HNum.Vector

Documentation

newtype Vector a

Constructors

Vector [a]

Instances

Functor Vector

Methods

fmap :: (a -> b) -> Vector a -> Vector b

(<$) :: a -> Vector b -> Vector a

Applicative Vector

Methods

pure :: a -> Vector a

(<*>) :: Vector (a -> b) -> Vector a -> Vector b

liftA2 :: (a -> b -> c) -> Vector a -> Vector b -> Vector c

(*>) :: Vector a -> Vector b -> Vector b

(<*) :: Vector a -> Vector b -> Vector a

Foldable Vector

Methods

fold :: Monoid m => Vector m -> m

foldMap :: Monoid m => (a -> m) -> Vector a -> m

foldr :: (a -> b -> b) -> b -> Vector a -> b

foldr' :: (a -> b -> b) -> b -> Vector a -> b

foldl :: (b -> a -> b) -> b -> Vector a -> b

foldl' :: (b -> a -> b) -> b -> Vector a -> b

foldr1 :: (a -> a -> a) -> Vector a -> a

foldl1 :: (a -> a -> a) -> Vector a -> a

toList :: Vector a -> [a]

null :: Vector a -> Bool

length :: Vector a -> Int

elem :: Eq a => a -> Vector a -> Bool

maximum :: Ord a => Vector a -> a

minimum :: Ord a => Vector a -> a

sum :: Num a => Vector a -> a

product :: Num a => Vector a -> a

Concatable Vector

Methods

hcat :: Vector a -> Vector a -> Vector a

vcat :: Vector a -> Vector a -> Matrix a

VecOps Vector

Methods

(.+) :: Num a => Vector a -> a -> Vector a

(.-) :: Num a => Vector a -> a -> Vector a

(.*) :: Num a => Vector a -> a -> Vector a

(./) :: Fractional a => Vector a -> a -> Vector a

(.^) :: Floating a => Vector a -> a -> Vector a

(.*.) :: Num a => Vector a -> Vector a -> a

norm :: Floating a => Vector a -> a

List Vector

Methods

toList :: Vector a -> [a]

fromList :: [a] -> Vector a

Writable Vector

Methods

toString :: Show a => Vector a -> String

writeCSV :: Show a => String -> Vector a -> IO ()

Statistical Vector

Methods

mean :: Fractional a => Vector a -> a

cov' :: Floating a => Vector a -> Vector a -> a

cov :: Floating a => Vector a -> Vector a -> Matrix a

var :: Floating a => Vector a -> a

std :: Floating a => Vector a -> a

se :: Floating a => Vector a -> a

cor :: Floating a => Vector a -> Vector a -> a

med :: (Ord a, Floating a) => Vector a -> a

mode :: Eq a => Vector a -> a

cv :: Floating a => Vector a -> a

moment :: Floating a => a -> Vector a -> a

skew :: Floating a => Vector a -> a

skew' :: Floating a => Vector a -> a

kurt :: Floating a => Vector a -> a

Eq a => Eq (Vector a)

Methods

(==) :: Vector a -> Vector a -> Bool

(/=) :: Vector a -> Vector a -> Bool

Floating a => Floating (Vector a)

Methods

pi :: Vector a

exp :: Vector a -> Vector a

log :: Vector a -> Vector a

sqrt :: Vector a -> Vector a

(**) :: Vector a -> Vector a -> Vector a

logBase :: Vector a -> Vector a -> Vector a

sin :: Vector a -> Vector a

cos :: Vector a -> Vector a

tan :: Vector a -> Vector a

asin :: Vector a -> Vector a

acos :: Vector a -> Vector a

atan :: Vector a -> Vector a

sinh :: Vector a -> Vector a

cosh :: Vector a -> Vector a

tanh :: Vector a -> Vector a

asinh :: Vector a -> Vector a

acosh :: Vector a -> Vector a

atanh :: Vector a -> Vector a

log1p :: Vector a -> Vector a

expm1 :: Vector a -> Vector a

log1pexp :: Vector a -> Vector a

log1mexp :: Vector a -> Vector a

Fractional a => Fractional (Vector a)

Methods

(/) :: Vector a -> Vector a -> Vector a

recip :: Vector a -> Vector a

fromRational :: Rational -> Vector a

Num a => Num (Vector a)

Methods

(+) :: Vector a -> Vector a -> Vector a

(-) :: Vector a -> Vector a -> Vector a

(*) :: Vector a -> Vector a -> Vector a

negate :: Vector a -> Vector a

abs :: Vector a -> Vector a

signum :: Vector a -> Vector a

fromInteger :: Integer -> Vector a

Show a => Show (Vector a)

Methods

showsPrec :: Int -> Vector a -> ShowS

show :: Vector a -> String

showList :: [Vector a] -> ShowS

vector :: [a] -> Vector a

vec :: [a] -> Vector a

class List m where

Minimal complete definition

toList, fromList

Methods

toList :: m a -> [a]

fromList :: [a] -> m a

Instances

List Vector

Methods

toList :: Vector a -> [a]

fromList :: [a] -> Vector a

data Matrix a

Definition of Matrix

Constructors

Matrix

Fields

• val :: Vector a
• row :: Int
• col :: Int
• byRow :: Bool

Instances

Functor Matrix

Methods

fmap :: (a -> b) -> Matrix a -> Matrix b

(<$) :: a -> Matrix b -> Matrix a

Applicative Matrix

Methods

pure :: a -> Matrix a

(<*>) :: Matrix (a -> b) -> Matrix a -> Matrix b

liftA2 :: (a -> b -> c) -> Matrix a -> Matrix b -> Matrix c

(*>) :: Matrix a -> Matrix b -> Matrix b

(<*) :: Matrix a -> Matrix b -> Matrix a

Foldable Matrix

Methods

fold :: Monoid m => Matrix m -> m

foldMap :: Monoid m => (a -> m) -> Matrix a -> m

foldr :: (a -> b -> b) -> b -> Matrix a -> b

foldr' :: (a -> b -> b) -> b -> Matrix a -> b

foldl :: (b -> a -> b) -> b -> Matrix a -> b

foldl' :: (b -> a -> b) -> b -> Matrix a -> b

foldr1 :: (a -> a -> a) -> Matrix a -> a

foldl1 :: (a -> a -> a) -> Matrix a -> a

toList :: Matrix a -> [a]

null :: Matrix a -> Bool

length :: Matrix a -> Int

elem :: Eq a => a -> Matrix a -> Bool

maximum :: Ord a => Matrix a -> a

minimum :: Ord a => Matrix a -> a

sum :: Num a => Matrix a -> a

product :: Num a => Matrix a -> a

Concatable Matrix

Methods

hcat :: Matrix a -> Matrix a -> Matrix a

vcat :: Matrix a -> Matrix a -> Matrix a

MatOps Matrix

Methods

(%*%) :: Num a => Matrix a -> Matrix a -> Matrix a

(%/%) :: (Eq a, Fractional a) => Matrix a -> Matrix a -> Matrix a

det :: (Eq a, Fractional a) => Matrix a -> a

inv :: (Eq a, Fractional a) => Matrix a -> Matrix a

transpose :: Matrix a -> Matrix a

VecOps Matrix

Methods

(.+) :: Num a => Matrix a -> a -> Matrix a

(.-) :: Num a => Matrix a -> a -> Matrix a

(.*) :: Num a => Matrix a -> a -> Matrix a

(./) :: Fractional a => Matrix a -> a -> Matrix a

(.^) :: Floating a => Matrix a -> a -> Matrix a

(.*.) :: Num a => Matrix a -> Matrix a -> a

norm :: Floating a => Matrix a -> a

Matrices Matrix

Methods

matForm :: Matrix a -> [[a]]

formMat :: [[a]] -> Matrix a

Writable Matrix

Methods

toString :: Show a => Matrix a -> String

writeCSV :: Show a => String -> Matrix a -> IO ()

Eq a => Eq (Matrix a)

Methods

(==) :: Matrix a -> Matrix a -> Bool

(/=) :: Matrix a -> Matrix a -> Bool

Floating a => Floating (Matrix a)

Methods

pi :: Matrix a

exp :: Matrix a -> Matrix a

log :: Matrix a -> Matrix a

sqrt :: Matrix a -> Matrix a

(**) :: Matrix a -> Matrix a -> Matrix a

logBase :: Matrix a -> Matrix a -> Matrix a

sin :: Matrix a -> Matrix a

cos :: Matrix a -> Matrix a

tan :: Matrix a -> Matrix a

asin :: Matrix a -> Matrix a

acos :: Matrix a -> Matrix a

atan :: Matrix a -> Matrix a

sinh :: Matrix a -> Matrix a

cosh :: Matrix a -> Matrix a

tanh :: Matrix a -> Matrix a

asinh :: Matrix a -> Matrix a

acosh :: Matrix a -> Matrix a

atanh :: Matrix a -> Matrix a

log1p :: Matrix a -> Matrix a

expm1 :: Matrix a -> Matrix a

log1pexp :: Matrix a -> Matrix a

log1mexp :: Matrix a -> Matrix a

Fractional a => Fractional (Matrix a)

Methods

(/) :: Matrix a -> Matrix a -> Matrix a

recip :: Matrix a -> Matrix a

fromRational :: Rational -> Matrix a

Num a => Num (Matrix a)

Methods

(+) :: Matrix a -> Matrix a -> Matrix a

(-) :: Matrix a -> Matrix a -> Matrix a

(*) :: Matrix a -> Matrix a -> Matrix a

negate :: Matrix a -> Matrix a

abs :: Matrix a -> Matrix a

signum :: Matrix a -> Matrix a

fromInteger :: Integer -> Matrix a

Show a => Show (Matrix a)

Methods

showsPrec :: Int -> Matrix a -> ShowS

show :: Matrix a -> String

showList :: [Matrix a] -> ShowS

matrix :: [[a]] -> Matrix a

matrix is syntactic sugar to create Matrix

class Matrices m where

Matrices is necessary class for Matrix

Minimal complete definition

matForm, formMat

Methods

matForm :: m a -> [[a]]

formMat :: [[a]] -> m a

Instances

Matrices Matrix

Methods

matForm :: Matrix a -> [[a]]

formMat :: [[a]] -> Matrix a

class Functor f => VecOps f where

(.ops) is an operation Vector(or Matrix) with Constant. Dot means position of Vector. Example: a .* 2 = twice whole elements of a a .*. b = Dot product

Minimal complete definition

(.+), (.-), (.*), (./), (.^), (.*.), norm

Methods

(.+) :: Num a => f a -> a -> f a

(.-) :: Num a => f a -> a -> f a

(.*) :: Num a => f a -> a -> f a

(./) :: Fractional a => f a -> a -> f a

(.^) :: Floating a => f a -> a -> f a

(.*.) :: Num a => f a -> f a -> a

norm :: Floating a => f a -> a

Instances

VecOps Matrix

Methods

(.+) :: Num a => Matrix a -> a -> Matrix a

(.-) :: Num a => Matrix a -> a -> Matrix a

(.*) :: Num a => Matrix a -> a -> Matrix a

(./) :: Fractional a => Matrix a -> a -> Matrix a

(.^) :: Floating a => Matrix a -> a -> Matrix a

(.*.) :: Num a => Matrix a -> Matrix a -> a

norm :: Floating a => Matrix a -> a

VecOps Vector

Methods

(.+) :: Num a => Vector a -> a -> Vector a

(.-) :: Num a => Vector a -> a -> Vector a

(.*) :: Num a => Vector a -> a -> Vector a

(./) :: Fractional a => Vector a -> a -> Vector a

(.^) :: Floating a => Vector a -> a -> Vector a

(.*.) :: Num a => Vector a -> Vector a -> a

norm :: Floating a => Vector a -> a

class Functor f => MatOps f where

Minimal complete definition

(%*%), (%/%), det, inv, transpose

Methods

(%*%) :: Num a => f a -> f a -> f a

(%/%) :: (Eq a, Fractional a) => f a -> f a -> f a

det :: (Eq a, Fractional a) => f a -> a

inv :: (Eq a, Fractional a) => f a -> f a

transpose :: f a -> f a

Instances

MatOps Matrix

Methods

(%*%) :: Num a => Matrix a -> Matrix a -> Matrix a

(%/%) :: (Eq a, Fractional a) => Matrix a -> Matrix a -> Matrix a

det :: (Eq a, Fractional a) => Matrix a -> a

inv :: (Eq a, Fractional a) => Matrix a -> Matrix a

transpose :: Matrix a -> Matrix a

bp :: Int -> Matrix a -> Matrix a

Block Partitioning

class Functor f => Concatable f where

Minimal complete definition

hcat, vcat

Methods

hcat :: f a -> f a -> f a

vcat :: f a -> f a -> Matrix a

Instances

Concatable Matrix

Methods

hcat :: Matrix a -> Matrix a -> Matrix a

vcat :: Matrix a -> Matrix a -> Matrix a

Concatable Vector

Methods

hcat :: Vector a -> Vector a -> Vector a

vcat :: Vector a -> Vector a -> Matrix a

(.:) :: Vector a -> Matrix a -> Matrix a

(.:) inserts vector to head of matrix.

qsort :: Ord a => Vector a -> Vector a

Quick Sort

transposeMat :: [[a]] -> [[a]]

Merge Sort msort :: Ord a => Vector a -> Vector a msort

indexMat :: [[a]] -> [[(Int, Int)]]

dropAtMat :: Int -> Int -> [[a]] -> [[a]]

postSplitAt :: ([a], [a]) -> [a]

dropAt :: Int -> [a] -> [a]

dropAtMat' :: Int -> [[a]] -> [[a]]

bpMat :: Int -> [[a]] -> [[a]]

(%-+-%) :: Num a => [[a]] -> [[a]] -> [[a]]

negMap :: Num a => [[a]] -> [[a]]

(%---%) :: Num a => [[a]] -> [[a]] -> [[a]]

(%-*-%) :: Num a => [[a]] -> [[a]] -> [[a]]

zerosVec :: Int -> [Int]

eyeMat :: Int -> [[Int]]

basisVec :: Int -> Int -> [Int]

permMat :: Int -> Int -> [[a]] -> [[Int]]

whichMax :: Ord a => [a] -> Int

colMat :: [[a]] -> Int -> [a]

colMaxIdx :: Ord a => [[a]] -> Int -> Int

cycleMat :: [[a]] -> [[a]]

bpMat' :: Int -> [[a]] -> [[a]]

Another Block Partitioning

detMat :: (Eq a, Fractional a) => [[a]] -> a

Determinant for Double List - Order ~ 4^n

invMat :: (Eq a, Fractional a) => [[a]] -> [[a]]

Inverse for Double List - Order ~ n * 2^n