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

Vector

type ℝ = Double Source #

data R n Source #

Instances

Domain ℝ R L Source #
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 #
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 #
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 #
Methods (/) :: R n -> R n -> R n # recip :: R n -> R n # fromRational :: Rational -> R n #
Num (R n) Source #
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 #
Methods showsPrec :: Int -> R n -> ShowS # show :: R n -> String # showList :: [R n] -> ShowS #
Generic (R n) Source #
Associated Types type Rep (R n) :: * -> * # Methods from :: R n -> Rep (R n) x # to :: Rep (R n) x -> R n #
KnownNat n => Binary (R n) Source #
Methods put :: R n -> Put # get :: Get (R n) # putList :: [R n] -> Put #
NFData (R n) Source #
Methods rnf :: R n -> () #
Additive (R n) Source #
Methods add :: R n -> R n -> R n Source #
KnownNat n => Disp (R n) Source #
Methods disp :: Int -> R n -> IO () Source #
KnownNat n => Eigen (Sym n) (R n) (L n n) Source #
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 #
Methods takeDiag :: L n n -> R n Source #
type Rep (R n) Source #
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, 1 <= 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 #
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 #
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 #
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 #
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 #
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 #
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 #
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 #
Methods showsPrec :: Int -> L m n -> ShowS # show :: L m n -> String # showList :: [L m n] -> ShowS #
Generic (L m n) Source #
Associated Types type Rep (L m n) :: * -> * # Methods from :: L m n -> Rep (L m n) x # to :: Rep (L m n) x -> L m n #
(KnownNat n, KnownNat m) => Binary (L m n) Source #
Methods put :: L m n -> Put # get :: Get (L m n) # putList :: [L m n] -> Put #
NFData (L n m) Source #
Methods rnf :: L n m -> () #
(KnownNat m, KnownNat n) => Additive (L m n) Source #
Methods add :: L m n -> L m n -> L m n Source #
(KnownNat m, KnownNat n) => Disp (L m n) Source #
Methods disp :: Int -> L m n -> IO () Source #
KnownNat n => Diag (L n n) (R n) Source #
Methods takeDiag :: L n n -> R n Source #
(KnownNat n, KnownNat m) => Transposable (L m n) (L n m) Source #
Methods tr :: L m n -> L n m Source # tr' :: L m n -> L n m Source #
type Rep (L m n) Source #
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 r2, KnownNat r1, KnownNat ((+) r1 r2), KnownNat c) => 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 #
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 #
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 #
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 #
Methods (/) :: C n -> C n -> C n # recip :: C n -> C n # fromRational :: Rational -> C n #
Num (C n) Source #
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 #
Methods showsPrec :: Int -> C n -> ShowS # show :: C n -> String # showList :: [C n] -> ShowS #
Generic (C n) Source #
Associated Types type Rep (C n) :: * -> * # Methods from :: C n -> Rep (C n) x # to :: Rep (C n) x -> C n #
NFData (C n) Source #
Methods rnf :: C n -> () #
Additive (C n) Source #
Methods add :: C n -> C n -> C n Source #
KnownNat n => Disp (C n) Source #
Methods disp :: Int -> C n -> IO () Source #
KnownNat n => Eigen (Sq n) (C n) (M n n) Source #
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 #
Methods takeDiag :: M n n -> C n Source #
type Rep (C n) Source #
type Rep (C n)

data M m n Source #

Instances

Domain ℂ C M Source #
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 #
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 #
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 #
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 #
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 #
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 #
Methods showsPrec :: Int -> M m n -> ShowS # show :: M m n -> String # showList :: [M m n] -> ShowS #
Generic (M m n) Source #
Associated Types type Rep (M m n) :: * -> * # Methods from :: M m n -> Rep (M m n) x # to :: Rep (M m n) x -> M m n #
NFData (M n m) Source #
Methods rnf :: M n m -> () #
(KnownNat m, KnownNat n) => Additive (M m n) Source #
Methods add :: M m n -> M m n -> M m n Source #
(KnownNat m, KnownNat n) => Disp (M m n) Source #
Methods disp :: Int -> M m n -> IO () Source #
KnownNat n => Diag (M n n) (C n) Source #
Methods takeDiag :: M n n -> C n Source #
(KnownNat n, KnownNat m) => Transposable (M m n) (M n m) Source #
Methods tr :: M m n -> M n m Source # tr' :: M m n -> M n m Source #
type Rep (M m n) Source #
type Rep (M m n)

data Her n Source #

Instances

KnownNat n => Disp (Her n) Source #
Methods disp :: Int -> Her n -> IO () Source #
KnownNat n => Transposable (Her n) (Her n) Source #
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 #

Minimal complete definition

eigensystem, eigenvalues

Methods

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

eigenvalues :: m -> l Source #

Instances

KnownNat n => Eigen (Sym n) (R n) (L n n) Source #
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 #
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

Minimal complete definition

norm_0, norm_1, norm_2, norm_Inf

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 #
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 #
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 #
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 #
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 #
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 #
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 #
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 #
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 #
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 #
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 #

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 #
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 #

Minimal complete definition

disp

Methods

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

Instances

KnownNat n => Disp (C n) Source #
Methods disp :: Int -> C n -> IO () Source #
KnownNat n => Disp (R n) Source #
Methods disp :: Int -> R n -> IO () Source #
KnownNat n => Disp (Her n) Source #
Methods disp :: Int -> Her n -> IO () Source #
KnownNat n => Disp (Sym n) Source #
Methods disp :: Int -> Sym n -> IO () Source #
(KnownNat m, KnownNat n) => Disp (M m n) Source #
Methods disp :: Int -> M m n -> IO () Source #
(KnownNat m, KnownNat n) => Disp (L m n) Source #
Methods disp :: Int -> L m n -> IO () Source #

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

Minimal complete definition

mul, app, dot, cross, diagR, dvmap, dmmap, outer, zipWithVector, det, invlndet, expm, sqrtm, inv

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 #
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 #
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 #

Minimal complete definition

konst, unwrap, fromList, extract, create, size

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 #
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 #
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 #
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 #
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 #

Minimal complete definition

takeDiag

Methods

takeDiag :: m -> d Source #

Instances

KnownNat n => Diag (M n n) (C n) Source #
Methods takeDiag :: M n n -> C n Source #
KnownNat n => Diag (L n n) (R n) Source #
Methods takeDiag :: L n n -> R n Source #

data Sym n Source #

Instances

KnownNat n => Floating (Sym n) Source #
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 #
Methods (/) :: Sym n -> Sym n -> Sym n # recip :: Sym n -> Sym n # fromRational :: Rational -> Sym n #
KnownNat n => Num (Sym n) Source #
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 #
Methods showsPrec :: Int -> Sym n -> ShowS # show :: Sym n -> String # showList :: [Sym n] -> ShowS #
KnownNat n => Additive (Sym n) Source #
Methods add :: Sym n -> Sym n -> Sym n Source #
KnownNat n => Disp (Sym n) Source #
Methods disp :: Int -> Sym n -> IO () Source #
KnownNat n => Transposable (Sym n) (Sym n) Source #
Methods tr :: Sym n -> Sym n Source # tr' :: Sym n -> Sym n Source #
KnownNat n => Eigen (Sym n) (R n) (L n n) Source #
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 #
Methods norm_0 :: R n -> R Source # norm_1 :: R n -> R Source # norm_2 :: R n -> R Source # norm_Inf :: R n -> R Source #
(KnownNat n', KnownNat m') => Testable (L n' m') Source #
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 #
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 #