Numeric.LAPACK.Matrix.Triangular

Synopsis

• type Triangular lo diag up sh = Array (Triangular lo diag up sh)
• type UpLo lo up = (UpLoC lo up, UpLoC up lo)
• type Diagonal sh = FlexDiagonal NonUnit sh
• type Upper sh = FlexUpper NonUnit sh
• type FlexUpper diag sh = Array (UpperTriangular diag sh)
• type UnitUpper sh = FlexUpper Unit sh
• type Lower sh = FlexLower NonUnit sh
• type FlexLower diag sh = Array (LowerTriangular diag sh)
• type UnitLower sh = FlexLower Unit sh
• type Symmetric sh = Array (Symmetric sh)
• type FlexSymmetric diag sh = Array (FlexSymmetric diag sh)
• fromList :: (Content lo, Content up, C sh, Storable a) => Order -> sh -> [a] -> Triangular lo NonUnit up sh a
• autoFromList :: (Content lo, Content up, Storable a) => Order -> [a] -> Triangular lo NonUnit up ZeroInt a
• lowerFromList :: (C sh, Storable a) => Order -> sh -> [a] -> Lower sh a
• autoLowerFromList :: Storable a => Order -> [a] -> Lower ZeroInt a
• upperFromList :: (C sh, Storable a) => Order -> sh -> [a] -> Upper sh a
• autoUpperFromList :: Storable a => Order -> [a] -> Upper ZeroInt a
• symmetricFromList :: (C sh, Storable a) => Order -> sh -> [a] -> Symmetric sh a
• autoSymmetricFromList :: Storable a => Order -> [a] -> Symmetric ZeroInt a
• diagonalFromList :: (C sh, Storable a) => Order -> sh -> [a] -> Diagonal sh a
• autoDiagonalFromList :: Storable a => Order -> [a] -> Diagonal ZeroInt a
• relaxUnitDiagonal :: TriDiag diag => Triangular lo Unit up sh a -> Triangular lo diag up sh a
• strictNonUnitDiagonal :: TriDiag diag => Triangular lo diag up sh a -> Triangular lo NonUnit up sh a
• asDiagonal :: FlexDiagonal diag sh a -> FlexDiagonal diag sh a
• asLower :: FlexLower diag sh a -> FlexLower diag sh a
• asUpper :: FlexUpper diag sh a -> FlexUpper diag sh a
• asSymmetric :: FlexSymmetric diag sh a -> FlexSymmetric diag sh a
• forceUnitDiagonal :: Triangular lo Unit up sh a -> Triangular lo Unit up sh a
• forceNonUnitDiagonal :: Triangular lo NonUnit up sh a -> Triangular lo NonUnit up sh a
• identity :: (Content lo, Content up, C sh, Floating a) => Order -> sh -> Triangular lo Unit up sh a
• diagonal :: (Content lo, Content up, C sh, Floating a) => Order -> Vector sh a -> Triangular lo NonUnit up sh a
• takeDiagonal :: (Content lo, Content up, C sh, Floating a) => Triangular lo diag up sh a -> Vector sh a
• transpose :: (Content lo, Content up, TriDiag diag) => Triangular lo diag up sh a -> Triangular up diag lo sh a
• adjoint :: (Content lo, Content up, TriDiag diag, C sh, Floating a) => Triangular lo diag up sh a -> Triangular up diag lo sh a
• stackLower :: (TriDiag diag, C sh0, Eq sh0, C sh1, Eq sh1, Floating a) => FlexLower diag sh0 a -> General sh1 sh0 a -> FlexLower diag sh1 a -> FlexLower diag (sh0 :+: sh1) a
• stackUpper :: (TriDiag diag, C sh0, Eq sh0, C sh1, Eq sh1, Floating a) => FlexUpper diag sh0 a -> General sh0 sh1 a -> FlexUpper diag sh1 a -> FlexUpper diag (sh0 :+: sh1) a
• stackSymmetric :: (TriDiag diag, C sh0, Eq sh0, C sh1, Eq sh1, Floating a) => FlexSymmetric diag sh0 a -> General sh0 sh1 a -> FlexSymmetric diag sh1 a -> FlexSymmetric diag (sh0 :+: sh1) a
• toSquare :: (Content lo, Content up, C sh, Floating a) => Triangular lo diag up sh a -> Square sh a
• takeLower :: (C horiz, C height, C width, Floating a) => Full Small horiz height width a -> Lower height a
• takeUpper :: (C vert, C height, C width, Floating a) => Full vert Small height width a -> Upper width a
• fromLowerRowMajor :: (C sh, Floating a) => Array (Triangular Lower sh) a -> Lower sh a
• toLowerRowMajor :: (C sh, Floating a) => Lower sh a -> Array (Triangular Lower sh) a
• fromUpperRowMajor :: (C sh, Floating a) => Array (Triangular Upper sh) a -> Upper sh a
• toUpperRowMajor :: (C sh, Floating a) => Upper sh a -> Array (Triangular Upper sh) a
• forceOrder :: (Content lo, Content up, TriDiag diag, C sh, Floating a) => Order -> Triangular lo diag up sh a -> Triangular lo diag up sh a
• adaptOrder :: (Content lo, Content up, TriDiag diag, C sh, Floating a) => Triangular lo diag up sh a -> Triangular lo diag up sh a -> Triangular lo diag up sh a
• add :: (Content lo, Content up, Eq lo, Eq up, Eq sh, C sh, Floating a) => Triangular lo NonUnit up sh a -> Triangular lo NonUnit up sh a -> Triangular lo NonUnit up sh a
• sub :: (Content lo, Content up, Eq lo, Eq up, Eq sh, C sh, Floating a) => Triangular lo NonUnit up sh a -> Triangular lo NonUnit up sh a -> Triangular lo NonUnit up sh a
• type family PowerDiag lo up diag
• multiplyVector :: (Content lo, Content up, TriDiag diag, C sh, Eq sh, Floating a) => Triangular lo diag up sh a -> Vector sh a -> Vector sh a
• square :: (DiagUpLo lo up, TriDiag diag, C sh, Eq sh, Floating a) => Triangular lo diag up sh a -> Triangular lo diag up sh a
• squareGeneric :: (Content lo, Content up, TriDiag diag, C sh, Eq sh, Floating a) => Triangular lo diag up sh a -> Triangular lo (PowerDiag lo up diag) up sh a
• multiply :: (DiagUpLo lo up, TriDiag diag, C sh, Eq sh, Floating a) => Triangular lo diag up sh a -> Triangular lo diag up sh a -> Triangular lo diag up sh a
• multiplyFull :: (Content lo, Content up, TriDiag diag, C vert, C horiz, C height, Eq height, C width, Floating a) => Triangular lo diag up height a -> Full vert horiz height width a -> Full vert horiz height width a
• solve :: (Content lo, Content up, TriDiag diag, C vert, C horiz, C sh, Eq sh, C nrhs, Floating a) => Triangular lo diag up sh a -> Full vert horiz sh nrhs a -> Full vert horiz sh nrhs a
• inverse :: (DiagUpLo lo up, TriDiag diag, C sh, Floating a) => Triangular lo diag up sh a -> Triangular lo diag up sh a
• inverseGeneric :: (Content lo, Content up, TriDiag diag, C sh, Floating a) => Triangular lo diag up sh a -> Triangular lo (PowerDiag lo up diag) up sh a
• determinant :: (Content lo, Content up, TriDiag diag, C sh, Floating a) => Triangular lo diag up sh a -> a
• size :: Triangular lo diag up sh a -> sh
• eigenvalues :: (DiagUpLo lo up, C sh, Floating a) => Triangular lo diag up sh a -> Vector sh a
• eigensystem :: (DiagUpLo lo up, C sh, Floating a) => Triangular lo NonUnit up sh a -> (Triangular lo NonUnit up sh a, Vector sh a, Triangular lo NonUnit up sh a)

Documentation

 toSquare (stack a b c)

 =

 toSquare a ||| b
 ===
 constant 0 ||| toSquare c

(vr,d,vlAdj) = eigensystem a

 let scal = Array.map recip $ takeDiagonal $ vlAdj <#> vr
 a == vr <#> diagonal d <#> diagonal scal <#> vlAdj