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Language	Haskell2010

Math.Matrix.Vector1

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Orphan instances

Documentation

grid :: (Applicative n, Applicative (f \\\ n), ProjectionSpace f n, ProjectionSpace g n', ProjectionSpace g n'') => (n :*: n') a -> (n :*: (g \\\ n')) a -> ((f \\\ n) :*: n'') a -> ((f \\\ n) :*: (g \\\ n'')) a -> (f :*: g) a Source #

prefixMatrix :: (Applicative (f \\\ Vector1), ProjectionSpace f Vector1, ProjectionSpace g Vector1) => a -> (f \\\ Vector1) a -> (g \\\ Vector1) a -> ((f \\\ Vector1) :*: (g \\\ Vector1)) a -> (f :*: g) a Source #

vertical :: Functor v => v a -> (v :*: Vector1) a Source #

horizontal :: Functor v => v a -> (Vector1 :*: v) a Source #

bra :: (Functor v, RealFloat a) => v (Complex a) -> (Vector1 :*: v) (Complex a) Source #

ket :: Functor m => m a -> (m :*: Vector1) a Source #

(%<|>%) :: (Scalar (g (Complex a)) ~ Complex a, InnerProductSpace (g (Complex a)), Transposable g Vector1 (Complex a), RealFloat a) => g (Complex a) -> g (Complex a) -> Scalar (g (Complex a)) Source #

type Matrix1 a = (Vector1 :*: Vector1) a Source #

matrix1 :: a -> Matrix1 a Source #

inVector1 :: (Vector1 a -> Vector1 b) -> a -> b Source #

inVector1_binary :: (Vector1 a -> Vector1 b -> Vector1 c) -> a -> b -> c Source #

diagonal_projections1 :: Vector1 (Vector1 a -> a) Source #

Orphan instances

Foldable Vector1 Source #
Instance details Methods fold :: Monoid m => Vector1 m -> m # foldMap :: Monoid m => (a -> m) -> Vector1 a -> m # foldMap' :: Monoid m => (a -> m) -> Vector1 a -> m # foldr :: (a -> b -> b) -> b -> Vector1 a -> b # foldr' :: (a -> b -> b) -> b -> Vector1 a -> b # foldl :: (b -> a -> b) -> b -> Vector1 a -> b # foldl' :: (b -> a -> b) -> b -> Vector1 a -> b # foldr1 :: (a -> a -> a) -> Vector1 a -> a # foldl1 :: (a -> a -> a) -> Vector1 a -> a # toList :: Vector1 a -> [a] # null :: Vector1 a -> Bool # length :: Vector1 a -> Int # elem :: Eq a => a -> Vector1 a -> Bool # maximum :: Ord a => Vector1 a -> a # minimum :: Ord a => Vector1 a -> a # sum :: Num a => Vector1 a -> a # product :: Num a => Vector1 a -> a #
Traversable Vector1 Source #
Instance details Methods traverse :: Applicative f => (a -> f b) -> Vector1 a -> f (Vector1 b) # sequenceA :: Applicative f => Vector1 (f a) -> f (Vector1 a) # mapM :: Monad m => (a -> m b) -> Vector1 a -> m (Vector1 b) # sequence :: Monad m => Vector1 (m a) -> m (Vector1 a) #
Applicative Vector1 Source #
Instance details Methods pure :: a -> Vector1 a # (<>) :: Vector1 (a -> b) -> Vector1 a -> Vector1 b # liftA2 :: (a -> b -> c) -> Vector1 a -> Vector1 b -> Vector1 c # (>) :: Vector1 a -> Vector1 b -> Vector1 b # (<*) :: Vector1 a -> Vector1 b -> Vector1 a #
Functor Vector1 Source #
Instance details Methods fmap :: (a -> b) -> Vector1 a -> Vector1 b # (<$) :: a -> Vector1 b -> Vector1 a #
Monad Vector1 Source #
Instance details Methods (>>=) :: Vector1 a -> (a -> Vector1 b) -> Vector1 b # (>>) :: Vector1 a -> Vector1 b -> Vector1 b # return :: a -> Vector1 a #
PpShowF Vector1 Source #
Instance details Methods ppf :: PpShow a => Vector1 a -> Doc Source #
PpShowVerticalF Vector1 Source #
Instance details Methods ppf_vertical :: PpShow a => Vector1 a -> Doc Source #
Num a => Diagonalizable Vector1 a Source #
Instance details Methods identity_impl :: Vector1 Integer -> (Vector1 :: Vector1) a Source # identity :: (Vector1 :: Vector1) a Source # diagonal_impl :: (Vector1 :: Vector1) a -> Vector1 a Source # diagonal_matrix_impl :: Vector1 a -> (Vector1 :: Vector1) a Source #
Num a => Indexable Vector1 a Source #
Instance details Methods diagonal_projections :: Vector1 (Index Vector1 a) Source # basis_vector :: Index Vector1 a -> Vector1 a Source # index_project :: Index Vector1 a -> Vector1 a -> a Source # indexable_indices :: Vector1 a Source #
ProjectionSpace Vector1 Vector1 Source #
Instance details Associated Types data (Vector1 \\\ Vector1) a Source # Methods project_first :: Vector1 a -> Vector1 a Source # project_second :: Vector1 a -> (Vector1 \\\ Vector1) a Source # join_vector :: Vector1 a -> (Vector1 \\\ Vector1) a -> Vector1 a Source #
Num a => Traceable Vector1 a Source #
Instance details Methods trace_impl :: (Vector1 :: Vector1) a -> a Source # determinant_impl :: (Vector1 :: Vector1) a -> a Source # vector_dimension :: Vector1 a -> a Source #
Num a => LinearTransform Vector1 Vector1 a Source #
Instance details Methods (<>>) :: Vector1 a -> (Vector1 :: Vector1) a -> Vector1 a Source # (<<>) :: (Vector1 :: Vector1) a -> Vector1 a -> Vector1 a Source #
Transposable Vector1 Vector1 a Source #
Instance details Methods transpose_impl :: (Vector1 :: Vector1) a -> (Vector1 :: Vector1) a Source #
Transposable Stream Vector1 a Source #
Instance details Methods transpose_impl :: (Stream :: Vector1) a -> (Vector1 :: Stream) a Source #
FunctorArrow Vector1 (->) (->) Source #
Instance details Methods amap :: forall (c :: k) (d :: k). (c -> d) -> Vector1 c -> Vector1 d Source #
Infinitesimal str a => Infinitesimal str (Vector1 a) Source #
Instance details Methods epsilon_closure :: Closure str (Vector1 a) Source # infinite_closure :: Closure str (Vector1 a) Source # minus_infinite_closure :: Closure str (Vector1 a) Source # nan_closure :: Closure str (Vector1 a) Source # epsilon_stream :: str (Vector1 a) Source # infinite_stream :: str (Vector1 a) Source # minus_infinite_stream :: str (Vector1 a) Source #
Limiting str a => Limiting str (Vector1 a) Source #
Instance details Associated Types data Closure str (Vector1 a) Source # Methods limit :: str (Vector1 a) -> Closure str (Vector1 a) Source # approximations :: Closure str (Vector1 a) -> str (Vector1 a) Source #
Transposable Vector1 ((->) row) a Source #
Instance details Methods transpose_impl :: (Vector1 :: (->) row) a -> ((->) row :: Vector1) a Source #
Data a => Data (Vector1 a) Source #
Instance details Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Vector1 a -> c (Vector1 a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Vector1 a) # toConstr :: Vector1 a -> Constr # dataTypeOf :: Vector1 a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Vector1 a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Vector1 a)) # gmapT :: (forall b. Data b => b -> b) -> Vector1 a -> Vector1 a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Vector1 a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Vector1 a -> r # gmapQ :: (forall d. Data d => d -> u) -> Vector1 a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Vector1 a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Vector1 a -> m (Vector1 a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Vector1 a -> m (Vector1 a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Vector1 a -> m (Vector1 a) #
Num a => Monoid (Vector1 a) Source #
Instance details Methods mempty :: Vector1 a # mappend :: Vector1 a -> Vector1 a -> Vector1 a # mconcat :: [Vector1 a] -> Vector1 a #
Num a => Semigroup (Vector1 a) Source #
Instance details Methods (<>) :: Vector1 a -> Vector1 a -> Vector1 a # sconcat :: NonEmpty (Vector1 a) -> Vector1 a # stimes :: Integral b => b -> Vector1 a -> Vector1 a #
Floating a => Floating (Vector1 a) Source #
Instance details Methods pi :: Vector1 a # exp :: Vector1 a -> Vector1 a # log :: Vector1 a -> Vector1 a # sqrt :: Vector1 a -> Vector1 a # (**) :: Vector1 a -> Vector1 a -> Vector1 a # logBase :: Vector1 a -> Vector1 a -> Vector1 a # sin :: Vector1 a -> Vector1 a # cos :: Vector1 a -> Vector1 a # tan :: Vector1 a -> Vector1 a # asin :: Vector1 a -> Vector1 a # acos :: Vector1 a -> Vector1 a # atan :: Vector1 a -> Vector1 a # sinh :: Vector1 a -> Vector1 a # cosh :: Vector1 a -> Vector1 a # tanh :: Vector1 a -> Vector1 a # asinh :: Vector1 a -> Vector1 a # acosh :: Vector1 a -> Vector1 a # atanh :: Vector1 a -> Vector1 a # log1p :: Vector1 a -> Vector1 a # expm1 :: Vector1 a -> Vector1 a # log1pexp :: Vector1 a -> Vector1 a # log1mexp :: Vector1 a -> Vector1 a #
Generic a => Generic (Vector1 a) Source #
Instance details Associated Types type Rep (Vector1 a) :: Type -> Type # Methods from :: Vector1 a -> Rep (Vector1 a) x # to :: Rep (Vector1 a) x -> Vector1 a #
Num a => Num (Vector1 a) Source #
Instance details Methods (+) :: Vector1 a -> Vector1 a -> Vector1 a # (-) :: Vector1 a -> Vector1 a -> Vector1 a # (*) :: Vector1 a -> Vector1 a -> Vector1 a # negate :: Vector1 a -> Vector1 a # abs :: Vector1 a -> Vector1 a # signum :: Vector1 a -> Vector1 a # fromInteger :: Integer -> Vector1 a #
Read a => Read (Vector1 a) Source #
Instance details Methods readsPrec :: Int -> ReadS (Vector1 a) # readList :: ReadS [Vector1 a] # readPrec :: ReadPrec (Vector1 a) # readListPrec :: ReadPrec [Vector1 a] #
Fractional a => Fractional (Vector1 a) Source #
Instance details Methods (/) :: Vector1 a -> Vector1 a -> Vector1 a # recip :: Vector1 a -> Vector1 a # fromRational :: Rational -> Vector1 a #
Show a => Show (Vector1 a) Source #
Instance details Methods showsPrec :: Int -> Vector1 a -> ShowS # show :: Vector1 a -> String # showList :: [Vector1 a] -> ShowS #
Binary s => Binary (Vector1 s) Source #
Instance details Methods put :: Vector1 s -> Put # get :: Get (Vector1 s) # putList :: [Vector1 s] -> Put #
ConjugateSymmetric a => ConjugateSymmetric (Vector1 a) Source #
Instance details Methods conj :: Vector1 a -> Vector1 a Source #
Num a => CoordinateSpace (Vector1 a) Source #
Instance details Associated Types type Coordinate (Vector1 a) Source # Methods index :: Coordinate (Vector1 a) -> Vector1 a -> Scalar (Vector1 a) Source # listVector :: [Scalar (Vector1 a)] -> Vector1 a Source # dimension_size :: Vector1 a -> Int Source # coordinates :: Vector1 a -> [Coordinate (Vector1 a)] Source #
(Num a, ConjugateSymmetric a) => InnerProductSpace (Vector1 a) Source #
Instance details Methods (%.) :: Vector1 a -> Vector1 a -> Scalar (Vector1 a) Source #
(Floating a, ConjugateSymmetric a) => NormedSpace (Vector1 a) Source #
Instance details Methods norm :: Vector1 a -> Scalar (Vector1 a) Source # norm_squared :: Vector1 a -> Scalar (Vector1 a) Source #
Num a => StandardBasis (Vector1 a) Source #
Instance details Methods unit_vectors :: [Vector1 a] Source #
Num a => VectorSpace (Vector1 a) Source #
Instance details Associated Types type Scalar (Vector1 a) Source # Methods vzero :: Vector1 a Source # vnegate :: Vector1 a -> Vector1 a Source # (%+) :: Vector1 a -> Vector1 a -> Vector1 a Source # (%*) :: Scalar (Vector1 a) -> Vector1 a -> Vector1 a Source #
DifferentiallyClosed a => DifferentiallyClosed (Vector1 a) Source #
Instance details Methods derivate :: (Vector1 a -> Vector1 a) -> Vector1 a -> Vector1 a Source # integral :: (Vector1 a, Vector1 a) -> (Vector1 a -> Vector1 a) -> Vector1 a Source #
MedianAlgebra a => MedianAlgebra (Vector1 a) Source #
Instance details Methods med :: Vector1 a -> Vector1 a -> Vector1 a -> Vector1 a Source #
PpShow a => PpShow (Vector1 a) Source #
Instance details Methods pp :: Vector1 a -> Doc Source #
Universe a => Universe (Vector1 a) Source #
Instance details Methods all_elements :: [Vector1 a] Source #
Eq a => Eq (Vector1 a) Source #
Instance details Methods (==) :: Vector1 a -> Vector1 a -> Bool # (/=) :: Vector1 a -> Vector1 a -> Bool #
Ord a => Ord (Vector1 a) Source #
Instance details Methods compare :: Vector1 a -> Vector1 a -> Ordering # (<) :: Vector1 a -> Vector1 a -> Bool # (<=) :: Vector1 a -> Vector1 a -> Bool # (>) :: Vector1 a -> Vector1 a -> Bool # (>=) :: Vector1 a -> Vector1 a -> Bool # max :: Vector1 a -> Vector1 a -> Vector1 a # min :: Vector1 a -> Vector1 a -> Vector1 a #
Functor (Vector1 \\\ Vector1) Source #
Instance details Methods fmap :: (a -> b) -> (Vector1 \\\ Vector1) a -> (Vector1 \\\ Vector1) b # (<$) :: a -> (Vector1 \\\ Vector1) b -> (Vector1 \\\ Vector1) a #
Transposable ((->) row) Vector1 a Source #
Instance details Methods transpose_impl :: ((->) row :: Vector1) a -> (Vector1 :: (->) row) a Source #
Show (f a) => Show ((Vector1 :*: f) a) Source #
Instance details Methods showsPrec :: Int -> (Vector1 :: f) a -> ShowS # show :: (Vector1 :: f) a -> String # showList :: [(Vector1 :*: f) a] -> ShowS #
Num a => VectorSpace ((Vector1 :*: Vector1) a) Source #
Instance details Associated Types type Scalar ((Vector1 :: Vector1) a) Source # Methods vzero :: (Vector1 :: Vector1) a Source # vnegate :: (Vector1 :: Vector1) a -> (Vector1 :: Vector1) a Source # (%+) :: (Vector1 :: Vector1) a -> (Vector1 :: Vector1) a -> (Vector1 :: Vector1) a Source # (%) :: Scalar ((Vector1 :: Vector1) a) -> (Vector1 :: Vector1) a -> (Vector1 :*: Vector1) a Source #