MonadZip Vector2 Source #
Instance details Methods mzip :: Vector2 a -> Vector2 b -> Vector2 (a, b) # mzipWith :: (a -> b -> c) -> Vector2 a -> Vector2 b -> Vector2 c # munzip :: Vector2 (a, b) -> (Vector2 a, Vector2 b) #
Foldable Vector2 Source #
Instance details Methods fold :: Monoid m => Vector2 m -> m # foldMap :: Monoid m => (a -> m) -> Vector2 a -> m # foldMap' :: Monoid m => (a -> m) -> Vector2 a -> m # foldr :: (a -> b -> b) -> b -> Vector2 a -> b # foldr' :: (a -> b -> b) -> b -> Vector2 a -> b # foldl :: (b -> a -> b) -> b -> Vector2 a -> b # foldl' :: (b -> a -> b) -> b -> Vector2 a -> b # foldr1 :: (a -> a -> a) -> Vector2 a -> a # foldl1 :: (a -> a -> a) -> Vector2 a -> a # toList :: Vector2 a -> [a] # null :: Vector2 a -> Bool # length :: Vector2 a -> Int # elem :: Eq a => a -> Vector2 a -> Bool # maximum :: Ord a => Vector2 a -> a # minimum :: Ord a => Vector2 a -> a # sum :: Num a => Vector2 a -> a # product :: Num a => Vector2 a -> a #
Traversable Vector2 Source #
Instance details Methods traverse :: Applicative f => (a -> f b) -> Vector2 a -> f (Vector2 b) # sequenceA :: Applicative f => Vector2 (f a) -> f (Vector2 a) # mapM :: Monad m => (a -> m b) -> Vector2 a -> m (Vector2 b) # sequence :: Monad m => Vector2 (m a) -> m (Vector2 a) #
Applicative Vector2 Source #
Instance details Methods pure :: a -> Vector2 a # (<>) :: Vector2 (a -> b) -> Vector2 a -> Vector2 b # liftA2 :: (a -> b -> c) -> Vector2 a -> Vector2 b -> Vector2 c # (>) :: Vector2 a -> Vector2 b -> Vector2 b # (<*) :: Vector2 a -> Vector2 b -> Vector2 a #
Functor Vector2 Source #
Instance details Methods fmap :: (a -> b) -> Vector2 a -> Vector2 b # (<$) :: a -> Vector2 b -> Vector2 a #
Monad Vector2 Source #
Instance details Methods (>>=) :: Vector2 a -> (a -> Vector2 b) -> Vector2 b # (>>) :: Vector2 a -> Vector2 b -> Vector2 b # return :: a -> Vector2 a #
UpdateableMatrixDimension Vector2 Source #
Instance details Methods write_row :: Applicative h => h a -> Vector2 ((Vector2 :: h) a -> (Vector2 :: h) a) Source # write_column :: Applicative h => h a -> Vector2 ((h :: Vector2) a -> (h :: Vector2) a) Source #
DifferentialOperator Vector2 Source #
Instance details Methods partial :: DifferentiallyClosed a => (Vector2 a -> a) -> Vector2 a -> Vector2 a Source #
CircularComonad Vector2 Source #
Instance details Methods rotate :: Vector2 a -> Vector2 a Source #
Comonad Vector2 Source #
Instance details Methods extract :: Vector2 a -> a Source # duplicate :: Vector2 a -> Vector2 (Vector2 a) Source # extend :: (Vector2 a -> b) -> Vector2 a -> Vector2 b Source # (=>>) :: Vector2 a -> (Vector2 a -> b) -> Vector2 b Source # (.>>) :: Vector2 a -> b -> Vector2 b Source #
PpShowF Vector2 Source #
Instance details Methods ppf :: PpShow a => Vector2 a -> Doc Source #
PpShowVerticalF Vector2 Source #
Instance details Methods ppf_vertical :: PpShow a => Vector2 a -> Doc Source #
AppendableVector Vector1 Vector1 Source #
Instance details Associated Types type Vector1 :+: Vector1 :: Type -> Type Source # Methods (\|\|>>) :: Vector1 a -> Vector1 a -> (Vector1 :+: Vector1) a Source #
CodiagonalMatrix Vector2 a Source #
Instance details Associated Types data Codiagonal Vector2 a Source # type Vector2 \\ a Source # Methods codiagonal_impl :: (Vector2 :: Vector2) a -> Codiagonal Vector2 a Source # (\|\\|) :: Vector2 a -> Codiagonal Vector2 a -> (Vector2 :: Vector2) a Source # down_project :: Codiagonal Vector2 a -> Vector2 \\ a Source # right_project :: Codiagonal Vector2 a -> Vector2 \\ a Source #
Num a => Diagonalizable Vector2 a Source #
Instance details Methods identity_impl :: Vector2 Integer -> (Vector2 :: Vector2) a Source # identity :: (Vector2 :: Vector2) a Source # diagonal_impl :: (Vector2 :: Vector2) a -> Vector2 a Source # diagonal_matrix_impl :: Vector2 a -> (Vector2 :: Vector2) a Source #
Floating a => EigenDecomposable Vector2 a Source #
Instance details Methods eigenvalues :: (Vector2 :*: Vector2) a -> Vector2 a Source #
Num a => Indexable Vector2 a Source #
Instance details Methods diagonal_projections :: Vector2 (Index Vector2 a) Source # basis_vector :: Index Vector2 a -> Vector2 a Source # index_project :: Index Vector2 a -> Vector2 a -> a Source # indexable_indices :: Vector2 a Source #
Fractional a => Invertible Vector2 a Source #
Instance details Methods cofactor_impl :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a Source # adjucate_impl :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a Source # inverse_impl :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a Source #
ProjectionSpace Vector2 Vector1 Source #
Instance details Associated Types data (Vector2 \\\ Vector1) a Source # Methods project_first :: Vector2 a -> Vector1 a Source # project_second :: Vector2 a -> (Vector2 \\\ Vector1) a Source # join_vector :: Vector1 a -> (Vector2 \\\ Vector1) a -> Vector2 a Source #
SplittableVector Vector1 Vector1 Source #
Instance details Methods vsplit :: (Vector1 :+: Vector1) a -> (Vector1 a, Vector1 a) Source #
Num a => Traceable Vector2 a Source #
Instance details Methods trace_impl :: (Vector2 :: Vector2) a -> a Source # determinant_impl :: (Vector2 :: Vector2) a -> a Source # vector_dimension :: Vector2 a -> a Source #
(ConjugateSymmetric a, Num a) => LinearTransform Vector1 Vector2 a Source #
Instance details Methods (<>>) :: Vector2 a -> (Vector1 :: Vector2) a -> Vector1 a Source # (<<>) :: (Vector1 :: Vector2) a -> Vector1 a -> Vector2 a Source #
(ConjugateSymmetric a, Num a) => LinearTransform Vector2 Vector1 a Source #
Instance details Methods (<>>) :: Vector1 a -> (Vector2 :: Vector1) a -> Vector2 a Source # (<<>) :: (Vector2 :: Vector1) a -> Vector2 a -> Vector1 a Source #
(ConjugateSymmetric a, Num a) => LinearTransform Vector2 Vector2 a Source #
Instance details Methods (<>>) :: Vector2 a -> (Vector2 :: Vector2) a -> Vector2 a Source # (<<>) :: (Vector2 :: Vector2) a -> Vector2 a -> Vector2 a Source #
Transposable Vector1 Vector2 a Source #
Instance details Methods transpose_impl :: (Vector1 :: Vector2) a -> (Vector2 :: Vector1) a Source #
Transposable Vector2 Vector1 a Source #
Instance details Methods transpose_impl :: (Vector2 :: Vector1) a -> (Vector1 :: Vector2) a Source #
Transposable Vector2 Vector2 a Source #
Instance details Methods transpose_impl :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a Source #
Transposable Stream Vector2 a Source #
Instance details Methods transpose_impl :: (Stream :: Vector2) a -> (Vector2 :: Stream) a Source #
FunctorArrow Vector2 (:==:) (:==:) Source #
Instance details Methods amap :: forall (c :: k) (d :: k). (c :==: d) -> Vector2 c :==: Vector2 d Source #
(Limiting str a, Monad str) => Limiting str (Vector2 a) Source #
Instance details Associated Types data Closure str (Vector2 a) Source # Methods limit :: str (Vector2 a) -> Closure str (Vector2 a) Source # approximations :: Closure str (Vector2 a) -> str (Vector2 a) Source #
Transposable Vector2 ((->) row) a Source #
Instance details Methods transpose_impl :: (Vector2 :: (->) row) a -> ((->) row :: Vector2) a Source #
Data a => Data (Vector2 a) Source #
Instance details Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Vector2 a -> c (Vector2 a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Vector2 a) # toConstr :: Vector2 a -> Constr # dataTypeOf :: Vector2 a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Vector2 a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Vector2 a)) # gmapT :: (forall b. Data b => b -> b) -> Vector2 a -> Vector2 a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Vector2 a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Vector2 a -> r # gmapQ :: (forall d. Data d => d -> u) -> Vector2 a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Vector2 a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Vector2 a -> m (Vector2 a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Vector2 a -> m (Vector2 a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Vector2 a -> m (Vector2 a) #
Applicative (Codiagonal Vector2) Source #
Instance details Methods pure :: a -> Codiagonal Vector2 a # (<>) :: Codiagonal Vector2 (a -> b) -> Codiagonal Vector2 a -> Codiagonal Vector2 b # liftA2 :: (a -> b -> c) -> Codiagonal Vector2 a -> Codiagonal Vector2 b -> Codiagonal Vector2 c # (>) :: Codiagonal Vector2 a -> Codiagonal Vector2 b -> Codiagonal Vector2 b # (<*) :: Codiagonal Vector2 a -> Codiagonal Vector2 b -> Codiagonal Vector2 a #
Functor (Codiagonal Vector2) Source #
Instance details Methods fmap :: (a -> b) -> Codiagonal Vector2 a -> Codiagonal Vector2 b # (<$) :: a -> Codiagonal Vector2 b -> Codiagonal Vector2 a #
Num s => Monoid (Vector2 s) Source #
Instance details Methods mempty :: Vector2 s # mappend :: Vector2 s -> Vector2 s -> Vector2 s # mconcat :: [Vector2 s] -> Vector2 s #
Num s => Semigroup (Vector2 s) Source #
Instance details Methods (<>) :: Vector2 s -> Vector2 s -> Vector2 s # sconcat :: NonEmpty (Vector2 s) -> Vector2 s # stimes :: Integral b => b -> Vector2 s -> Vector2 s #
Generic a => Generic (Vector2 a) Source #
Instance details Associated Types type Rep (Vector2 a) :: Type -> Type # Methods from :: Vector2 a -> Rep (Vector2 a) x # to :: Rep (Vector2 a) x -> Vector2 a #
Num a => Num (Vector2 a) Source #
Instance details Methods (+) :: Vector2 a -> Vector2 a -> Vector2 a # (-) :: Vector2 a -> Vector2 a -> Vector2 a # (*) :: Vector2 a -> Vector2 a -> Vector2 a # negate :: Vector2 a -> Vector2 a # abs :: Vector2 a -> Vector2 a # signum :: Vector2 a -> Vector2 a # fromInteger :: Integer -> Vector2 a #
Read a => Read (Vector2 a) Source #
Instance details Methods readsPrec :: Int -> ReadS (Vector2 a) # readList :: ReadS [Vector2 a] # readPrec :: ReadPrec (Vector2 a) # readListPrec :: ReadPrec [Vector2 a] #
Show a => Show (Vector2 a) Source #
Instance details Methods showsPrec :: Int -> Vector2 a -> ShowS # show :: Vector2 a -> String # showList :: [Vector2 a] -> ShowS #
Binary s => Binary (Vector2 s) Source #
Instance details Methods put :: Vector2 s -> Put # get :: Get (Vector2 s) # putList :: [Vector2 s] -> Put #
ConjugateSymmetric a => ConjugateSymmetric (Vector2 a) Source #
Instance details Methods conj :: Vector2 a -> Vector2 a Source #
Num a => CoordinateSpace (Vector2 a) Source #
Instance details Associated Types type Coordinate (Vector2 a) Source # Methods index :: Coordinate (Vector2 a) -> Vector2 a -> Scalar (Vector2 a) Source # listVector :: [Scalar (Vector2 a)] -> Vector2 a Source # dimension_size :: Vector2 a -> Int Source # coordinates :: Vector2 a -> [Coordinate (Vector2 a)] Source #
(Num a, ConjugateSymmetric a) => InnerProductSpace (Vector2 a) Source #
Instance details Methods (%.) :: Vector2 a -> Vector2 a -> Scalar (Vector2 a) Source #
(Floating a, ConjugateSymmetric a) => NormedSpace (Vector2 a) Source #
Instance details Methods norm :: Vector2 a -> Scalar (Vector2 a) Source # norm_squared :: Vector2 a -> Scalar (Vector2 a) Source #
StandardBasis (Vector2 (Vector2 Int)) Source #
Instance details Methods unit_vectors :: [Vector2 (Vector2 Int)] Source #
StandardBasis (Vector2 Int) Source #
Instance details Methods unit_vectors :: [Vector2 Int] Source #
Num a => StandardBasis (Vector2 a) Source #
Instance details Methods unit_vectors :: [Vector2 a] Source #
Num a => VectorSpace (Vector2 a) Source #
Instance details Associated Types type Scalar (Vector2 a) Source # Methods vzero :: Vector2 a Source # vnegate :: Vector2 a -> Vector2 a Source # (%+) :: Vector2 a -> Vector2 a -> Vector2 a Source # (%*) :: Scalar (Vector2 a) -> Vector2 a -> Vector2 a Source #
MedianAlgebra s => MedianAlgebra (Vector2 s) Source #
Instance details Methods med :: Vector2 s -> Vector2 s -> Vector2 s -> Vector2 s Source #
PpShow a => PpShow (Vector2 a) Source #
Instance details Methods pp :: Vector2 a -> Doc Source #
Universe a => Universe (Vector2 a) Source #
Instance details Methods all_elements :: [Vector2 a] Source #
Visitor (Vector2 a) Source #
Instance details Associated Types data Fold (Vector2 a) :: Type -> Type Source # Methods visit :: Fold (Vector2 a) a0 -> Vector2 a -> a0 Source #
Eq a => Eq (Vector2 a) Source #
Instance details Methods (==) :: Vector2 a -> Vector2 a -> Bool # (/=) :: Vector2 a -> Vector2 a -> Bool #
Ord a => Ord (Vector2 a) Source #
Instance details Methods compare :: Vector2 a -> Vector2 a -> Ordering # (<) :: Vector2 a -> Vector2 a -> Bool # (<=) :: Vector2 a -> Vector2 a -> Bool # (>) :: Vector2 a -> Vector2 a -> Bool # (>=) :: Vector2 a -> Vector2 a -> Bool # max :: Vector2 a -> Vector2 a -> Vector2 a # min :: Vector2 a -> Vector2 a -> Vector2 a #
Applicative (Vector2 \\\ Vector1) Source #
Instance details Methods pure :: a -> (Vector2 \\\ Vector1) a # (<>) :: (Vector2 \\\ Vector1) (a -> b) -> (Vector2 \\\ Vector1) a -> (Vector2 \\\ Vector1) b # liftA2 :: (a -> b -> c) -> (Vector2 \\\ Vector1) a -> (Vector2 \\\ Vector1) b -> (Vector2 \\\ Vector1) c # (>) :: (Vector2 \\\ Vector1) a -> (Vector2 \\\ Vector1) b -> (Vector2 \\\ Vector1) b # (<*) :: (Vector2 \\\ Vector1) a -> (Vector2 \\\ Vector1) b -> (Vector2 \\\ Vector1) a #
Functor (Vector2 \\\ Vector1) Source #
Instance details Methods fmap :: (a -> b) -> (Vector2 \\\ Vector1) a -> (Vector2 \\\ Vector1) b # (<$) :: a -> (Vector2 \\\ Vector1) b -> (Vector2 \\\ Vector1) a #
Show a => Show (Codiagonal Vector2 a) Source #
Instance details Methods showsPrec :: Int -> Codiagonal Vector2 a -> ShowS # show :: Codiagonal Vector2 a -> String # showList :: [Codiagonal Vector2 a] -> ShowS #
Transposable ((->) row) Vector2 a Source #
Instance details Methods transpose_impl :: ((->) row :: Vector2) a -> (Vector2 :: (->) row) a Source #
Num a => Indexable (Vector2 :*: Vector2) a Source #
Instance details Methods diagonal_projections :: (Vector2 :: Vector2) (Index (Vector2 :: Vector2) a) Source # basis_vector :: Index (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a Source # index_project :: Index (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a -> a Source # indexable_indices :: (Vector2 :*: Vector2) a Source #
(Num a, ConjugateSymmetric a) => Monoid ((Vector2 :*: Vector2) a) Source #	see "Lawvere,Rosebrugh: Sets for mathematics", pg. 167.
Instance details Methods mempty :: (Vector2 :: Vector2) a # mappend :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a # mconcat :: [(Vector2 :: Vector2) a] -> (Vector2 :: Vector2) a #
(Num a, ConjugateSymmetric a) => Semigroup ((Vector2 :*: Vector2) a) Source #	see "Lawvere,Rosebrugh: Sets for mathematics", pg. 167.
Instance details Methods (<>) :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a # sconcat :: NonEmpty ((Vector2 :: Vector2) a) -> (Vector2 :: Vector2) a # stimes :: Integral b => b -> (Vector2 :: Vector2) a -> (Vector2 :*: Vector2) a #
(Num a, ConjugateSymmetric a) => Num ((Vector2 :*: Vector2) a) Source #
Instance details Methods (+) :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a # (-) :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a # () :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a # negate :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a # abs :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a # signum :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a # fromInteger :: Integer -> (Vector2 :*: Vector2) a #
Show (f a) => Show ((Vector2 :*: f) a) Source #
Instance details Methods showsPrec :: Int -> (Vector2 :: f) a -> ShowS # show :: (Vector2 :: f) a -> String # showList :: [(Vector2 :*: f) a] -> ShowS #
(Num a, ConjugateSymmetric a) => ConjugateSymmetric ((Vector2 :*: Vector2) a) Source #	https://en.wikipedia.org/wiki/Conjugate_transpose
Instance details Methods conj :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a Source #
Num a => VectorSpace ((Vector1 :*: Vector2) a) Source #
Instance details Associated Types type Scalar ((Vector1 :: Vector2) a) Source # Methods vzero :: (Vector1 :: Vector2) a Source # vnegate :: (Vector1 :: Vector2) a -> (Vector1 :: Vector2) a Source # (%+) :: (Vector1 :: Vector2) a -> (Vector1 :: Vector2) a -> (Vector1 :: Vector2) a Source # (%) :: Scalar ((Vector1 :: Vector2) a) -> (Vector1 :: Vector2) a -> (Vector1 :*: Vector2) a Source #
Num a => VectorSpace ((Vector2 :*: Vector1) a) Source #
Instance details Associated Types type Scalar ((Vector2 :: Vector1) a) Source # Methods vzero :: (Vector2 :: Vector1) a Source # vnegate :: (Vector2 :: Vector1) a -> (Vector2 :: Vector1) a Source # (%+) :: (Vector2 :: Vector1) a -> (Vector2 :: Vector1) a -> (Vector2 :: Vector1) a Source # (%) :: Scalar ((Vector2 :: Vector1) a) -> (Vector2 :: Vector1) a -> (Vector2 :*: Vector1) a Source #
Num a => VectorSpace ((Vector2 :*: Vector2) a) Source #
Instance details Associated Types type Scalar ((Vector2 :: Vector2) a) Source # Methods vzero :: (Vector2 :: Vector2) a Source # vnegate :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a Source # (%+) :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a Source # (%) :: Scalar ((Vector2 :: Vector2) a) -> (Vector2 :: Vector2) a -> (Vector2 :*: Vector2) a Source #
(Fractional a, ConjugateSymmetric a) => Group ((Vector2 :*: Vector2) a) Source #
Instance details Methods ginvert :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a Source #
PpShow (f a) => PpShow ((Vector2 :*: f) a) Source #
Instance details Methods pp :: (Vector2 :*: f) a -> Doc Source #