Safe Haskell	None
Language	Haskell98

Numeric.LAPACK.Orthogonal.Householder

Synopsis

type Householder vert horiz height width = Matrix (Hh vert horiz height width)
type General height width = Householder Big Big height width
type Tall height width = Householder Big Small height width
type Wide height width = Householder Small Big height width
type Square sh = Householder Small Small sh sh
mapExtent :: (C vertA, C horizA) => (C vertB, C horizB) => Map vertA horizA vertB horizB height width -> Householder vertA horizA height width a -> Householder vertB horizB height width a
fromMatrix :: (C vert, C horiz, C height, C width, Floating a) => Full vert horiz height width a -> Householder vert horiz height width a
determinant :: (C sh, Floating a) => Square sh a -> a
determinantAbsolute :: (C vert, C horiz, C height, C width, Floating a) => Householder vert horiz height width a -> RealOf a
leastSquares :: (C vert, C horiz, C height, Eq height, C width, Eq width, C nrhs, Floating a) => Householder horiz Small height width a -> Full vert horiz height nrhs a -> Full vert horiz width nrhs a
minimumNorm :: (C vert, C horiz, C height, Eq height, C width, Eq width, C nrhs, Floating a) => Householder vert Small width height a -> Full vert horiz height nrhs a -> Full vert horiz width nrhs a
data Transposition
- = NonTransposed
- | Transposed
data Conjugation
- = NonConjugated
- | Conjugated
extractQ :: (C vert, C horiz, C height, C width, Floating a) => Householder vert horiz height width a -> Square height a
extractR :: (C vert, C horiz, C height, C width, Floating a) => Householder vert horiz height width a -> Full vert horiz height width a
multiplyQ :: (C vertA, C horizA, C widthA, C vertB, C horizB, C widthB, C height, Eq height, Floating a) => Transposition -> Conjugation -> Householder vertA horizA height widthA a -> Full vertB horizB height widthB a -> Full vertB horizB height widthB a
tallExtractQ :: (C vert, C height, C width, Floating a) => Householder vert Small height width a -> Full vert Small height width a
tallExtractR :: (C vert, C height, C width, Floating a) => Householder vert Small height width a -> Upper width a
tallMultiplyQ :: (C vert, C horiz, C height, Eq height, C width, C fuse, Eq fuse, Floating a) => Householder vert Small height fuse a -> Full vert horiz fuse width a -> Full vert horiz height width a
tallMultiplyQAdjoint :: (C vert, C horiz, C height, C width, C fuse, Eq fuse, Floating a) => Householder horiz Small fuse height a -> Full vert horiz fuse width a -> Full vert horiz height width a
tallMultiplyR :: (C vertA, C vert, C horiz, C height, Eq height, C heightA, C widthB, Floating a) => Transposition -> Householder vertA Small heightA height a -> Full vert horiz height widthB a -> Full vert horiz height widthB a
tallSolveR :: (C vertA, C vert, C horiz, C height, C width, Eq width, C nrhs, Floating a) => Transposition -> Conjugation -> Householder vertA Small height width a -> Full vert horiz width nrhs a -> Full vert horiz width nrhs a

Documentation

type Householder vert horiz height width = Matrix (Hh vert horiz height width) Source #

type General height width = Householder Big Big height width Source #

type Tall height width = Householder Big Small height width Source #

type Wide height width = Householder Small Big height width Source #

type Square sh = Householder Small Small sh sh Source #

mapExtent :: (C vertA, C horizA) => (C vertB, C horizB) => Map vertA horizA vertB horizB height width -> Householder vertA horizA height width a -> Householder vertB horizB height width a Source #

fromMatrix :: (C vert, C horiz, C height, C width, Floating a) => Full vert horiz height width a -> Householder vert horiz height width a Source #

determinant :: (C sh, Floating a) => Square sh a -> a Source #

determinantAbsolute :: (C vert, C horiz, C height, C width, Floating a) => Householder vert horiz height width a -> RealOf a Source #

leastSquares :: (C vert, C horiz, C height, Eq height, C width, Eq width, C nrhs, Floating a) => Householder horiz Small height width a -> Full vert horiz height nrhs a -> Full vert horiz width nrhs a Source #

minimumNorm :: (C vert, C horiz, C height, Eq height, C width, Eq width, C nrhs, Floating a) => Householder vert Small width height a -> Full vert horiz height nrhs a -> Full vert horiz width nrhs a Source #

HH.minimumNorm (HH.fromMatrix a) b
==
Ortho.minimumNorm (adjoint a) b

data Transposition Source #

Constructors

NonTransposed
Transposed

Instances

Instances details

Bounded Transposition Source #
Instance details Defined in Numeric.LAPACK.Matrix.Modifier Methods minBound :: Transposition # maxBound :: Transposition #
Enum Transposition Source #
Instance details Defined in Numeric.LAPACK.Matrix.Modifier Methods succ :: Transposition -> Transposition # pred :: Transposition -> Transposition # toEnum :: Int -> Transposition # fromEnum :: Transposition -> Int # enumFrom :: Transposition -> [Transposition] # enumFromThen :: Transposition -> Transposition -> [Transposition] # enumFromTo :: Transposition -> Transposition -> [Transposition] # enumFromThenTo :: Transposition -> Transposition -> Transposition -> [Transposition] #
Eq Transposition Source #
Instance details Defined in Numeric.LAPACK.Matrix.Modifier Methods (==) :: Transposition -> Transposition -> Bool # (/=) :: Transposition -> Transposition -> Bool #
Show Transposition Source #
Instance details Defined in Numeric.LAPACK.Matrix.Modifier Methods showsPrec :: Int -> Transposition -> ShowS # show :: Transposition -> String # showList :: [Transposition] -> ShowS #
Semigroup Transposition Source #
Instance details Defined in Numeric.LAPACK.Matrix.Modifier Methods (<>) :: Transposition -> Transposition -> Transposition # sconcat :: NonEmpty Transposition -> Transposition # stimes :: Integral b => b -> Transposition -> Transposition #
Monoid Transposition Source #
Instance details Defined in Numeric.LAPACK.Matrix.Modifier Methods mempty :: Transposition # mappend :: Transposition -> Transposition -> Transposition # mconcat :: [Transposition] -> Transposition #

data Conjugation Source #

Constructors

NonConjugated
Conjugated

Instances

Instances details

Bounded Conjugation Source #
Instance details Defined in Numeric.LAPACK.Matrix.Modifier Methods minBound :: Conjugation # maxBound :: Conjugation #
Enum Conjugation Source #
Instance details Defined in Numeric.LAPACK.Matrix.Modifier Methods succ :: Conjugation -> Conjugation # pred :: Conjugation -> Conjugation # toEnum :: Int -> Conjugation # fromEnum :: Conjugation -> Int # enumFrom :: Conjugation -> [Conjugation] # enumFromThen :: Conjugation -> Conjugation -> [Conjugation] # enumFromTo :: Conjugation -> Conjugation -> [Conjugation] # enumFromThenTo :: Conjugation -> Conjugation -> Conjugation -> [Conjugation] #
Eq Conjugation Source #
Instance details Defined in Numeric.LAPACK.Matrix.Modifier Methods (==) :: Conjugation -> Conjugation -> Bool # (/=) :: Conjugation -> Conjugation -> Bool #
Show Conjugation Source #
Instance details Defined in Numeric.LAPACK.Matrix.Modifier Methods showsPrec :: Int -> Conjugation -> ShowS # show :: Conjugation -> String # showList :: [Conjugation] -> ShowS #
Semigroup Conjugation Source #
Instance details Defined in Numeric.LAPACK.Matrix.Modifier Methods (<>) :: Conjugation -> Conjugation -> Conjugation # sconcat :: NonEmpty Conjugation -> Conjugation # stimes :: Integral b => b -> Conjugation -> Conjugation #
Monoid Conjugation Source #
Instance details Defined in Numeric.LAPACK.Matrix.Modifier Methods mempty :: Conjugation # mappend :: Conjugation -> Conjugation -> Conjugation # mconcat :: [Conjugation] -> Conjugation #

extractQ :: (C vert, C horiz, C height, C width, Floating a) => Householder vert horiz height width a -> Square height a Source #

extractR :: (C vert, C horiz, C height, C width, Floating a) => Householder vert horiz height width a -> Full vert horiz height width a Source #

multiplyQ :: (C vertA, C horizA, C widthA, C vertB, C horizB, C widthB, C height, Eq height, Floating a) => Transposition -> Conjugation -> Householder vertA horizA height widthA a -> Full vertB horizB height widthB a -> Full vertB horizB height widthB a Source #

tallExtractQ :: (C vert, C height, C width, Floating a) => Householder vert Small height width a -> Full vert Small height width a Source #

tallExtractR :: (C vert, C height, C width, Floating a) => Householder vert Small height width a -> Upper width a Source #

tallMultiplyQ :: (C vert, C horiz, C height, Eq height, C width, C fuse, Eq fuse, Floating a) => Householder vert Small height fuse a -> Full vert horiz fuse width a -> Full vert horiz height width a Source #

tallMultiplyQAdjoint :: (C vert, C horiz, C height, C width, C fuse, Eq fuse, Floating a) => Householder horiz Small fuse height a -> Full vert horiz fuse width a -> Full vert horiz height width a Source #

tallMultiplyR :: (C vertA, C vert, C horiz, C height, Eq height, C heightA, C widthB, Floating a) => Transposition -> Householder vertA Small heightA height a -> Full vert horiz height widthB a -> Full vert horiz height widthB a Source #

tallSolveR :: (C vertA, C vert, C horiz, C height, C width, Eq width, C nrhs, Floating a) => Transposition -> Conjugation -> Householder vertA Small height width a -> Full vert horiz width nrhs a -> Full vert horiz width nrhs a Source #