Safe Haskell	None
Language	Haskell2010

Numeric.Matrix.Bidiagonal

Synopsis

data BiDiag (t :: Type) (n :: Nat) (m :: Nat) = BiDiag {
- bdU :: Matrix t n n
- bdUDet :: Scalar t
- bdAlpha :: Vector t (Min n m)
- bdBeta :: Vector t (Min n m)
- bdV :: Matrix t m m
- bdVDet :: Scalar t
}
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
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

Documentation

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

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

Constructors

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 details

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

Put two vectors on the main and first upper diagonal.

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

The first returned number