Numeric.LAPACK.Matrix.Symmetric

Documentation

type Symmetric sh = FlexSymmetric NonUnit sh

size :: Symmetric sh a -> sh

fromList :: (C sh, Storable a) => Order -> sh -> [a] -> Symmetric sh a

autoFromList :: Storable a => Order -> [a] -> Symmetric ShapeInt a

identity :: (C sh, Floating a) => Order -> sh -> Symmetric sh a

diagonal :: (C sh, Floating a) => Order -> Vector sh a -> Symmetric sh a

takeDiagonal :: (C sh, Floating a) => Symmetric sh a -> Vector sh a

transpose :: Symmetric sh a -> Symmetric sh a

adjoint :: (C sh, Floating a) => Symmetric sh a -> Symmetric sh a

stack :: (C sh0, Eq sh0, C sh1, Eq sh1, Floating a) => Symmetric sh0 a -> General sh0 sh1 a -> Symmetric sh1 a -> Symmetric (sh0 :+: sh1) a

(#%%%#) :: (C sh0, Eq sh0, C sh1, Eq sh1, Floating a) => (Symmetric sh0 a, General sh0 sh1 a) -> Symmetric sh1 a -> Symmetric (sh0 :+: sh1) a infixr 2

split :: (C sh0, Eq sh0, C sh1, Eq sh1, Floating a) => Symmetric (sh0 :+: sh1) a -> (Symmetric sh0 a, General sh0 sh1 a, Symmetric sh1 a)

toSquare :: (C sh, Floating a) => Symmetric sh a -> Square sh a

fromHermitian :: (C sh, Real a) => Hermitian sh a -> Symmetric sh a

gramian :: (C height, C width, Floating a) => General height width a -> Symmetric width a

gramian A = A^T * A

gramianTransposed :: (C height, C width, Floating a) => General height width a -> Symmetric height a

gramianTransposed A = A * A^T = gramian (A^T)

congruenceDiagonal :: (C height, Eq height, C width, Floating a) => Vector height a -> General height width a -> Symmetric width a

congruenceDiagonal D A = A^T * D * A

congruenceDiagonalTransposed :: (C height, C width, Eq width, Floating a) => General height width a -> Vector width a -> Symmetric height a

congruenceDiagonalTransposed A D = A * D * A^T

congruence :: (C height, Eq height, C width, Floating a) => Symmetric height a -> General height width a -> Symmetric width a

congruence B A = A^T * B * A

congruenceTransposed :: (C height, C width, Eq width, Floating a) => General height width a -> Symmetric width a -> Symmetric height a

congruenceTransposed B A = A * B * A^T

anticommutator :: (C vert, C horiz, C height, Eq height, C width, Eq width, Floating a) => Full vert horiz height width a -> Full vert horiz height width a -> Symmetric width a

anticommutator A B = A^T * B + B^T * A

Not exactly a matrix anticommutator, thus I like to call it Symmetric anticommutator.

anticommutatorTransposed :: (C vert, C horiz, C height, Eq height, C width, Eq width, Floating a) => Full vert horiz height width a -> Full vert horiz height width a -> Symmetric height a

anticommutatorTransposed A B = A * B^T + B * A^T = anticommutator (transpose A) (transpose B)