Numeric.LAPACK.Matrix.Block

Matrices that are assembled from smaller matrices.

We can nest block matrices, but we still not have appropriate type classes for their multiplications. E.g. a Square matrix with more than 2x2 blocks would have the top-level structure:

Quadratic   Block.Beside
Block.Above Block.Square

Thus we would need e.g. multiplication Beside times Above with Quadratic result and multiplication Beside times Square with Above result.

Documentation

data family Matrix typ extraLower extraUpper lower upper meas vert horiz height width a

Instances

(C height, Eq height) => Eq (Matrix Permutation xl xu lower upper meas vert horiz height width a)

Defined in Numeric.LAPACK.Matrix.Type.Private

Methods

(==) :: Matrix Permutation xl xu lower upper meas vert horiz height width a -> Matrix Permutation xl xu lower upper meas vert horiz height width a -> Bool

(/=) :: Matrix Permutation xl xu lower upper meas vert horiz height width a -> Matrix Permutation xl xu lower upper meas vert horiz height width a -> Bool

(C height, Show height) => Show (Matrix Permutation xl xu lower upper meas vert horiz height width a)

Defined in Numeric.LAPACK.Matrix.Type.Private

Methods

showsPrec :: Int -> Matrix Permutation xl xu lower upper meas vert horiz height width a -> ShowS

show :: Matrix Permutation xl xu lower upper meas vert horiz height width a -> String

showList :: [Matrix Permutation xl xu lower upper meas vert horiz height width a] -> ShowS

(C height, Show height, Show a) => Show (Matrix Scale xl xu lower upper meas vert horiz height width a)

Defined in Numeric.LAPACK.Matrix.Type.Private

Methods

showsPrec :: Int -> Matrix Scale xl xu lower upper meas vert horiz height width a -> ShowS

show :: Matrix Scale xl xu lower upper meas vert horiz height width a -> String

showList :: [Matrix Scale xl xu lower upper meas vert horiz height width a] -> ShowS

(Measure meas, C vert, C horiz, C height, C width, Storable a, Show height, Show width, Show a) => Show (Matrix (Array pack prop) xl xu lower upper meas vert horiz height width a)

Defined in Numeric.LAPACK.Matrix.Array.Private

Methods

showsPrec :: Int -> Matrix (Array pack prop) xl xu lower upper meas vert horiz height width a -> ShowS

show :: Matrix (Array pack prop) xl xu lower upper meas vert horiz height width a -> String

showList :: [Matrix (Array pack prop) xl xu lower upper meas vert horiz height width a] -> ShowS

(Show (Quadratic typ0 (Symmetric0 xl) (Symmetric0 xu) lower upper (ShapeHead height) a), Show (Quadratic typ1 (Symmetric1 xl) (Symmetric1 xu) lower upper (ShapeTail height) a), Show (Matrix typOff xlOff xuOff Filled Filled Size Big Big (ShapeHead height) (ShapeTail height) a), C height, C width, Show height, Show width, Show a) => Show (Matrix (Symmetric typ0 typOff xlOff xuOff typ1) xl xu lower upper meas vert horiz height width a)

Defined in Numeric.LAPACK.Matrix.Block.Private

Methods

showsPrec :: Int -> Matrix (Symmetric typ0 typOff xlOff xuOff typ1) xl xu lower upper meas vert horiz height width a -> ShowS

show :: Matrix (Symmetric typ0 typOff xlOff xuOff typ1) xl xu lower upper meas vert horiz height width a -> String

showList :: [Matrix (Symmetric typ0 typOff xlOff xuOff typ1) xl xu lower upper meas vert horiz height width a] -> ShowS

(Show (Quadratic typ0 (Triangular0 xl) (Triangular0 xu) lower upper (ShapeHead height) a), Show (Quadratic typ1 (Triangular1 xl) (Triangular1 xu) lower upper (ShapeTail height) a), Show (Matrix typOff (TriangularOff xl) (TriangularOff xu) Filled Filled Size Big Big (TriangularFstShape xl xu height) (TriangularSndShape xl xu height) a), C height, C width, Show height, Show width, Show a) => Show (Matrix (Triangular typ0 typOff typ1) xl xu lower upper meas vert horiz height width a)

Defined in Numeric.LAPACK.Matrix.Block.Private

Methods

showsPrec :: Int -> Matrix (Triangular typ0 typOff typ1) xl xu lower upper meas vert horiz height width a -> ShowS

show :: Matrix (Triangular typ0 typOff typ1) xl xu lower upper meas vert horiz height width a -> String

showList :: [Matrix (Triangular typ0 typOff typ1) xl xu lower upper meas vert horiz height width a] -> ShowS

(Show (Matrix typ0 (Append0 xl) (Append0 xu) lower upper meas vert horiz (AppendSelectShape xl height sh0) (AppendSelectShape xu width sh0) a), Show (Matrix typ1 (Append1 xl) (Append1 xu) lower upper meas vert horiz (AppendSelectShape xl height sh1) (AppendSelectShape xu width sh1) a), C height, C width, Show height, Show width, Show a) => Show (Matrix (Append typ0 typ1 sh0 sh1) xl xu lower upper meas vert horiz height width a)

Defined in Numeric.LAPACK.Matrix.Block.Private

Methods

showsPrec :: Int -> Matrix (Append typ0 typ1 sh0 sh1) xl xu lower upper meas vert horiz height width a -> ShowS

show :: Matrix (Append typ0 typ1 sh0 sh1) xl xu lower upper meas vert horiz height width a -> String

showList :: [Matrix (Append typ0 typ1 sh0 sh1) xl xu lower upper meas vert horiz height width a] -> ShowS

(Show (Quadratic typ00 (Square00 xl) (Square00 xu) Filled Filled (ShapeHead height) a), Show (Quadratic typ11 (Square11 xl) (Square11 xu) Filled Filled (ShapeTail height) a), Show (Matrix (SquareType xu) (Square01 xu) (Square10 xu) Filled Filled measOff vertOff horizOff (ShapeHead height) (ShapeTail width) a), Show (Matrix (SquareType xl) (Square10 xl) (Square01 xl) Filled Filled measOff horizOff vertOff (ShapeTail height) (ShapeHead width) a), C height, C width, Show height, Show width, Show a) => Show (Matrix (Square typ00 measOff vertOff horizOff typ11) xl xu lower upper meas vert horiz height width a)

Defined in Numeric.LAPACK.Matrix.Block.Private

Methods

showsPrec :: Int -> Matrix (Square typ00 measOff vertOff horizOff typ11) xl xu lower upper meas vert horiz height width a -> ShowS

show :: Matrix (Square typ00 measOff vertOff horizOff typ11) xl xu lower upper meas vert horiz height width a -> String

showList :: [Matrix (Square typ00 measOff vertOff horizOff typ11) xl xu lower upper meas vert horiz height width a] -> ShowS

(Show (Quadratic typ0 (Diagonal0 xl) (Diagonal0 xu) lower upper (ShapeHead height) a), Show (Quadratic typ1 (Diagonal1 xl) (Diagonal1 xu) lower upper (ShapeTail height) a), C height, C width, Show height, Show width, Show a) => Show (Matrix (Diagonal typ0 typ1) xl xu lower upper meas vert horiz height width a)

Defined in Numeric.LAPACK.Matrix.Block.Private

Methods

showsPrec :: Int -> Matrix (Diagonal typ0 typ1) xl xu lower upper meas vert horiz height width a -> ShowS

show :: Matrix (Diagonal typ0 typ1) xl xu lower upper meas vert horiz height width a -> String

showList :: [Matrix (Diagonal typ0 typ1) xl xu lower upper meas vert horiz height width a] -> ShowS

(MultiplySame typ, MultiplySameExtra typ xl, MultiplySameExtra typ xu, PowerStrip lower, PowerStrip upper, Measure meas, C vert, C horiz, C height, Eq height, height ~ width, Floating a) => Semigroup (Matrix typ xl xu lower upper meas vert horiz height width a)

Defined in Numeric.LAPACK.Matrix.Type.Private

Methods

(<>) :: Matrix typ xl xu lower upper meas vert horiz height width a -> Matrix typ xl xu lower upper meas vert horiz height width a -> Matrix typ xl xu lower upper meas vert horiz height width a

sconcat :: NonEmpty (Matrix typ xl xu lower upper meas vert horiz height width a) -> Matrix typ xl xu lower upper meas vert horiz height width a

stimes :: Integral b => b -> Matrix typ xl xu lower upper meas vert horiz height width a -> Matrix typ xl xu lower upper meas vert horiz height width a

(MultiplySame typ, StaticIdentity typ, MultiplySameExtra typ xl, MultiplySameExtra typ xu, StaticIdentityExtra typ xl, StaticIdentityStrip typ lower, StaticIdentityExtra typ xu, StaticIdentityStrip typ upper, PowerStrip lower, PowerStrip upper, meas ~ Shape, vert ~ Small, horiz ~ Small, Static height, Eq height, height ~ width, Floating a) => Monoid (Matrix typ xl xu lower upper meas vert horiz height width a)

Defined in Numeric.LAPACK.Matrix.Type.Private

Methods

mempty :: Matrix typ xl xu lower upper meas vert horiz height width a

mappend :: Matrix typ xl xu lower upper meas vert horiz height width a -> Matrix typ xl xu lower upper meas vert horiz height width a -> Matrix typ xl xu lower upper meas vert horiz height width a

mconcat :: [Matrix typ xl xu lower upper meas vert horiz height width a] -> Matrix typ xl xu lower upper meas vert horiz height width a

(NFData typ, Measure meas, C vert, C horiz, NFData height, NFData width, NFData a) => NFData (Matrix typ xl xu lower upper meas vert horiz height width a)

Defined in Numeric.LAPACK.Matrix.Type.Private

Methods

rnf :: Matrix typ xl xu lower upper meas vert horiz height width a -> ()

(Format typ, FormatExtra typ xl, FormatExtra typ xu, Measure meas, C vert, C horiz, C height, C width, Floating a) => Display (Matrix typ xl xu lower upper meas vert horiz height width a)

Defined in Numeric.LAPACK.Matrix.Type.Private

Methods

display :: Matrix typ xl xu lower upper meas vert horiz height width a -> Graphic

displayIO :: Matrix typ xl xu lower upper meas vert horiz height width a -> IO Graphic

(Format typ, FormatExtra typ xl, FormatExtra typ xu, Measure meas, C vert, C horiz, C height, C width, Floating a) => Format (Matrix typ xl xu lower upper meas vert horiz height width a)

Defined in Numeric.LAPACK.Format

Methods

format :: Output out => Config -> Matrix typ xl xu lower upper meas vert horiz height width a -> out

data Matrix Permutation xl xu lower upper meas vert horiz height width a

Defined in Numeric.LAPACK.Matrix.Type.Private

data Matrix Permutation xl xu lower upper meas vert horiz height width a where

• Permutation :: forall xl xu lower upper meas vert horiz sh width a. Permutation sh -> Quadratic Permutation () () lower upper sh a

data Matrix Identity xl xu lower upper meas vert horiz height width a

Defined in Numeric.LAPACK.Matrix.Type.Private

data Matrix Identity xl xu lower upper meas vert horiz height width a where

• Identity :: forall xl xu lower upper meas vert horiz height width a. Measure meas => Extent meas Small Small height width -> QuadraticMeas Identity () () Empty Empty meas height width a

data Matrix Scale xl xu lower upper meas vert horiz height width a

Defined in Numeric.LAPACK.Matrix.Type.Private

data Matrix Scale xl xu lower upper meas vert horiz height width a where

• Scale :: forall xl xu lower upper meas vert horiz sh width a. sh -> a -> Quadratic Scale () () Empty Empty sh a

data Matrix (Product fuse) xl xu lower upper meas vert horiz height width a

Defined in Numeric.LAPACK.Matrix.Type.Private

data Matrix (Product fuse) xl xu lower upper meas vert horiz height width a where

• Product :: forall fuse xl xu lowerC upperC meas vert horiz height width a lowerA lowerB upperA upperB typA xlA xuA typB xlB xuB. (MultipliedBands lowerA lowerB ~ lowerC, MultipliedBands lowerB lowerA ~ lowerC, MultipliedBands upperA upperB ~ upperC, MultipliedBands upperB upperA ~ upperC) => Matrix typA xlA xuA lowerA upperA meas vert horiz height fuse a -> Matrix typB xlB xuB lowerB upperB meas vert horiz fuse width a -> Matrix (Product fuse) (typA, xlA, xuA, lowerA, upperA) (typB, xuB, xlB, upperB, lowerB) lowerC upperC meas vert horiz height width a

data Matrix (FillStrips typ) extraLower extraUpper lower upper meas vert horiz height width a

Defined in Numeric.LAPACK.Matrix.Wrapper

data Matrix (FillStrips typ) extraLower extraUpper lower upper meas vert horiz height width a where

• FillStrips :: forall typ extraLower extraUpper lower upper meas vert horiz height width a lower upper xl xu. (Strip lower, Strip upper) => Matrix typ xl xu lower upper meas vert horiz height width a -> Matrix (FillStrips typ) (xl, lower) (xu, upper) Filled Filled meas vert horiz height width a

data Matrix (Inverse typ) extraLower extraUpper lowerf upperf meas vert horiz height width a

Defined in Numeric.LAPACK.Matrix.Inverse

data Matrix (Inverse typ) extraLower extraUpper lowerf upperf meas vert horiz height width a where

• Inverse :: forall typ extraLower extraUpper lower upper meas vert horiz height width a xl xu. QuadraticMeas typ xl xu upper lower meas width height a -> QuadraticMeas (Inverse typ) (xl, lower) (xu, upper) lower upper meas height width a

data Matrix (Array pack prop) xl xu lower upper meas vert horiz height width a

Defined in Numeric.LAPACK.Matrix.Array.Private

data Matrix (Array pack prop) xl xu lower upper meas vert horiz height width a where

• Array :: forall pack prop xl xu lower upper meas vert horiz height width a. OmniArray pack prop lower upper meas vert horiz height width a -> Matrix (Array pack prop) () () lower upper meas vert horiz height width a

data Matrix (MapExtent typ meas) extraLower extraUpper lower upper meas1 vert1 horiz1 height width a

Defined in Numeric.LAPACK.Matrix.Wrapper

data Matrix (MapExtent typ meas) extraLower extraUpper lower upper meas1 vert1 horiz1 height width a where

• MapExtent :: forall typ meas0 extraLower extraUpper lower upper meas1 vert1 horiz1 height width a vert0 horiz0 xl xu. (C vert0, C horiz0) => Map meas0 vert0 horiz0 meas1 vert1 horiz1 height width -> Matrix typ xl xu lower upper meas0 vert0 horiz0 height width a -> Matrix (MapExtent typ meas0) (xl, vert0) (xu, horiz0) lower upper meas1 vert1 horiz1 height width a

data Matrix (Diagonal typ0 typ1) xl xu lower upper meas vert horiz height width a

Defined in Numeric.LAPACK.Matrix.Block.Private

data Matrix (Diagonal typ0 typ1) xl xu lower upper meas vert horiz height width a where

• Diagonal :: forall typ0 typ1 xl xu lower upper meas vert horiz height width a sh0 sh1 xl0 xu0 xl1 xu1. (C sh0, Eq sh0, C sh1, Eq sh1) => Quadratic typ0 xl0 xu0 lower upper sh0 a -> Quadratic typ1 xl1 xu1 lower upper sh1 a -> Quadratic (Diagonal typ0 typ1) (xl0, xl1) (xu0, xu1) lower upper (sh0 ::+ sh1) a

data Matrix (Triangular typ0 typOff typ1) xl xu lower upper meas vert horiz height width a

Defined in Numeric.LAPACK.Matrix.Block.Private

data Matrix (Triangular typ0 typOff typ1) xl xu lower upper meas vert horiz height width a where

• Upper :: forall typ0 typOff typ1 xl xu lower upper meas vert horiz height width a sh0 sh1 xl0 xu0 xlOff xuOff xl1 xu1. (C sh0, Eq sh0, C sh1, Eq sh1) => Quadratic typ0 xl0 xu0 lower Filled sh0 a -> Matrix typOff xlOff xuOff Filled Filled Size Big Big sh0 sh1 a -> Quadratic typ1 xl1 xu1 lower Filled sh1 a -> Quadratic (Triangular typ0 typOff typ1) (xl0, xlOff, xl1, False) (xu0, xuOff, xu1, True) lower Filled (sh0 ::+ sh1) a
• Lower :: forall typ0 typOff typ1 xl xu lower upper meas vert horiz height width a sh0 sh1 xl0 xu0 xlOff xuOff xl1 xu1. (C sh0, Eq sh0, C sh1, Eq sh1) => Quadratic typ0 xl0 xu0 Filled upper sh0 a -> Matrix typOff xlOff xuOff Filled Filled Size Big Big sh1 sh0 a -> Quadratic typ1 xl1 xu1 Filled upper sh1 a -> Quadratic (Triangular typ0 typOff typ1) (xl0, xlOff, xl1, True) (xu0, xuOff, xu1, False) Filled upper (sh0 ::+ sh1) a

data Matrix (Append typ0 typ1 sh0 sh1) xl xu lower upper meas vert horiz height width a

Defined in Numeric.LAPACK.Matrix.Block.Private

data Matrix (Append typ0 typ1 sh0 sh1) xl xu lower upper meas vert horiz height width a where

• Above :: forall typ0 typ1 sh0 sh1 xl xu lower upper meas vert horiz height width a xl0 xu0 xl1 xu1. (C sh0, C sh1, Eq width) => Matrix typ0 xl0 xu0 Filled Filled Size Big horiz sh0 width a -> Matrix typ1 xl1 xu1 Filled Filled Size Big horiz sh1 width a -> Matrix (Append typ0 typ1 sh0 sh1) (xl0, xl1, False) (xu0, xu1, True) Filled Filled Size Big horiz (sh0 ::+ sh1) width a
• Beside :: forall typ0 typ1 sh0 sh1 xl xu lower upper meas vert horiz height width a xl0 xu0 xl1 xu1. (C sh0, C sh1, Eq height) => Matrix typ0 xl0 xu0 Filled Filled Size vert Big height sh0 a -> Matrix typ1 xl1 xu1 Filled Filled Size vert Big height sh1 a -> Matrix (Append typ0 typ1 sh0 sh1) (xl0, xl1, True) (xu0, xu1, False) Filled Filled Size vert Big height (sh0 ::+ sh1) a

data Matrix (Symmetric typ0 typOff xlOff xuOff typ1) xl xu lower upper meas vert horiz height width a

Defined in Numeric.LAPACK.Matrix.Block.Private

data Matrix (Symmetric typ0 typOff xlOff xuOff typ1) xl xu lower upper meas vert horiz height width a where

• Symmetric :: forall typ0 typOff xlOff xuOff typ1 xl xu lower upper meas vert horiz height width a sh0 sh1 xl0 xu0 xl1 xu1. (C sh0, Eq sh0, C sh1, Eq sh1) => Quadratic typ0 xl0 xu0 Filled Filled sh0 a -> Matrix typOff xlOff xuOff Filled Filled Size Big Big sh0 sh1 a -> Quadratic typ1 xl1 xu1 Filled Filled sh1 a -> Quadratic (Symmetric typ0 typOff xlOff xuOff typ1) (xl0, xl1) (xu0, xu1) Filled Filled (sh0 ::+ sh1) a

data Matrix (Square typ00 measOff vertOff horizOff typ11) xl xu lower upper meas vert horiz height width a

Defined in Numeric.LAPACK.Matrix.Block.Private

data Matrix (Square typ00 measOff vertOff horizOff typ11) xl xu lower upper meas vert horiz height width a where

• Square :: forall typ00 measOff vertOff horizOff typ11 xl xu lower upper meas vert horiz height width a sh0 sh1 xl00 xu00 typ01 xl01 xu01 typ10 xl10 xu10 xl11 xu11. (Measure measOff, C vertOff, C horizOff, C sh0, Eq sh0, C sh1, Eq sh1) => Quadratic typ00 xl00 xu00 Filled Filled sh0 a -> Matrix typ01 xl01 xu01 Filled Filled measOff vertOff horizOff sh0 sh1 a -> Matrix typ10 xl10 xu10 Filled Filled measOff horizOff vertOff sh1 sh0 a -> Quadratic typ11 xl11 xu11 Filled Filled sh1 a -> Quadratic (Square typ00 measOff vertOff horizOff typ11) (xl00, xl11, (typ10, xl10, xu10)) (xu00, xu11, (typ01, xu01, xl01)) Filled Filled (sh0 ::+ sh1) a

type Diagonal typ0 xl0 xu0 typ1 xl1 xu1 lower upper sh0 sh1 = Quadratic (Diagonal typ0 typ1) (xl0, xl1) (xu0, xu1) lower upper (sh0 ::+ sh1)

type Above typ0 xl0 xu0 typ1 xl1 xu1 horiz height0 height1 width = Matrix (Append typ0 typ1 height0 height1) (xl0, xl1, False) (xu0, xu1, True) Filled Filled Size Big horiz (height0 ::+ height1) width

type Beside typ0 xl0 xu0 typ1 xl1 xu1 vert height width0 width1 = Matrix (Append typ0 typ1 width0 width1) (xl0, xl1, True) (xu0, xu1, False) Filled Filled Size vert Big height (width0 ::+ width1)

aboveFromFull :: (C height0, Eq height0, C height1, Eq height1, C width, Eq width, Floating a) => General (height0 ::+ height1) width a -> AboveGeneral height0 height1 width a

besideFromFull :: (C height, Eq height, C width0, Eq width0, C width1, Eq width1, Floating a) => General height (width0 ::+ width1) a -> BesideGeneral height width0 width1 a

type Square typ00 xl00 xu00 typ01 xl01 xu01 typ10 xl10 xu10 typ11 xl11 xu11 measOff vertOff horizOff sh0 sh1 = Quadratic (Square typ00 measOff vertOff horizOff typ11) (xl00, xl11, (typ10, xl10, xu10)) (xu00, xu11, (typ01, xu01, xl01)) Filled Filled (sh0 ::+ sh1)

type LowerTriangular typ0 xl0 xu0 typOff xlOff xuOff typ1 xl1 xu1 upper sh0 sh1 = Quadratic (Triangular typ0 typOff typ1) (xl0, xlOff, xl1, True) (xu0, xuOff, xu1, False) Filled upper (sh0 ::+ sh1)

type UpperTriangular typ0 xl0 xu0 typOff xlOff xuOff typ1 xl1 xu1 lower sh0 sh1 = Quadratic (Triangular typ0 typOff typ1) (xl0, xlOff, xl1, False) (xu0, xuOff, xu1, True) lower Filled (sh0 ::+ sh1)

type Symmetric typ0 xl0 xu0 typOff xlOff xuOff typ1 xl1 xu1 sh0 sh1 = Quadratic (Symmetric typ0 typOff xlOff xuOff typ1) (xl0, xl1) (xu0, xu1) Filled Filled (sh0 ::+ sh1)

squareFromSymmetric :: (Transpose typOff, TransposeExtra typOff xlOff, TransposeExtra typOff xuOff, Floating a) => Quadratic (Symmetric typ0 typOff xlOff xuOff typ1) (xl0, xl1) (xu0, xu1) lower upper sh a -> Quadratic (Square typ0 Size Big Big typ1) (xl0, xl1, (typOff, xuOff, xlOff)) (xu0, xu1, (typOff, xuOff, xlOff)) lower upper sh a

schurComplement :: (Solve typ11, SolveExtra typ11 xl11, SolveExtra typ11 xu11, Floating a) => Quadratic (Square TypeFull measOff vertOff horizOff typ11) ((), xl11, (TypeFull, (), ())) ((), xu11, (TypeFull, (), ())) Filled Filled (sh0 ::+ sh1) a -> Square sh0 a