Numeric.LinearAlgebra.Static

Contents

• Vector
• Matrix
• Complex
• Products
• Linear Systems
• Factorizations
• Norms
• Random arrays
• Misc

Description

Synopsis

• type ℝ = Double
• data R n
• vec2 :: ℝ -> ℝ -> R 2
• vec3 :: ℝ -> ℝ -> ℝ -> R 3
• vec4 :: ℝ -> ℝ -> ℝ -> ℝ -> R 4
• (&) :: forall n. (KnownNat n, 1 <= n) => R n -> ℝ -> R (n + 1)
• (#) :: forall n m. (KnownNat n, KnownNat m) => R n -> R m -> R (n + m)
• split :: forall p n. (KnownNat p, KnownNat n, p <= n) => R n -> (R p, R (n - p))
• headTail :: (KnownNat n, 1 <= n) => R n -> (ℝ, R (n - 1))
• vector :: KnownNat n => [ℝ] -> R n
• linspace :: forall n. KnownNat n => (ℝ, ℝ) -> R n
• range :: forall n. KnownNat n => R n
• dim :: forall n. KnownNat n => R n
• data L m n
• type Sq n = L n n
• build :: forall m n. (KnownNat n, KnownNat m) => (ℝ -> ℝ -> ℝ) -> L m n
• row :: R n -> L 1 n
• col :: KnownNat n => R n -> L n 1
• (|||) :: (KnownNat r1, KnownNat c, KnownNat r2, KnownNat ((+) r1 r2)) => L c r1 -> L c r2 -> L c ((+) r1 r2)
• (===) :: (KnownNat r1, KnownNat r2, KnownNat c) => L r1 c -> L r2 c -> L (r1 + r2) c
• splitRows :: forall p m n. (KnownNat p, KnownNat m, KnownNat n, p <= m) => L m n -> (L p n, L (m - p) n)
• splitCols :: forall p m n. (KnownNat p, KnownNat m, KnownNat n, KnownNat (n - p), p <= n) => L m n -> (L m p, L m (n - p))
• unrow :: L 1 n -> R n
• uncol :: KnownNat n => L n 1 -> R n
• tr :: Transposable m mt => m -> mt
• eye :: KnownNat n => Sq n
• diag :: KnownNat n => R n -> Sq n
• blockAt :: forall m n. (KnownNat m, KnownNat n) => ℝ -> Int -> Int -> Matrix Double -> L m n
• matrix :: (KnownNat m, KnownNat n) => [ℝ] -> L m n
• type ℂ = Complex Double
• data C n
• data M m n
• data Her n
• her :: KnownNat n => M n n -> Her n
• 𝑖 :: Sized ℂ s c => s
• (<>) :: forall m k n. (KnownNat m, KnownNat k, KnownNat n) => L m k -> L k n -> L m n
• (#>) :: (KnownNat m, KnownNat n) => L m n -> R n -> R m
• (<.>) :: R n -> R n -> ℝ
• linSolve :: (KnownNat m, KnownNat n) => L m m -> L m n -> Maybe (L m n)
• (<\>) :: (KnownNat m, KnownNat n, KnownNat r) => L m n -> L m r -> L n r
• svd :: (KnownNat m, KnownNat n) => L m n -> (L m m, R n, L n n)
• withCompactSVD :: forall m n z. (KnownNat m, KnownNat n) => L m n -> (forall k. KnownNat k => (L m k, R k, L n k) -> z) -> z
• svdTall :: (KnownNat m, KnownNat n, n <= m) => L m n -> (L m n, R n, L n n)
• svdFlat :: (KnownNat m, KnownNat n, m <= n) => L m n -> (L m m, R m, L n m)
• class Eigen m l v | m -> l, m -> v where
  • eigensystem :: m -> (l, v)
  • eigenvalues :: m -> l
• withNullspace :: forall m n z. (KnownNat m, KnownNat n) => L m n -> (forall k. KnownNat k => L n k -> z) -> z
• withOrth :: forall m n z. (KnownNat m, KnownNat n) => L m n -> (forall k. KnownNat k => L n k -> z) -> z
• qr :: (KnownNat m, KnownNat n) => L m n -> (L m m, L m n)
• chol :: KnownNat n => Sym n -> Sq n
• class Normed a where
  • norm_0 :: a -> R
  • norm_1 :: a -> R
  • norm_2 :: a -> R
  • norm_Inf :: a -> R
• type Seed = Int
• data RandDist
  • = Uniform
  • | Gaussian
• randomVector :: forall n. KnownNat n => Seed -> RandDist -> R n
• rand :: forall m n. (KnownNat m, KnownNat n) => IO (L m n)
• randn :: forall m n. (KnownNat m, KnownNat n) => IO (L m n)
• gaussianSample :: forall m n. (KnownNat m, KnownNat n) => Seed -> R n -> Sym n -> L m n
• uniformSample :: forall m n. (KnownNat m, KnownNat n) => Seed -> R n -> R n -> L m n
• mean :: (KnownNat n, 1 <= n) => R n -> ℝ
• meanCov :: forall m n. (KnownNat m, KnownNat n, 1 <= m) => L m n -> (R n, Sym n)
• class Disp t where
  • disp :: Int -> t -> IO ()
• class Domain field vec mat | mat -> vec field, vec -> mat field, field -> mat vec where
  • mul :: forall m k n. (KnownNat m, KnownNat k, KnownNat n) => mat m k -> mat k n -> mat m n
  • app :: forall m n. (KnownNat m, KnownNat n) => mat m n -> vec n -> vec m
  • dot :: forall n. KnownNat n => vec n -> vec n -> field
  • cross :: vec 3 -> vec 3 -> vec 3
  • diagR :: forall m n k. (KnownNat m, KnownNat n, KnownNat k) => field -> vec k -> mat m n
  • dvmap :: forall n. KnownNat n => (field -> field) -> vec n -> vec n
  • dmmap :: forall n m. (KnownNat m, KnownNat n) => (field -> field) -> mat n m -> mat n m
  • outer :: forall n m. (KnownNat m, KnownNat n) => vec n -> vec m -> mat n m
  • zipWithVector :: forall n. KnownNat n => (field -> field -> field) -> vec n -> vec n -> vec n
  • det :: forall n. KnownNat n => mat n n -> field
  • invlndet :: forall n. KnownNat n => mat n n -> (mat n n, (field, field))
  • expm :: forall n. KnownNat n => mat n n -> mat n n
  • sqrtm :: forall n. KnownNat n => mat n n -> mat n n
  • inv :: forall n. KnownNat n => mat n n -> mat n n
• withVector :: forall z. Vector ℝ -> (forall n. KnownNat n => R n -> z) -> z
• withMatrix :: forall z. Matrix ℝ -> (forall m n. (KnownNat m, KnownNat n) => L m n -> z) -> z
• exactLength :: forall n m. (KnownNat n, KnownNat m) => R m -> Maybe (R n)
• exactDims :: forall n m j k. (KnownNat n, KnownNat m, KnownNat j, KnownNat k) => L m n -> Maybe (L j k)
• toRows :: forall m n. (KnownNat m, KnownNat n) => L m n -> [R n]
• toColumns :: forall m n. (KnownNat m, KnownNat n) => L m n -> [R m]
• withRows :: forall n z. KnownNat n => [R n] -> (forall m. KnownNat m => L m n -> z) -> z
• withColumns :: forall m z. KnownNat m => [R m] -> (forall n. KnownNat n => L m n -> z) -> z
• class Num t => Sized t s d | s -> t, s -> d where
  • konst :: t -> s
  • unwrap :: s -> d t
  • fromList :: [t] -> s
  • extract :: s -> d t
  • create :: d t -> Maybe s
  • size :: s -> IndexOf d
• class Diag m d | m -> d where
  • takeDiag :: m -> d
• data Sym n
• sym :: KnownNat n => Sq n -> Sym n
• mTm :: (KnownNat m, KnownNat n) => L m n -> Sym n
• unSym :: Sym n -> Sq n
• <·> :: R n -> R n -> ℝ

Vector

Matrix

Complex

Products

Linear Systems

Factorizations

Norms

Random arrays

Misc