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)

(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)

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

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

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

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

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

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

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

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

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

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

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

(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 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)

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

Show Order

NFData 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

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

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

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

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

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

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

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

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

data Triangle

Constructors

Triangle

Instances

Eq Triangle

Show Triangle

NFData Triangle

data Reflector

Constructors

Reflector

Instances

Eq Reflector

Show Reflector

NFData 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)

Show size => Show (Hermitian size)

C size => C (Hermitian size)

Indexed size => Indexed (Hermitian size)

InvIndexed size => InvIndexed (Hermitian size)

NFData size => NFData (Hermitian size)

C size => FormatArray (Hermitian size)

(Eq shape, C shape) => MultiplyLeft (Hermitian shape)

(Eq shape, C shape) => MultiplyRight (Hermitian shape)

C shape => Inverse (Hermitian shape)

C shape => Solve (Hermitian shape)

(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)

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

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

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

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

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

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

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

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

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

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

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

(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)

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)

data Unit

Constructors

Unit

Instances

Eq Unit

Show Unit

TriDiag Unit

data NonUnit

Constructors

NonUnit

Instances

Eq NonUnit

Show NonUnit

TriDiag 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)

(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)

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

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

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

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

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

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

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

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

(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)

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)

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

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 TriDiag diag where

Methods

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

Instances

TriDiag NonUnit

TriDiag Unit

class Content c

Instances

Content Filled

Content Empty

data BandedHermitian off size

Constructors

BandedHermitian

Fields

bandedHermitianOffDiagonals :: UnaryProxy off

bandedHermitianOrder :: Order

bandedHermitianSize :: size

Instances

Eq size => Eq (BandedHermitian off size)

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

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

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

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

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

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

(Natural offDiag, C size, Eq size) => MultiplyLeft (BandedHermitian offDiag size)

(Natural offDiag, C size, Eq size) => MultiplyRight (BandedHermitian offDiag size)

(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.

(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)

(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)

(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)

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