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Numeric.LAPACK.Matrix.Shape

Synopsis

Documentation

type General height width = Full Big Big height widthSource

type Tall height width = Full Big Small height widthSource

type Wide height width = Full Small Big height widthSource

type Square size = Full Small Small size sizeSource

data Full vert horiz height width Source

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) => Box (Full vert horiz height width)
(C vert, C horiz, C height, C width) => FormatArray (Full vert horiz height width)
(~ * Small vert, ~ * Small horiz, C height, ~ * height width) => SquareShape (Full vert horiz height width)
(C vert, C horiz, C height, Eq height, C width, Eq width) => Additive (Full vert horiz height width)
(C vert, C horiz, C height, C width) => ShapeOrder (Full vert horiz height width)
(C vert, C horiz, C height, C width) => Homogeneous (Full vert horiz height width)
(C vert, C horiz, C height, C width) => Complex (Full vert horiz height width)
(C vert, C horiz, C height, C width) => Admissible (Full vert horiz height width)
(C vert, C horiz, C height, Eq height, ~ * height width) => MultiplySame (Full vert horiz height width)
(~ * Small vert, ~ * Small horiz, C height, ~ * height width) => Power (Full vert horiz height width)
(~ * vert Small, ~ * horiz Small, C height, ~ * height width) => MultiplySquare (Full vert horiz height width)
(C vert, C horiz, C width, C height) => MultiplyVector (Full vert horiz height width)
(C vert, C horiz, C height, C width) => Scale (Full vert horiz height width)
(~ * vert Small, ~ * horiz Small, C height, ~ * height width) => Inverse (Full vert horiz height width)
(~ * vert Small, ~ * horiz Small, C height, ~ * height width) => Solve (Full vert horiz height width)
(~ * vert Small, ~ * horiz Small, C height, ~ * height width) => Determinant (Full vert horiz height width)
(C vert, C horiz, Indexed height, Indexed width) => Indexed (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 -> heightSource

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

data Order Source

Constructors

RowMajor
ColumnMajor

Instances

Eq Order
Show Order
NFData Order

flipOrder :: Order -> Order Source

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

square :: Order -> sh -> Square shSource

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

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

data Split lower vert horiz height width Source

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) => Box (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 widthSource

data Triangle Source

Constructors

Triangle

Instances

Eq Triangle
Show Triangle
NFData Triangle

data Reflector Source

Constructors

Reflector

Instances

Eq Reflector
Show Reflector
NFData Reflector

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

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

data Hermitian size Source

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 => Box (Hermitian size)
C size => FormatArray (Hermitian size)
C size => SquareShape (Hermitian size)
(C size, Eq size) => Additive (Hermitian size)
C size => ShapeOrder (Hermitian size)
C size => Homogeneous (Hermitian size)
C size => Complex (Hermitian size)
C size => Admissible (Hermitian size)
C size => Power (Hermitian size)
C shape => MultiplySquare (Hermitian shape)
C shape => MultiplyVector (Hermitian shape)
C shape => Inverse (Hermitian shape)
C shape => Solve (Hermitian shape)
C shape => Determinant (Hermitian shape)
Indexed size => Indexed (Hermitian size)
(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 sizeSource

data Triangular lo diag up size Source

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, TriDiag diag, Content up, C size) => Box (Triangular lo diag up size)
(Content lo, Content up, TriDiag diag, C size) => FormatArray (Triangular lo diag up size)
(Content lo, TriDiag diag, Content up, C size) => SquareShape (Triangular lo diag up size)
(Content lo, Eq lo, ~ * NonUnit diag, Content up, Eq up, C size, Eq size) => Additive (Triangular lo diag up size)
(Content lo, TriDiag diag, Content up, C size) => ShapeOrder (Triangular lo diag up size)
(Content lo, ~ * NonUnit diag, Content up, C size) => Homogeneous (Triangular lo diag up size)
(Content lo, TriDiag diag, Content up, C size) => Complex (Triangular lo diag up size)
(Content lo, TriDiag diag, Content up, C size) => Admissible (Triangular lo diag up size)
(DiagUpLo lo up, TriDiag diag, C size, Eq size) => MultiplySame (Triangular lo diag up size)
(PowerContentDiag lo diag up, C size) => Power (Triangular lo diag up size)
(Content lo, Content up, TriDiag diag, C shape) => MultiplySquare (Triangular lo diag up shape)
(Content lo, Content up, TriDiag diag, C shape) => MultiplyVector (Triangular lo diag up shape)
(Content lo, Content up, ~ * diag NonUnit, C size) => Scale (Triangular lo diag up size)
(PowerContentDiag lo diag up, C shape) => Inverse (Triangular lo diag up shape)
(Content lo, Content up, TriDiag diag, C shape) => Solve (Triangular lo diag up shape)
(Content lo, Content up, TriDiag diag, C shape) => Determinant (Triangular lo diag up shape)
(Content lo, TriDiag diag, Content up, Indexed size) => Indexed (Triangular lo diag up 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)

type Identity = Triangular Empty Unit EmptySource

type Diagonal = Triangular Empty NonUnit EmptySource

type LowerTriangular diag = Triangular Filled diag EmptySource

type UpperTriangular diag = Triangular Empty diag FilledSource

type Symmetric = FlexSymmetric NonUnit Source

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

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

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

symmetric :: Order -> size -> Symmetric sizeSource

autoDiag :: TriDiag diag => diagSource

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

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

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

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

class TriDiag diag whereSource

Methods

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

Instances

TriDiag NonUnit
TriDiag Unit

data Unit Source

Constructors

Unit

Instances

Eq Unit
Show Unit
TriDiag Unit

data NonUnit Source

Constructors

NonUnit

Instances

Eq NonUnit
Show NonUnit
TriDiag NonUnit

data Banded sub super vert horiz height width Source

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) => Box (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, ~ * Small vert, ~ * Small horiz, C height, ~ * height width) => SquareShape (Banded sub super vert horiz height width)
(Natural sub, Natural super, C vert, C horiz, C height, C width) => Homogeneous (Banded sub super vert horiz height width)
(Natural sub, Natural super, C vert, C horiz, C height, C width) => Complex (Banded sub super vert horiz height width)
(Natural sub, Natural super, C vert, C horiz, C height, C width) => Admissible (Banded sub super vert horiz height width)
(Natural sub, Natural super, ~ * vert Small, ~ * horiz Small, C height, ~ * height width) => MultiplySquare (Banded sub super vert horiz height width)
(Natural sub, Natural super, C vert, C horiz, C height, C width) => MultiplyVector (Banded sub super vert horiz height width)
(Natural sub, Natural super, C vert, C horiz, C height, C width) => Scale (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 sub, Natural super, ~ * vert Small, ~ * horiz Small, C width, C height, ~ * width height) => Determinant (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 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 Source

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

type BandedLowerTriangular sub size = BandedSquare sub U0 sizeSource

type BandedUpperTriangular super size = BandedSquare U0 super sizeSource

type BandedDiagonal size = BandedSquare U0 U0 sizeSource

data BandedIndex row column Source

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 widthSource

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

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

type UnaryProxy a = Proxy (Un a)Source

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))Source

class Content c Source

Instances

Content Filled
Content Empty

data BandedHermitian off size Source

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 off, C size) => Box (BandedHermitian off size)
(Natural offDiag, C size) => FormatArray (BandedHermitian offDiag size)
(Natural offDiag, C size) => SquareShape (BandedHermitian offDiag size)
(Natural off, C size) => Homogeneous (BandedHermitian off size)
(Natural off, C size) => Complex (BandedHermitian off size)
(Natural off, C size) => Admissible (BandedHermitian off size)
(Natural offDiag, C size) => MultiplySquare (BandedHermitian offDiag size)
(Natural offDiag, C size) => MultiplyVector (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 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.
(Natural off, Indexed size) => Indexed (BandedHermitian off size)
(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 sizeSource

class C shape => Box shape whereSource

Associated Types

type HeightOf shape Source

type WidthOf shape Source

Methods

height :: shape -> HeightOf shapeSource

width :: shape -> WidthOf shapeSource

Instances

C size => Box (Hermitian size)
(Natural off, C size) => Box (BandedHermitian off size)
(Content lo, TriDiag diag, Content up, C size) => Box (Triangular lo diag up size)
(C vert, C horiz, C height, C width) => Box (Full vert horiz height width)
(Eq lower, C vert, C horiz, C height, C width) => Box (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)