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