Numeric.Matrix.LU

Documentation

class (KnownDim n, Ord t, Fractional t, PrimBytes t, KnownBackend t '[n, n]) => MatrixLU t (n :: Nat) where

Methods

lu :: Matrix t n n -> LU t n

Compute LU factorization with Partial Pivoting

Instances

(KnownDim n, Ord t, Fractional t, PrimBytes t, KnownBackend t '[n, n]) => MatrixLU t n

Defined in Numeric.Matrix.LU

Methods

lu :: Matrix t n n -> LU t n

data LU (t :: Type) (n :: Nat)

Result of LU factorization with Partial Pivoting \( PA = LU \).

Constructors

LU

Fields

• luLower :: Matrix t n n

  Unit lower triangular matrix \(L\). All elements on the diagonal of L equal 1. The rest of the elements satisfy \(|l_{ij}| \leq 1\).

• luUpper :: Matrix t n n

  Upper triangular matrix \(U\)

• luPerm :: Matrix t n n

  Row permutation matrix \(P\)

• luPermDet :: Scalar t

  Sign of permutation luPermDet == det . luPerm; \(|P| = \pm 1\).

Instances

(Eq (Matrix t n n), Eq t) => Eq (LU t n)

Defined in Numeric.Matrix.LU

Methods

(==) :: LU t n -> LU t n -> Bool

(/=) :: LU t n -> LU t n -> Bool

(Show t, PrimBytes t, KnownDim n) => Show (LU t n)

Defined in Numeric.Matrix.LU

Methods

showsPrec :: Int -> LU t n -> ShowS

show :: LU t n -> String

showList :: [LU t n] -> ShowS

luSolveR :: forall t (n :: Nat) (ds :: [Nat]). (MatrixLU t n, Dimensions ds) => LU t n -> DataFrame t (n :+ ds) -> DataFrame t (n :+ ds)

Solve Ax = b problem given LU decomposition of A.

luSolveL :: forall t (n :: Nat) (ds :: [Nat]). (MatrixLU t n, Dimensions ds) => LU t n -> DataFrame t (ds +: n) -> DataFrame t (ds +: n)

Solve xA = b problem given LU decomposition of A.

detViaLU :: forall (t :: Type) (n :: Nat). MatrixLU t n => Matrix t n n -> Scalar t

Calculate determinant of a matrix via LU decomposition

inverseViaLU :: forall (t :: Type) (n :: Nat). MatrixLU t n => Matrix t n n -> Matrix t n n

Calculate inverse of a matrix via LU decomposition