Numeric.LAPACK.Matrix.Array

Documentation

data family Matrix typ a

type ArrayMatrix shape = Matrix (Array shape)

data Array shape

Instances

Box sh => Box (Array sh)

MultiplySame sh => MultiplySame (Array sh)

FormatArray sh => FormatMatrix (Array sh)

NFData shape => NFData (Array shape)

Indexed sh => Indexed (Array sh)

Power shape => Power (Array shape)

MultiplySquare shape => MultiplySquare (Array shape)

MultiplyVector shape => MultiplyVector (Array shape)

Inverse shape => Inverse (Array shape)

Solve shape => Solve (Array shape)

Determinant shape => Determinant (Array shape)

SquareShape sh => SquareShape (Array sh)

Complex sh => Complex (Array sh)

(C shapeA, Eq shapeA, ~ * shapeA (HeightOf shapeB), Box shapeB, Scale shapeB) => Multiply (Scale shapeA) (Array shapeB)

(Box shapeA, Scale shapeA, ~ * (WidthOf shapeA) shapeB, C shapeB, Eq shapeB) => Multiply (Array shapeA) (Scale shapeB)

(Box shapeA, Box shapeB, Multiply shapeA shapeB) => Multiply (Array shapeA) (Array shapeB)

(Show shape, Show a, Storable a, C shape) => Show (Matrix (Array shape) a)

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 :: (Admissible sh, Floating a) => Array sh a -> ArrayMatrix sh a

lift0 :: Array shA a -> ArrayMatrix shA a

lift0 is a synonym for fromVector but lacks the admissibility check. You may thus fool the type tags. This applies to the other lift functions, too.

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

lift4 :: (Array shA a -> Array shB b -> Array shC c -> Array shD d -> Array shE e) -> ArrayMatrix shA a -> ArrayMatrix shB b -> ArrayMatrix shC c -> ArrayMatrix shD d -> ArrayMatrix shE e

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

Instances

C size => Homogeneous (Hermitian size)

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

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

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

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

zero :: (Homogeneous shape, Floating a) => shape -> ArrayMatrix shape a

negate :: (Homogeneous shape, Floating a) => ArrayMatrix shape a -> ArrayMatrix shape a

scaleReal :: (Homogeneous shape, 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

Methods

shapeOrder :: shape -> Order

Instances

C size => ShapeOrder (Hermitian size)

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

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

forceOrder :: (ShapeOrder shape, Floating a) => Order -> ArrayMatrix shape a -> ArrayMatrix shape a

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

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

class (Homogeneous shape, Eq shape) => Additive shape

Instances

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

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

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

add :: (Additive shape, Floating a) => ArrayMatrix shape a -> ArrayMatrix shape a -> ArrayMatrix shape a

sub :: (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

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

class C shape => Complex shape

Instances

C size => Complex (Hermitian size)

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

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

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

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

class (Box shape, HeightOf shape ~ WidthOf shape) => SquareShape shape

Instances

C size => SquareShape (Hermitian size)

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

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

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

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

class Box shape => MultiplyVector shape

Instances

C shape => MultiplyVector (Hermitian shape)

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

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

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

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

class SquareShape shape => MultiplySquare shape

Instances

C shape => MultiplySquare (Hermitian shape)

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

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

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

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

class SquareShape shape => Power shape

Instances

C size => Power (Hermitian size)

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

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

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

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. MultiplyVector and MultiplySquare are much less problematic, because the input and output are always dense vectors or dense matrices.

Instances

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

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

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

(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)

(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)

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

(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)

(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)

(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)

(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)

(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)

(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)

(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)

(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)

(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)

class SquareShape shape => Determinant shape

Instances

C shape => Determinant (Hermitian shape)

(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.

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

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

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

class SquareShape shape => Solve shape

Instances

C shape => Solve (Hermitian shape)

(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.

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

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

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

class (Solve shape, Power shape) => Inverse shape

Instances

C shape => Inverse (Hermitian shape)

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

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