Numeric.LAPACK.Matrix.BandedHermitianPositiveDefinite

Documentation

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

Instances

Semidefinite True False

Defined in Numeric.LAPACK.Matrix.Array.Hermitian

Semidefinite False True

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

solve :: (Natural offDiag, C size, Eq size, Measure meas, C vert, C horiz, C nrhs, Floating a) => HermitianPosDef offDiag size a -> Full meas vert horiz size nrhs a -> Full meas vert horiz size nrhs a

solveDecomposed :: (Natural offDiag, C size, Eq size, Measure meas, C vert, C horiz, C nrhs, Floating a) => Upper offDiag size a -> Full meas vert horiz size nrhs a -> Full meas vert horiz size nrhs a

solve a b == solveDecomposed (decompose a) b
solve (gramian u) b == solveDecomposed u b

decompose :: (Natural offDiag, C size, Floating a) => HermitianPosDef offDiag size a -> Upper offDiag size a

Cholesky decomposition

determinant :: (Natural offDiag, C size, Floating a) => HermitianPosDef offDiag size a -> RealOf a