Numeric.LAPACK.Matrix.BandedHermitian

Documentation

type BandedHermitian offDiag sh = Hermitian offDiag sh

data Transposition

Constructors

NonTransposed

Transposed

Instances

Monoid Transposition

Defined in Numeric.BLAS.Matrix.Modifier

Methods

mempty :: Transposition

mappend :: Transposition -> Transposition -> Transposition

mconcat :: [Transposition] -> Transposition

Semigroup Transposition

Defined in Numeric.BLAS.Matrix.Modifier

Methods

(<>) :: Transposition -> Transposition -> Transposition

sconcat :: NonEmpty Transposition -> Transposition

stimes :: Integral b => b -> Transposition -> Transposition

Bounded Transposition

Defined in Numeric.BLAS.Matrix.Modifier

Methods

minBound :: Transposition

maxBound :: Transposition

Enum Transposition

Defined in Numeric.BLAS.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]

Show Transposition

Defined in Numeric.BLAS.Matrix.Modifier

Methods

showsPrec :: Int -> Transposition -> ShowS

show :: Transposition -> String

showList :: [Transposition] -> ShowS

Eq Transposition

Defined in Numeric.BLAS.Matrix.Modifier

Methods

(==) :: Transposition -> Transposition -> Bool

(/=) :: Transposition -> Transposition -> Bool

class (C neg, C pos) => Semidefinite neg pos

Instances

Semidefinite False True

Defined in Numeric.LAPACK.Matrix.Array.Hermitian

Semidefinite True False

Defined in Numeric.LAPACK.Matrix.Array.Hermitian

assureFullRank :: (Semidefinite neg pos, C zero) => AnyHermitianP pack neg zero pos bands sh a -> AnyHermitianP pack neg False pos bands sh a

assureAnyRank :: (Semidefinite neg pos, C zero) => AnyHermitianP pack neg True pos bands sh a -> AnyHermitianP pack neg zero pos bands sh a

relaxSemidefinite :: (C neg, C zero, C pos) => AnyHermitianP pack neg False pos bands sh a -> AnyHermitianP pack neg zero pos bands sh a

relaxIndefinite :: (C neg, C zero, C pos) => AnyHermitianP pack neg zero pos bands sh a -> Quadratic pack HermitianUnknownDefiniteness bands bands sh a

assurePositiveDefiniteness :: (C neg, C zero, C pos) => AnyHermitianP pack neg zero pos bands sh a -> Quadratic pack HermitianPositiveDefinite bands bands sh a

relaxDefiniteness :: (C neg, C zero, C pos) => Quadratic pack HermitianPositiveDefinite bands bands sh a -> AnyHermitianP pack neg zero pos bands sh a

size :: BandedHermitian offDiag sh a -> sh

fromList :: (Natural offDiag, C size, Floating a) => UnaryProxy offDiag -> Order -> size -> [a] -> BandedHermitian offDiag size a

identity :: (C sh, Floating a) => sh -> HermitianPosDef U0 sh a

diagonal :: (C sh, Floating a) => Vector sh (RealOf a) -> Diagonal sh a

takeDiagonal :: (C neg, C zero, C pos) => (Natural offDiag, C size, Floating a) => FlexHermitian neg zero pos offDiag size a -> Vector size (RealOf a)

toHermitian :: (C neg, C zero, C pos) => (Natural offDiag, C size, Floating a) => FlexHermitian neg zero pos offDiag size a -> FlexHermitian neg zero pos size a

toBanded :: (C neg, C zero, C pos, Natural offDiag, C size, Floating a) => FlexHermitian neg zero pos offDiag size a -> Square offDiag offDiag size a

forceOrder :: (C neg, C zero, C pos, Natural offDiag, C size, Floating a) => Order -> FlexHermitian neg zero pos offDiag size a -> FlexHermitian neg zero pos offDiag size a

takeTopLeft :: (C neg, C zero, C pos, Natural offDiag, C sh0, C sh1, Floating a) => FlexHermitian neg zero pos offDiag (sh0 ::+ sh1) a -> FlexHermitian neg zero pos offDiag sh0 a

takeBottomRight :: (C neg, C zero, C pos, Natural offDiag, C sh0, C sh1, Floating a) => FlexHermitian neg zero pos offDiag (sh0 ::+ sh1) a -> FlexHermitian neg zero pos offDiag sh1 a

negate :: (C neg, C zero, C pos, Natural offDiag, C sh, Floating a) => FlexHermitian neg zero pos offDiag sh a -> FlexHermitian pos zero neg offDiag sh a

multiplyVector :: (C neg, C zero, C pos, Natural offDiag, C size, Eq size, Floating a) => Transposition -> FlexHermitian neg zero pos offDiag size a -> Vector size a -> Vector size a

multiplyFull :: (C neg, C zero, C pos, Natural offDiag, Measure meas, C vert, C horiz, C height, Eq height, C width, Floating a) => Transposition -> FlexHermitian neg zero pos offDiag height a -> Full meas vert horiz height width a -> Full meas vert horiz height width a

gramian :: (C size, Eq size, Floating a, Natural sub, Natural super) => Square sub super size a -> HermitianPosSemidef (sub :+: super) size a

sumRank1 :: (Natural k, Indexed sh, Floating a) => Order -> sh -> [(RealOf a, (Index sh, StaticVector (Succ k) a))] -> HermitianPosSemidef k sh a

The list represents ragged rows of a sparse matrix.

eigenvalues :: (C neg, C zero, C pos, Natural offDiag) => (Permutable sh, Floating a) => FlexHermitian neg zero pos offDiag sh a -> Vector sh (RealOf a)

eigensystem :: (C neg, C zero, C pos, Natural offDiag) => (Permutable sh, Floating a) => FlexHermitian neg zero pos offDiag sh a -> (Square sh a, Vector sh (RealOf a))

For symmetric eigenvalue problems, eigensystem and schur coincide.