Safe Haskell	Safe-Inferred
Language	Haskell98

Numeric.LAPACK.Orthogonal.Householder

Synopsis

type Householder = HouseholderFlex Filled Filled
type General height width = Householder Size Big Big height width
type Tall height width = Householder Size Big Small height width
type Wide height width = Householder Size Small Big height width
type Square sh = SquareMeas Shape sh sh
type LiberalSquare height width = SquareMeas Size height width
mapExtent :: (Measure measA, C vertA, C horizA) => (Measure measB, C vertB, C horizB) => Map measA vertA horizA measB vertB horizB height width -> Householder measA vertA horizA height width a -> Householder measB vertB horizB height width a
fromMatrix :: (Measure meas, C vert, C horiz, C height, C width, Floating a) => Full meas vert horiz height width a -> Householder meas vert horiz height width a
determinant :: (C sh, Floating a) => HouseholderFlex lower upper Shape Small Small sh sh a -> a
determinantAbsolute :: (Measure meas, C vert, C horiz, C height, C width, Floating a) => Householder meas vert horiz height width a -> RealOf a
leastSquares :: (Measure meas, C vert, C horiz, C height, Eq height, C width, Eq width, C nrhs, Floating a) => Householder meas horiz Small height width a -> Full meas vert horiz height nrhs a -> Full meas vert horiz width nrhs a
minimumNorm :: (Measure meas, C vert, C horiz, C height, Eq height, C width, Eq width, C nrhs, Floating a) => Householder meas vert Small width height a -> Full meas vert horiz height nrhs a -> Full meas vert horiz width nrhs a
data Transposition
- = NonTransposed
- | Transposed
data Conjugation
- = NonConjugated
- | Conjugated
extractQ :: (Measure meas, C vert, C horiz, Permutable height, C width, Floating a) => Householder meas vert horiz height width a -> Square height a
extractR :: (Measure meas, C vert, C horiz, Permutable height, C width, Floating a) => Householder meas vert horiz height width a -> UpperTrapezoid meas vert horiz height width a
multiplyQ :: (Measure measA, C vertA, C horizA, C widthA, Measure measB, C vertB, C horizB, C widthB, Permutable height, Eq height, Floating a) => Transposition -> Conjugation -> Householder measA vertA horizA height widthA a -> Full measB vertB horizB height widthB a -> Full measB vertB horizB height widthB a
tallExtractQ :: (Measure meas, C vert, C height, Permutable width, Floating a) => Householder meas vert Small height width a -> Full meas vert Small height width a
tallExtractR :: (Measure meas, C vert, C height, Permutable width, Floating a) => Householder meas vert Small height width a -> Upper width a
tallMultiplyQ :: (Measure meas, C vert, C horiz, Permutable height, Eq height, C width, C fuse, Eq fuse, Floating a) => Householder meas vert Small height fuse a -> Full meas vert horiz fuse width a -> Full meas vert horiz height width a
tallMultiplyQAdjoint :: (Measure meas, C vert, C horiz, Permutable height, C width, C fuse, Eq fuse, Floating a) => Householder meas horiz Small fuse height a -> Full meas vert horiz fuse width a -> Full meas vert horiz height width a
tallMultiplyR :: (Measure measA, C vertA, Measure meas, C vert, C horiz, Permutable height, Eq height, C heightA, C widthB, Floating a) => Transposition -> Householder measA vertA Small heightA height a -> Full meas vert horiz height widthB a -> Full meas vert horiz height widthB a
tallSolveR :: (Measure measA, C vertA, Measure meas, C vert, C horiz, C height, Permutable width, Eq width, C nrhs, Floating a) => Transposition -> Conjugation -> Householder measA vertA Small height width a -> Full meas vert horiz width nrhs a -> Full meas vert horiz width nrhs a

Documentation

type Householder = HouseholderFlex Filled Filled Source #

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

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

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

type Square sh = SquareMeas Shape sh sh Source #

type LiberalSquare height width = SquareMeas Size height width Source #

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

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

determinant :: (C sh, Floating a) => HouseholderFlex lower upper Shape Small Small sh sh a -> a Source #

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

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

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

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

data Transposition #

Constructors

NonTransposed
Transposed

Instances

Instances details

Monoid Transposition
Instance details Defined in Numeric.Netlib.Modifier Methods mempty :: Transposition # mappend :: Transposition -> Transposition -> Transposition # mconcat :: [Transposition] -> Transposition #
Semigroup Transposition
Instance details Defined in Numeric.Netlib.Modifier Methods (<>) :: Transposition -> Transposition -> Transposition # sconcat :: NonEmpty Transposition -> Transposition # stimes :: Integral b => b -> Transposition -> Transposition #
Bounded Transposition
Instance details Defined in Numeric.Netlib.Modifier Methods minBound :: Transposition # maxBound :: Transposition #
Enum Transposition
Instance details Defined in Numeric.Netlib.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] #
Show Transposition
Instance details Defined in Numeric.Netlib.Modifier Methods showsPrec :: Int -> Transposition -> ShowS # show :: Transposition -> String # showList :: [Transposition] -> ShowS #
Eq Transposition
Instance details Defined in Numeric.Netlib.Modifier Methods (==) :: Transposition -> Transposition -> Bool # (/=) :: Transposition -> Transposition -> Bool #

data Conjugation #

Constructors

NonConjugated
Conjugated

Instances

Instances details

Monoid Conjugation
Instance details Defined in Numeric.Netlib.Modifier Methods mempty :: Conjugation # mappend :: Conjugation -> Conjugation -> Conjugation # mconcat :: [Conjugation] -> Conjugation #
Semigroup Conjugation
Instance details Defined in Numeric.Netlib.Modifier Methods (<>) :: Conjugation -> Conjugation -> Conjugation # sconcat :: NonEmpty Conjugation -> Conjugation # stimes :: Integral b => b -> Conjugation -> Conjugation #
Bounded Conjugation
Instance details Defined in Numeric.Netlib.Modifier Methods minBound :: Conjugation # maxBound :: Conjugation #
Enum Conjugation
Instance details Defined in Numeric.Netlib.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] #
Show Conjugation
Instance details Defined in Numeric.Netlib.Modifier Methods showsPrec :: Int -> Conjugation -> ShowS # show :: Conjugation -> String # showList :: [Conjugation] -> ShowS #
Eq Conjugation
Instance details Defined in Numeric.Netlib.Modifier Methods (==) :: Conjugation -> Conjugation -> Bool # (/=) :: Conjugation -> Conjugation -> Bool #

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

extractR :: (Measure meas, C vert, C horiz, Permutable height, C width, Floating a) => Householder meas vert horiz height width a -> UpperTrapezoid meas vert horiz height width a Source #

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

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

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

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

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

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

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