Copyright	(c) Alberto Ruiz 2014
License	BSD3
Stability	experimental
Safe Haskell	None
Language	Haskell98

Numeric.LinearAlgebra.Static

Contents

Vector
Matrix
Complex
Products
Linear Systems
Factorizations
Norms
Random arrays
Misc
Orphan instances

Description

Experimental interface with statically checked dimensions.

See code examples at http://dis.um.es/~alberto/hmatrix/static.html.

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 => 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 c, KnownNat (r1 + r2), KnownNat r1, KnownNat 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
(<.>) :: KnownNat n => 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
(<·>) :: KnownNat n => R n -> R n -> ℝ

Vector

type ℝ = Double Source #

data R n Source #

Instances

Domain ℝ R L Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods mul :: (KnownNat m, KnownNat k, KnownNat n) => L m k -> L k n -> L m n Source # app :: (KnownNat m, KnownNat n) => L m n -> R n -> R m Source # dot :: KnownNat n => R n -> R n -> ℝ Source # cross :: R 3 -> R 3 -> R 3 Source # diagR :: (KnownNat m, KnownNat n, KnownNat k) => ℝ -> R k -> L m n Source # dvmap :: KnownNat n => (ℝ -> ℝ) -> R n -> R n Source # dmmap :: (KnownNat m, KnownNat n) => (ℝ -> ℝ) -> L n m -> L n m Source # outer :: (KnownNat m, KnownNat n) => R n -> R m -> L n m Source # zipWithVector :: KnownNat n => (ℝ -> ℝ -> ℝ) -> R n -> R n -> R n Source # det :: KnownNat n => L n n -> ℝ Source # invlndet :: KnownNat n => L n n -> (L n n, (ℝ, ℝ)) Source # expm :: KnownNat n => L n n -> L n n Source # sqrtm :: KnownNat n => L n n -> L n n Source # inv :: KnownNat n => L n n -> L n n Source #
KnownNat n => Sized ℝ (R n) Vector Source #
Instance details Defined in Internal.Static Methods konst :: ℝ -> R n Source # unwrap :: R n -> Vector ℝ Source # fromList :: [ℝ] -> R n Source # extract :: R n -> Vector ℝ Source # create :: Vector ℝ -> Maybe (R n) Source # size :: R n -> IndexOf Vector Source #
Floating (R n) Source #
Instance details Defined in Internal.Static Methods pi :: R n # exp :: R n -> R n # log :: R n -> R n # sqrt :: R n -> R n # (**) :: R n -> R n -> R n # logBase :: R n -> R n -> R n # sin :: R n -> R n # cos :: R n -> R n # tan :: R n -> R n # asin :: R n -> R n # acos :: R n -> R n # atan :: R n -> R n # sinh :: R n -> R n # cosh :: R n -> R n # tanh :: R n -> R n # asinh :: R n -> R n # acosh :: R n -> R n # atanh :: R n -> R n # log1p :: R n -> R n # expm1 :: R n -> R n # log1pexp :: R n -> R n # log1mexp :: R n -> R n #
Fractional (R n) Source #
Instance details Defined in Internal.Static Methods (/) :: R n -> R n -> R n # recip :: R n -> R n # fromRational :: Rational -> R n #
Num (R n) Source #
Instance details Defined in Internal.Static Methods (+) :: R n -> R n -> R n # (-) :: R n -> R n -> R n # (*) :: R n -> R n -> R n # negate :: R n -> R n # abs :: R n -> R n # signum :: R n -> R n # fromInteger :: Integer -> R n #
KnownNat n => Show (R n) Source #
Instance details Defined in Internal.Static Methods showsPrec :: Int -> R n -> ShowS # show :: R n -> String # showList :: [R n] -> ShowS #
Generic (R n) Source #
Instance details Defined in Internal.Static Associated Types type Rep (R n) :: Type -> Type # Methods from :: R n -> Rep (R n) x # to :: Rep (R n) x -> R n #
KnownNat n => Binary (R n) Source #
Instance details Defined in Internal.Static Methods put :: R n -> Put # get :: Get (R n) # putList :: [R n] -> Put #
NFData (R n) Source #
Instance details Defined in Internal.Static Methods rnf :: R n -> () #
Additive (R n) Source #
Instance details Defined in Internal.Static Methods add :: R n -> R n -> R n Source #
KnownNat n => Normed (R n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods norm_0 :: R n -> R0 Source # norm_1 :: R n -> R0 Source # norm_2 :: R n -> R0 Source # norm_Inf :: R n -> R0 Source #
KnownNat n => Disp (R n) Source #
Instance details Defined in Internal.Static Methods disp :: Int -> R n -> IO () Source #
KnownNat n => Eigen (Sym n) (R n) (L n n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods eigensystem :: Sym n -> (R n, L n n) Source # eigenvalues :: Sym n -> R n Source #
KnownNat n => Diag (L n n) (R n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods takeDiag :: L n n -> R n Source #
type Rep (R n) Source #
Instance details Defined in Internal.Static type Rep (R n)

vec2 :: ℝ -> ℝ -> R 2 Source #

vec3 :: ℝ -> ℝ -> ℝ -> R 3 Source #

vec4 :: ℝ -> ℝ -> ℝ -> ℝ -> R 4 Source #

(&) :: forall n. KnownNat n => R n -> ℝ -> R (n + 1) infixl 4 Source #

(#) :: forall n m. (KnownNat n, KnownNat m) => R n -> R m -> R (n + m) infixl 4 Source #

split :: forall p n. (KnownNat p, KnownNat n, p <= n) => R n -> (R p, R (n - p)) Source #

headTail :: (KnownNat n, 1 <= n) => R n -> (ℝ, R (n - 1)) Source #

vector :: KnownNat n => [ℝ] -> R n Source #

linspace :: forall n. KnownNat n => (ℝ, ℝ) -> R n Source #

range :: forall n. KnownNat n => R n Source #

dim :: forall n. KnownNat n => R n Source #

Matrix

data L m n Source #

Instances

Domain ℝ R L Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods mul :: (KnownNat m, KnownNat k, KnownNat n) => L m k -> L k n -> L m n Source # app :: (KnownNat m, KnownNat n) => L m n -> R n -> R m Source # dot :: KnownNat n => R n -> R n -> ℝ Source # cross :: R 3 -> R 3 -> R 3 Source # diagR :: (KnownNat m, KnownNat n, KnownNat k) => ℝ -> R k -> L m n Source # dvmap :: KnownNat n => (ℝ -> ℝ) -> R n -> R n Source # dmmap :: (KnownNat m, KnownNat n) => (ℝ -> ℝ) -> L n m -> L n m Source # outer :: (KnownNat m, KnownNat n) => R n -> R m -> L n m Source # zipWithVector :: KnownNat n => (ℝ -> ℝ -> ℝ) -> R n -> R n -> R n Source # det :: KnownNat n => L n n -> ℝ Source # invlndet :: KnownNat n => L n n -> (L n n, (ℝ, ℝ)) Source # expm :: KnownNat n => L n n -> L n n Source # sqrtm :: KnownNat n => L n n -> L n n Source # inv :: KnownNat n => L n n -> L n n Source #
(KnownNat m, KnownNat n) => Sized ℝ (L m n) Matrix Source #
Instance details Defined in Internal.Static Methods konst :: ℝ -> L m n Source # unwrap :: L m n -> Matrix ℝ Source # fromList :: [ℝ] -> L m n Source # extract :: L m n -> Matrix ℝ Source # create :: Matrix ℝ -> Maybe (L m n) Source # size :: L m n -> IndexOf Matrix Source #
KnownNat n => Eigen (Sym n) (R n) (L n n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods eigensystem :: Sym n -> (R n, L n n) Source # eigenvalues :: Sym n -> R n Source #
KnownNat n => Eigen (Sq n) (C n) (M n n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods eigensystem :: Sq n -> (C n, M n n) Source # eigenvalues :: Sq n -> C n Source #
(KnownNat n, KnownNat m) => Floating (L n m) Source #
Instance details Defined in Internal.Static Methods pi :: L n m # exp :: L n m -> L n m # log :: L n m -> L n m # sqrt :: L n m -> L n m # (**) :: L n m -> L n m -> L n m # logBase :: L n m -> L n m -> L n m # sin :: L n m -> L n m # cos :: L n m -> L n m # tan :: L n m -> L n m # asin :: L n m -> L n m # acos :: L n m -> L n m # atan :: L n m -> L n m # sinh :: L n m -> L n m # cosh :: L n m -> L n m # tanh :: L n m -> L n m # asinh :: L n m -> L n m # acosh :: L n m -> L n m # atanh :: L n m -> L n m # log1p :: L n m -> L n m # expm1 :: L n m -> L n m # log1pexp :: L n m -> L n m # log1mexp :: L n m -> L n m #
(KnownNat n, KnownNat m) => Fractional (L n m) Source #
Instance details Defined in Internal.Static Methods (/) :: L n m -> L n m -> L n m # recip :: L n m -> L n m # fromRational :: Rational -> L n m #
(KnownNat n, KnownNat m) => Num (L n m) Source #
Instance details Defined in Internal.Static Methods (+) :: L n m -> L n m -> L n m # (-) :: L n m -> L n m -> L n m # (*) :: L n m -> L n m -> L n m # negate :: L n m -> L n m # abs :: L n m -> L n m # signum :: L n m -> L n m # fromInteger :: Integer -> L n m #
(KnownNat m, KnownNat n) => Show (L m n) Source #
Instance details Defined in Internal.Static Methods showsPrec :: Int -> L m n -> ShowS # show :: L m n -> String # showList :: [L m n] -> ShowS #
Generic (L m n) Source #
Instance details Defined in Internal.Static Associated Types type Rep (L m n) :: Type -> Type # Methods from :: L m n -> Rep (L m n) x # to :: Rep (L m n) x -> L m n #
(KnownNat m, KnownNat n) => Binary (L m n) Source #
Instance details Defined in Internal.Static Methods put :: L m n -> Put # get :: Get (L m n) # putList :: [L m n] -> Put #
NFData (L n m) Source #
Instance details Defined in Internal.Static Methods rnf :: L n m -> () #
(KnownNat n', KnownNat m') => Testable (L n' m') Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods checkT :: L n' m' -> (Bool, IO ()) Source # ioCheckT :: L n' m' -> IO (Bool, IO ()) Source #
(KnownNat m, KnownNat n) => Additive (L m n) Source #
Instance details Defined in Internal.Static Methods add :: L m n -> L m n -> L m n Source #
(KnownNat m, KnownNat n) => Normed (L m n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods norm_0 :: L m n -> R Source # norm_1 :: L m n -> R Source # norm_2 :: L m n -> R Source # norm_Inf :: L m n -> R Source #
(KnownNat m, KnownNat n) => Disp (L m n) Source #
Instance details Defined in Internal.Static Methods disp :: Int -> L m n -> IO () Source #
KnownNat n => Diag (L n n) (R n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods takeDiag :: L n n -> R n Source #
(KnownNat n, KnownNat m) => Transposable (L m n) (L n m) Source #
Instance details Defined in Internal.Static Methods tr :: L m n -> L n m Source # tr' :: L m n -> L n m Source #
type Rep (L m n) Source #
Instance details Defined in Internal.Static type Rep (L m n)

type Sq n = L n n Source #

build :: forall m n. (KnownNat n, KnownNat m) => (ℝ -> ℝ -> ℝ) -> L m n Source #

row :: R n -> L 1 n Source #

col :: KnownNat n => R n -> L n 1 Source #

(|||) :: (KnownNat c, KnownNat (r1 + r2), KnownNat r1, KnownNat r2) => L c r1 -> L c r2 -> L c (r1 + r2) infixl 3 Source #

(===) :: (KnownNat r1, KnownNat r2, KnownNat c) => L r1 c -> L r2 c -> L (r1 + r2) c infixl 2 Source #

splitRows :: forall p m n. (KnownNat p, KnownNat m, KnownNat n, p <= m) => L m n -> (L p n, L (m - p) n) Source #

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)) Source #

unrow :: L 1 n -> R n Source #

uncol :: KnownNat n => L n 1 -> R n Source #

tr :: Transposable m mt => m -> mt Source #

conjugate transpose

eye :: KnownNat n => Sq n Source #

diag :: KnownNat n => R n -> Sq n Source #

blockAt :: forall m n. (KnownNat m, KnownNat n) => ℝ -> Int -> Int -> Matrix Double -> L m n Source #

matrix :: (KnownNat m, KnownNat n) => [ℝ] -> L m n Source #

Complex

type ℂ = Complex Double Source #

data C n Source #

Instances

Domain ℂ C M Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods mul :: (KnownNat m, KnownNat k, KnownNat n) => M m k -> M k n -> M m n Source # app :: (KnownNat m, KnownNat n) => M m n -> C n -> C m Source # dot :: KnownNat n => C n -> C n -> ℂ Source # cross :: C 3 -> C 3 -> C 3 Source # diagR :: (KnownNat m, KnownNat n, KnownNat k) => ℂ -> C k -> M m n Source # dvmap :: KnownNat n => (ℂ -> ℂ) -> C n -> C n Source # dmmap :: (KnownNat m, KnownNat n) => (ℂ -> ℂ) -> M n m -> M n m Source # outer :: (KnownNat m, KnownNat n) => C n -> C m -> M n m Source # zipWithVector :: KnownNat n => (ℂ -> ℂ -> ℂ) -> C n -> C n -> C n Source # det :: KnownNat n => M n n -> ℂ Source # invlndet :: KnownNat n => M n n -> (M n n, (ℂ, ℂ)) Source # expm :: KnownNat n => M n n -> M n n Source # sqrtm :: KnownNat n => M n n -> M n n Source # inv :: KnownNat n => M n n -> M n n Source #
KnownNat n => Sized ℂ (C n) Vector Source #
Instance details Defined in Internal.Static Methods konst :: ℂ -> C n Source # unwrap :: C n -> Vector ℂ Source # fromList :: [ℂ] -> C n Source # extract :: C n -> Vector ℂ Source # create :: Vector ℂ -> Maybe (C n) Source # size :: C n -> IndexOf Vector Source #
Floating (C n) Source #
Instance details Defined in Internal.Static Methods pi :: C n # exp :: C n -> C n # log :: C n -> C n # sqrt :: C n -> C n # (**) :: C n -> C n -> C n # logBase :: C n -> C n -> C n # sin :: C n -> C n # cos :: C n -> C n # tan :: C n -> C n # asin :: C n -> C n # acos :: C n -> C n # atan :: C n -> C n # sinh :: C n -> C n # cosh :: C n -> C n # tanh :: C n -> C n # asinh :: C n -> C n # acosh :: C n -> C n # atanh :: C n -> C n # log1p :: C n -> C n # expm1 :: C n -> C n # log1pexp :: C n -> C n # log1mexp :: C n -> C n #
Fractional (C n) Source #
Instance details Defined in Internal.Static Methods (/) :: C n -> C n -> C n # recip :: C n -> C n # fromRational :: Rational -> C n #
Num (C n) Source #
Instance details Defined in Internal.Static Methods (+) :: C n -> C n -> C n # (-) :: C n -> C n -> C n # (*) :: C n -> C n -> C n # negate :: C n -> C n # abs :: C n -> C n # signum :: C n -> C n # fromInteger :: Integer -> C n #
KnownNat n => Show (C n) Source #
Instance details Defined in Internal.Static Methods showsPrec :: Int -> C n -> ShowS # show :: C n -> String # showList :: [C n] -> ShowS #
Generic (C n) Source #
Instance details Defined in Internal.Static Associated Types type Rep (C n) :: Type -> Type # Methods from :: C n -> Rep (C n) x # to :: Rep (C n) x -> C n #
NFData (C n) Source #
Instance details Defined in Internal.Static Methods rnf :: C n -> () #
Additive (C n) Source #
Instance details Defined in Internal.Static Methods add :: C n -> C n -> C n Source #
KnownNat n => Disp (C n) Source #
Instance details Defined in Internal.Static Methods disp :: Int -> C n -> IO () Source #
KnownNat n => Eigen (Sq n) (C n) (M n n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods eigensystem :: Sq n -> (C n, M n n) Source # eigenvalues :: Sq n -> C n Source #
KnownNat n => Diag (M n n) (C n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods takeDiag :: M n n -> C n Source #
type Rep (C n) Source #
Instance details Defined in Internal.Static type Rep (C n)

data M m n Source #

Instances

Domain ℂ C M Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods mul :: (KnownNat m, KnownNat k, KnownNat n) => M m k -> M k n -> M m n Source # app :: (KnownNat m, KnownNat n) => M m n -> C n -> C m Source # dot :: KnownNat n => C n -> C n -> ℂ Source # cross :: C 3 -> C 3 -> C 3 Source # diagR :: (KnownNat m, KnownNat n, KnownNat k) => ℂ -> C k -> M m n Source # dvmap :: KnownNat n => (ℂ -> ℂ) -> C n -> C n Source # dmmap :: (KnownNat m, KnownNat n) => (ℂ -> ℂ) -> M n m -> M n m Source # outer :: (KnownNat m, KnownNat n) => C n -> C m -> M n m Source # zipWithVector :: KnownNat n => (ℂ -> ℂ -> ℂ) -> C n -> C n -> C n Source # det :: KnownNat n => M n n -> ℂ Source # invlndet :: KnownNat n => M n n -> (M n n, (ℂ, ℂ)) Source # expm :: KnownNat n => M n n -> M n n Source # sqrtm :: KnownNat n => M n n -> M n n Source # inv :: KnownNat n => M n n -> M n n Source #
(KnownNat m, KnownNat n) => Sized ℂ (M m n) Matrix Source #
Instance details Defined in Internal.Static Methods konst :: ℂ -> M m n Source # unwrap :: M m n -> Matrix ℂ Source # fromList :: [ℂ] -> M m n Source # extract :: M m n -> Matrix ℂ Source # create :: Matrix ℂ -> Maybe (M m n) Source # size :: M m n -> IndexOf Matrix Source #
KnownNat n => Eigen (Sq n) (C n) (M n n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods eigensystem :: Sq n -> (C n, M n n) Source # eigenvalues :: Sq n -> C n Source #
(KnownNat n, KnownNat m) => Floating (M n m) Source #
Instance details Defined in Internal.Static Methods pi :: M n m # exp :: M n m -> M n m # log :: M n m -> M n m # sqrt :: M n m -> M n m # (**) :: M n m -> M n m -> M n m # logBase :: M n m -> M n m -> M n m # sin :: M n m -> M n m # cos :: M n m -> M n m # tan :: M n m -> M n m # asin :: M n m -> M n m # acos :: M n m -> M n m # atan :: M n m -> M n m # sinh :: M n m -> M n m # cosh :: M n m -> M n m # tanh :: M n m -> M n m # asinh :: M n m -> M n m # acosh :: M n m -> M n m # atanh :: M n m -> M n m # log1p :: M n m -> M n m # expm1 :: M n m -> M n m # log1pexp :: M n m -> M n m # log1mexp :: M n m -> M n m #
(KnownNat n, KnownNat m) => Fractional (M n m) Source #
Instance details Defined in Internal.Static Methods (/) :: M n m -> M n m -> M n m # recip :: M n m -> M n m # fromRational :: Rational -> M n m #
(KnownNat n, KnownNat m) => Num (M n m) Source #
Instance details Defined in Internal.Static Methods (+) :: M n m -> M n m -> M n m # (-) :: M n m -> M n m -> M n m # (*) :: M n m -> M n m -> M n m # negate :: M n m -> M n m # abs :: M n m -> M n m # signum :: M n m -> M n m # fromInteger :: Integer -> M n m #
(KnownNat m, KnownNat n) => Show (M m n) Source #
Instance details Defined in Internal.Static Methods showsPrec :: Int -> M m n -> ShowS # show :: M m n -> String # showList :: [M m n] -> ShowS #
Generic (M m n) Source #
Instance details Defined in Internal.Static Associated Types type Rep (M m n) :: Type -> Type # Methods from :: M m n -> Rep (M m n) x # to :: Rep (M m n) x -> M m n #
NFData (M n m) Source #
Instance details Defined in Internal.Static Methods rnf :: M n m -> () #
(KnownNat m, KnownNat n) => Additive (M m n) Source #
Instance details Defined in Internal.Static Methods add :: M m n -> M m n -> M m n Source #
(KnownNat m, KnownNat n) => Disp (M m n) Source #
Instance details Defined in Internal.Static Methods disp :: Int -> M m n -> IO () Source #
KnownNat n => Diag (M n n) (C n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods takeDiag :: M n n -> C n Source #
(KnownNat n, KnownNat m) => Transposable (M m n) (M n m) Source #
Instance details Defined in Internal.Static Methods tr :: M m n -> M n m Source # tr' :: M m n -> M n m Source #
type Rep (M m n) Source #
Instance details Defined in Internal.Static type Rep (M m n)

data Her n Source #

Instances

KnownNat n => Disp (Her n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods disp :: Int -> Her n -> IO () Source #
KnownNat n => Transposable (Her n) (Her n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods tr :: Her n -> Her n Source # tr' :: Her n -> Her n Source #

her :: KnownNat n => M n n -> Her n Source #

𝑖 :: Sized ℂ s c => s Source #

Products

(<>) :: forall m k n. (KnownNat m, KnownNat k, KnownNat n) => L m k -> L k n -> L m n infixr 8 Source #

(#>) :: (KnownNat m, KnownNat n) => L m n -> R n -> R m infixr 8 Source #

(<.>) :: KnownNat n => R n -> R n -> ℝ infixr 8 Source #

Linear Systems

linSolve :: (KnownNat m, KnownNat n) => L m m -> L m n -> Maybe (L m n) Source #

(<\>) :: (KnownNat m, KnownNat n, KnownNat r) => L m n -> L m r -> L n r Source #

Factorizations

svd :: (KnownNat m, KnownNat n) => L m n -> (L m m, R n, L n n) Source #

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 Source #

svdTall :: (KnownNat m, KnownNat n, n <= m) => L m n -> (L m n, R n, L n n) Source #

svdFlat :: (KnownNat m, KnownNat n, m <= n) => L m n -> (L m m, R m, L n m) Source #

class Eigen m l v | m -> l, m -> v where Source #

Methods

eigensystem :: m -> (l, v) Source #

eigenvalues :: m -> l Source #

Instances

KnownNat n => Eigen (Sym n) (R n) (L n n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods eigensystem :: Sym n -> (R n, L n n) Source # eigenvalues :: Sym n -> R n Source #
KnownNat n => Eigen (Sq n) (C n) (M n n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods eigensystem :: Sq n -> (C n, M n n) Source # eigenvalues :: Sq n -> C n Source #

withNullspace :: forall m n z. (KnownNat m, KnownNat n) => L m n -> (forall k. KnownNat k => L n k -> z) -> z Source #

withOrth :: forall m n z. (KnownNat m, KnownNat n) => L m n -> (forall k. KnownNat k => L n k -> z) -> z Source #

qr :: (KnownNat m, KnownNat n) => L m n -> (L m m, L m n) Source #

chol :: KnownNat n => Sym n -> Sq n Source #

Norms

class Normed a where Source #

p-norm for vectors, operator norm for matrices

Methods

norm_0 :: a -> R Source #

norm_1 :: a -> R Source #

norm_2 :: a -> R Source #

norm_Inf :: a -> R Source #

Instances

Normed (Vector Float) Source #
Instance details Defined in Internal.Util Methods norm_0 :: Vector Float -> R Source # norm_1 :: Vector Float -> R Source # norm_2 :: Vector Float -> R Source # norm_Inf :: Vector Float -> R Source #
Normed (Vector (Complex Float)) Source #
Instance details Defined in Internal.Util Methods norm_0 :: Vector (Complex Float) -> R Source # norm_1 :: Vector (Complex Float) -> R Source # norm_2 :: Vector (Complex Float) -> R Source # norm_Inf :: Vector (Complex Float) -> R Source #
Normed (Vector C) Source #
Instance details Defined in Internal.Util Methods norm_0 :: Vector C -> R Source # norm_1 :: Vector C -> R Source # norm_2 :: Vector C -> R Source # norm_Inf :: Vector C -> R Source #
Normed (Vector R) Source #
Instance details Defined in Internal.Util Methods norm_0 :: Vector R -> R Source # norm_1 :: Vector R -> R Source # norm_2 :: Vector R -> R Source # norm_Inf :: Vector R -> R Source #
Normed (Vector Z) Source #
Instance details Defined in Internal.Util Methods norm_0 :: Vector Z -> R Source # norm_1 :: Vector Z -> R Source # norm_2 :: Vector Z -> R Source # norm_Inf :: Vector Z -> R Source #
Normed (Vector I) Source #
Instance details Defined in Internal.Util Methods norm_0 :: Vector I -> R Source # norm_1 :: Vector I -> R Source # norm_2 :: Vector I -> R Source # norm_Inf :: Vector I -> R Source #
KnownNat m => Normed (Vector (Mod m Z)) Source #
Instance details Defined in Internal.Modular Methods norm_0 :: Vector (Mod m Z) -> R Source # norm_1 :: Vector (Mod m Z) -> R Source # norm_2 :: Vector (Mod m Z) -> R Source # norm_Inf :: Vector (Mod m Z) -> R Source #
KnownNat m => Normed (Vector (Mod m I)) Source #
Instance details Defined in Internal.Modular Methods norm_0 :: Vector (Mod m I) -> R Source # norm_1 :: Vector (Mod m I) -> R Source # norm_2 :: Vector (Mod m I) -> R Source # norm_Inf :: Vector (Mod m I) -> R Source #
Normed (Matrix C) Source #
Instance details Defined in Internal.Util Methods norm_0 :: Matrix C -> R Source # norm_1 :: Matrix C -> R Source # norm_2 :: Matrix C -> R Source # norm_Inf :: Matrix C -> R Source #
Normed (Matrix R) Source #
Instance details Defined in Internal.Util Methods norm_0 :: Matrix R -> R Source # norm_1 :: Matrix R -> R Source # norm_2 :: Matrix R -> R Source # norm_Inf :: Matrix R -> R Source #
KnownNat n => Normed (R n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods norm_0 :: R n -> R0 Source # norm_1 :: R n -> R0 Source # norm_2 :: R n -> R0 Source # norm_Inf :: R n -> R0 Source #
(KnownNat m, KnownNat n) => Normed (L m n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods norm_0 :: L m n -> R Source # norm_1 :: L m n -> R Source # norm_2 :: L m n -> R Source # norm_Inf :: L m n -> R Source #

Random arrays

type Seed = Int Source #

data RandDist Source #

Constructors

Uniform	uniform distribution in [0,1)
Gaussian	normal distribution with mean zero and standard deviation one

Instances

Enum RandDist Source #
Instance details Defined in Internal.Vectorized Methods succ :: RandDist -> RandDist # pred :: RandDist -> RandDist # toEnum :: Int -> RandDist # fromEnum :: RandDist -> Int # enumFrom :: RandDist -> [RandDist] # enumFromThen :: RandDist -> RandDist -> [RandDist] # enumFromTo :: RandDist -> RandDist -> [RandDist] # enumFromThenTo :: RandDist -> RandDist -> RandDist -> [RandDist] #

randomVector :: forall n. KnownNat n => Seed -> RandDist -> R n Source #

rand :: forall m n. (KnownNat m, KnownNat n) => IO (L m n) Source #

randn :: forall m n. (KnownNat m, KnownNat n) => IO (L m n) Source #

gaussianSample :: forall m n. (KnownNat m, KnownNat n) => Seed -> R n -> Sym n -> L m n Source #

uniformSample Source #

Arguments

:: (KnownNat m, KnownNat n)
=> Seed
-> R n	minimums of each row
-> R n	maximums of each row
-> L m n

Misc

mean :: (KnownNat n, 1 <= n) => R n -> ℝ Source #

meanCov :: forall m n. (KnownNat m, KnownNat n, 1 <= m) => L m n -> (R n, Sym n) Source #

class Disp t where Source #

Methods

disp :: Int -> t -> IO () Source #

Instances

KnownNat n => Disp (C n) Source #
Instance details Defined in Internal.Static Methods disp :: Int -> C n -> IO () Source #
KnownNat n => Disp (R n) Source #
Instance details Defined in Internal.Static Methods disp :: Int -> R n -> IO () Source #
KnownNat n => Disp (Her n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods disp :: Int -> Her n -> IO () Source #
KnownNat n => Disp (Sym n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods disp :: Int -> Sym n -> IO () Source #
(KnownNat m, KnownNat n) => Disp (M m n) Source #
Instance details Defined in Internal.Static Methods disp :: Int -> M m n -> IO () Source #
(KnownNat m, KnownNat n) => Disp (L m n) Source #
Instance details Defined in Internal.Static Methods disp :: Int -> L m n -> IO () Source #

class Domain field vec mat | mat -> vec field, vec -> mat field, field -> mat vec where Source #

Methods

mul :: forall m k n. (KnownNat m, KnownNat k, KnownNat n) => mat m k -> mat k n -> mat m n Source #

app :: forall m n. (KnownNat m, KnownNat n) => mat m n -> vec n -> vec m Source #

dot :: forall n. KnownNat n => vec n -> vec n -> field Source #

cross :: vec 3 -> vec 3 -> vec 3 Source #

diagR :: forall m n k. (KnownNat m, KnownNat n, KnownNat k) => field -> vec k -> mat m n Source #

dvmap :: forall n. KnownNat n => (field -> field) -> vec n -> vec n Source #

dmmap :: forall n m. (KnownNat m, KnownNat n) => (field -> field) -> mat n m -> mat n m Source #

outer :: forall n m. (KnownNat m, KnownNat n) => vec n -> vec m -> mat n m Source #

zipWithVector :: forall n. KnownNat n => (field -> field -> field) -> vec n -> vec n -> vec n Source #

det :: forall n. KnownNat n => mat n n -> field Source #

invlndet :: forall n. KnownNat n => mat n n -> (mat n n, (field, field)) Source #

expm :: forall n. KnownNat n => mat n n -> mat n n Source #

sqrtm :: forall n. KnownNat n => mat n n -> mat n n Source #

inv :: forall n. KnownNat n => mat n n -> mat n n Source #

Instances

Domain ℂ C M Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods mul :: (KnownNat m, KnownNat k, KnownNat n) => M m k -> M k n -> M m n Source # app :: (KnownNat m, KnownNat n) => M m n -> C n -> C m Source # dot :: KnownNat n => C n -> C n -> ℂ Source # cross :: C 3 -> C 3 -> C 3 Source # diagR :: (KnownNat m, KnownNat n, KnownNat k) => ℂ -> C k -> M m n Source # dvmap :: KnownNat n => (ℂ -> ℂ) -> C n -> C n Source # dmmap :: (KnownNat m, KnownNat n) => (ℂ -> ℂ) -> M n m -> M n m Source # outer :: (KnownNat m, KnownNat n) => C n -> C m -> M n m Source # zipWithVector :: KnownNat n => (ℂ -> ℂ -> ℂ) -> C n -> C n -> C n Source # det :: KnownNat n => M n n -> ℂ Source # invlndet :: KnownNat n => M n n -> (M n n, (ℂ, ℂ)) Source # expm :: KnownNat n => M n n -> M n n Source # sqrtm :: KnownNat n => M n n -> M n n Source # inv :: KnownNat n => M n n -> M n n Source #
Domain ℝ R L Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods mul :: (KnownNat m, KnownNat k, KnownNat n) => L m k -> L k n -> L m n Source # app :: (KnownNat m, KnownNat n) => L m n -> R n -> R m Source # dot :: KnownNat n => R n -> R n -> ℝ Source # cross :: R 3 -> R 3 -> R 3 Source # diagR :: (KnownNat m, KnownNat n, KnownNat k) => ℝ -> R k -> L m n Source # dvmap :: KnownNat n => (ℝ -> ℝ) -> R n -> R n Source # dmmap :: (KnownNat m, KnownNat n) => (ℝ -> ℝ) -> L n m -> L n m Source # outer :: (KnownNat m, KnownNat n) => R n -> R m -> L n m Source # zipWithVector :: KnownNat n => (ℝ -> ℝ -> ℝ) -> R n -> R n -> R n Source # det :: KnownNat n => L n n -> ℝ Source # invlndet :: KnownNat n => L n n -> (L n n, (ℝ, ℝ)) Source # expm :: KnownNat n => L n n -> L n n Source # sqrtm :: KnownNat n => L n n -> L n n Source # inv :: KnownNat n => L n n -> L n n Source #

withVector :: forall z. Vector ℝ -> (forall n. KnownNat n => R n -> z) -> z Source #

withMatrix :: forall z. Matrix ℝ -> (forall m n. (KnownNat m, KnownNat n) => L m n -> z) -> z Source #

exactLength :: forall n m. (KnownNat n, KnownNat m) => R m -> Maybe (R n) Source #

Useful for constraining two dependently typed vectors to match each other in length when they are unknown at compile-time.

exactDims :: forall n m j k. (KnownNat n, KnownNat m, KnownNat j, KnownNat k) => L m n -> Maybe (L j k) Source #

Useful for constraining two dependently typed matrices to match each other in dimensions when they are unknown at compile-time.

toRows :: forall m n. (KnownNat m, KnownNat n) => L m n -> [R n] Source #

toColumns :: forall m n. (KnownNat m, KnownNat n) => L m n -> [R m] Source #

withRows :: forall n z. KnownNat n => [R n] -> (forall m. KnownNat m => L m n -> z) -> z Source #

withColumns :: forall m z. KnownNat m => [R m] -> (forall n. KnownNat n => L m n -> z) -> z Source #

class Num t => Sized t s d | s -> t, s -> d where Source #

Methods

konst :: t -> s Source #

unwrap :: s -> d t Source #

fromList :: [t] -> s Source #

extract :: s -> d t Source #

create :: d t -> Maybe s Source #

size :: s -> IndexOf d Source #

Instances

KnownNat n => Sized ℂ (C n) Vector Source #
Instance details Defined in Internal.Static Methods konst :: ℂ -> C n Source # unwrap :: C n -> Vector ℂ Source # fromList :: [ℂ] -> C n Source # extract :: C n -> Vector ℂ Source # create :: Vector ℂ -> Maybe (C n) Source # size :: C n -> IndexOf Vector Source #
KnownNat n => Sized ℝ (R n) Vector Source #
Instance details Defined in Internal.Static Methods konst :: ℝ -> R n Source # unwrap :: R n -> Vector ℝ Source # fromList :: [ℝ] -> R n Source # extract :: R n -> Vector ℝ Source # create :: Vector ℝ -> Maybe (R n) Source # size :: R n -> IndexOf Vector Source #
(KnownNat m, KnownNat n) => Sized ℂ (M m n) Matrix Source #
Instance details Defined in Internal.Static Methods konst :: ℂ -> M m n Source # unwrap :: M m n -> Matrix ℂ Source # fromList :: [ℂ] -> M m n Source # extract :: M m n -> Matrix ℂ Source # create :: Matrix ℂ -> Maybe (M m n) Source # size :: M m n -> IndexOf Matrix Source #
(KnownNat m, KnownNat n) => Sized ℝ (L m n) Matrix Source #
Instance details Defined in Internal.Static Methods konst :: ℝ -> L m n Source # unwrap :: L m n -> Matrix ℝ Source # fromList :: [ℝ] -> L m n Source # extract :: L m n -> Matrix ℝ Source # create :: Matrix ℝ -> Maybe (L m n) Source # size :: L m n -> IndexOf Matrix Source #

class Diag m d | m -> d where Source #

Methods

takeDiag :: m -> d Source #

Instances

KnownNat n => Diag (M n n) (C n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods takeDiag :: M n n -> C n Source #
KnownNat n => Diag (L n n) (R n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods takeDiag :: L n n -> R n Source #

data Sym n Source #

Instances

KnownNat n => Floating (Sym n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods pi :: Sym n # exp :: Sym n -> Sym n # log :: Sym n -> Sym n # sqrt :: Sym n -> Sym n # (**) :: Sym n -> Sym n -> Sym n # logBase :: Sym n -> Sym n -> Sym n # sin :: Sym n -> Sym n # cos :: Sym n -> Sym n # tan :: Sym n -> Sym n # asin :: Sym n -> Sym n # acos :: Sym n -> Sym n # atan :: Sym n -> Sym n # sinh :: Sym n -> Sym n # cosh :: Sym n -> Sym n # tanh :: Sym n -> Sym n # asinh :: Sym n -> Sym n # acosh :: Sym n -> Sym n # atanh :: Sym n -> Sym n # log1p :: Sym n -> Sym n # expm1 :: Sym n -> Sym n # log1pexp :: Sym n -> Sym n # log1mexp :: Sym n -> Sym n #
KnownNat n => Fractional (Sym n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods (/) :: Sym n -> Sym n -> Sym n # recip :: Sym n -> Sym n # fromRational :: Rational -> Sym n #
KnownNat n => Num (Sym n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods (+) :: Sym n -> Sym n -> Sym n # (-) :: Sym n -> Sym n -> Sym n # (*) :: Sym n -> Sym n -> Sym n # negate :: Sym n -> Sym n # abs :: Sym n -> Sym n # signum :: Sym n -> Sym n # fromInteger :: Integer -> Sym n #
KnownNat n => Show (Sym n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods showsPrec :: Int -> Sym n -> ShowS # show :: Sym n -> String # showList :: [Sym n] -> ShowS #
KnownNat n => Additive (Sym n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods add :: Sym n -> Sym n -> Sym n Source #
KnownNat n => Disp (Sym n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods disp :: Int -> Sym n -> IO () Source #
KnownNat n => Transposable (Sym n) (Sym n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods tr :: Sym n -> Sym n Source # tr' :: Sym n -> Sym n Source #
KnownNat n => Eigen (Sym n) (R n) (L n n) Source #
Instance details Defined in Numeric.LinearAlgebra.Static Methods eigensystem :: Sym n -> (R n, L n n) Source # eigenvalues :: Sym n -> R n Source #

sym :: KnownNat n => Sq n -> Sym n Source #

mTm :: (KnownNat m, KnownNat n) => L m n -> Sym n Source #

unSym :: Sym n -> Sq n Source #

(<·>) :: KnownNat n => R n -> R n -> ℝ infixr 8 Source #

Orphan instances

KnownNat n => Normed (R n) Source #
Instance details Methods norm_0 :: R n -> R0 Source # norm_1 :: R n -> R0 Source # norm_2 :: R n -> R0 Source # norm_Inf :: R n -> R0 Source #
(KnownNat n', KnownNat m') => Testable (L n' m') Source #
Instance details Methods checkT :: L n' m' -> (Bool, IO ()) Source # ioCheckT :: L n' m' -> IO (Bool, IO ()) Source #
(KnownNat m, KnownNat n) => Normed (L m n) Source #
Instance details Methods norm_0 :: L m n -> R Source # norm_1 :: L m n -> R Source # norm_2 :: L m n -> R Source # norm_Inf :: L m n -> R Source #