{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE RankNTypes #-}
module Nonlinear.Matrix
( (!*!),
(!*),
(*!),
(!!*),
(*!!),
(!!/),
column,
diagonal,
trace,
M22,
M23,
M24,
M32,
M33,
M34,
M42,
M43,
M44,
det22,
det33,
det44,
inv22,
inv33,
inv44,
identity,
transpose,
fromQuaternion,
_m22,
_m23,
_m24,
_m32,
_m33,
_m34,
_m42,
_m43,
_m44,
)
where
import Control.Applicative
import Control.Monad (join)
import Data.Foldable as Foldable
import Nonlinear.Internal (Lens', lens, set, view)
import Nonlinear.Quaternion
import Nonlinear.V2
import Nonlinear.V3
import Nonlinear.V4
import Nonlinear.Vector (Vec, scaled, (*^))
column ::
Vec v =>
Lens' a b ->
Lens' (v a) (v b)
column :: Lens' a b -> Lens' (v a) (v b)
column Lens' a b
l = (v a -> v b) -> (v a -> v b -> v a) -> Lens' (v a) (v b)
forall s a. (s -> a) -> (s -> a -> s) -> Lens' s a
lens ((a -> b) -> v a -> v b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ((a -> b) -> v a -> v b) -> (a -> b) -> v a -> v b
forall a b. (a -> b) -> a -> b
$ Lens' a b -> a -> b
forall s a. Lens' s a -> s -> a
view Lens' a b
l) ((a -> b -> a) -> v a -> v b -> v a
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 ((b -> a -> a) -> a -> b -> a
forall a b c. (a -> b -> c) -> b -> a -> c
flip ((b -> a -> a) -> a -> b -> a) -> (b -> a -> a) -> a -> b -> a
forall a b. (a -> b) -> a -> b
$ ASetter' a b -> b -> a -> a
forall s a. ASetter' s a -> a -> s -> s
set ASetter' a b
Lens' a b
l))
{-# INLINE column #-}
diagonal :: Vec v => v (v a) -> v a
diagonal :: v (v a) -> v a
diagonal = v (v a) -> v a
forall (m :: * -> *) a. Monad m => m (m a) -> m a
join
trace :: (Vec v, Num a) => v (v a) -> a
trace :: v (v a) -> a
trace = v a -> a
forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a
sum (v a -> a) -> (v (v a) -> v a) -> v (v a) -> a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. v (v a) -> v a
forall (v :: * -> *) a. Vec v => v (v a) -> v a
diagonal
infixl 7 !*!
(!*!) :: (Vec m, Vec t, Vec n, Num a) => m (t a) -> t (n a) -> m (n a)
m (t a)
f !*! :: m (t a) -> t (n a) -> m (n a)
!*! t (n a)
g = (t a -> n a) -> m (t a) -> m (n a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (\t a
f' -> (n a -> n a -> n a) -> n a -> t (n a) -> n a
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
Foldable.foldl' ((a -> a -> a) -> n a -> n a -> n a
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 a -> a -> a
forall a. Num a => a -> a -> a
(+)) (a -> n a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
0) (t (n a) -> n a) -> t (n a) -> n a
forall a b. (a -> b) -> a -> b
$ (a -> n a -> n a) -> t a -> t (n a) -> t (n a)
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 a -> n a -> n a
forall (f :: * -> *) a. (Vec f, Num a) => a -> f a -> f a
(*^) t a
f' t (n a)
g) m (t a)
f
infixl 7 !*
(!*) :: (Vec m, Vec r, Num a) => m (r a) -> r a -> m a
m (r a)
m !* :: m (r a) -> r a -> m a
!* r a
v = (r a -> a) -> m (r a) -> m a
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (\r a
r -> r a -> a
forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a
Foldable.sum (r a -> a) -> r a -> a
forall a b. (a -> b) -> a -> b
$ (a -> a -> a) -> r a -> r a -> r a
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 a -> a -> a
forall a. Num a => a -> a -> a
(*) r a
r r a
v) m (r a)
m
infixl 7 *!
(*!) :: (Vec f, Vec t, Num a, Num (f a)) => t a -> t (f a) -> f a
t a
f *! :: t a -> t (f a) -> f a
*! t (f a)
g = t (f a) -> f a
forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a
sum (t (f a) -> f a) -> t (f a) -> f a
forall a b. (a -> b) -> a -> b
$ (a -> f a -> f a) -> t a -> t (f a) -> t (f a)
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 a -> f a -> f a
forall (f :: * -> *) a. (Vec f, Num a) => a -> f a -> f a
(*^) t a
f t (f a)
g
infixl 7 *!!
(*!!) :: (Vec m, Vec r, Num a) => a -> m (r a) -> m (r a)
a
s *!! :: a -> m (r a) -> m (r a)
*!! m (r a)
m = (r a -> r a) -> m (r a) -> m (r a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (a
s a -> r a -> r a
forall (f :: * -> *) a. (Vec f, Num a) => a -> f a -> f a
*^) m (r a)
m
{-# INLINE (*!!) #-}
infixl 7 !!*
(!!*) :: (Vec m, Vec r, Num a) => m (r a) -> a -> m (r a)
!!* :: m (r a) -> a -> m (r a)
(!!*) = (a -> m (r a) -> m (r a)) -> m (r a) -> a -> m (r a)
forall a b c. (a -> b -> c) -> b -> a -> c
flip a -> m (r a) -> m (r a)
forall (m :: * -> *) (r :: * -> *) a.
(Vec m, Vec r, Num a) =>
a -> m (r a) -> m (r a)
(*!!)
{-# INLINE (!!*) #-}
infixl 7 !!/
(!!/) :: (Vec r, Vec m, Fractional (r a), Fractional a) => m (r a) -> a -> m (r a)
m (r a)
m !!/ :: m (r a) -> a -> m (r a)
!!/ a
s = (r a -> r a) -> m (r a) -> m (r a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (r a -> r a -> r a
forall a. Fractional a => a -> a -> a
/ a -> r a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
s) m (r a)
m
{-# INLINE (!!/) #-}
type M22 a = V2 (V2 a)
type M23 a = V2 (V3 a)
type M24 a = V2 (V4 a)
type M32 a = V3 (V2 a)
type M33 a = V3 (V3 a)
type M34 a = V3 (V4 a)
type M42 a = V4 (V2 a)
type M43 a = V4 (V3 a)
type M44 a = V4 (V4 a)
fromQuaternion :: Num a => Quaternion a -> M33 a
fromQuaternion :: Quaternion a -> M33 a
fromQuaternion (Quaternion a
w (V3 a
x a
y a
z)) =
V3 a -> V3 a -> V3 a -> M33 a
forall a. a -> a -> a -> V3 a
V3
(a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 (a
1 a -> a -> a
forall a. Num a => a -> a -> a
- a
2 a -> a -> a
forall a. Num a => a -> a -> a
* (a
y2 a -> a -> a
forall a. Num a => a -> a -> a
+ a
z2)) (a
2 a -> a -> a
forall a. Num a => a -> a -> a
* (a
xy a -> a -> a
forall a. Num a => a -> a -> a
- a
zw)) (a
2 a -> a -> a
forall a. Num a => a -> a -> a
* (a
xz a -> a -> a
forall a. Num a => a -> a -> a
+ a
yw)))
(a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 (a
2 a -> a -> a
forall a. Num a => a -> a -> a
* (a
xy a -> a -> a
forall a. Num a => a -> a -> a
+ a
zw)) (a
1 a -> a -> a
forall a. Num a => a -> a -> a
- a
2 a -> a -> a
forall a. Num a => a -> a -> a
* (a
x2 a -> a -> a
forall a. Num a => a -> a -> a
+ a
z2)) (a
2 a -> a -> a
forall a. Num a => a -> a -> a
* (a
yz a -> a -> a
forall a. Num a => a -> a -> a
- a
xw)))
(a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 (a
2 a -> a -> a
forall a. Num a => a -> a -> a
* (a
xz a -> a -> a
forall a. Num a => a -> a -> a
- a
yw)) (a
2 a -> a -> a
forall a. Num a => a -> a -> a
* (a
yz a -> a -> a
forall a. Num a => a -> a -> a
+ a
xw)) (a
1 a -> a -> a
forall a. Num a => a -> a -> a
- a
2 a -> a -> a
forall a. Num a => a -> a -> a
* (a
x2 a -> a -> a
forall a. Num a => a -> a -> a
+ a
y2)))
where
x2 :: a
x2 = a
x a -> a -> a
forall a. Num a => a -> a -> a
* a
x
y2 :: a
y2 = a
y a -> a -> a
forall a. Num a => a -> a -> a
* a
y
z2 :: a
z2 = a
z a -> a -> a
forall a. Num a => a -> a -> a
* a
z
xy :: a
xy = a
x a -> a -> a
forall a. Num a => a -> a -> a
* a
y
xz :: a
xz = a
x a -> a -> a
forall a. Num a => a -> a -> a
* a
z
xw :: a
xw = a
x a -> a -> a
forall a. Num a => a -> a -> a
* a
w
yz :: a
yz = a
y a -> a -> a
forall a. Num a => a -> a -> a
* a
z
yw :: a
yw = a
y a -> a -> a
forall a. Num a => a -> a -> a
* a
w
zw :: a
zw = a
z a -> a -> a
forall a. Num a => a -> a -> a
* a
w
{-# INLINE fromQuaternion #-}
identity :: (Vec v, Num a) => v (v a)
identity :: v (v a)
identity = v a -> v (v a)
forall (t :: * -> *) a. (Vec t, Num a) => t a -> t (t a)
scaled (a -> v a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
1)
{-# INLINE identity #-}
_m22 :: (Vec t, R2 t, R2 v) => Lens' (t (v a)) (M22 a)
_m22 :: Lens' (t (v a)) (M22 a)
_m22 = Lens' (v a) (V2 a) -> Lens' (t (v a)) (t (V2 a))
forall (v :: * -> *) a b. Vec v => Lens' a b -> Lens' (v a) (v b)
column Lens' (v a) (V2 a)
forall (t :: * -> *) a. R2 t => Lens' (t a) (V2 a)
_xy ((t (V2 a) -> m (t (V2 a))) -> t (v a) -> m (t (v a)))
-> ((M22 a -> m (M22 a)) -> t (V2 a) -> m (t (V2 a)))
-> (M22 a -> m (M22 a))
-> t (v a)
-> m (t (v a))
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (M22 a -> m (M22 a)) -> t (V2 a) -> m (t (V2 a))
forall (t :: * -> *) a. R2 t => Lens' (t a) (V2 a)
_xy
_m23 :: (Vec t, R2 t, R3 v) => Lens' (t (v a)) (M23 a)
_m23 :: Lens' (t (v a)) (M23 a)
_m23 = Lens' (v a) (V3 a) -> Lens' (t (v a)) (t (V3 a))
forall (v :: * -> *) a b. Vec v => Lens' a b -> Lens' (v a) (v b)
column Lens' (v a) (V3 a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((t (V3 a) -> m (t (V3 a))) -> t (v a) -> m (t (v a)))
-> ((M23 a -> m (M23 a)) -> t (V3 a) -> m (t (V3 a)))
-> (M23 a -> m (M23 a))
-> t (v a)
-> m (t (v a))
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (M23 a -> m (M23 a)) -> t (V3 a) -> m (t (V3 a))
forall (t :: * -> *) a. R2 t => Lens' (t a) (V2 a)
_xy
_m24 :: (Vec t, R2 t, R4 v) => Lens' (t (v a)) (M24 a)
_m24 :: Lens' (t (v a)) (M24 a)
_m24 = Lens' (v a) (V4 a) -> Lens' (t (v a)) (t (V4 a))
forall (v :: * -> *) a b. Vec v => Lens' a b -> Lens' (v a) (v b)
column Lens' (v a) (V4 a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((t (V4 a) -> m (t (V4 a))) -> t (v a) -> m (t (v a)))
-> ((M24 a -> m (M24 a)) -> t (V4 a) -> m (t (V4 a)))
-> (M24 a -> m (M24 a))
-> t (v a)
-> m (t (v a))
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (M24 a -> m (M24 a)) -> t (V4 a) -> m (t (V4 a))
forall (t :: * -> *) a. R2 t => Lens' (t a) (V2 a)
_xy
_m32 :: (Vec t, R3 t, R2 v) => Lens' (t (v a)) (M32 a)
_m32 :: Lens' (t (v a)) (M32 a)
_m32 = Lens' (v a) (V2 a) -> Lens' (t (v a)) (t (V2 a))
forall (v :: * -> *) a b. Vec v => Lens' a b -> Lens' (v a) (v b)
column Lens' (v a) (V2 a)
forall (t :: * -> *) a. R2 t => Lens' (t a) (V2 a)
_xy ((t (V2 a) -> m (t (V2 a))) -> t (v a) -> m (t (v a)))
-> ((M32 a -> m (M32 a)) -> t (V2 a) -> m (t (V2 a)))
-> (M32 a -> m (M32 a))
-> t (v a)
-> m (t (v a))
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (M32 a -> m (M32 a)) -> t (V2 a) -> m (t (V2 a))
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz
_m33 :: (Vec t, R3 t, R3 v) => Lens' (t (v a)) (M33 a)
_m33 :: Lens' (t (v a)) (M33 a)
_m33 = Lens' (v a) (V3 a) -> Lens' (t (v a)) (t (V3 a))
forall (v :: * -> *) a b. Vec v => Lens' a b -> Lens' (v a) (v b)
column Lens' (v a) (V3 a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((t (V3 a) -> m (t (V3 a))) -> t (v a) -> m (t (v a)))
-> ((M33 a -> m (M33 a)) -> t (V3 a) -> m (t (V3 a)))
-> (M33 a -> m (M33 a))
-> t (v a)
-> m (t (v a))
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (M33 a -> m (M33 a)) -> t (V3 a) -> m (t (V3 a))
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz
_m34 :: (Vec t, R3 t, R4 v) => Lens' (t (v a)) (M34 a)
_m34 :: Lens' (t (v a)) (M34 a)
_m34 = Lens' (v a) (V4 a) -> Lens' (t (v a)) (t (V4 a))
forall (v :: * -> *) a b. Vec v => Lens' a b -> Lens' (v a) (v b)
column Lens' (v a) (V4 a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((t (V4 a) -> m (t (V4 a))) -> t (v a) -> m (t (v a)))
-> ((M34 a -> m (M34 a)) -> t (V4 a) -> m (t (V4 a)))
-> (M34 a -> m (M34 a))
-> t (v a)
-> m (t (v a))
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (M34 a -> m (M34 a)) -> t (V4 a) -> m (t (V4 a))
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz
_m42 :: (Vec t, R4 t, R2 v) => Lens' (t (v a)) (M42 a)
_m42 :: Lens' (t (v a)) (M42 a)
_m42 = Lens' (v a) (V2 a) -> Lens' (t (v a)) (t (V2 a))
forall (v :: * -> *) a b. Vec v => Lens' a b -> Lens' (v a) (v b)
column Lens' (v a) (V2 a)
forall (t :: * -> *) a. R2 t => Lens' (t a) (V2 a)
_xy ((t (V2 a) -> m (t (V2 a))) -> t (v a) -> m (t (v a)))
-> ((M42 a -> m (M42 a)) -> t (V2 a) -> m (t (V2 a)))
-> (M42 a -> m (M42 a))
-> t (v a)
-> m (t (v a))
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (M42 a -> m (M42 a)) -> t (V2 a) -> m (t (V2 a))
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw
_m43 :: (Vec t, R4 t, R3 v) => Lens' (t (v a)) (M43 a)
_m43 :: Lens' (t (v a)) (M43 a)
_m43 = Lens' (v a) (V3 a) -> Lens' (t (v a)) (t (V3 a))
forall (v :: * -> *) a b. Vec v => Lens' a b -> Lens' (v a) (v b)
column Lens' (v a) (V3 a)
forall (t :: * -> *) a. R3 t => Lens' (t a) (V3 a)
_xyz ((t (V3 a) -> m (t (V3 a))) -> t (v a) -> m (t (v a)))
-> ((M43 a -> m (M43 a)) -> t (V3 a) -> m (t (V3 a)))
-> (M43 a -> m (M43 a))
-> t (v a)
-> m (t (v a))
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (M43 a -> m (M43 a)) -> t (V3 a) -> m (t (V3 a))
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw
_m44 :: (Vec t, R4 t, R4 v) => Lens' (t (v a)) (M44 a)
_m44 :: Lens' (t (v a)) (M44 a)
_m44 = Lens' (v a) (V4 a) -> Lens' (t (v a)) (t (V4 a))
forall (v :: * -> *) a b. Vec v => Lens' a b -> Lens' (v a) (v b)
column Lens' (v a) (V4 a)
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw ((t (V4 a) -> m (t (V4 a))) -> t (v a) -> m (t (v a)))
-> ((M44 a -> m (M44 a)) -> t (V4 a) -> m (t (V4 a)))
-> (M44 a -> m (M44 a))
-> t (v a)
-> m (t (v a))
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (M44 a -> m (M44 a)) -> t (V4 a) -> m (t (V4 a))
forall (t :: * -> *) a. R4 t => Lens' (t a) (V4 a)
_xyzw
det22 :: Num a => M22 a -> a
det22 :: M22 a -> a
det22 (V2 (V2 a
a a
b) (V2 a
c a
d)) = a
a a -> a -> a
forall a. Num a => a -> a -> a
* a
d a -> a -> a
forall a. Num a => a -> a -> a
- a
b a -> a -> a
forall a. Num a => a -> a -> a
* a
c
{-# INLINE det22 #-}
det33 :: Num a => M33 a -> a
det33 :: M33 a -> a
det33
( V3
(V3 a
a a
b a
c)
(V3 a
d a
e a
f)
(V3 a
g a
h a
i)
) = a
a a -> a -> a
forall a. Num a => a -> a -> a
* (a
e a -> a -> a
forall a. Num a => a -> a -> a
* a
i a -> a -> a
forall a. Num a => a -> a -> a
- a
f a -> a -> a
forall a. Num a => a -> a -> a
* a
h) a -> a -> a
forall a. Num a => a -> a -> a
- a
d a -> a -> a
forall a. Num a => a -> a -> a
* (a
b a -> a -> a
forall a. Num a => a -> a -> a
* a
i a -> a -> a
forall a. Num a => a -> a -> a
- a
c a -> a -> a
forall a. Num a => a -> a -> a
* a
h) a -> a -> a
forall a. Num a => a -> a -> a
+ a
g a -> a -> a
forall a. Num a => a -> a -> a
* (a
b a -> a -> a
forall a. Num a => a -> a -> a
* a
f a -> a -> a
forall a. Num a => a -> a -> a
- a
c a -> a -> a
forall a. Num a => a -> a -> a
* a
e)
{-# INLINE det33 #-}
det44 :: Num a => M44 a -> a
det44 :: M44 a -> a
det44
( V4
(V4 a
i00 a
i01 a
i02 a
i03)
(V4 a
i10 a
i11 a
i12 a
i13)
(V4 a
i20 a
i21 a
i22 a
i23)
(V4 a
i30 a
i31 a
i32 a
i33)
) =
let s0 :: a
s0 = a
i00 a -> a -> a
forall a. Num a => a -> a -> a
* a
i11 a -> a -> a
forall a. Num a => a -> a -> a
- a
i10 a -> a -> a
forall a. Num a => a -> a -> a
* a
i01
s1 :: a
s1 = a
i00 a -> a -> a
forall a. Num a => a -> a -> a
* a
i12 a -> a -> a
forall a. Num a => a -> a -> a
- a
i10 a -> a -> a
forall a. Num a => a -> a -> a
* a
i02
s2 :: a
s2 = a
i00 a -> a -> a
forall a. Num a => a -> a -> a
* a
i13 a -> a -> a
forall a. Num a => a -> a -> a
- a
i10 a -> a -> a
forall a. Num a => a -> a -> a
* a
i03
s3 :: a
s3 = a
i01 a -> a -> a
forall a. Num a => a -> a -> a
* a
i12 a -> a -> a
forall a. Num a => a -> a -> a
- a
i11 a -> a -> a
forall a. Num a => a -> a -> a
* a
i02
s4 :: a
s4 = a
i01 a -> a -> a
forall a. Num a => a -> a -> a
* a
i13 a -> a -> a
forall a. Num a => a -> a -> a
- a
i11 a -> a -> a
forall a. Num a => a -> a -> a
* a
i03
s5 :: a
s5 = a
i02 a -> a -> a
forall a. Num a => a -> a -> a
* a
i13 a -> a -> a
forall a. Num a => a -> a -> a
- a
i12 a -> a -> a
forall a. Num a => a -> a -> a
* a
i03
c5 :: a
c5 = a
i22 a -> a -> a
forall a. Num a => a -> a -> a
* a
i33 a -> a -> a
forall a. Num a => a -> a -> a
- a
i32 a -> a -> a
forall a. Num a => a -> a -> a
* a
i23
c4 :: a
c4 = a
i21 a -> a -> a
forall a. Num a => a -> a -> a
* a
i33 a -> a -> a
forall a. Num a => a -> a -> a
- a
i31 a -> a -> a
forall a. Num a => a -> a -> a
* a
i23
c3 :: a
c3 = a
i21 a -> a -> a
forall a. Num a => a -> a -> a
* a
i32 a -> a -> a
forall a. Num a => a -> a -> a
- a
i31 a -> a -> a
forall a. Num a => a -> a -> a
* a
i22
c2 :: a
c2 = a
i20 a -> a -> a
forall a. Num a => a -> a -> a
* a
i33 a -> a -> a
forall a. Num a => a -> a -> a
- a
i30 a -> a -> a
forall a. Num a => a -> a -> a
* a
i23
c1 :: a
c1 = a
i20 a -> a -> a
forall a. Num a => a -> a -> a
* a
i32 a -> a -> a
forall a. Num a => a -> a -> a
- a
i30 a -> a -> a
forall a. Num a => a -> a -> a
* a
i22
c0 :: a
c0 = a
i20 a -> a -> a
forall a. Num a => a -> a -> a
* a
i31 a -> a -> a
forall a. Num a => a -> a -> a
- a
i30 a -> a -> a
forall a. Num a => a -> a -> a
* a
i21
in a
s0 a -> a -> a
forall a. Num a => a -> a -> a
* a
c5 a -> a -> a
forall a. Num a => a -> a -> a
- a
s1 a -> a -> a
forall a. Num a => a -> a -> a
* a
c4 a -> a -> a
forall a. Num a => a -> a -> a
+ a
s2 a -> a -> a
forall a. Num a => a -> a -> a
* a
c3 a -> a -> a
forall a. Num a => a -> a -> a
+ a
s3 a -> a -> a
forall a. Num a => a -> a -> a
* a
c2 a -> a -> a
forall a. Num a => a -> a -> a
- a
s4 a -> a -> a
forall a. Num a => a -> a -> a
* a
c1 a -> a -> a
forall a. Num a => a -> a -> a
+ a
s5 a -> a -> a
forall a. Num a => a -> a -> a
* a
c0
{-# INLINE det44 #-}
inv22 :: Fractional a => M22 a -> M22 a
inv22 :: M22 a -> M22 a
inv22 m :: M22 a
m@(V2 (V2 a
a a
b) (V2 a
c a
d)) = (a
1 a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
det) a -> M22 a -> M22 a
forall (m :: * -> *) (r :: * -> *) a.
(Vec m, Vec r, Num a) =>
a -> m (r a) -> m (r a)
*!! V2 a -> V2 a -> M22 a
forall a. a -> a -> V2 a
V2 (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
d (-a
b)) (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 (-a
c) a
a)
where
det :: a
det = M22 a -> a
forall a. Num a => M22 a -> a
det22 M22 a
m
{-# INLINE inv22 #-}
inv33 :: Fractional a => M33 a -> M33 a
inv33 :: M33 a -> M33 a
inv33
m :: M33 a
m@( V3
(V3 a
a a
b a
c)
(V3 a
d a
e a
f)
(V3 a
g a
h a
i)
) =
(a
1 a -> a -> a
forall a. Fractional a => a -> a -> a
/ a
det)
a -> M33 a -> M33 a
forall (m :: * -> *) (r :: * -> *) a.
(Vec m, Vec r, Num a) =>
a -> m (r a) -> m (r a)
*!! V3 a -> V3 a -> V3 a -> M33 a
forall a. a -> a -> a -> V3 a
V3
(a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
a' a
b' a
c')
(a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
d' a
e' a
f')
(a -> a -> a -> V3 a
forall a. a -> a -> a -> V3 a
V3 a
g' a
h' a
i')
where
a' :: a
a' = (a, a, a, a) -> a
forall a. Num a => (a, a, a, a) -> a
cofactor (a
e, a
f, a
h, a
i)
b' :: a
b' = (a, a, a, a) -> a
forall a. Num a => (a, a, a, a) -> a
cofactor (a
c, a
b, a
i, a
h)
c' :: a
c' = (a, a, a, a) -> a
forall a. Num a => (a, a, a, a) -> a
cofactor (a
b, a
c, a
e, a
f)
d' :: a
d' = (a, a, a, a) -> a
forall a. Num a => (a, a, a, a) -> a
cofactor (a
f, a
d, a
i, a
g)
e' :: a
e' = (a, a, a, a) -> a
forall a. Num a => (a, a, a, a) -> a
cofactor (a
a, a
c, a
g, a
i)
f' :: a
f' = (a, a, a, a) -> a
forall a. Num a => (a, a, a, a) -> a
cofactor (a
c, a
a, a
f, a
d)
g' :: a
g' = (a, a, a, a) -> a
forall a. Num a => (a, a, a, a) -> a
cofactor (a
d, a
e, a
g, a
h)
h' :: a
h' = (a, a, a, a) -> a
forall a. Num a => (a, a, a, a) -> a
cofactor (a
b, a
a, a
h, a
g)
i' :: a
i' = (a, a, a, a) -> a
forall a. Num a => (a, a, a, a) -> a
cofactor (a
a, a
b, a
d, a
e)
cofactor :: (a, a, a, a) -> a
cofactor (a
q, a
r, a
s, a
t) = M22 a -> a
forall a. Num a => M22 a -> a
det22 (V2 a -> V2 a -> M22 a
forall a. a -> a -> V2 a
V2 (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
q a
r) (a -> a -> V2 a
forall a. a -> a -> V2 a
V2 a
s a
t))
det :: a
det = M33 a -> a
forall a. Num a => M33 a -> a
det33 M33 a
m
{-# INLINE inv33 #-}
transpose :: (Vec f, Vec g) => f (g a) -> g (f a)
transpose :: f (g a) -> g (f a)
transpose = f (g a) -> g (f a)
forall (t :: * -> *) (f :: * -> *) a.
(Traversable t, Applicative f) =>
t (f a) -> f (t a)
sequenceA
{-# INLINE transpose #-}
inv44 :: Fractional a => M44 a -> M44 a
inv44 :: M44 a -> M44 a
inv44
( V4
(V4 a
i00 a
i01 a
i02 a
i03)
(V4 a
i10 a
i11 a
i12 a
i13)
(V4 a
i20 a
i21 a
i22 a
i23)
(V4 a
i30 a
i31 a
i32 a
i33)
) =
let s0 :: a
s0 = a
i00 a -> a -> a
forall a. Num a => a -> a -> a
* a
i11 a -> a -> a
forall a. Num a => a -> a -> a
- a
i10 a -> a -> a
forall a. Num a => a -> a -> a
* a
i01
s1 :: a
s1 = a
i00 a -> a -> a
forall a. Num a => a -> a -> a
* a
i12 a -> a -> a
forall a. Num a => a -> a -> a
- a
i10 a -> a -> a
forall a. Num a => a -> a -> a
* a
i02
s2 :: a
s2 = a
i00 a -> a -> a
forall a. Num a => a -> a -> a
* a
i13 a -> a -> a
forall a. Num a => a -> a -> a
- a
i10 a -> a -> a
forall a. Num a => a -> a -> a
* a
i03
s3 :: a
s3 = a
i01 a -> a -> a
forall a. Num a => a -> a -> a
* a
i12 a -> a -> a
forall a. Num a => a -> a -> a
- a
i11 a -> a -> a
forall a. Num a => a -> a -> a
* a
i02
s4 :: a
s4 = a
i01 a -> a -> a
forall a. Num a => a -> a -> a
* a
i13 a -> a -> a
forall a. Num a => a -> a -> a
- a
i11 a -> a -> a
forall a. Num a => a -> a -> a
* a
i03
s5 :: a
s5 = a
i02 a -> a -> a
forall a. Num a => a -> a -> a
* a
i13 a -> a -> a
forall a. Num a => a -> a -> a
- a
i12 a -> a -> a
forall a. Num a => a -> a -> a
* a
i03
c5 :: a
c5 = a
i22 a -> a -> a
forall a. Num a => a -> a -> a
* a
i33 a -> a -> a
forall a. Num a => a -> a -> a
- a
i32 a -> a -> a
forall a. Num a => a -> a -> a
* a
i23
c4 :: a
c4 = a
i21 a -> a -> a
forall a. Num a => a -> a -> a
* a
i33 a -> a -> a
forall a. Num a => a -> a -> a
- a
i31 a -> a -> a
forall a. Num a => a -> a -> a
* a
i23
c3 :: a
c3 = a
i21 a -> a -> a
forall a. Num a => a -> a -> a
* a
i32 a -> a -> a
forall a. Num a => a -> a -> a
- a
i31 a -> a -> a
forall a. Num a => a -> a -> a
* a
i22
c2 :: a
c2 = a
i20 a -> a -> a
forall a. Num a => a -> a -> a
* a
i33 a -> a -> a
forall a. Num a => a -> a -> a
- a
i30 a -> a -> a
forall a. Num a => a -> a -> a
* a
i23
c1 :: a
c1 = a
i20 a -> a -> a
forall a. Num a => a -> a -> a
* a
i32 a -> a -> a
forall a. Num a => a -> a -> a
- a
i30 a -> a -> a
forall a. Num a => a -> a -> a
* a
i22
c0 :: a
c0 = a
i20 a -> a -> a
forall a. Num a => a -> a -> a
* a
i31 a -> a -> a
forall a. Num a => a -> a -> a
- a
i30 a -> a -> a
forall a. Num a => a -> a -> a
* a
i21
det :: a
det = a
s0 a -> a -> a
forall a. Num a => a -> a -> a
* a
c5 a -> a -> a
forall a. Num a => a -> a -> a
- a
s1 a -> a -> a
forall a. Num a => a -> a -> a
* a
c4 a -> a -> a
forall a. Num a => a -> a -> a
+ a
s2 a -> a -> a
forall a. Num a => a -> a -> a
* a
c3 a -> a -> a
forall a. Num a => a -> a -> a
+ a
s3 a -> a -> a
forall a. Num a => a -> a -> a
* a
c2 a -> a -> a
forall a. Num a => a -> a -> a
- a
s4 a -> a -> a
forall a. Num a => a -> a -> a
* a
c1 a -> a -> a
forall a. Num a => a -> a -> a
+ a
s5 a -> a -> a
forall a. Num a => a -> a -> a
* a
c0
invDet :: a
invDet = a -> a
forall a. Fractional a => a -> a
recip a
det
in a
invDet
a -> M44 a -> M44 a
forall (m :: * -> *) (r :: * -> *) a.
(Vec m, Vec r, Num a) =>
a -> m (r a) -> m (r a)
*!! V4 a -> V4 a -> V4 a -> V4 a -> M44 a
forall a. a -> a -> a -> a -> V4 a
V4
( a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4
(a
i11 a -> a -> a
forall a. Num a => a -> a -> a
* a
c5 a -> a -> a
forall a. Num a => a -> a -> a
- a
i12 a -> a -> a
forall a. Num a => a -> a -> a
* a
c4 a -> a -> a
forall a. Num a => a -> a -> a
+ a
i13 a -> a -> a
forall a. Num a => a -> a -> a
* a
c3)
(-a
i01 a -> a -> a
forall a. Num a => a -> a -> a
* a
c5 a -> a -> a
forall a. Num a => a -> a -> a
+ a
i02 a -> a -> a
forall a. Num a => a -> a -> a
* a
c4 a -> a -> a
forall a. Num a => a -> a -> a
- a
i03 a -> a -> a
forall a. Num a => a -> a -> a
* a
c3)
(a
i31 a -> a -> a
forall a. Num a => a -> a -> a
* a
s5 a -> a -> a
forall a. Num a => a -> a -> a
- a
i32 a -> a -> a
forall a. Num a => a -> a -> a
* a
s4 a -> a -> a
forall a. Num a => a -> a -> a
+ a
i33 a -> a -> a
forall a. Num a => a -> a -> a
* a
s3)
(-a
i21 a -> a -> a
forall a. Num a => a -> a -> a
* a
s5 a -> a -> a
forall a. Num a => a -> a -> a
+ a
i22 a -> a -> a
forall a. Num a => a -> a -> a
* a
s4 a -> a -> a
forall a. Num a => a -> a -> a
- a
i23 a -> a -> a
forall a. Num a => a -> a -> a
* a
s3)
)
( a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4
(-a
i10 a -> a -> a
forall a. Num a => a -> a -> a
* a
c5 a -> a -> a
forall a. Num a => a -> a -> a
+ a
i12 a -> a -> a
forall a. Num a => a -> a -> a
* a
c2 a -> a -> a
forall a. Num a => a -> a -> a
- a
i13 a -> a -> a
forall a. Num a => a -> a -> a
* a
c1)
(a
i00 a -> a -> a
forall a. Num a => a -> a -> a
* a
c5 a -> a -> a
forall a. Num a => a -> a -> a
- a
i02 a -> a -> a
forall a. Num a => a -> a -> a
* a
c2 a -> a -> a
forall a. Num a => a -> a -> a
+ a
i03 a -> a -> a
forall a. Num a => a -> a -> a
* a
c1)
(-a
i30 a -> a -> a
forall a. Num a => a -> a -> a
* a
s5 a -> a -> a
forall a. Num a => a -> a -> a
+ a
i32 a -> a -> a
forall a. Num a => a -> a -> a
* a
s2 a -> a -> a
forall a. Num a => a -> a -> a
- a
i33 a -> a -> a
forall a. Num a => a -> a -> a
* a
s1)
(a
i20 a -> a -> a
forall a. Num a => a -> a -> a
* a
s5 a -> a -> a
forall a. Num a => a -> a -> a
- a
i22 a -> a -> a
forall a. Num a => a -> a -> a
* a
s2 a -> a -> a
forall a. Num a => a -> a -> a
+ a
i23 a -> a -> a
forall a. Num a => a -> a -> a
* a
s1)
)
( a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4
(a
i10 a -> a -> a
forall a. Num a => a -> a -> a
* a
c4 a -> a -> a
forall a. Num a => a -> a -> a
- a
i11 a -> a -> a
forall a. Num a => a -> a -> a
* a
c2 a -> a -> a
forall a. Num a => a -> a -> a
+ a
i13 a -> a -> a
forall a. Num a => a -> a -> a
* a
c0)
(-a
i00 a -> a -> a
forall a. Num a => a -> a -> a
* a
c4 a -> a -> a
forall a. Num a => a -> a -> a
+ a
i01 a -> a -> a
forall a. Num a => a -> a -> a
* a
c2 a -> a -> a
forall a. Num a => a -> a -> a
- a
i03 a -> a -> a
forall a. Num a => a -> a -> a
* a
c0)
(a
i30 a -> a -> a
forall a. Num a => a -> a -> a
* a
s4 a -> a -> a
forall a. Num a => a -> a -> a
- a
i31 a -> a -> a
forall a. Num a => a -> a -> a
* a
s2 a -> a -> a
forall a. Num a => a -> a -> a
+ a
i33 a -> a -> a
forall a. Num a => a -> a -> a
* a
s0)
(-a
i20 a -> a -> a
forall a. Num a => a -> a -> a
* a
s4 a -> a -> a
forall a. Num a => a -> a -> a
+ a
i21 a -> a -> a
forall a. Num a => a -> a -> a
* a
s2 a -> a -> a
forall a. Num a => a -> a -> a
- a
i23 a -> a -> a
forall a. Num a => a -> a -> a
* a
s0)
)
( a -> a -> a -> a -> V4 a
forall a. a -> a -> a -> a -> V4 a
V4
(-a
i10 a -> a -> a
forall a. Num a => a -> a -> a
* a
c3 a -> a -> a
forall a. Num a => a -> a -> a
+ a
i11 a -> a -> a
forall a. Num a => a -> a -> a
* a
c1 a -> a -> a
forall a. Num a => a -> a -> a
- a
i12 a -> a -> a
forall a. Num a => a -> a -> a
* a
c0)
(a
i00 a -> a -> a
forall a. Num a => a -> a -> a
* a
c3 a -> a -> a
forall a. Num a => a -> a -> a
- a
i01 a -> a -> a
forall a. Num a => a -> a -> a
* a
c1 a -> a -> a
forall a. Num a => a -> a -> a
+ a
i02 a -> a -> a
forall a. Num a => a -> a -> a
* a
c0)
(-a
i30 a -> a -> a
forall a. Num a => a -> a -> a
* a
s3 a -> a -> a
forall a. Num a => a -> a -> a
+ a
i31 a -> a -> a
forall a. Num a => a -> a -> a
* a
s1 a -> a -> a
forall a. Num a => a -> a -> a
- a
i32 a -> a -> a
forall a. Num a => a -> a -> a
* a
s0)
(a
i20 a -> a -> a
forall a. Num a => a -> a -> a
* a
s3 a -> a -> a
forall a. Num a => a -> a -> a
- a
i21 a -> a -> a
forall a. Num a => a -> a -> a
* a
s1 a -> a -> a
forall a. Num a => a -> a -> a
+ a
i22 a -> a -> a
forall a. Num a => a -> a -> a
* a
s0)
)
{-# INLINE inv44 #-}