linear-1.19.1.3: Linear Algebra

Copyright(C) 2012-2015 Edward Kmett
LicenseBSD-style (see the file LICENSE)
MaintainerEdward Kmett <ekmett@gmail.com>
Stabilityexperimental
Portabilitynon-portable
Safe HaskellTrustworthy
LanguageHaskell98

Linear.V3

Description

3-D Vectors

Synopsis

Documentation

data V3 a Source

A 3-dimensional vector

Constructors

V3 !a !a !a 

Instances

Monad V3 Source 
Functor V3 Source 
MonadFix V3 Source 
Applicative V3 Source 
Foldable V3 Source 
Traversable V3 Source 
Generic1 V3 Source 
Distributive V3 Source 
Representable V3 Source 
MonadZip V3 Source 
Serial1 V3 Source 
Traversable1 V3 Source 
Apply V3 Source 
Bind V3 Source 
Foldable1 V3 Source 
Eq1 V3 Source 
Ord1 V3 Source 
Read1 V3 Source 
Show1 V3 Source 
Additive V3 Source 
Metric V3 Source 
R1 V3 Source 
R2 V3 Source 
R3 V3 Source 
Trace V3 Source 
Affine V3 Source 
Unbox a => Vector Vector (V3 a) Source 
Unbox a => MVector MVector (V3 a) Source 
Num r => Coalgebra r (E V3) Source 
Bounded a => Bounded (V3 a) Source 
Eq a => Eq (V3 a) Source 
Floating a => Floating (V3 a) Source 
Fractional a => Fractional (V3 a) Source 
Data a => Data (V3 a) Source 
Num a => Num (V3 a) Source 
Ord a => Ord (V3 a) Source 
Read a => Read (V3 a) Source 
Show a => Show (V3 a) Source 
Ix a => Ix (V3 a) Source 
Generic (V3 a) Source 
Storable a => Storable (V3 a) Source 
Binary a => Binary (V3 a) Source 
Serial a => Serial (V3 a) Source 
Serialize a => Serialize (V3 a) Source 
NFData a => NFData (V3 a) Source 
Hashable a => Hashable (V3 a) Source 
Unbox a => Unbox (V3 a) Source 
Ixed (V3 a) Source 
Epsilon a => Epsilon (V3 a) Source 
FunctorWithIndex (E V3) V3 Source 
FoldableWithIndex (E V3) V3 Source 
TraversableWithIndex (E V3) V3 Source 
Each (V3 a) (V3 b) a b Source 
type Rep1 V3 Source 
type Rep V3 = E V3 Source 
type Diff V3 = V3 Source 
data MVector s (V3 a) = MV_V3 !Int (MVector s a) Source 
type Rep (V3 a) Source 
data Vector (V3 a) = V_V3 !Int (Vector a) Source 
type Index (V3 a) = E V3 Source 
type IxValue (V3 a) = a Source 

cross :: Num a => V3 a -> V3 a -> V3 a Source

cross product

triple :: Num a => V3 a -> V3 a -> V3 a -> a Source

scalar triple product

class R1 t where Source

A space that has at least 1 basis vector _x.

Minimal complete definition

Nothing

Methods

_x :: Lens' (t a) a Source

>>> V1 2 ^._x
2
>>> V1 2 & _x .~ 3
V1 3

class R1 t => R2 t where Source

A space that distinguishes 2 orthogonal basis vectors _x and _y, but may have more.

Minimal complete definition

Nothing

Methods

_y :: Lens' (t a) a Source

>>> V2 1 2 ^._y
2
>>> V2 1 2 & _y .~ 3
V2 1 3

_xy :: Lens' (t a) (V2 a) Source

Instances

_yx :: R2 t => Lens' (t a) (V2 a) Source

>>> V2 1 2 ^. _yx
V2 2 1

class R2 t => R3 t where Source

A space that distinguishes 3 orthogonal basis vectors: _x, _y, and _z. (It may have more)

Minimal complete definition

Nothing

Methods

_z :: Lens' (t a) a Source

>>> V3 1 2 3 ^. _z
3

_xyz :: Lens' (t a) (V3 a) Source

Instances

_xz :: R3 t => Lens' (t a) (V2 a) Source

_yz :: R3 t => Lens' (t a) (V2 a) Source

_zx :: R3 t => Lens' (t a) (V2 a) Source

_zy :: R3 t => Lens' (t a) (V2 a) Source

_xzy :: R3 t => Lens' (t a) (V3 a) Source

_yxz :: R3 t => Lens' (t a) (V3 a) Source

_yzx :: R3 t => Lens' (t a) (V3 a) Source

_zxy :: R3 t => Lens' (t a) (V3 a) Source

_zyx :: R3 t => Lens' (t a) (V3 a) Source

ex :: R1 t => E t Source

ey :: R2 t => E t Source

ez :: R3 t => E t Source