lapack-0.5: Numerical Linear Algebra using LAPACK

Numeric.LAPACK.Matrix.HermitianPositiveDefinite

Synopsis

# Documentation

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

#### Instances

Instances details
 Source # Instance detailsDefined in Numeric.LAPACK.Matrix.Array.Hermitian Source # Instance detailsDefined 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 Source #

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

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

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

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

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

solve :: (Measure meas, C vert, C horiz, Packing pack, C sh, Eq sh, C nrhs, Floating a) => HermitianPosDefP pack sh a -> Full meas vert horiz sh nrhs a -> Full meas vert horiz sh nrhs a Source #

solveDecomposed :: (Measure meas, C vert, C horiz, Packing pack, C sh, Eq sh, C nrhs, Floating a) => UpperP pack sh a -> Full meas vert horiz sh nrhs a -> Full meas vert horiz sh nrhs a Source #

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

inverse :: (Packing pack, C sh, Floating a) => HermitianPosDefP pack sh a -> HermitianPosDefP pack sh a Source #

decompose :: (Packing pack, C sh, Floating a) => HermitianPosDefP pack sh a -> UpperP pack sh a Source #

Cholesky decomposition

determinant :: (Packing pack, C sh, Floating a) => HermitianPosDefP pack sh a -> RealOf a Source #