Numeric.Matrix.Bidiagonal

Documentation

data BiDiag (t :: Type) (n :: Nat) (m :: Nat)

Decomposition of a matrix \( A = U B V^\intercal \) such that \( U \) and \( V \) are orthogonal and \( B \) is bidiagonal.

Constructors

BiDiag

Fields

• bdU :: Matrix t n n

  \( U \) left orthogonal matrix

• bdUDet :: Scalar t

  A shortcut for evaluating a determinant of \( |U| = \pm 1 \)

• bdAlpha :: Vector t (Min n m)

  Main diagonal of \( B \)

• bdBeta :: Vector t (Min n m)

  First upper diagonal of \( B \); its last element equals zero if \( n \geq m \)

• bdV :: Matrix t m m

  \( B \) left orthogonal matrix

• bdVDet :: Scalar t

  A shortcut for evaluating a determinant of \( |V| = \pm 1 \)

Instances

(Eq t, PrimBytes t, KnownDim n, KnownDim m, KnownDim (Min n m), KnownBackend t '[Min n m]) => Eq (BiDiag t n m)

Defined in Numeric.Matrix.Bidiagonal

Methods

(==) :: BiDiag t n m -> BiDiag t n m -> Bool

(/=) :: BiDiag t n m -> BiDiag t n m -> Bool

(Show t, PrimBytes t, KnownDim n, KnownDim m, KnownDim (Min n m)) => Show (BiDiag t n m)

Defined in Numeric.Matrix.Bidiagonal

Methods

showsPrec :: Int -> BiDiag t n m -> ShowS

show :: BiDiag t n m -> String

showList :: [BiDiag t n m] -> ShowS

biDiag :: forall (t :: Type) (n :: Nat) (m :: Nat). (PrimBytes t, Num t) => Dims '[n, m] -> Vector t (Min n m) -> Vector t (Min n m) -> Matrix t n m

Put two vectors on the main and first upper diagonal.

bidiagonalHouseholder :: forall (t :: Type) (n :: Nat) (m :: Nat). (PrimBytes t, Ord t, Epsilon t, KnownDim n, KnownDim m) => Matrix t n m -> BiDiag t n m

Decompose a matrix \( A = U B V^\intercal \) such that ( U ) and \( V \) are orthogonal and \( B \) is bidiagonal.

The first returned number