrder :: Floating a => Order -> Array (Triangular lo diag up size) a -> Array (Triangular lo diag up size) a

shapeOrder :: Triangular lo diag up size -> Order

(Content lo, NonUnit ~ diag, Content up, C size) => Homogeneous (Triangular lo diag up size)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

zero :: Floating a => Triangular lo diag up size -> Array (Triangular lo diag up size) a

negate :: Floating a => Array (Triangular lo diag up size) a -> Array (Triangular lo diag up size) a

scaleReal :: Floating a => RealOf a -> Array (Triangular lo diag up size) a -> Array (Triangular lo diag up size) a

(Content lo, TriDiag diag, Content up, C size) => Complex (Triangular lo diag up size)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

conjugate :: Floating a => Array (Triangular lo diag up size) a -> Array (Triangular lo diag up size) a

fromReal :: Floating a => Array (Triangular lo diag up size) (RealOf a) -> Array (Triangular lo diag up size) a

toComplex :: Floating a => Array (Triangular lo diag up size) a -> Array (Triangular lo diag up size) (ComplexOf a)

(PowerContentDiag lo diag up, C size) => Power (Triangular lo diag up size)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Methods

square :: Floating a => Array (Triangular lo diag up size) a -> Array (Triangular lo diag up size) a

power :: Floating a => Int -> Array (Triangular lo diag up size) a -> Array (Triangular lo diag up size) a

(Content lo, Content up, TriDiag diag, C shape) => MultiplySquare (Triangular lo diag up shape)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Methods

transposableSquare :: (HeightOf (Triangular lo diag up shape) ~ height, Eq height, C width, C vert, C horiz, 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 vert, C horiz, 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 vert, C horiz, Floating a) => Full vert horiz height width a -> Array (Triangular lo diag up shape) a -> Full vert horiz height width a

(Content lo, Content up, TriDiag diag, C shape) => MultiplyVector (Triangular lo diag up shape)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Methods

matrixVector :: (WidthOf (Triangular lo diag up shape) ~ width, Eq width, Floating a) => Array (Triangular lo diag up shape) a -> Vector width a -> Vector (HeightOf (Triangular lo diag up shape)) a

vectorMatrix :: (HeightOf (Triangular lo diag up shape) ~ height, Eq height, Floating a) => Vector height a -> Array (Triangular lo diag up shape) a -> Vector (WidthOf (Triangular lo diag up shape)) a

(PowerContentDiag lo diag up, C shape) => Inverse (Triangular lo diag up shape)

Defined in Numeric.LAPACK.Matrix.Plain.Divide

Methods

inverse :: Floating a => Array (Triangular lo diag up shape) a -> Array (Triangular lo diag up shape) a

(Content lo, Content up, TriDiag diag, C shape) => Solve (Triangular lo diag up shape)

Defined in Numeric.LAPACK.Matrix.Plain.Divide

Methods

solve :: (Floating a, HeightOf (Triangular lo diag up shape) ~ height, Eq height, C vert, C horiz, C width) => Transposition -> Array (Triangular lo diag up shape) a -> Full vert horiz height width a -> Full vert horiz height width a

solveRight :: (Floating a, HeightOf (Triangular lo diag up shape) ~ height, Eq height, C vert, C horiz, C width) => Array (Triangular lo diag up shape) a -> Full vert horiz height width a -> Full vert horiz height width a

solveLeft :: (Floating a, HeightOf (Triangular lo diag up shape) ~ width, Eq width, C vert, C horiz, C height) => Full vert horiz height width a -> Array (Triangular lo diag up shape) a -> Full vert horiz height width a

(Content lo, Content up, TriDiag diag, C shape) => Determinant (Triangular lo diag up shape)

Defined in Numeric.LAPACK.Matrix.Plain.Divide

Methods

determinant :: Floating a => Array (Triangular lo diag up shape) a -> 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)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (Triangular loA diagA upA sizeA) (Triangular loB diagB upB sizeB)

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)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (Triangular lo diag up size) (Full vert horiz height width)

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)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (Full vert horiz height width) (Triangular lo diag up size)

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

type Index (Triangular lo diag up size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type Index (Triangular lo diag up size) = (Index size, Index size)

type HeightOf (Triangular lo diag up size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type HeightOf (Triangular lo diag up size) = size

type WidthOf (Triangular lo diag up size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type WidthOf (Triangular lo diag up size) = size

type Identity = Triangular Empty Unit Empty

type Diagonal = Triangular Empty NonUnit Empty

type LowerTriangular diag = Triangular Filled diag Empty

type UpperTriangular diag = Triangular Empty diag Filled

type Symmetric = FlexSymmetric NonUnit

diagonal :: Order -> size -> Triangular Empty NonUnit Empty size

lowerTriangular :: Order -> size -> LowerTriangular NonUnit size

upperTriangular :: Order -> size -> UpperTriangular NonUnit size

symmetric :: Order -> size -> Symmetric size

autoDiag :: TriDiag diag => diag

autoUplo :: (Content lo, Content up) => (lo, up)

type DiagUpLo lo up = (DiagUpLoC lo up, DiagUpLoC up lo)

switchDiagUpLo :: DiagUpLoC lo up => f Empty Empty -> f Empty Filled -> f Filled Empty -> f lo up

switchDiagUpLoSym :: (Content lo, Content up) => f Empty Empty -> f Empty Filled -> f Filled Empty -> f Filled Filled -> f lo up

class TriDiag diag

Minimal complete definition

switchTriDiag

Instances

TriDiag NonUnit

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

switchTriDiag :: f Unit -> f NonUnit -> f NonUnit

TriDiag Unit

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

switchTriDiag :: f Unit -> f NonUnit -> f Unit

switchTriDiag :: TriDiag diag => f Unit -> f NonUnit -> f diag

data Unit

Constructors

Unit

Instances

Eq Unit

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

(==) :: Unit -> Unit -> Bool

(/=) :: Unit -> Unit -> Bool

Show Unit

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

showsPrec :: Int -> Unit -> ShowS

show :: Unit -> String

showList :: [Unit] -> ShowS

TriDiag Unit

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

switchTriDiag :: f Unit -> f NonUnit -> f Unit

data NonUnit

Constructors

NonUnit

Instances

Eq NonUnit

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

(==) :: NonUnit -> NonUnit -> Bool

(/=) :: NonUnit -> NonUnit -> Bool

Show NonUnit

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

showsPrec :: Int -> NonUnit -> ShowS

show :: NonUnit -> String

showList :: [NonUnit] -> ShowS

TriDiag NonUnit

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

switchTriDiag :: f Unit -> f NonUnit -> f NonUnit

data Banded sub super vert horiz height width

Constructors

Banded

Fields

• bandedOffDiagonals :: (UnaryProxy sub, UnaryProxy super)
• bandedOrder :: Order
• bandedExtent :: Extent vert horiz height width

Instances

(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)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (BandedHermitian offDiag size) (Banded sub super vert horiz height width)

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

(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)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (Full vertA horizA heightA widthA) (Banded sub super vertB horizB heightB widthB)

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

(C vert, C horiz, Eq height, Eq width) => Eq (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

(==) :: Banded sub super vert horiz height width -> Banded sub super vert horiz height width -> Bool

(/=) :: Banded sub super vert horiz height width -> Banded sub super vert horiz height width -> Bool

(Natural sub, Natural super, C vert, C horiz, Show height, Show width) => Show (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

showsPrec :: Int -> Banded sub super vert horiz height width -> ShowS

show :: Banded sub super vert horiz height width -> String

showList :: [Banded sub super vert horiz height width] -> ShowS

(Natural sub, Natural super, C vert, C horiz, C height, C width) => C (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

size :: Banded sub super vert horiz height width -> Int

uncheckedSize :: Banded sub super vert horiz height width -> Int

(Natural sub, Natural super, C vert, C horiz, Indexed height, Indexed width) => Indexed (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Associated Types

type Index (Banded sub super vert horiz height width)

Methods

indices :: Banded sub super vert horiz height width -> [Index (Banded sub super vert horiz height width)]

offset :: Banded sub super vert horiz height width -> Index (Banded sub super vert horiz height width) -> Int

uncheckedOffset :: Banded sub super vert horiz height width -> Index (Banded sub super vert horiz height width) -> Int

inBounds :: Banded sub super vert horiz height width -> Index (Banded sub super vert horiz height width) -> Bool

sizeOffset :: Banded sub super vert horiz height width -> (Int, Index (Banded sub super vert horiz height width) -> Int)

uncheckedSizeOffset :: Banded sub super vert horiz height width -> (Int, Index (Banded sub super vert horiz height width) -> Int)

(Natural sub, Natural super, C vert, C horiz, InvIndexed height, InvIndexed width) => InvIndexed (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

indexFromOffset :: Banded sub super vert horiz height width -> Int -> Index (Banded sub super vert horiz height width)

uncheckedIndexFromOffset :: Banded sub super vert horiz height width -> Int -> Index (Banded sub super vert horiz height width)

(Natural sub, Natural super, C vert, C horiz, NFData height, NFData width) => NFData (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

rnf :: Banded sub super vert horiz height width -> ()

(Natural sub, Natural super, C vert, C horiz, C height, C width) => Box (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Associated Types

type HeightOf (Banded sub super vert horiz height width)

type WidthOf (Banded sub super vert horiz height width)

Methods

height :: Banded sub super vert horiz height width -> HeightOf (Banded sub super vert horiz height width)

width :: Banded sub super vert horiz height width -> WidthOf (Banded sub super vert horiz height width)

(Natural sub, Natural super, C vert, C horiz, C height, C width) => FormatArray (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Format

Methods

formatArray :: (Floating a, Output out) => String -> Array (Banded sub super vert horiz height width) a -> out

(Natural sub, Natural super, Small ~ vert, Small ~ horiz, C height, height ~ width) => SquareShape (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

toSquare :: (HeightOf (Banded sub super vert horiz height width) ~ sh, Floating a) => Array (Banded sub super vert horiz height width) a -> Square sh a

identityOrder :: (HeightOf (Banded sub super vert horiz height width) ~ sh, Floating a) => Order -> sh -> Array (Banded sub super vert horiz height width) a

takeDiagonal :: (HeightOf (Banded sub super vert horiz height width) ~ sh, Floating a) => Array (Banded sub super vert horiz height width) a -> Vector sh a

(Natural sub, Natural super, C vert, C horiz, C height, C width) => Homogeneous (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

zero :: Floating a => Banded sub super vert horiz height width -> Array (Banded sub super vert horiz height width) a

negate :: Floating a => Array (Banded sub super vert horiz height width) a -> Array (Banded sub super vert horiz height width) a

scaleReal :: Floating a => RealOf a -> Array (Banded sub super vert horiz height width) a -> Array (Banded sub super vert horiz height width) a

(Natural sub, Natural super, C vert, C horiz, C height, C width) => Complex (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

conjugate :: Floating a => Array (Banded sub super vert horiz height width) a -> Array (Banded sub super vert horiz height width) a

fromReal :: Floating a => Array (Banded sub super vert horiz height width) (RealOf a) -> Array (Banded sub super vert horiz height width) a

toComplex :: Floating a => Array (Banded sub super vert horiz height width) a -> Array (Banded sub super vert horiz height width) (ComplexOf a)

(Natural sub, Natural super, vert ~ Small, horiz ~ Small, C height, height ~ width) => MultiplySquare (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Methods

transposableSquare :: (HeightOf (Banded sub super vert horiz height width) ~ height0, Eq height0, C width0, C vert0, C horiz0, 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 vert0, C horiz0, 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 vert0, C horiz0, Floating a) => Full vert0 horiz0 height0 width0 a -> Array (Banded sub super vert horiz height width) a -> Full vert0 horiz0 height0 width0 a

(Natural sub, Natural super, C vert, C horiz, C height, C width) => MultiplyVector (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Methods

matrixVector :: (WidthOf (Banded sub super vert horiz height width) ~ width0, Eq width0, Floating a) => Array (Banded sub super vert horiz height width) a -> Vector width0 a -> Vector (HeightOf (Banded sub super vert horiz height width)) a

vectorMatrix :: (HeightOf (Banded sub super vert horiz height width) ~ height0, Eq height0, Floating a) => Vector height0 a -> Array (Banded sub super vert horiz height width) a -> Vector (WidthOf (Banded sub super vert horiz height width)) a

(Natural sub, Natural super, vert ~ Small, horiz ~ Small, C width, C height, width ~ height) => Solve (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Divide

Methods

solve :: (Floating a, HeightOf (Banded sub super vert horiz height width) ~ height0, Eq height0, C vert0, C horiz0, C width0) => Transposition -> Array (Banded sub super vert horiz height width) a -> Full vert0 horiz0 height0 width0 a -> Full vert0 horiz0 height0 width0 a

solveRight :: (Floating a, HeightOf (Banded sub super vert horiz height width) ~ height0, Eq height0, C vert0, C horiz0, C width0) => Array (Banded sub super vert horiz height width) a -> Full vert0 horiz0 height0 width0 a -> Full vert0 horiz0 height0 width0 a

solveLeft :: (Floating a, HeightOf (Banded sub super vert horiz height width) ~ width0, Eq width0, C vert0, C horiz0, C height0) => Full vert0 horiz0 height0 width0 a -> Array (Banded sub super vert horiz height width) a -> Full vert0 horiz0 height0 width0 a

(Natural sub, Natural super, vert ~ Small, horiz ~ Small, C width, C height, width ~ height) => Determinant (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Plain.Divide

Methods

determinant :: Floating a => Array (Banded sub super vert horiz height width) a -> 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)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (Banded sub super vert horiz height width) (BandedHermitian offDiag size)

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)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (Banded sub super vertA horizA heightA widthA) (Full vertB horizB heightB widthB)

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)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (Banded subA superA vertA horizA heightA widthA) (Banded subB superB vertB horizB heightB widthB)

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

type Index (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type Index (Banded sub super vert horiz height width) = BandedIndex (Index height) (Index width)

type HeightOf (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type HeightOf (Banded sub super vert horiz height width) = height

type WidthOf (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type WidthOf (Banded sub super vert horiz height width) = width

type BandedGeneral sub super = Banded sub super Big Big

type BandedSquare sub super size = Banded sub super Small Small size size

type BandedLowerTriangular sub size = BandedSquare sub U0 size

type BandedUpperTriangular super size = BandedSquare U0 super size

type BandedDiagonal size = BandedSquare U0 U0 size

data BandedIndex row column

Constructors

InsideBox row column

VertOutsideBox Int column

HorizOutsideBox row Int

Instances

(Eq row, Eq column) => Eq (BandedIndex row column)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

(==) :: BandedIndex row column -> BandedIndex row column -> Bool

(/=) :: BandedIndex row column -> BandedIndex row column -> Bool

(Show row, Show column) => Show (BandedIndex row column)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

showsPrec :: Int -> BandedIndex row column -> ShowS

show :: BandedIndex row column -> String

showList :: [BandedIndex row column] -> ShowS

bandedGeneral :: (UnaryProxy sub, UnaryProxy super) -> Order -> height -> width -> Banded sub super Big Big height width

bandedSquare :: (UnaryProxy sub, UnaryProxy super) -> Order -> size -> Banded sub super Small Small size size

bandedFromFull :: (UnaryProxy sub, UnaryProxy super) -> Full vert horiz height width -> Banded sub super vert horiz height width

type UnaryProxy a = Proxy (Un a)

addOffDiagonals :: (Natural subA, Natural superA, Natural subB, Natural superB, (subA :+: subB) ~ subC, (superA :+: superB) ~ superC) => (UnaryProxy subA, UnaryProxy superA) -> (UnaryProxy subB, UnaryProxy superB) -> ((Nat subC, Nat superC), (UnaryProxy subC, UnaryProxy superC))

class Content c

Minimal complete definition

switchContent

data BandedHermitian off size

Constructors

BandedHermitian

Fields

• bandedHermitianOffDiagonals :: UnaryProxy off
• bandedHermitianOrder :: Order
• bandedHermitianSize :: size

Instances

Eq size => Eq (BandedHermitian off size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

(==) :: BandedHermitian off size -> BandedHermitian off size -> Bool

(/=) :: BandedHermitian off size -> BandedHermitian off size -> Bool

(Natural off, Show size) => Show (BandedHermitian off size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

showsPrec :: Int -> BandedHermitian off size -> ShowS

show :: BandedHermitian off size -> String

showList :: [BandedHermitian off size] -> ShowS

(Natural off, C size) => C (BandedHermitian off size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

size :: BandedHermitian off size -> Int

uncheckedSize :: BandedHermitian off size -> Int

(Natural off, Indexed size) => Indexed (BandedHermitian off size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Associated Types

type Index (BandedHermitian off size)

Methods

indices :: BandedHermitian off size -> [Index (BandedHermitian off size)]

offset :: BandedHermitian off size -> Index (BandedHermitian off size) -> Int

uncheckedOffset :: BandedHermitian off size -> Index (BandedHermitian off size) -> Int

inBounds :: BandedHermitian off size -> Index (BandedHermitian off size) -> Bool

sizeOffset :: BandedHermitian off size -> (Int, Index (BandedHermitian off size) -> Int)

uncheckedSizeOffset :: BandedHermitian off size -> (Int, Index (BandedHermitian off size) -> Int)

(Natural off, InvIndexed size) => InvIndexed (BandedHermitian off size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

indexFromOffset :: BandedHermitian off size -> Int -> Index (BandedHermitian off size)

uncheckedIndexFromOffset :: BandedHermitian off size -> Int -> Index (BandedHermitian off size)

(Natural off, NFData size) => NFData (BandedHermitian off size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Methods

rnf :: BandedHermitian off size -> ()

(Natural off, C size) => Box (BandedHermitian off size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Associated Types

type HeightOf (BandedHermitian off size)

type WidthOf (BandedHermitian off size)

Methods

height :: BandedHermitian off size -> HeightOf (BandedHermitian off size)

width :: BandedHermitian off size -> WidthOf (BandedHermitian off size)

(Natural offDiag, C size) => FormatArray (BandedHermitian offDiag size)

Defined in Numeric.LAPACK.Matrix.Plain.Format

Methods

formatArray :: (Floating a, Output out) => String -> Array (BandedHermitian offDiag size) a -> out

(Natural offDiag, C size) => SquareShape (BandedHermitian offDiag size)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

toSquare :: (HeightOf (BandedHermitian offDiag size) ~ sh, Floating a) => Array (BandedHermitian offDiag size) a -> Square sh a

identityOrder :: (HeightOf (BandedHermitian offDiag size) ~ sh, Floating a) => Order -> sh -> Array (BandedHermitian offDiag size) a

takeDiagonal :: (HeightOf (BandedHermitian offDiag size) ~ sh, Floating a) => Array (BandedHermitian offDiag size) a -> Vector sh a

(Natural off, C size) => Homogeneous (BandedHermitian off size)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

zero :: Floating a => BandedHermitian off size -> Array (BandedHermitian off size) a

negate :: Floating a => Array (BandedHermitian off size) a -> Array (BandedHermitian off size) a

scaleReal :: Floating a => RealOf a -> Array (BandedHermitian off size) a -> Array (BandedHermitian off size) a

(Natural off, C size) => Complex (BandedHermitian off size)

Defined in Numeric.LAPACK.Matrix.Plain.Class

Methods

conjugate :: Floating a => Array (BandedHermitian off size) a -> Array (BandedHermitian off size) a

fromReal :: Floating a => Array (BandedHermitian off size) (RealOf a) -> Array (BandedHermitian off size) a

toComplex :: Floating a => Array (BandedHermitian off size) a -> Array (BandedHermitian off size) (ComplexOf a)

(Natural offDiag, C size) => MultiplySquare (BandedHermitian offDiag size)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Methods

transposableSquare :: (HeightOf (BandedHermitian offDiag size) ~ height, Eq height, C width, C vert, C horiz, 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 vert, C horiz, 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 vert, C horiz, Floating a) => Full vert horiz height width a -> Array (BandedHermitian offDiag size) a -> Full vert horiz height width a

(Natural offDiag, C size) => MultiplyVector (BandedHermitian offDiag size)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Methods

matrixVector :: (WidthOf (BandedHermitian offDiag size) ~ width, Eq width, Floating a) => Array (BandedHermitian offDiag size) a -> Vector width a -> Vector (HeightOf (BandedHermitian offDiag size)) a

vectorMatrix :: (HeightOf (BandedHermitian offDiag size) ~ height, Eq height, Floating a) => Vector height a -> Array (BandedHermitian offDiag size) a -> Vector (WidthOf (BandedHermitian offDiag size)) a

(Natural offDiag, C size) => Solve (BandedHermitian offDiag size)

There is no solver for indefinite matrices. Thus the instance will fail for indefinite but solvable systems.

Defined in Numeric.LAPACK.Matrix.Plain.Divide

Methods

solve :: (Floating a, HeightOf (BandedHermitian offDiag size) ~ height, Eq height, C vert, C horiz, C width) => Transposition -> Array (BandedHermitian offDiag size) a -> Full vert horiz height width a -> Full vert horiz height width a

solveRight :: (Floating a, HeightOf (BandedHermitian offDiag size) ~ height, Eq height, C vert, C horiz, C width) => Array (BandedHermitian offDiag size) a -> Full vert horiz height width a -> Full vert horiz height width a

solveLeft :: (Floating a, HeightOf (BandedHermitian offDiag size) ~ width, Eq width, C vert, C horiz, C height) => Full vert horiz height width a -> Array (BandedHermitian offDiag size) a -> Full vert horiz height width a

(Natural offDiag, C size) => Determinant (BandedHermitian offDiag size)

There is no solver for general banded Hermitian matrices. Thus the instance will fail for an indefinite matrix.

Defined in Numeric.LAPACK.Matrix.Plain.Divide

Methods

determinant :: Floating a => Array (BandedHermitian offDiag size) a -> a

(Natural offDiagA, Natural offDiagB, C sizeA, sizeA ~ sizeB, C sizeB, Eq sizeB) => Multiply (BandedHermitian offDiagA sizeA) (BandedHermitian offDiagB sizeB)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (BandedHermitian offDiagA sizeA) (BandedHermitian offDiagB sizeB)

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)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (BandedHermitian offDiag size) (Full vert horiz height width)

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)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (BandedHermitian offDiag size) (Banded sub super vert horiz height width)

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

(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)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (Full vert horiz height width) (BandedHermitian offDiag size)

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

(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)

Defined in Numeric.LAPACK.Matrix.Plain.Multiply

Associated Types

type Multiplied (Banded sub super vert horiz height width) (BandedHermitian offDiag size)

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

type Index (BandedHermitian off size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type Index (BandedHermitian off size) = BandedIndex (Index size) (Index size)

type HeightOf (BandedHermitian off size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type HeightOf (BandedHermitian off size) = size

type WidthOf (BandedHermitian off size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type WidthOf (BandedHermitian off size) = size

bandedHermitian :: UnaryProxy off -> Order -> size -> BandedHermitian off size

class C shape => Box shape

Minimal complete definition

height, width

Instances

C size => Box (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Associated Types

type HeightOf (Hermitian size)

type WidthOf (Hermitian size)

Methods

height :: Hermitian size -> HeightOf (Hermitian size)

width :: Hermitian size -> WidthOf (Hermitian size)

(Natural off, C size) => Box (BandedHermitian off size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Associated Types

type HeightOf (BandedHermitian off size)

type WidthOf (BandedHermitian off size)

Methods

height :: BandedHermitian off size -> HeightOf (BandedHermitian off size)

width :: BandedHermitian off size -> WidthOf (BandedHermitian off size)

(Content lo, TriDiag diag, Content up, C size) => Box (Triangular lo diag up size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Associated Types

type HeightOf (Triangular lo diag up size)

type WidthOf (Triangular lo diag up size)

Methods

height :: Triangular lo diag up size -> HeightOf (Triangular lo diag up size)

width :: Triangular lo diag up size -> WidthOf (Triangular lo diag up size)

(C vert, C horiz, C height, C width) => Box (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Associated Types

type HeightOf (Full vert horiz height width)

type WidthOf (Full vert horiz height width)

Methods

height :: Full vert horiz height width -> HeightOf (Full vert horiz height width)

width :: Full vert horiz height width -> WidthOf (Full vert horiz height width)

(Eq lower, C vert, C horiz, C height, C width) => Box (Split lower vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Associated Types

type HeightOf (Split lower vert horiz height width)

type WidthOf (Split lower vert horiz height width)

Methods

height :: Split lower vert horiz height width -> HeightOf (Split lower vert horiz height width)

width :: Split lower vert horiz height width -> WidthOf (Split lower vert horiz height width)

(Natural sub, Natural super, C vert, C horiz, C height, C width) => Box (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

Associated Types

type HeightOf (Banded sub super vert horiz height width)

type WidthOf (Banded sub super vert horiz height width)

Methods

height :: Banded sub super vert horiz height width -> HeightOf (Banded sub super vert horiz height width)

width :: Banded sub super vert horiz height width -> WidthOf (Banded sub super vert horiz height width)

type family HeightOf shape

Instances

type HeightOf (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type HeightOf (Hermitian size) = size

type HeightOf (BandedHermitian off size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type HeightOf (BandedHermitian off size) = size

type HeightOf (Triangular lo diag up size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type HeightOf (Triangular lo diag up size) = size

type HeightOf (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type HeightOf (Full vert horiz height width) = height

type HeightOf (Split lower vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type HeightOf (Split lower vert horiz height width) = height

type HeightOf (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type HeightOf (Banded sub super vert horiz height width) = height

type family WidthOf shape

Instances

type WidthOf (Hermitian size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type WidthOf (Hermitian size) = size

type WidthOf (BandedHermitian off size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type WidthOf (BandedHermitian off size) = size

type WidthOf (Triangular lo diag up size)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type WidthOf (Triangular lo diag up size) = size

type WidthOf (Full vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type WidthOf (Full vert horiz height width) = width

type WidthOf (Split lower vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type WidthOf (Split lower vert horiz height width) = width

type WidthOf (Banded sub super vert horiz height width)

Defined in Numeric.LAPACK.Matrix.Shape.Private

type WidthOf (Banded sub super vert horiz height width) = width

height :: Box shape => shape -> HeightOf shape

width :: Box shape => shape -> WidthOf shape