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Language	Haskell2010

Math.Matrix.Vector3

Contents

Orphan instances

Synopsis

data Vector3 s = Vector3 {
- xcoord3 :: !s
- ycoord3 :: !s
- zcoord3 :: !s
}
type ComplexVector3 a = (Vector3 :*: Complex) a
dim3 :: Vector3 Integer
i3 :: Num a => Vector3 a
j3 :: Num a => Vector3 a
k3 :: Num a => Vector3 a
type Matrix3 a = (Vector3 :*: Vector3) a
vec3 :: (a, a, a) -> Vector3 a
finite3 :: Vector3 a -> Vec 3 a
constant3 :: a -> Vector3 a
vec3Unit :: a -> Scalar (Vector3 a)
vec3Counit :: Vector3 (Scalar (Vector3 a)) -> Vector3 a
destructvec3 :: Vector3 a -> (a, a, a)
setx3 :: s -> Vector3 s -> Vector3 s
sety3 :: s -> Vector3 s -> Vector3 s
setz3 :: s -> Vector3 s -> Vector3 s
setEndo :: Vector3 s -> Vector3 (Endo (Vector3 s))
setVectorAction :: Vector3 s -> Vector3 (Vector3 s -> Vector3 s)
updateRow3 :: g a -> Vector3 ((Vector3 :*: g) a -> (Vector3 :*: g) a)
updateColumn3 :: Applicative f => f a -> Vector3 ((f :*: Vector3) a -> (f :*: Vector3) a)
removex3 :: Vector3 a -> Vector2 a
removey3 :: Vector3 a -> Vector2 a
removez3 :: Vector3 a -> Vector2 a
remove3 :: Vector3 (Vector3 a -> Vector2 a)
determinancett3 :: Num a => Determinance Vector3 Vector3 Vector2 Vector2 Vector2 a a a
remove_index3 :: Matrix3 a -> Matrix3 (Matrix2 a)
cofactor3 :: Num a => Matrix3 a -> Matrix3 a
adjucate3 :: Num a => Matrix3 a -> Matrix3 a
inverse3 :: Fractional a => Matrix3 a -> Matrix3 a
set3 :: Vector3 a -> Vector3 a -> (Vector3 :*: Vector3) a
swap3 :: (Vector3 :*: Vector3) (Vector3 a -> Vector3 a)
mul3 :: VectorSpace s => Scalar s -> Vector3 (Vector3 s -> Vector3 s)
add3Matrix :: VectorSpace a => Scalar a -> ((Vector3 :*: Vector3) :*: Vector3) a -> ((Vector3 :*: Vector3) :*: Vector3) a
add3 :: VectorSpace s => Scalar s -> (Vector3 :*: Vector3) (Vector3 s -> Vector3 s)
swapxy3 :: Vector3 a -> Vector3 a
swapxz3 :: Vector3 a -> Vector3 a
swapyz3 :: Vector3 a -> Vector3 a
mul3Matrix :: (Num a, VectorSpace a) => Scalar a -> Vector3 ((Vector3 :*: Vector3) a)
signs3 :: Integral a => Matrix3 a
dx3_endo :: Num a => a -> Endo (Vector3 a)
dy3_endo :: Num a => a -> Endo (Vector3 a)
dz3_endo :: Num a => a -> Endo (Vector3 a)
dx3 :: Num a => a -> Vector3 a -> Vector3 a
dy3 :: Num a => a -> Vector3 a -> Vector3 a
dz3 :: Num a => a -> Vector3 a -> Vector3 a
op_dot :: Num b => Vector3 (a -> b) -> a -> b
applicative_matrix :: Num b => Vector3 (b -> b) -> (Vector3 :*: Vector3) b
sum_coordinates3 :: Num a => Vector3 a -> a
cube_norm3 :: Floating a => Vector3 a -> a
nth_norm3 :: Floating a => a -> Vector3 a -> a
index3 :: Vector3 (Vector3 a -> a)
mapBasis :: Numeric a => (Vector3 a -> Vector3 a) -> Vector3 a -> Vector3 a
functionMatrix3 :: Numeric a => (Vector3 a -> Vector3 a) -> Matrix3 a
splitx :: Vector3 s -> (Vector2 s, Vector1 s)
splity :: Vector3 s -> (Vector2 s, Vector1 s)
splitz :: Vector3 s -> (Vector2 s, Vector1 s)
trace3 :: Num a => Matrix3 a -> a
vector3 :: [a] -> Vector3 a
cross_product :: Num a => Vector3 a -> Vector3 a -> Vector3 a
cross_product3 :: Num a => (Vector2 :*: Vector3) a -> Vector3 a
xid :: Num a => Vector3 a
yid :: Num a => Vector3 a
zid :: Num a => Vector3 a
identity3 :: Num a => Matrix3 a
matrixPower3 :: (Ord a, ConjugateSymmetric a, Numeric a) => Matrix3 a -> Integer -> Matrix3 a
vectorIndices3 :: Integral a => Vector3 a
matrixIndices3 :: Integral a => (Vector3 :*: Vector3) (a, a)
matrixMultiply3 :: (Ord a, ConjugateSymmetric a, Num a) => Matrix3 a -> Matrix3 a -> Matrix3 a
dot3 :: (Num a, ConjugateSymmetric a) => Vector3 a -> Vector3 a -> a
leftMultiply3Gen :: (Functor f, Num a, ConjugateSymmetric a) => Vector3 a -> (f :*: Vector3) a -> f a
rightMultiply3Gen :: (VectorSpace (f a), ConjugateSymmetric a, Scalar (f a) ~ a) => (Vector3 :*: f) a -> Vector3 a -> f a
leftMultiply3 :: (Num a, ConjugateSymmetric a) => Vector3 a -> Matrix3 a -> Vector3 a
rightMultiply3 :: (Num a, ConjugateSymmetric a) => Matrix3 a -> Vector3 a -> Vector3 a
transpose3 :: Num a => Matrix3 a -> Matrix3 a
transpose3Impl :: Matrix3 a -> Matrix3 a
outer3 :: (a -> b -> c) -> Vector3 a -> Vector3 b -> Matrix3 c
zipWithV3 :: (a -> b -> c) -> Vector3 a -> Vector3 b -> Vector3 c
rotate_x :: Floating a => a -> Matrix3 a
rotate_y :: Floating a => a -> Matrix3 a
rotate_z :: Floating a => a -> Matrix3 a
rotate_coordinates3 :: Vector3 a -> Vector3 a
zero_codiagonal3 :: Num a => Codiagonal Vector3 a
diagonal_matrix3 :: Vector3 a -> (Vector3 :*: Vector3) a -> (Vector3 :*: Vector3) a
matrix3 :: Vector3 a -> Codiagonal Vector3 a -> (Vector3 :*: Vector3) a
codiag3 :: Matrix3 a -> Codiagonal Vector3 a
codiagonal3 :: Matrix3 a -> Vector2 (Vector2 a, Vector2 a)
diagonal3 :: Matrix3 a -> Vector3 a
diagonal_projections3 :: Vector3 (Index Vector3 a)
diagonal3x :: Num a => Matrix3 a -> Vector3 a
diagonal3y :: Num a => Matrix3 a -> Vector3 a
diagonal3z :: Num a => Matrix3 a -> Vector3 a
determinant3 :: Num a => Matrix3 a -> a
determinant3_ :: Num a => Matrix3 a -> a
gram_schmidt3 :: (Fractional (Scalar a), Num a, InnerProductSpace a, VectorSpace a) => Vector3 a -> Vector3 a
eigenvalue3 :: (Floating a, Ord a, ConjugateSymmetric a) => (Vector3 :*: Vector3) a -> Vector3 a
levi_civita3 :: ((Vector3 :*: Vector3) :*: Vector3) Int
cycle3 :: StreamBuilder str => Vector3 a -> str a

Documentation

data Vector3 s Source #

Three element vector

Constructors

Vector3
Fields xcoord3 :: !s ycoord3 :: !s zcoord3 :: !s

Instances

Instances details

MonadZip Vector3 Source #
Instance details Defined in Math.Matrix.Vector3 Methods mzip :: Vector3 a -> Vector3 b -> Vector3 (a, b) # mzipWith :: (a -> b -> c) -> Vector3 a -> Vector3 b -> Vector3 c # munzip :: Vector3 (a, b) -> (Vector3 a, Vector3 b) #
Foldable Vector3 Source #
Instance details Defined in Math.Matrix.Vector3 Methods fold :: Monoid m => Vector3 m -> m # foldMap :: Monoid m => (a -> m) -> Vector3 a -> m # foldMap' :: Monoid m => (a -> m) -> Vector3 a -> m # foldr :: (a -> b -> b) -> b -> Vector3 a -> b # foldr' :: (a -> b -> b) -> b -> Vector3 a -> b # foldl :: (b -> a -> b) -> b -> Vector3 a -> b # foldl' :: (b -> a -> b) -> b -> Vector3 a -> b # foldr1 :: (a -> a -> a) -> Vector3 a -> a # foldl1 :: (a -> a -> a) -> Vector3 a -> a # toList :: Vector3 a -> [a] # null :: Vector3 a -> Bool # length :: Vector3 a -> Int # elem :: Eq a => a -> Vector3 a -> Bool # maximum :: Ord a => Vector3 a -> a # minimum :: Ord a => Vector3 a -> a # sum :: Num a => Vector3 a -> a # product :: Num a => Vector3 a -> a #
Traversable Vector3 Source #
Instance details Defined in Math.Matrix.Vector3 Methods traverse :: Applicative f => (a -> f b) -> Vector3 a -> f (Vector3 b) # sequenceA :: Applicative f => Vector3 (f a) -> f (Vector3 a) # mapM :: Monad m => (a -> m b) -> Vector3 a -> m (Vector3 b) # sequence :: Monad m => Vector3 (m a) -> m (Vector3 a) #
Applicative Vector3 Source #
Instance details Defined in Math.Matrix.Vector3 Methods pure :: a -> Vector3 a # (<>) :: Vector3 (a -> b) -> Vector3 a -> Vector3 b # liftA2 :: (a -> b -> c) -> Vector3 a -> Vector3 b -> Vector3 c # (>) :: Vector3 a -> Vector3 b -> Vector3 b # (<*) :: Vector3 a -> Vector3 b -> Vector3 a #
Functor Vector3 Source #
Instance details Defined in Math.Matrix.Vector3 Methods fmap :: (a -> b) -> Vector3 a -> Vector3 b # (<$) :: a -> Vector3 b -> Vector3 a #
Monad Vector3 Source #
Instance details Defined in Math.Matrix.Vector3 Methods (>>=) :: Vector3 a -> (a -> Vector3 b) -> Vector3 b # (>>) :: Vector3 a -> Vector3 b -> Vector3 b # return :: a -> Vector3 a #
UpdateableMatrixDimension Vector3 Source #
Instance details Defined in Math.Matrix.Vector3 Methods writeRow :: Applicative h => h a -> Vector3 ((Vector3 :: h) a -> (Vector3 :: h) a) Source # writeColumn :: Applicative h => h a -> Vector3 ((h :: Vector3) a -> (h :: Vector3) a) Source #
DifferentialOperator Vector3 Source #
Instance details Defined in Math.Matrix.Linear Methods partial :: DifferentiallyClosed a => (Vector3 a -> a) -> Vector3 a -> Vector3 a Source #
CircularComonad Vector3 Source #
Instance details Defined in Math.Matrix.Vector3 Methods rotate :: Vector3 a -> Vector3 a Source #
Coapplicative Vector3 Source #
Instance details Defined in Math.Matrix.Vector3 Methods coeval :: Vector3 a -> a Source # colambda :: (Vector3 a -> Vector3 b) -> Vector3 (a -> b) Source #
Comonad Vector3 Source #
Instance details Defined in Math.Matrix.Vector3 Methods extract :: Vector3 a -> a Source # duplicate :: Vector3 a -> Vector3 (Vector3 a) Source # extend :: (Vector3 a -> b) -> Vector3 a -> Vector3 b Source # (=>>) :: Vector3 a -> (Vector3 a -> b) -> Vector3 b Source # (.>>) :: Vector3 a -> b -> Vector3 b Source #
FiniteComonad Vector3 Source #
Instance details Defined in Math.Matrix.Vector3 Methods inverseRotate :: Vector3 a -> Vector3 a Source #
PpShowF Vector3 Source #
Instance details Defined in Math.Matrix.Vector3 Methods ppf :: PpShow a => Vector3 a -> Doc Source #
PpShowVerticalF Vector3 Source #
Instance details Defined in Math.Matrix.Vector3 Methods ppfVertical :: PpShow a => Vector3 a -> Doc Source #
Unfoldable Vector3 Source #
Instance details Defined in Math.Matrix.Vector3 Methods unfoldF :: forall (m :: Type -> Type) s a. Monad m => StateT s m a -> StateT s m (Vector3 a) Source #
AppendableVector Vector1 Vector3 Source #
Instance details Defined in Math.Matrix.Vector4 Associated Types type Vector1 :+: Vector3 :: Type -> Type Source # Methods (\|\|>>) :: Vector1 a -> Vector3 a -> (Vector1 :+: Vector3) a Source #
AppendableVector Vector3 Vector1 Source #
Instance details Defined in Math.Matrix.Vector4 Associated Types type Vector3 :+: Vector1 :: Type -> Type Source # Methods (\|\|>>) :: Vector3 a -> Vector1 a -> (Vector3 :+: Vector1) a Source #
AppendableVector Vector3 Stream Source #
Instance details Defined in Math.Number.Stream Associated Types type Vector3 :+: Stream :: Type -> Type Source # Methods (\|\|>>) :: Vector3 a -> Stream a -> (Vector3 :+: Stream) a Source #
CodiagonalMatrix Vector3 a Source #
Instance details Defined in Math.Matrix.Vector3 Associated Types data Codiagonal Vector3 a Source # type Vector3 \\ a Source # Methods codiagonalImpl :: (Vector3 :: Vector3) a -> Codiagonal Vector3 a Source # (\|\\|) :: Vector3 a -> Codiagonal Vector3 a -> (Vector3 :: Vector3) a Source # downProject :: Codiagonal Vector3 a -> Vector3 \\ a Source # rightProject :: Codiagonal Vector3 a -> Vector3 \\ a Source #
Diagonalizable Vector3 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods identity :: (Vector3 :: Vector3) a Source # diagonalImpl :: (Vector3 :: Vector3) a -> Vector3 a Source # diagonalMatrixImpl :: Vector3 a -> (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a Source #
(Floating a, Ord a, ConjugateSymmetric a) => EigenDecomposable Vector3 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods eigenvalues :: (Vector3 :*: Vector3) a -> Vector3 a Source #
Indexable Vector3 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods diagonalProjections :: Vector3 (Index Vector3 a) Source # basisVector :: Index Vector3 a -> a -> Vector3 a -> Vector3 a Source # indexProject :: Index Vector3 a -> Vector3 a -> a Source # indexableIndices :: Vector3 a Source #
(ConjugateSymmetric a, Num a) => InnerProductSpaceFunctor Vector3 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods innerProductF :: Vector3 a -> Vector3 a -> a Source #
Fractional a => Invertible Vector3 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods cofactorImpl :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a Source # adjucateImpl :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a Source # inverseImpl :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a Source #
ProjectionSpace Vector3 Vector1 Source #
Instance details Defined in Math.Matrix.Vector3 Associated Types data (Vector3 \\\ Vector1) a Source # Methods projectFirst :: Vector3 a -> Vector1 a Source # projectSecond :: Vector3 a -> (Vector3 \\\ Vector1) a Source # joinVector :: Vector1 a -> (Vector3 \\\ Vector1) a -> Vector3 a Source #
ProjectionSpace Vector3 Vector2 Source #
Instance details Defined in Math.Matrix.Vector3 Associated Types data (Vector3 \\\ Vector2) a Source # Methods projectFirst :: Vector3 a -> Vector2 a Source # projectSecond :: Vector3 a -> (Vector3 \\\ Vector2) a Source # joinVector :: Vector2 a -> (Vector3 \\\ Vector2) a -> Vector3 a Source #
SplittableVector Vector1 Vector3 Source #
Instance details Defined in Math.Matrix.Vector4 Methods vsplit :: (Vector1 :+: Vector3) a -> (Vector1 a, Vector3 a) Source #
SplittableVector Vector3 Vector1 Source #
Instance details Defined in Math.Matrix.Vector4 Methods vsplit :: (Vector3 :+: Vector1) a -> (Vector3 a, Vector1 a) Source #
Num a => Traceable Vector3 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods traceImpl :: (Vector3 :: Vector3) a -> a Source # determinantImpl :: (Vector3 :: Vector3) a -> a Source # vectorDimension :: Vector3 a -> a Source #
HasIdentityLinear Vector3 LinearMap Source #
Instance details Defined in Math.Matrix.Linear Methods matIdentity :: (Ord a, Num a, ConjugateSymmetric a) => LinearMap (Vector3 a) (Vector3 a) Source #
(ConjugateSymmetric a, Fractional a, Ord a) => LinearInvertible LinearMap Vector3 a Source #
Instance details Defined in Math.Matrix.Linear Methods cofactor :: LinearMap (Vector3 a) (Vector3 a) -> LinearMap (Vector3 a) (Vector3 a) Source # adjucate :: LinearMap (Vector3 a) (Vector3 a) -> LinearMap (Vector3 a) (Vector3 a) Source # inverse :: LinearMap (Vector3 a) (Vector3 a) -> LinearMap (Vector3 a) (Vector3 a) Source #
(ConjugateSymmetric a, Num a, Ord a) => LinearTraceable LinearMap Vector3 a Source #
Instance details Defined in Math.Matrix.Linear Methods determinant :: LinearMap (Vector3 a) (Vector3 a) -> a Source # trace :: LinearMap (Vector3 a) (Vector3 a) -> a Source #
(Num a, Ord a, ConjugateSymmetric a) => LinearTransform Vector1 Vector3 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods (<>>) :: Vector3 a -> (Vector1 :: Vector3) a -> Vector1 a Source # (<<>) :: (Vector1 :: Vector3) a -> Vector1 a -> Vector3 a Source #
(Num a, ConjugateSymmetric a) => LinearTransform Vector2 Vector3 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods (<>>) :: Vector3 a -> (Vector2 :: Vector3) a -> Vector2 a Source # (<<>) :: (Vector2 :: Vector3) a -> Vector2 a -> Vector3 a Source #
(Num a, ConjugateSymmetric a) => LinearTransform Vector3 Vector1 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods (<>>) :: Vector1 a -> (Vector3 :: Vector1) a -> Vector3 a Source # (<<>) :: (Vector3 :: Vector1) a -> Vector3 a -> Vector1 a Source #
(Num a, ConjugateSymmetric a) => LinearTransform Vector3 Vector2 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods (<>>) :: Vector2 a -> (Vector3 :: Vector2) a -> Vector3 a Source # (<<>) :: (Vector3 :: Vector2) a -> Vector3 a -> Vector2 a Source #
LinearTransform Vector3 Vector3 Float Source #
Instance details Defined in Math.Matrix.SIMD Methods (<>>) :: Vector3 Float -> (Vector3 :: Vector3) Float -> Vector3 Float Source # (<<>) :: (Vector3 :: Vector3) Float -> Vector3 Float -> Vector3 Float Source #
(Num a, ConjugateSymmetric a) => LinearTransform Vector3 Vector3 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods (<>>) :: Vector3 a -> (Vector3 :: Vector3) a -> Vector3 a Source # (<<>) :: (Vector3 :: Vector3) a -> Vector3 a -> Vector3 a Source #
(Num a, ConjugateSymmetric a) => LinearTransform Vector3 Vector4 a Source #
Instance details Defined in Math.Matrix.Vector4 Methods (<>>) :: Vector4 a -> (Vector3 :: Vector4) a -> Vector3 a Source # (<<>) :: (Vector3 :: Vector4) a -> Vector3 a -> Vector4 a Source #
(Num a, ConjugateSymmetric a) => LinearTransform Vector4 Vector3 a Source #
Instance details Defined in Math.Matrix.Vector4 Methods (<>>) :: Vector3 a -> (Vector4 :: Vector3) a -> Vector4 a Source # (<<>) :: (Vector4 :: Vector3) a -> Vector4 a -> Vector3 a Source #
(Num a, Ord a, ConjugateSymmetric a) => ProjectionDual Vector3 Dual a Source #
Instance details Defined in Math.Matrix.Linear Methods projectionDual :: Vector3 (Dual (Vector3 a)) Source #
Transposable Vector1 Vector3 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods transposeImpl :: (Vector1 :: Vector3) a -> (Vector3 :: Vector1) a Source #
Transposable Vector2 Vector3 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods transposeImpl :: (Vector2 :: Vector3) a -> (Vector3 :: Vector2) a Source #
Transposable Vector3 Vector1 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods transposeImpl :: (Vector3 :: Vector1) a -> (Vector1 :: Vector3) a Source #
Transposable Vector3 Vector2 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods transposeImpl :: (Vector3 :: Vector2) a -> (Vector2 :: Vector3) a Source #
Transposable Vector3 Vector3 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods transposeImpl :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a Source #
Transposable Vector3 Vector4 a Source #	3 x 4 matrices
Instance details Defined in Math.Matrix.Vector4 Methods transposeImpl :: (Vector3 :: Vector4) a -> (Vector4 :: Vector3) a Source #
Transposable Vector4 Vector3 a Source #	4 x 3 matrices:
Instance details Defined in Math.Matrix.Vector4 Methods transposeImpl :: (Vector4 :: Vector3) a -> (Vector3 :: Vector4) a Source #
Transposable Stream Vector3 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods transposeImpl :: (Stream :: Vector3) a -> (Vector3 :: Stream) a Source #
(Scalar a ~ a, Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Dual Vector3 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Dual a) (Vector3 a) -> (Dual :: Vector3) a Source # linear :: (Dual :: Vector3) a -> LinearMap (Dual a) (Vector3 a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector1 Vector3 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector1 a) (Vector3 a) -> (Vector1 :: Vector3) a Source # linear :: (Vector1 :: Vector3) a -> LinearMap (Vector1 a) (Vector3 a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector2 Vector3 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector2 a) (Vector3 a) -> (Vector2 :: Vector3) a Source # linear :: (Vector2 :: Vector3) a -> LinearMap (Vector2 a) (Vector3 a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector3 Vector1 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector3 a) (Vector1 a) -> (Vector3 :: Vector1) a Source # linear :: (Vector3 :: Vector1) a -> LinearMap (Vector3 a) (Vector1 a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector3 Vector2 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector3 a) (Vector2 a) -> (Vector3 :: Vector2) a Source # linear :: (Vector3 :: Vector2) a -> LinearMap (Vector3 a) (Vector2 a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector3 Vector3 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector3 a) (Vector3 a) -> (Vector3 :: Vector3) a Source # linear :: (Vector3 :: Vector3) a -> LinearMap (Vector3 a) (Vector3 a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector3 Vector4 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector3 a) (Vector4 a) -> (Vector3 :: Vector4) a Source # linear :: (Vector3 :: Vector4) a -> LinearMap (Vector3 a) (Vector4 a) Source #
(Num a, ConjugateSymmetric a, InnerProductSpaceFunctor Stream a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector3 Stream (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector3 a) (Stream a) -> (Vector3 :: Stream) a Source # linear :: (Vector3 :: Stream) a -> LinearMap (Vector3 a) (Stream a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector4 Vector3 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector4 a) (Vector3 a) -> (Vector4 :: Vector3) a Source # linear :: (Vector4 :: Vector3) a -> LinearMap (Vector4 a) (Vector3 a) Source #
(Num a, ConjugateSymmetric a, InnerProductSpaceFunctor Stream a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Stream Vector3 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Stream a) (Vector3 a) -> (Stream :: Vector3) a Source # linear :: (Stream :: Vector3) a -> LinearMap (Stream a) (Vector3 a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector3 Dual (f a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector3 (f a)) (Dual (f a)) -> (Vector3 :: Dual) (f a) Source # linear :: (Vector3 :: Dual) (f a) -> LinearMap (Vector3 (f a)) (Dual (f a)) Source #
(InnerProductSpaceFunctor ((->) col) a, ConjugateSymmetric a, Universe col) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector3 ((->) col :: Type -> Type) (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector3 a) (col -> a) -> (Vector3 :: (->) col) a Source # linear :: (Vector3 :: (->) col) a -> LinearMap (Vector3 a) (col -> a) Source #
(InnerProductSpaceFunctor ((->) row) a, ConjugateSymmetric a, Universe row) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) ((->) row :: Type -> Type) Vector3 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (row -> a) (Vector3 a) -> ((->) row :: Vector3) a Source # linear :: ((->) row :: Vector3) a -> LinearMap (row -> a) (Vector3 a) Source #
Limiting Stream a => Limiting Stream (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 Associated Types data Closure Stream (Vector3 a) Source # Methods limit :: Stream (Vector3 a) -> Closure Stream (Vector3 a) Source # approximations :: Closure Stream (Vector3 a) -> Stream (Vector3 a) Source #
Lift a => Lift (Vector3 a :: Type) Source #
Instance details Defined in Math.Matrix.QuasiQuoter Methods lift :: Quote m => Vector3 a -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Vector3 a -> Code m (Vector3 a) #
(Ord a, Closed a, Num a, ConjugateSymmetric a) => VectorCrossProduct (Vector3 a :: Type) LinearMap Source #
Instance details Defined in Math.Matrix.Linear Methods curl :: LinearMap (Vector3 a) (Vector3 a) -> LinearMap (Vector3 a) (Vector3 a) Source #
(Ord a, Closed a, Num a, ConjugateSymmetric a) => VectorLaplacian (Vector3 a :: Type) LinearMap Source #
Instance details Defined in Math.Matrix.Linear Methods vectorLaplace :: LinearMap (Vector3 a) (Vector3 a) -> LinearMap (Vector3 a) (Vector3 a) Source #
(Num a, Universe col) => LinearTransform Vector3 ((->) col) a Source #
Instance details Defined in Math.Matrix.Simple Methods (<>>) :: (col -> a) -> (Vector3 :: (->) col) a -> Vector3 a Source # (<<>) :: (Vector3 :: (->) col) a -> Vector3 a -> col -> a Source #
Transposable Vector3 ((->) row) a Source #
Instance details Defined in Math.Matrix.Vector3 Methods transposeImpl :: (Vector3 :: (->) row) a -> ((->) row :: Vector3) a Source #
Lift ((Vector3 :*: Vector3) Integer) Source #
Instance details Defined in Math.Matrix.QuasiQuoter Methods lift :: Quote m => (Vector3 :: Vector3) Integer -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => (Vector3 :: Vector3) Integer -> Code m ((Vector3 :*: Vector3) Integer) #
Data a => Data (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Vector3 a -> c (Vector3 a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Vector3 a) # toConstr :: Vector3 a -> Constr # dataTypeOf :: Vector3 a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Vector3 a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Vector3 a)) # gmapT :: (forall b. Data b => b -> b) -> Vector3 a -> Vector3 a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Vector3 a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Vector3 a -> r # gmapQ :: (forall d. Data d => d -> u) -> Vector3 a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Vector3 a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Vector3 a -> m (Vector3 a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Vector3 a -> m (Vector3 a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Vector3 a -> m (Vector3 a) #
Applicative (Codiagonal Vector3) Source #
Instance details Defined in Math.Matrix.Vector3 Methods pure :: a -> Codiagonal Vector3 a # (<>) :: Codiagonal Vector3 (a -> b) -> Codiagonal Vector3 a -> Codiagonal Vector3 b # liftA2 :: (a -> b -> c) -> Codiagonal Vector3 a -> Codiagonal Vector3 b -> Codiagonal Vector3 c # (>) :: Codiagonal Vector3 a -> Codiagonal Vector3 b -> Codiagonal Vector3 b # (<*) :: Codiagonal Vector3 a -> Codiagonal Vector3 b -> Codiagonal Vector3 a #
Functor (Codiagonal Vector3) Source #
Instance details Defined in Math.Matrix.Vector3 Methods fmap :: (a -> b) -> Codiagonal Vector3 a -> Codiagonal Vector3 b # (<$) :: a -> Codiagonal Vector3 b -> Codiagonal Vector3 a #
Num s => Monoid (Vector3 s) Source #
Instance details Defined in Math.Matrix.Vector3 Methods mempty :: Vector3 s # mappend :: Vector3 s -> Vector3 s -> Vector3 s # mconcat :: [Vector3 s] -> Vector3 s #
Num s => Semigroup (Vector3 s) Source #
Instance details Defined in Math.Matrix.Vector3 Methods (<>) :: Vector3 s -> Vector3 s -> Vector3 s # sconcat :: NonEmpty (Vector3 s) -> Vector3 s # stimes :: Integral b => b -> Vector3 s -> Vector3 s #
Generic a => Generic (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 Associated Types type Rep (Vector3 a) :: Type -> Type # Methods from :: Vector3 a -> Rep (Vector3 a) x # to :: Rep (Vector3 a) x -> Vector3 a #
Num a => Num (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods (+) :: Vector3 a -> Vector3 a -> Vector3 a # (-) :: Vector3 a -> Vector3 a -> Vector3 a # (*) :: Vector3 a -> Vector3 a -> Vector3 a # negate :: Vector3 a -> Vector3 a # abs :: Vector3 a -> Vector3 a # signum :: Vector3 a -> Vector3 a # fromInteger :: Integer -> Vector3 a #
Read a => Read (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods readsPrec :: Int -> ReadS (Vector3 a) # readList :: ReadS [Vector3 a] # readPrec :: ReadPrec (Vector3 a) # readListPrec :: ReadPrec [Vector3 a] #
Show a => Show (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods showsPrec :: Int -> Vector3 a -> ShowS # show :: Vector3 a -> String # showList :: [Vector3 a] -> ShowS #
Binary s => Binary (Vector3 s) Source #
Instance details Defined in Math.Matrix.Vector3 Methods put :: Vector3 s -> Put # get :: Get (Vector3 s) # putList :: [Vector3 s] -> Put #
ConjugateSymmetric a => ConjugateSymmetric (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods conj :: Vector3 a -> Vector3 a Source #
Num a => CoordinateSpace (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 Associated Types type Coordinate (Vector3 a) Source # Methods index :: Coordinate (Vector3 a) -> Vector3 a -> Scalar (Vector3 a) Source # listVector :: [Scalar (Vector3 a)] -> Vector3 a Source # dimensionSize :: Vector3 a -> Int Source # coordinates :: Vector3 a -> [Coordinate (Vector3 a)] Source #
InnerProductSpace (Vector3 Float) Source #
Instance details Defined in Math.Matrix.SIMD Methods (%.) :: Vector3 Float -> Vector3 Float -> Scalar (Vector3 Float) Source # areOrthogonal :: Vector3 Float -> Vector3 Float -> Bool Source # canonicalNorm :: Vector3 Float -> Scalar (Vector3 Float) Source #
(ConjugateSymmetric a, Num a) => InnerProductSpace (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods (%.) :: Vector3 a -> Vector3 a -> Scalar (Vector3 a) Source # areOrthogonal :: Vector3 a -> Vector3 a -> Bool Source # canonicalNorm :: Vector3 a -> Scalar (Vector3 a) Source #
Num a => LieAlgebra (Vector3 a) Source #	https://en.wikipedia.org/wiki/Lie_algebra
Instance details Defined in Math.Matrix.Vector3 Methods (%<>%) :: Vector3 a -> Vector3 a -> Vector3 a Source #
(MetricSpace a, Floating (Distance a)) => MetricSpace (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 Associated Types type Distance (Vector3 a) Source # Methods distance :: Vector3 a -> Vector3 a -> Distance (Vector3 a) Source #
(Ord a, Floating a, ConjugateSymmetric a) => NormedSpace (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods norm :: Vector3 a -> Scalar (Vector3 a) Source # normSquared :: Vector3 a -> Scalar (Vector3 a) Source #
Numeric a => StandardBasis (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods unitVectors :: [Vector3 a] Source #
Num a => VectorSpace (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 Associated Types type Scalar (Vector3 a) Source # Methods vzero :: Vector3 a Source # vnegate :: Vector3 a -> Vector3 a Source # (%+) :: Vector3 a -> Vector3 a -> Vector3 a Source # (%*) :: Scalar (Vector3 a) -> Vector3 a -> Vector3 a Source #
Optimal (Vector3 Float) Source #
Instance details Defined in Math.Matrix.SIMD Associated Types type Optimized (Vector3 Float) Source # Methods toO :: Vector3 Float -> Optimized (Vector3 Float) Source # fromO :: Optimized (Vector3 Float) -> Vector3 Float Source # zipO :: (Scalar (Vector3 Float) -> Scalar (Vector3 Float) -> Scalar (Vector3 Float)) -> Optimized (Vector3 Float) -> Optimized (Vector3 Float) -> Optimized (Vector3 Float) Source # mapO :: (Scalar (Vector3 Float) -> Scalar (Vector3 Float)) -> Optimized (Vector3 Float) -> Optimized (Vector3 Float) Source # sumCoordinatesO :: Optimized (Vector3 Float) -> Scalar (Vector3 Float) Source # constantO :: Scalar (Vector3 Float) -> Optimized (Vector3 Float) Source #
Num s => Group (Vector3 s) Source #
Instance details Defined in Math.Matrix.Vector3 Methods ginvert :: Vector3 s -> Vector3 s Source #
ShowPrecision s => ShowPrecision (Vector3 s) Source #
Instance details Defined in Math.Matrix.Vector3 Methods showAtPrecision :: Vector3 s -> Integer -> String Source #
MedianAlgebra s => MedianAlgebra (Vector3 s) Source #
Instance details Defined in Math.Matrix.Vector3 Methods med :: Vector3 s -> Vector3 s -> Vector3 s -> Vector3 s Source #
PpShow a => PpShow (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods pp :: Vector3 a -> Doc Source #
Universe a => Universe (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods allElements :: [Vector3 a] Source #
Visitor (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 Associated Types data Fold (Vector3 a) :: Type -> Type Source # Methods visit :: Fold (Vector3 a) a0 -> Vector3 a -> a0 Source #
Eq a => Eq (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods (==) :: Vector3 a -> Vector3 a -> Bool # (/=) :: Vector3 a -> Vector3 a -> Bool #
Ord a => Ord (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods compare :: Vector3 a -> Vector3 a -> Ordering # (<) :: Vector3 a -> Vector3 a -> Bool # (<=) :: Vector3 a -> Vector3 a -> Bool # (>) :: Vector3 a -> Vector3 a -> Bool # (>=) :: Vector3 a -> Vector3 a -> Bool # max :: Vector3 a -> Vector3 a -> Vector3 a # min :: Vector3 a -> Vector3 a -> Vector3 a #
(ConjugateSymmetric a, Num a) => Dualizable (Vector3 a) Dual Source #
Instance details Defined in Math.Matrix.Linear Methods covector :: (Vector3 a -> Scalar (Vector3 a)) -> Dual (Vector3 a) Source # bracket :: Dual (Vector3 a) -> Vector3 a -> Scalar (Vector3 a) Source #
(Closed a, Num a, ConjugateSymmetric a) => VectorDerivative (Vector3 a) Dual LinearMap Source #
Instance details Defined in Math.Matrix.Linear Methods divergence :: LinearMap (Vector3 a) (Vector3 a) -> Dual (Vector3 a) Source # grad :: Dual (Vector3 a) -> LinearMap (Vector3 a) (Vector3 a) Source # directionalDerivative :: Vector3 a -> Dual (Vector3 a) -> Dual (Vector3 a) Source # laplace :: Dual (Vector3 a) -> Dual (Vector3 a) Source #
Num a => DecomposableVectorSpace (Vector3 a) ((->) ThreeD) Source #
Instance details Defined in Math.Matrix.Simple Methods decompose :: (Scalar (Vector3 a) -> res) -> Vector3 a -> ThreeD -> res Source # project :: Vector3 a -> ThreeD -> Scalar (Vector3 a) Source #
Applicative (Vector3 \\\ Vector1) Source #
Instance details Defined in Math.Matrix.Vector3 Methods pure :: a -> (Vector3 \\\ Vector1) a # (<>) :: (Vector3 \\\ Vector1) (a -> b) -> (Vector3 \\\ Vector1) a -> (Vector3 \\\ Vector1) b # liftA2 :: (a -> b -> c) -> (Vector3 \\\ Vector1) a -> (Vector3 \\\ Vector1) b -> (Vector3 \\\ Vector1) c # (>) :: (Vector3 \\\ Vector1) a -> (Vector3 \\\ Vector1) b -> (Vector3 \\\ Vector1) b # (<*) :: (Vector3 \\\ Vector1) a -> (Vector3 \\\ Vector1) b -> (Vector3 \\\ Vector1) a #
Applicative (Vector3 \\\ Vector2) Source #
Instance details Defined in Math.Matrix.Vector3 Methods pure :: a -> (Vector3 \\\ Vector2) a # (<>) :: (Vector3 \\\ Vector2) (a -> b) -> (Vector3 \\\ Vector2) a -> (Vector3 \\\ Vector2) b # liftA2 :: (a -> b -> c) -> (Vector3 \\\ Vector2) a -> (Vector3 \\\ Vector2) b -> (Vector3 \\\ Vector2) c # (>) :: (Vector3 \\\ Vector2) a -> (Vector3 \\\ Vector2) b -> (Vector3 \\\ Vector2) b # (<*) :: (Vector3 \\\ Vector2) a -> (Vector3 \\\ Vector2) b -> (Vector3 \\\ Vector2) a #
Functor (Vector3 \\\ Vector1) Source #
Instance details Defined in Math.Matrix.Vector3 Methods fmap :: (a -> b) -> (Vector3 \\\ Vector1) a -> (Vector3 \\\ Vector1) b # (<$) :: a -> (Vector3 \\\ Vector1) b -> (Vector3 \\\ Vector1) a #
Functor (Vector3 \\\ Vector2) Source #
Instance details Defined in Math.Matrix.Vector3 Methods fmap :: (a -> b) -> (Vector3 \\\ Vector2) a -> (Vector3 \\\ Vector2) b # (<$) :: a -> (Vector3 \\\ Vector2) b -> (Vector3 \\\ Vector2) a #
Show a => Show (Codiagonal Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods showsPrec :: Int -> Codiagonal Vector3 a -> ShowS # show :: Codiagonal Vector3 a -> String # showList :: [Codiagonal Vector3 a] -> ShowS #
(Show a, Limiting Stream a) => Show (Closure Stream (Vector3 a)) Source #
Instance details Defined in Math.Matrix.Vector3 Methods showsPrec :: Int -> Closure Stream (Vector3 a) -> ShowS # show :: Closure Stream (Vector3 a) -> String # showList :: [Closure Stream (Vector3 a)] -> ShowS #
(PpShow a, Limiting Stream a) => PpShow (Closure Stream (Vector3 a)) Source #
Instance details Defined in Math.Matrix.Vector3 Methods pp :: Closure Stream (Vector3 a) -> Doc Source #
ProjectionSpace (Vector3 \\\ Vector1) Vector1 Source #
Instance details Defined in Math.Matrix.Vector3 Associated Types data ((Vector3 \\\ Vector1) \\\ Vector1) a Source # Methods projectFirst :: (Vector3 \\\ Vector1) a -> Vector1 a Source # projectSecond :: (Vector3 \\\ Vector1) a -> ((Vector3 \\\ Vector1) \\\ Vector1) a Source # joinVector :: Vector1 a -> ((Vector3 \\\ Vector1) \\\ Vector1) a -> (Vector3 \\\ Vector1) a Source #
Show a => Show ((Vector3 \\\ Vector1) a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods showsPrec :: Int -> (Vector3 \\\ Vector1) a -> ShowS # show :: (Vector3 \\\ Vector1) a -> String # showList :: [(Vector3 \\\ Vector1) a] -> ShowS #
Show a => Show ((Vector3 \\\ Vector2) a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods showsPrec :: Int -> (Vector3 \\\ Vector2) a -> ShowS # show :: (Vector3 \\\ Vector2) a -> String # showList :: [(Vector3 \\\ Vector2) a] -> ShowS #
(Universe row, Num a) => LinearTransform ((->) row) Vector3 a Source #
Instance details Defined in Math.Matrix.Simple Methods (<>>) :: Vector3 a -> ((->) row :: Vector3) a -> row -> a Source # (<<>) :: ((->) row :: Vector3) a -> (row -> a) -> Vector3 a Source #
Transposable ((->) row) Vector3 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods transposeImpl :: ((->) row :: Vector3) a -> (Vector3 :: (->) row) a Source #
(Ord a, Num a, ConjugateSymmetric a) => Monoid ((Vector3 :*: Vector3) a) Source #	see "Lawvere,Rosebrugh: Sets for mathematics", pg. 167.
Instance details Defined in Math.Matrix.Vector3 Methods mempty :: (Vector3 :: Vector3) a # mappend :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a # mconcat :: [(Vector3 :: Vector3) a] -> (Vector3 :: Vector3) a #
(Ord a, ConjugateSymmetric a, Num a) => Semigroup ((Vector3 :*: Vector3) a) Source #	see "Lawvere,Rosebrugh: Sets for mathematics", pg. 167.
Instance details Defined in Math.Matrix.Vector3 Methods (<>) :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a # sconcat :: NonEmpty ((Vector3 :: Vector3) a) -> (Vector3 :: Vector3) a # stimes :: Integral b => b -> (Vector3 :: Vector3) a -> (Vector3 :*: Vector3) a #
(Ord a, Numeric a, ConjugateSymmetric a) => Num ((Vector3 :*: Vector3) a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods (+) :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a # (-) :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a # () :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a # negate :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a # abs :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a # signum :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a # fromInteger :: Integer -> (Vector3 :*: Vector3) a #
(Ord a, NumFractional a, ConjugateSymmetric a) => Fractional ((Vector3 :*: Vector3) a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods (/) :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a # recip :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a # fromRational :: Rational -> (Vector3 :: Vector3) a #
Show (f a) => Show ((Vector3 :*: f) a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods showsPrec :: Int -> (Vector3 :: f) a -> ShowS # show :: (Vector3 :: f) a -> String # showList :: [(Vector3 :*: f) a] -> ShowS #
(ConjugateSymmetric a, Num a) => ConjugateSymmetric ((Vector3 :*: Vector3) a) Source #	https://en.wikipedia.org/wiki/Conjugate_transpose
Instance details Defined in Math.Matrix.Vector3 Methods conj :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a Source #
SupportsMatrixMultiplication Vector3 Vector3 Vector3 a => InnerProductSpace ((Vector3 :*: Vector3) a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods (%.) :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a -> Scalar ((Vector3 :: Vector3) a) Source # areOrthogonal :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a -> Bool Source # canonicalNorm :: (Vector3 :: Vector3) a -> Scalar ((Vector3 :*: Vector3) a) Source #
(Num a, ConjugateSymmetric a) => LieAlgebra ((Vector3 :*: Vector3) a) Source #
Instance details Defined in Math.Matrix.Matrix Methods (%<>%) :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a -> (Vector3 :*: Vector3) a Source #
(Floating a, ConjugateSymmetric a, AdditiveIdentity a, MultiplicativeIdentity a) => NormedSpace ((Vector3 :*: Vector3) a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods norm :: (Vector3 :: Vector3) a -> Scalar ((Vector3 :: Vector3) a) Source # normSquared :: (Vector3 :: Vector3) a -> Scalar ((Vector3 :: Vector3) a) Source #
(Num a, ConjugateSymmetric a) => StandardBasis ((Dual :*: Vector3) a) Source #	https://en.wikipedia.org/wiki/Dual_space
Instance details Defined in Math.Matrix.Linear Methods unitVectors :: [(Dual :*: Vector3) a] Source #
Num a => VectorSpace ((Vector1 :*: Vector3) a) Source #	1 x 3 matrices:
Instance details Defined in Math.Matrix.Vector3 Associated Types type Scalar ((Vector1 :: Vector3) a) Source # Methods vzero :: (Vector1 :: Vector3) a Source # vnegate :: (Vector1 :: Vector3) a -> (Vector1 :: Vector3) a Source # (%+) :: (Vector1 :: Vector3) a -> (Vector1 :: Vector3) a -> (Vector1 :: Vector3) a Source # (%) :: Scalar ((Vector1 :: Vector3) a) -> (Vector1 :: Vector3) a -> (Vector1 :*: Vector3) a Source #
Num a => VectorSpace ((Vector2 :*: Vector3) a) Source #	2 x 3 matrices:
Instance details Defined in Math.Matrix.Vector3 Associated Types type Scalar ((Vector2 :: Vector3) a) Source # Methods vzero :: (Vector2 :: Vector3) a Source # vnegate :: (Vector2 :: Vector3) a -> (Vector2 :: Vector3) a Source # (%+) :: (Vector2 :: Vector3) a -> (Vector2 :: Vector3) a -> (Vector2 :: Vector3) a Source # (%) :: Scalar ((Vector2 :: Vector3) a) -> (Vector2 :: Vector3) a -> (Vector2 :*: Vector3) a Source #
Num a => VectorSpace ((Vector3 :*: Vector1) a) Source #	3 x 1 matrices:
Instance details Defined in Math.Matrix.Vector3 Associated Types type Scalar ((Vector3 :: Vector1) a) Source # Methods vzero :: (Vector3 :: Vector1) a Source # vnegate :: (Vector3 :: Vector1) a -> (Vector3 :: Vector1) a Source # (%+) :: (Vector3 :: Vector1) a -> (Vector3 :: Vector1) a -> (Vector3 :: Vector1) a Source # (%) :: Scalar ((Vector3 :: Vector1) a) -> (Vector3 :: Vector1) a -> (Vector3 :*: Vector1) a Source #
Num a => VectorSpace ((Vector3 :*: Vector2) a) Source #	3 x 2 matrices
Instance details Defined in Math.Matrix.Vector3 Associated Types type Scalar ((Vector3 :: Vector2) a) Source # Methods vzero :: (Vector3 :: Vector2) a Source # vnegate :: (Vector3 :: Vector2) a -> (Vector3 :: Vector2) a Source # (%+) :: (Vector3 :: Vector2) a -> (Vector3 :: Vector2) a -> (Vector3 :: Vector2) a Source # (%) :: Scalar ((Vector3 :: Vector2) a) -> (Vector3 :: Vector2) a -> (Vector3 :*: Vector2) a Source #
Num a => VectorSpace ((Vector3 :*: Vector3) a) Source #	3 x 3 matrices:
Instance details Defined in Math.Matrix.Vector3 Associated Types type Scalar ((Vector3 :: Vector3) a) Source # Methods vzero :: (Vector3 :: Vector3) a Source # vnegate :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a Source # (%+) :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a Source # (%) :: Scalar ((Vector3 :: Vector3) a) -> (Vector3 :: Vector3) a -> (Vector3 :*: Vector3) a Source #
Num a => VectorSpace ((Vector3 :*: Vector4) a) Source #	3 x 4 matrices
Instance details Defined in Math.Matrix.Vector4 Associated Types type Scalar ((Vector3 :: Vector4) a) Source # Methods vzero :: (Vector3 :: Vector4) a Source # vnegate :: (Vector3 :: Vector4) a -> (Vector3 :: Vector4) a Source # (%+) :: (Vector3 :: Vector4) a -> (Vector3 :: Vector4) a -> (Vector3 :: Vector4) a Source # (%) :: Scalar ((Vector3 :: Vector4) a) -> (Vector3 :: Vector4) a -> (Vector3 :*: Vector4) a Source #
Num a => VectorSpace ((Vector3 :*: (->) col) a) Source #
Instance details Defined in Math.Matrix.Simple Associated Types type Scalar ((Vector3 :: (->) col) a) Source # Methods vzero :: (Vector3 :: (->) col) a Source # vnegate :: (Vector3 :: (->) col) a -> (Vector3 :: (->) col) a Source # (%+) :: (Vector3 :: (->) col) a -> (Vector3 :: (->) col) a -> (Vector3 :: (->) col) a Source # (%) :: Scalar ((Vector3 :: (->) col) a) -> (Vector3 :: (->) col) a -> (Vector3 :*: (->) col) a Source #
Num a => VectorSpace ((Vector4 :*: Vector3) a) Source #	4 x 3 matrices:
Instance details Defined in Math.Matrix.Vector4 Associated Types type Scalar ((Vector4 :: Vector3) a) Source # Methods vzero :: (Vector4 :: Vector3) a Source # vnegate :: (Vector4 :: Vector3) a -> (Vector4 :: Vector3) a Source # (%+) :: (Vector4 :: Vector3) a -> (Vector4 :: Vector3) a -> (Vector4 :: Vector3) a Source # (%) :: Scalar ((Vector4 :: Vector3) a) -> (Vector4 :: Vector3) a -> (Vector4 :*: Vector3) a Source #
Num a => VectorSpace (((->) row :*: Vector3) a) Source #
Instance details Defined in Math.Matrix.Simple Associated Types type Scalar (((->) row :: Vector3) a) Source # Methods vzero :: ((->) row :: Vector3) a Source # vnegate :: ((->) row :: Vector3) a -> ((->) row :: Vector3) a Source # (%+) :: ((->) row :: Vector3) a -> ((->) row :: Vector3) a -> ((->) row :: Vector3) a Source # (%) :: Scalar (((->) row :: Vector3) a) -> ((->) row :: Vector3) a -> ((->) row :*: Vector3) a Source #
(Ord a, Fractional a, ConjugateSymmetric a) => Group ((Vector3 :*: Vector3) a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods ginvert :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a Source #
data Codiagonal Vector3 a Source #
Instance details Defined in Math.Matrix.Vector3 data Codiagonal Vector3 a = Codiagonal3 { downCodiagonal3 :: Vector2 a rightCodiagonal3 :: Vector2 a diagonalCodiagonal3 :: Codiagonal Vector2 a }
type Vector1 :+: Vector3 Source #
Instance details Defined in Math.Matrix.Vector4 type Vector1 :+: Vector3 = Vector4
type Vector3 :+: Vector1 Source #
Instance details Defined in Math.Matrix.Vector4 type Vector3 :+: Vector1 = Vector4
type Vector3 :+: Stream Source #
Instance details Defined in Math.Number.Stream type Vector3 :+: Stream = Stream
type Vector3 \\ a Source #
Instance details Defined in Math.Matrix.Vector3 type Vector3 \\ a = Vector2 a
data (Vector3 \\\ Vector1) a Source #
Instance details Defined in Math.Matrix.Vector3 data (Vector3 \\\ Vector1) a = S31Vector (Vector2 a)
data (Vector3 \\\ Vector2) a Source #
Instance details Defined in Math.Matrix.Vector3 data (Vector3 \\\ Vector2) a = S32Vector (Vector1 a)
data Closure Stream (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 data Closure Stream (Vector3 a) = Vector3Closure (Vector3 (Closure Stream a))
type Rep (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 type Rep (Vector3 a) = D1 ('MetaData "Vector3" "Math.Matrix.Vector3" "cifl-math-library-2.0.0.0-K3Wcv1zXOBxvFThQyThI4" 'False) (C1 ('MetaCons "Vector3" 'PrefixI 'True) (S1 ('MetaSel ('Just "xcoord3") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :: (S1 ('MetaSel ('Just "ycoord3") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :: S1 ('MetaSel ('Just "zcoord3") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a))))
type Coordinate (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 type Coordinate (Vector3 a) = Int
type Distance (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 type Distance (Vector3 a) = Distance a
type Scalar (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 type Scalar (Vector3 a) = a
type Optimized (Vector3 Float) Source #
Instance details Defined in Math.Matrix.SIMD type Optimized (Vector3 Float) = SIMDVec 4 Float
data Fold (Vector3 a) b Source #
Instance details Defined in Math.Matrix.Vector3 data Fold (Vector3 a) b = Vector3Fold (a -> a -> a -> b)
data ((Vector3 \\\ Vector1) \\\ Vector1) a Source #
Instance details Defined in Math.Matrix.Vector3 data ((Vector3 \\\ Vector1) \\\ Vector1) a = S311Vector (Vector1 a)
type Scalar ((Vector1 :*: Vector3) a) Source #
Instance details Defined in Math.Matrix.Vector3 type Scalar ((Vector1 :*: Vector3) a) = a
type Scalar ((Vector2 :*: Vector3) a) Source #
Instance details Defined in Math.Matrix.Vector3 type Scalar ((Vector2 :*: Vector3) a) = a
type Scalar ((Vector3 :*: Vector1) a) Source #
Instance details Defined in Math.Matrix.Vector3 type Scalar ((Vector3 :*: Vector1) a) = a
type Scalar ((Vector3 :*: Vector2) a) Source #
Instance details Defined in Math.Matrix.Vector3 type Scalar ((Vector3 :*: Vector2) a) = a
type Scalar ((Vector3 :*: Vector3) a) Source #
Instance details Defined in Math.Matrix.Vector3 type Scalar ((Vector3 :*: Vector3) a) = a
type Scalar ((Vector3 :*: Vector4) a) Source #
Instance details Defined in Math.Matrix.Vector4 type Scalar ((Vector3 :*: Vector4) a) = a
type Scalar ((Vector3 :*: (->) col) a) Source #
Instance details Defined in Math.Matrix.Simple type Scalar ((Vector3 :*: (->) col) a) = a
type Scalar ((Vector4 :*: Vector3) a) Source #
Instance details Defined in Math.Matrix.Vector4 type Scalar ((Vector4 :*: Vector3) a) = a
type Scalar (((->) row :*: Vector3) a) Source #
Instance details Defined in Math.Matrix.Simple type Scalar (((->) row :*: Vector3) a) = a

type ComplexVector3 a = (Vector3 :*: Complex) a Source #

dim3 :: Vector3 Integer Source #

i3 :: Num a => Vector3 a Source #

j3 :: Num a => Vector3 a Source #

k3 :: Num a => Vector3 a Source #

type Matrix3 a = (Vector3 :*: Vector3) a Source #

vec3 :: (a, a, a) -> Vector3 a Source #

finite3 :: Vector3 a -> Vec 3 a Source #

constant3 :: a -> Vector3 a Source #

vec3Unit :: a -> Scalar (Vector3 a) Source #

vec3Counit :: Vector3 (Scalar (Vector3 a)) -> Vector3 a Source #

destructvec3 :: Vector3 a -> (a, a, a) Source #

setx3 :: s -> Vector3 s -> Vector3 s Source #

sety3 :: s -> Vector3 s -> Vector3 s Source #

setz3 :: s -> Vector3 s -> Vector3 s Source #

setEndo :: Vector3 s -> Vector3 (Endo (Vector3 s)) Source #

setVectorAction :: Vector3 s -> Vector3 (Vector3 s -> Vector3 s) Source #

updateRow3 :: g a -> Vector3 ((Vector3 :*: g) a -> (Vector3 :*: g) a) Source #

update_column3 v is a vector of all update operations that replace one row with v

updateColumn3 :: Applicative f => f a -> Vector3 ((f :*: Vector3) a -> (f :*: Vector3) a) Source #

update_column3 v is a vector of all update operations that replace one column with v example use: update_column3 (Vector3 3 4 5) ycoord3 identity3 == [[1,3,0],[0,4,0],[0,5,1]].

removex3 :: Vector3 a -> Vector2 a Source #

removey3 :: Vector3 a -> Vector2 a Source #

removez3 :: Vector3 a -> Vector2 a Source #

remove3 :: Vector3 (Vector3 a -> Vector2 a) Source #

determinancett3 :: Num a => Determinance Vector3 Vector3 Vector2 Vector2 Vector2 a a a Source #

remove_index3 :: Matrix3 a -> Matrix3 (Matrix2 a) Source #

cofactor3 :: Num a => Matrix3 a -> Matrix3 a Source #

adjucate3 :: Num a => Matrix3 a -> Matrix3 a Source #

https://en.wikipedia.org/wiki/Adjugate_matrix

inverse3 :: Fractional a => Matrix3 a -> Matrix3 a Source #

https://en.wikipedia.org/wiki/Invertible_matrix

set3 :: Vector3 a -> Vector3 a -> (Vector3 :*: Vector3) a Source #

swap3 :: (Vector3 :*: Vector3) (Vector3 a -> Vector3 a) Source #

http://en.wikipedia.org/wiki/Elementary_matrix#Operations

mul3 :: VectorSpace s => Scalar s -> Vector3 (Vector3 s -> Vector3 s) Source #

add3Matrix :: VectorSpace a => Scalar a -> ((Vector3 :*: Vector3) :*: Vector3) a -> ((Vector3 :*: Vector3) :*: Vector3) a Source #

add3 :: VectorSpace s => Scalar s -> (Vector3 :*: Vector3) (Vector3 s -> Vector3 s) Source #

swapxy3 :: Vector3 a -> Vector3 a Source #

swapxz3 :: Vector3 a -> Vector3 a Source #

swapyz3 :: Vector3 a -> Vector3 a Source #

mul3Matrix :: (Num a, VectorSpace a) => Scalar a -> Vector3 ((Vector3 :*: Vector3) a) Source #

signs3 :: Integral a => Matrix3 a Source #

dx3_endo :: Num a => a -> Endo (Vector3 a) Source #

dy3_endo :: Num a => a -> Endo (Vector3 a) Source #

dz3_endo :: Num a => a -> Endo (Vector3 a) Source #

dx3 :: Num a => a -> Vector3 a -> Vector3 a Source #

dy3 :: Num a => a -> Vector3 a -> Vector3 a Source #

dz3 :: Num a => a -> Vector3 a -> Vector3 a Source #

op_dot :: Num b => Vector3 (a -> b) -> a -> b Source #

applicative_matrix :: Num b => Vector3 (b -> b) -> (Vector3 :*: Vector3) b Source #

sum_coordinates3 :: Num a => Vector3 a -> a Source #

cube_norm3 :: Floating a => Vector3 a -> a Source #

cube root of a sum of cubes.

nth_norm3 :: Floating a => a -> Vector3 a -> a Source #

nth root of a sum of nth powers

index3 :: Vector3 (Vector3 a -> a) Source #

mapBasis :: Numeric a => (Vector3 a -> Vector3 a) -> Vector3 a -> Vector3 a Source #

functionMatrix3 :: Numeric a => (Vector3 a -> Vector3 a) -> Matrix3 a Source #

splitx :: Vector3 s -> (Vector2 s, Vector1 s) Source #

splity :: Vector3 s -> (Vector2 s, Vector1 s) Source #

splitz :: Vector3 s -> (Vector2 s, Vector1 s) Source #

trace3 :: Num a => Matrix3 a -> a Source #

vector3 :: [a] -> Vector3 a Source #

cross_product :: Num a => Vector3 a -> Vector3 a -> Vector3 a Source #

https://en.wikipedia.org/wiki/Cross_product WARNING: a cross product produces an axial vector. https://en.wikipedia.org/wiki/Pseudovector

cross_product3 :: Num a => (Vector2 :*: Vector3) a -> Vector3 a Source #

cross_product3 computes the three dimensional vector that is orthogonal to both rows of the 2x3 vector.

xid :: Num a => Vector3 a Source #

yid :: Num a => Vector3 a Source #

zid :: Num a => Vector3 a Source #

identity3 :: Num a => Matrix3 a Source #

matrixPower3 :: (Ord a, ConjugateSymmetric a, Numeric a) => Matrix3 a -> Integer -> Matrix3 a Source #

vectorIndices3 :: Integral a => Vector3 a Source #

matrixIndices3 :: Integral a => (Vector3 :*: Vector3) (a, a) Source #

matrixMultiply3 :: (Ord a, ConjugateSymmetric a, Num a) => Matrix3 a -> Matrix3 a -> Matrix3 a Source #

dot3 :: (Num a, ConjugateSymmetric a) => Vector3 a -> Vector3 a -> a Source #

leftMultiply3Gen :: (Functor f, Num a, ConjugateSymmetric a) => Vector3 a -> (f :*: Vector3) a -> f a Source #

rightMultiply3Gen :: (VectorSpace (f a), ConjugateSymmetric a, Scalar (f a) ~ a) => (Vector3 :*: f) a -> Vector3 a -> f a Source #

leftMultiply3 :: (Num a, ConjugateSymmetric a) => Vector3 a -> Matrix3 a -> Vector3 a Source #

rightMultiply3 :: (Num a, ConjugateSymmetric a) => Matrix3 a -> Vector3 a -> Vector3 a Source #

transpose3 :: Num a => Matrix3 a -> Matrix3 a Source #

transpose3Impl :: Matrix3 a -> Matrix3 a Source #

outer3 :: (a -> b -> c) -> Vector3 a -> Vector3 b -> Matrix3 c Source #

zipWithV3 :: (a -> b -> c) -> Vector3 a -> Vector3 b -> Vector3 c Source #

rotate_x :: Floating a => a -> Matrix3 a Source #

rotate_y :: Floating a => a -> Matrix3 a Source #

rotate_z :: Floating a => a -> Matrix3 a Source #

rotate_coordinates3 :: Vector3 a -> Vector3 a Source #

zero_codiagonal3 :: Num a => Codiagonal Vector3 a Source #

diagonal_matrix3 :: Vector3 a -> (Vector3 :*: Vector3) a -> (Vector3 :*: Vector3) a Source #

matrix3 :: Vector3 a -> Codiagonal Vector3 a -> (Vector3 :*: Vector3) a Source #

codiag3 :: Matrix3 a -> Codiagonal Vector3 a Source #

codiagonal3 :: Matrix3 a -> Vector2 (Vector2 a, Vector2 a) Source #

diagonal3 :: Matrix3 a -> Vector3 a Source #

diagonal_projections3 :: Vector3 (Index Vector3 a) Source #

diagonal3x :: Num a => Matrix3 a -> Vector3 a Source #

diagonal3y :: Num a => Matrix3 a -> Vector3 a Source #

diagonal3z :: Num a => Matrix3 a -> Vector3 a Source #

determinant3 :: Num a => Matrix3 a -> a Source #

algorithm from http://en.wikipedia.org/wiki/Determinant

determinant3_ :: Num a => Matrix3 a -> a Source #

gram_schmidt3 :: (Fractional (Scalar a), Num a, InnerProductSpace a, VectorSpace a) => Vector3 a -> Vector3 a Source #

eigenvalue3 :: (Floating a, Ord a, ConjugateSymmetric a) => (Vector3 :*: Vector3) a -> Vector3 a Source #

https://en.wikipedia.org/wiki/Eigenvalue_algorithm based on algorithm by Smith, Oliver K.: Eigenvalues of symmetric 3x3 matrix, 1961, Communications of the ACM., doi:10.1145/355578.366316 The algorithm works reasonably when the matrix is real and symmetric.

levi_civita3 :: ((Vector3 :*: Vector3) :*: Vector3) Int Source #

https://en.wikipedia.org/wiki/Levi-Civita_symbol

cycle3 :: StreamBuilder str => Vector3 a -> str a Source #

Orphan instances

AppendableVector Vector1 Vector2 Source #
Instance details Associated Types type Vector1 :+: Vector2 :: Type -> Type Source # Methods (\|\|>>) :: Vector1 a -> Vector2 a -> (Vector1 :+: Vector2) a Source #
AppendableVector Vector2 Vector1 Source #
Instance details Associated Types type Vector2 :+: Vector1 :: Type -> Type Source # Methods (\|\|>>) :: Vector2 a -> Vector1 a -> (Vector2 :+: Vector1) a Source #
SplittableVector Vector1 Vector2 Source #
Instance details Methods vsplit :: (Vector1 :+: Vector2) a -> (Vector1 a, Vector2 a) Source #
SplittableVector Vector2 Vector1 Source #
Instance details Methods vsplit :: (Vector2 :+: Vector1) a -> (Vector2 a, Vector1 a) Source #