linear-1.20.4: 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.V4

Description

4-D Vectors

Synopsis

Documentation

data V4 a Source

A 4-dimensional vector.

Constructors

V4 !a !a !a !a 

Instances

Monad V4 Source 
Functor V4 Source 
MonadFix V4 Source 
Applicative V4 Source 
Foldable V4 Source 
Traversable V4 Source 
Generic1 V4 Source 
Distributive V4 Source 
Representable V4 Source 
MonadZip V4 Source 
Serial1 V4 Source 
Traversable1 V4 Source 
Apply V4 Source 
Bind V4 Source 
Foldable1 V4 Source 
Eq1 V4 Source 
Ord1 V4 Source 
Read1 V4 Source 
Show1 V4 Source 
Additive V4 Source 
Metric V4 Source 
R1 V4 Source 
R2 V4 Source 
R3 V4 Source 
R4 V4 Source 
Trace V4 Source 
Affine V4 Source 
Unbox a => Vector Vector (V4 a) Source 
Unbox a => MVector MVector (V4 a) Source 
Num r => Coalgebra r (E V4) Source 
Bounded a => Bounded (V4 a) Source 
Eq a => Eq (V4 a) Source 
Floating a => Floating (V4 a) Source 
Fractional a => Fractional (V4 a) Source 
Data a => Data (V4 a) Source 
Num a => Num (V4 a) Source 
Ord a => Ord (V4 a) Source 
Read a => Read (V4 a) Source 
Show a => Show (V4 a) Source 
Ix a => Ix (V4 a) Source 
Generic (V4 a) Source 
Storable a => Storable (V4 a) Source 
Binary a => Binary (V4 a) Source 
Serial a => Serial (V4 a) Source 
Serialize a => Serialize (V4 a) Source 
NFData a => NFData (V4 a) Source 
Hashable a => Hashable (V4 a) Source 
Unbox a => Unbox (V4 a) Source 
Ixed (V4 a) Source 
Epsilon a => Epsilon (V4 a) Source 
FunctorWithIndex (E V4) V4 Source 
FoldableWithIndex (E V4) V4 Source 
TraversableWithIndex (E V4) V4 Source 
Each (V4 a) (V4 b) a b Source 
type Rep1 V4 Source 
type Rep V4 = E V4 Source 
type Diff V4 = V4 Source 
data MVector s (V4 a) = MV_V4 !Int !(MVector s a) Source 
type Rep (V4 a) Source 
data Vector (V4 a) = V_V4 !Int !(Vector a) Source 
type Index (V4 a) = E V4 Source 
type IxValue (V4 a) = a Source 

vector :: Num a => V3 a -> V4 a Source

Convert a 3-dimensional affine vector into a 4-dimensional homogeneous vector.

point :: Num a => V3 a -> V4 a Source

Convert a 3-dimensional affine point into a 4-dimensional homogeneous vector.

normalizePoint :: Fractional a => V4 a -> V3 a Source

Convert 4-dimensional projective coordinates to a 3-dimensional point. This operation may be denoted, euclidean [x:y:z:w] = (x/w, y/w, z/w) where the projective, homogenous, coordinate [x:y:z:w] is one of many associated with a single point (x/w, y/w, z/w).

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

class R3 t => R4 t where Source

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

Minimal complete definition

Nothing

Methods

_w :: Lens' (t a) a Source

>>> V4 1 2 3 4 ^._w
4

_xyzw :: Lens' (t a) (V4 a) Source

Instances

R4 V4 Source 
R4 f => R4 (Point f) Source 

_xw :: R4 t => Lens' (t a) (V2 a) Source

_yw :: R4 t => Lens' (t a) (V2 a) Source

_zw :: R4 t => Lens' (t a) (V2 a) Source

_wx :: R4 t => Lens' (t a) (V2 a) Source

_wy :: R4 t => Lens' (t a) (V2 a) Source

_wz :: R4 t => Lens' (t a) (V2 a) Source

_xyw :: R4 t => Lens' (t a) (V3 a) Source

_xzw :: R4 t => Lens' (t a) (V3 a) Source

_xwy :: R4 t => Lens' (t a) (V3 a) Source

_xwz :: R4 t => Lens' (t a) (V3 a) Source

_yxw :: R4 t => Lens' (t a) (V3 a) Source

_yzw :: R4 t => Lens' (t a) (V3 a) Source

_ywx :: R4 t => Lens' (t a) (V3 a) Source

_ywz :: R4 t => Lens' (t a) (V3 a) Source

_zxw :: R4 t => Lens' (t a) (V3 a) Source

_zyw :: R4 t => Lens' (t a) (V3 a) Source

_zwx :: R4 t => Lens' (t a) (V3 a) Source

_zwy :: R4 t => Lens' (t a) (V3 a) Source

_wxy :: R4 t => Lens' (t a) (V3 a) Source

_wxz :: R4 t => Lens' (t a) (V3 a) Source

_wyx :: R4 t => Lens' (t a) (V3 a) Source

_wyz :: R4 t => Lens' (t a) (V3 a) Source

_wzx :: R4 t => Lens' (t a) (V3 a) Source

_wzy :: R4 t => Lens' (t a) (V3 a) Source

_xywz :: R4 t => Lens' (t a) (V4 a) Source

_xzyw :: R4 t => Lens' (t a) (V4 a) Source

_xzwy :: R4 t => Lens' (t a) (V4 a) Source

_xwyz :: R4 t => Lens' (t a) (V4 a) Source

_xwzy :: R4 t => Lens' (t a) (V4 a) Source

_yxzw :: R4 t => Lens' (t a) (V4 a) Source

_yxwz :: R4 t => Lens' (t a) (V4 a) Source

_yzxw :: R4 t => Lens' (t a) (V4 a) Source

_yzwx :: R4 t => Lens' (t a) (V4 a) Source

_ywxz :: R4 t => Lens' (t a) (V4 a) Source

_ywzx :: R4 t => Lens' (t a) (V4 a) Source

_zxyw :: R4 t => Lens' (t a) (V4 a) Source

_zxwy :: R4 t => Lens' (t a) (V4 a) Source

_zyxw :: R4 t => Lens' (t a) (V4 a) Source

_zywx :: R4 t => Lens' (t a) (V4 a) Source

_zwxy :: R4 t => Lens' (t a) (V4 a) Source

_zwyx :: R4 t => Lens' (t a) (V4 a) Source

_wxyz :: R4 t => Lens' (t a) (V4 a) Source

_wxzy :: R4 t => Lens' (t a) (V4 a) Source

_wyxz :: R4 t => Lens' (t a) (V4 a) Source

_wyzx :: R4 t => Lens' (t a) (V4 a) Source

_wzxy :: R4 t => Lens' (t a) (V4 a) Source

_wzyx :: R4 t => Lens' (t a) (V4 a) Source

ex :: R1 t => E t Source

ey :: R2 t => E t Source

ez :: R3 t => E t Source

ew :: R4 t => E t Source