module Linear.Mat
( M2(..) , M3(..) , M4(..)
, M2x3(..) , M2x4(..) , M3x2(..)
, M3x4(..) , M4x2(..) , M4x3(..)
, Ortho2 , Ortho3 , Ortho4
, Proj3 , Proj4
)
where
import Foreign.Storable
import Foreign.Ptr
import System.Random
import Linear.Class
import Linear.Vect
data M2 a = M2 !(V2 a) !(V2 a) deriving (Read,Show)
data M3 a = M3 !(V3 a) !(V3 a) !(V3 a) deriving (Read,Show)
data M4 a = M4 !(V4 a) !(V4 a) !(V4 a) !(V4 a) deriving (Read,Show)
data M2x3 a = M2x3 !a !a !a !a !a !a deriving (Read,Show)
data M2x4 a = M2x4 !a !a !a !a !a !a !a !a deriving (Read,Show)
data M3x2 a = M3x2 !a !a !a !a !a !a deriving (Read,Show)
data M3x4 a = M3x4 !a !a !a !a !a !a !a !a !a !a !a !a deriving (Read,Show)
data M4x2 a = M4x2 !a !a !a !a !a !a !a !a deriving (Read,Show)
data M4x3 a = M4x3 !a !a !a !a !a !a !a !a !a !a !a !a deriving (Read,Show)
newtype Ortho2 a = Ortho2 (M2 a) deriving (Read,Show,Storable,MultSemiGroup,Determinant a,Dimension)
newtype Ortho3 a = Ortho3 (M3 a) deriving (Read,Show,Storable,MultSemiGroup,Determinant a,Dimension)
newtype Ortho4 a = Ortho4 (M4 a) deriving (Read,Show,Storable,MultSemiGroup,Determinant a,Dimension)
newtype Proj3 a = Proj3 (M3 a) deriving (Read,Show,Storable,MultSemiGroup)
newtype Proj4 a = Proj4 (M4 a) deriving (Read,Show,Storable,MultSemiGroup)
instance Fractional a => Orthogonal a M2 Ortho2 where
fromOrtho (Ortho2 o) = o
toOrthoUnsafe = Ortho2
instance Fractional a => Orthogonal a M3 Ortho3 where
fromOrtho (Ortho3 o) = o
toOrthoUnsafe = Ortho3
instance Fractional a => Orthogonal a M4 Ortho4 where
fromOrtho (Ortho4 o) = o
toOrthoUnsafe = Ortho4
instance Transpose (Ortho2 a) (Ortho2 a) where
transpose (Ortho2 o) = Ortho2 (transpose o)
instance Fractional a => SquareMatrix (Ortho2 a) where
idmtx = Ortho2 idmtx
inverse = transpose
instance Transpose (Ortho3 a) (Ortho3 a) where
transpose (Ortho3 o) = Ortho3 (transpose o)
instance Fractional a => SquareMatrix (Ortho3 a) where
idmtx = Ortho3 idmtx
inverse = transpose
instance Transpose (Ortho4 a) (Ortho4 a) where
transpose (Ortho4 o) = Ortho4 (transpose o)
instance Fractional a => SquareMatrix (Ortho4 a) where
idmtx = Ortho4 idmtx
inverse = transpose
instance (Floating a, Ord a, Random a) => Random (Ortho2 a) where
random g = let (o,h) = _rndOrtho2 g in (toOrthoUnsafe (_flip1stRow2 o), h)
randomR _ = random
instance (Floating a, Ord a, Random a) => Random (Ortho3 a) where
random g = let (o,h) = _rndOrtho3 g in (toOrthoUnsafe ( o), h)
randomR _ = random
instance (Floating a, Ord a, Random a) => Random (Ortho4 a) where
random g = let (o,h) = _rndOrtho4 g in (toOrthoUnsafe (_flip1stRow4 o), h)
randomR _ = random
_rndOrtho2 :: (Floating a, Random a, Ord a, RandomGen g) => g -> (M2 a, g)
_rndOrtho2 g = (h2, g1) where
h2 = householder u2
(u2,g1) = random g
_rndOrtho3 :: (Floating a, Random a, Ord a, RandomGen g) => g -> (M3 a, g)
_rndOrtho3 g = ( (h3 .*. m3), g2) where
m3 = (extendWith :: Num a => a -> M2 a -> M3 a) 1 o2
h3 = householder u3
(u3,g1) = random g
(o2,g2) = _rndOrtho2 g1
_rndOrtho4 :: (Floating a, Random a, Ord a, RandomGen g) => g -> (M4 a, g)
_rndOrtho4 g = ( (h4 .*. m4), g2) where
m4 = (extendWith :: Num a => a -> M3 a -> M4 a) 1 o3
h4 = householder u4
(u4,g1) = random g
(o3,g2) = _rndOrtho3 g1
_flip1stRow2 :: Num a => M2 a -> M2 a
_flip1stRow2 (M2 a b) = M2 (neg a) b
_flip1stRow3 :: Num a => M3 a -> M3 a
_flip1stRow3 (M3 a b c) = M3 (neg a) b c
_flip1stRow4 :: Num a => M4 a -> M4 a
_flip1stRow4 (M4 a b c d) = M4 (neg a) b c d
instance Fractional a => Projective a V2 M2 Ortho2 M3 Proj3 where
fromProjective (Proj3 m) = m
toProjectiveUnsafe = Proj3
orthogonal = Proj3 . extendWith (1 :: a) . fromOrtho
linear = Proj3 . extendWith (1 :: a)
translation v = Proj3 $ M3 (V3 1 0 0) (V3 0 1 0) (extendWith (1 :: a) v)
scaling v = Proj3 $ diag (extendWith (1 :: a) v)
instance Fractional a => Projective a V3 M3 Ortho3 M4 Proj4 where
fromProjective (Proj4 m) = m
toProjectiveUnsafe = Proj4
orthogonal = Proj4 . extendWith (1 :: a) . fromOrtho
linear = Proj4 . extendWith (1 :: a)
translation v = Proj4 $ M4 (V4 1 0 0 0) (V4 0 1 0 0) (V4 0 0 1 0) (extendWith (1 :: a) v)
scaling v = Proj4 $ diag (extendWith (1 :: a) v)
instance Transpose (Proj3 a) (Proj3 a) where
transpose (Proj3 m) = Proj3 (transpose m)
instance Fractional a => SquareMatrix (Proj3 a) where
idmtx = Proj3 idmtx
inverse = _invertProj3
instance Transpose (Proj4 a) (Proj4 a) where
transpose (Proj4 m) = Proj4 (transpose m)
instance Fractional a => SquareMatrix (Proj4 a) where
idmtx = Proj4 idmtx
inverse = _invertProj4
_invertProj3 :: (Fractional a, Extend a V2 V3) => Proj3 a -> Proj3 a
_invertProj3 (Proj3 mat@(M3 _ _ t)) =
Proj3 $ M3 (extendZero a) (extendZero b) (extendWith 1 t')
where
t' = neg $ (trim :: Extend a V2 V3 => V3 a -> V2 a) t .* invm2
invm2@(M2 a b) = inverse $ trim mat
_invertProj4 :: Fractional a => Proj4 a -> Proj4 a
_invertProj4 (Proj4 mat@(M4 _ _ _ t)) =
Proj4 $ M4 (extendZero a) (extendZero b) (extendZero c) (extendWith 1 t')
where
t' = neg $ (trim :: Extend a V3 V4 => V4 a -> V3 a) t .* invm3
invm3@(M3 a b c) = inverse $ trim mat
instance Transpose (M2 a) (M2 a) where
transpose (M2 (V2 x1 y1) (V2 x2 y2)) =
M2 (V2 x1 x2)
(V2 y1 y2)
instance Fractional a => SquareMatrix (M2 a) where
idmtx = M2 (V2 1 0) (V2 0 1)
inverse (M2 (V2 a b) (V2 c d)) =
M2 (V2 (d*r) (b*r)) (V2 (c*r) (a*r))
where r = 1.0 / (a*d b*c)
instance Num a => AbelianGroup (M2 a) where
(&+) (M2 r1 r2) (M2 s1 s2) = M2 (r1 &+ s1) (r2 &+ s2)
(&-) (M2 r1 r2) (M2 s1 s2) = M2 (r1 &- s1) (r2 &- s2)
neg (M2 r1 r2) = M2 (neg r1) (neg r2)
zero = M2 zero zero
instance Num a => Vector a M2 where
scalarMul s (M2 r1 r2) = M2 (g r1) (g r2) where g = scalarMul s
mapVec f (M2 r1 r2) = M2 (g r1) (g r2) where g = mapVec f
instance Fractional a => MultSemiGroup (M2 a) where
(.*.) (M2 r1 r2) n =
let (M2 c1 c2) = transpose n
in M2 (V2 (r1 &. c1) (r1 &. c2))
(V2 (r2 &. c1) (r2 &. c2))
one = idmtx
instance Fractional a => Ring (M2 a)
instance Num a => LeftModule (M2 a) (V2 a) where
lmul (M2 row1 row2) v = V2 (row1 &. v) (row2 &. v)
instance Fractional a => RightModule (V2 a) (M2 a) where
rmul v mt = lmul (transpose mt) v
instance Num a => Diagonal (V2 a) (M2 a) where
diag (V2 x y) = M2 (V2 x 0) (V2 0 y)
instance Num a => Tensor (M2 a) (V2 a) where
outer (V2 a b) (V2 x y) = M2
(V2 (a*x) (a*y))
(V2 (b*x) (b*y))
instance Num a => Determinant a (M2 a) where
det (M2 (V2 a b) (V2 c d)) = a*d b*c
instance (Num a, Storable a) => Storable (M2 a) where
sizeOf _ = 2 * sizeOf (undefined :: V2 a)
alignment _ = alignment (undefined :: V2 a)
peek q = do
let p = castPtr q :: Ptr (V2 a)
k = sizeOf (undefined :: V2 a)
r1 <- peek p
r2 <- peekByteOff p k
return (M2 r1 r2)
poke q (M2 r1 r2) = do
let p = castPtr q :: Ptr (V2 a)
k = sizeOf (undefined :: V2 a)
poke p r1
pokeByteOff p k r2
instance (Num a, Random a) => Random (M2 a) where
random = randomR (M2 v1 v1 , M2 v2 v2) where
v1 = V2 (1) (1)
v2 = V2 1 1
randomR (M2 a b, M2 c d) gen =
let (x,gen1) = randomR (a,c) gen
(y,gen2) = randomR (b,d) gen1
in (M2 x y, gen2)
instance Num a => Dimension (M2 a) where dim _ = 2
instance (Floating a) => MatrixNorms a (M2 a) where
frobeniusNorm (M2 r1 r2) =
sqrt $
normsqr r1 +
normsqr r2
instance Num a => Pointwise (M2 a) where
pointwise (M2 x1 y1) (M2 x2 y2) = M2 (x1 &! x2) (y1 &! y2)
instance Transpose (M3 a) (M3 a) where
transpose (M3 (V3 x1 y1 z1) (V3 x2 y2 z2) (V3 x3 y3 z3)) =
M3 (V3 x1 x2 x3) (V3 y1 y2 y3) (V3 z1 z2 z3)
instance Fractional a => SquareMatrix (M3 a) where
idmtx = M3 (V3 1 0 0) (V3 0 1 0) (V3 0 0 1)
inverse (M3 (V3 a b c) (V3 e f g) (V3 i j k)) =
M3 (V3 (d11*r) (d21*r) (d31*r))
(V3 (d12*r) (d22*r) (d32*r))
(V3 (d13*r) (d23*r) (d33*r))
where
r = 1.0 / ( a*d11 + b*d12 + c*d13 )
d11 = f*k g*j
d12 = g*i e*k
d13 = e*j f*i
d31 = b*g c*f
d32 = c*e a*g
d33 = a*f b*e
d21 = c*j b*k
d22 = a*k c*i
d23 = b*i a*j
instance Num a => AbelianGroup (M3 a) where
(&+) (M3 r1 r2 r3) (M3 s1 s2 s3) = M3 (r1 &+ s1) (r2 &+ s2) (r3 &+ s3)
(&-) (M3 r1 r2 r3) (M3 s1 s2 s3) = M3 (r1 &- s1) (r2 &- s2) (r3 &- s3)
neg (M3 r1 r2 r3) = M3 (neg r1) (neg r2) (neg r3)
zero = M3 zero zero zero
instance Num a => Vector a M3 where
scalarMul s (M3 r1 r2 r3) = M3 (g r1) (g r2) (g r3) where g = scalarMul s
mapVec f (M3 r1 r2 r3) = M3 (g r1) (g r2) (g r3) where g = mapVec f
instance Fractional a => MultSemiGroup (M3 a) where
(.*.) (M3 r1 r2 r3) n =
let (M3 c1 c2 c3) = transpose n
in M3 (V3 (r1 &. c1) (r1 &. c2) (r1 &. c3))
(V3 (r2 &. c1) (r2 &. c2) (r2 &. c3))
(V3 (r3 &. c1) (r3 &. c2) (r3 &. c3))
one = idmtx
instance Fractional a => Ring (M3 a)
instance Num a => LeftModule (M3 a) (V3 a) where
lmul (M3 row1 row2 row3) v = V3 (row1 &. v) (row2 &. v) (row3 &. v)
instance Fractional a => RightModule (V3 a) (M3 a) where
rmul v mt = lmul (transpose mt) v
instance Num a => Diagonal (V3 a) (M3 a) where
diag (V3 x y z) = M3 (V3 x 0 0) (V3 0 y 0) (V3 0 0 z)
instance Num a => Tensor (M3 a) (V3 a) where
outer (V3 a b c) (V3 x y z) = M3
(V3 (a*x) (a*y) (a*z))
(V3 (b*x) (b*y) (b*z))
(V3 (c*x) (c*y) (c*z))
instance Num a => Determinant a (M3 a) where
det (M3 r1 r2 r3) = det (r1,r2,r3)
instance (Num a, Storable a) => Storable (M3 a) where
sizeOf _ = 3 * sizeOf (undefined::V3 a)
alignment _ = alignment (undefined::V3 a)
peek q = do
let p = castPtr q :: Ptr (V3 a)
k = sizeOf (undefined::V3 a)
r1 <- peek p
r2 <- peekByteOff p (k )
r3 <- peekByteOff p (k+k)
return (M3 r1 r2 r3)
poke q (M3 r1 r2 r3) = do
let p = castPtr q :: Ptr (V3 a)
k = sizeOf (undefined::V3 a)
poke p r1
pokeByteOff p (k ) r2
pokeByteOff p (k+k) r3
instance (Num a, Random a) => Random (M3 a) where
random = randomR (M3 v1 v1 v1 , M3 v2 v2 v2) where
v1 = V3 (1) (1) (1)
v2 = V3 1 1 1
randomR (M3 a b c, M3 d e f) gen =
let (x,gen1) = randomR (a,d) gen
(y,gen2) = randomR (b,e) gen1
(z,gen3) = randomR (c,f) gen2
in (M3 x y z, gen3)
instance Num a => Dimension (M3 a) where dim _ = 3
instance Floating a => MatrixNorms a (M3 a) where
frobeniusNorm (M3 r1 r2 r3) =
sqrt $
normsqr r1 +
normsqr r2 +
normsqr r3
instance Num a => Pointwise (M3 a) where
pointwise (M3 x1 y1 z1) (M3 x2 y2 z2) = M3 (x1 &! x2) (y1 &! y2) (z1 &! z2)
instance Transpose (M4 a) (M4 a) where
transpose (M4 (V4 x1 y1 z1 w1) (V4 x2 y2 z2 w2) (V4 x3 y3 z3 w3) (V4 x4 y4 z4 w4)) =
M4 (V4 x1 x2 x3 x4)
(V4 y1 y2 y3 y4)
(V4 z1 z2 z3 z4)
(V4 w1 w2 w3 w4)
instance Num a => SquareMatrix (M4 a) where
idmtx = M4 (V4 1 0 0 0) (V4 0 1 0 0) (V4 0 0 1 0) (V4 0 0 0 1)
inverse = error "inverse/M4: not implemented yet"
instance Num a => AbelianGroup (M4 a) where
(&+) (M4 r1 r2 r3 r4) (M4 s1 s2 s3 s4) = M4 (r1 &+ s1) (r2 &+ s2) (r3 &+ s3) (r4 &+ s4)
(&-) (M4 r1 r2 r3 r4) (M4 s1 s2 s3 s4) = M4 (r1 &- s1) (r2 &- s2) (r3 &- s3) (r4 &- s4)
neg (M4 r1 r2 r3 r4) = M4 (neg r1) (neg r2) (neg r3) (neg r4)
zero = M4 zero zero zero zero
instance Num a => Vector a M4 where
scalarMul s (M4 r1 r2 r3 r4) = M4 (g r1) (g r2) (g r3) (g r4) where g = scalarMul s
mapVec f (M4 r1 r2 r3 r4) = M4 (g r1) (g r2) (g r3) (g r4) where g = mapVec f
instance Num a => MultSemiGroup (M4 a) where
(.*.) (M4 r1 r2 r3 r4) n =
let (M4 c1 c2 c3 c4) = transpose n
in M4 (V4 (r1 &. c1) (r1 &. c2) (r1 &. c3) (r1 &. c4))
(V4 (r2 &. c1) (r2 &. c2) (r2 &. c3) (r2 &. c4))
(V4 (r3 &. c1) (r3 &. c2) (r3 &. c3) (r3 &. c4))
(V4 (r4 &. c1) (r4 &. c2) (r4 &. c3) (r4 &. c4))
one = idmtx
instance Num a => Ring (M4 a)
instance Num a => LeftModule (M4 a) (V4 a) where
lmul (M4 row1 row2 row3 row4) v = V4 (row1 &. v) (row2 &. v) (row3 &. v) (row4 &. v)
instance Num a => RightModule (V4 a) (M4 a) where
rmul v mt = lmul (transpose mt) v
instance Num a => Diagonal (V4 a) (M4 a) where
diag (V4 x y z w) = M4 (V4 x 0 0 0) (V4 0 y 0 0) (V4 0 0 z 0) (V4 0 0 0 w)
instance Num a => Tensor (M4 a) (V4 a) where
outer (V4 a b c d) (V4 x y z w) = M4
(V4 (a*x) (a*y) (a*z) (a*w))
(V4 (b*x) (b*y) (b*z) (b*w))
(V4 (c*x) (c*y) (c*z) (c*w))
(V4 (d*x) (d*y) (d*z) (d*w))
instance Num a => Determinant a (M4 a) where
det = error "det/M4: not implemented yet"
instance (Num a, Storable a) => Storable (M4 a) where
sizeOf _ = 4 * sizeOf (undefined::V4 a)
alignment _ = alignment (undefined::V4 a)
peek q = do
let p = castPtr q :: Ptr (V4 a)
k = sizeOf (undefined :: V4 a)
r1 <- peek p
r2 <- peekByteOff p (k )
r3 <- peekByteOff p (k+k)
r4 <- peekByteOff p (3*k)
return (M4 r1 r2 r3 r4)
poke q (M4 r1 r2 r3 r4) = do
let p = castPtr q :: Ptr (V4 a)
k = sizeOf (undefined :: V4 a)
poke p r1
pokeByteOff p (k ) r2
pokeByteOff p (k+k) r3
pokeByteOff p (3*k) r4
instance (Num a, Random a) => Random (M4 a) where
random = randomR (M4 v1 v1 v1 v1, M4 v2 v2 v2 v2) where
v1 = V4 (1) (1) (1) (1)
v2 = V4 1 1 1 1
randomR (M4 a b c d, M4 e f g h) gen =
let (x,gen1) = randomR (a,e) gen
(y,gen2) = randomR (b,f) gen1
(z,gen3) = randomR (c,g) gen2
(w,gen4) = randomR (d,h) gen3
in (M4 x y z w, gen4)
instance Num a => Dimension (M4 a) where dim _ = 4
instance Floating a => MatrixNorms a (M4 a) where
frobeniusNorm (M4 r1 r2 r3 r4) =
sqrt $
normsqr r1 +
normsqr r2 +
normsqr r3 +
normsqr r4
instance Num a => Pointwise (M4 a) where
pointwise (M4 x1 y1 z1 w1) (M4 x2 y2 z2 w2) = M4 (x1 &! x2) (y1 &! y2) (z1 &! z2) (w1 &! w2)
instance Num a => Extend a M2 M3 where
extendZero (M2 p q) = M3 (extendZero p) (extendZero q) zero
extendWith w (M2 p q) = M3 (extendZero p) (extendZero q) (V3 0 0 w)
trim (M3 p q _) = M2 (trim p) (trim q)
instance Num a => Extend a M2 M4 where
extendZero (M2 p q) = M4 (extendZero p) (extendZero q) zero zero
extendWith w (M2 p q) = M4 (extendZero p) (extendZero q) (V4 0 0 w 0) (V4 0 0 0 w)
trim (M4 p q _ _) = M2 (trim p) (trim q)
instance Num a => Extend a M3 M4 where
extendZero (M3 p q r) = M4 (extendZero p) (extendZero q) (extendZero r) zero
extendWith w (M3 p q r) = M4 (extendZero p) (extendZero q) (extendZero r) (V4 0 0 0 w)
trim (M4 p q r _) = M3 (trim p) (trim q) (trim r)
instance Transpose (M2x3 a) (M3x2 a) where
transpose (M2x3 a b c d e f) =
M3x2 a d b e c f
instance Transpose (M2x4 a) (M4x2 a) where
transpose (M2x4 a b c d e f g h) =
M4x2 a e b f c g d h
instance Transpose (M3x2 a) (M2x3 a) where
transpose (M3x2 a b c d e f) =
M2x3 a c e b d f
instance Transpose (M3x4 a) (M4x3 a) where
transpose (M3x4 a b c d e f g h i j k l) =
M4x3 a e i b f j c g k d h l
instance Transpose (M4x2 a) (M2x4 a) where
transpose (M4x2 a b c d e f g h) =
M2x4 a c e f b d f h
instance Transpose (M4x3 a) (M3x4 a) where
transpose (M4x3 a b c d e f g h i j k l) =
M3x4 a d g j b e h k c f i l
instance Storable a => Storable (M2x3 a) where
sizeOf _ = 6 * sizeOf (undefined :: a)
alignment _ = alignment (undefined :: a)
peek q = do
let p = castPtr q :: Ptr a
k = sizeOf (undefined :: a)
r1 <- peek p
r2 <- peekByteOff p (k )
r3 <- peekByteOff p (k+k)
r4 <- peekByteOff p (3*k)
r5 <- peekByteOff p (4*k)
r6 <- peekByteOff p (5*k)
return (M2x3 r1 r2 r3 r4 r5 r6)
poke q (M2x3 r1 r2 r3 r4 r5 r6) = do
let p = castPtr q :: Ptr a
k = sizeOf (undefined :: a)
poke p r1
pokeByteOff p (k ) r2
pokeByteOff p (k+k) r3
pokeByteOff p (3*k) r4
pokeByteOff p (4*k) r5
pokeByteOff p (5*k) r6
instance Storable a => Storable (M2x4 a) where
sizeOf _ = 8 * sizeOf (undefined :: a)
alignment _ = alignment (undefined :: a)
peek q = do
let p = castPtr q :: Ptr a
k = sizeOf (undefined :: a)
r1 <- peek p
r2 <- peekByteOff p (k )
r3 <- peekByteOff p (k+k)
r4 <- peekByteOff p (3*k)
r5 <- peekByteOff p (4*k)
r6 <- peekByteOff p (5*k)
r7 <- peekByteOff p (6*k)
r8 <- peekByteOff p (7*k)
return (M2x4 r1 r2 r3 r4 r5 r6 r7 r8)
poke q (M2x4 r1 r2 r3 r4 r5 r6 r7 r8) = do
let p = castPtr q :: Ptr a
k = sizeOf (undefined :: a)
poke p r1
pokeByteOff p (k ) r2
pokeByteOff p (k+k) r3
pokeByteOff p (3*k) r4
pokeByteOff p (4*k) r5
pokeByteOff p (5*k) r6
pokeByteOff p (6*k) r7
pokeByteOff p (7*k) r8
instance Storable a => Storable (M3x2 a) where
sizeOf _ = 6 * sizeOf (undefined :: a)
alignment _ = alignment (undefined :: a)
peek q = do
let p = castPtr q :: Ptr a
k = sizeOf (undefined :: a)
r1 <- peek p
r2 <- peekByteOff p (k )
r3 <- peekByteOff p (k+k)
r4 <- peekByteOff p (3*k)
r5 <- peekByteOff p (4*k)
r6 <- peekByteOff p (5*k)
return (M3x2 r1 r2 r3 r4 r5 r6)
poke q (M3x2 r1 r2 r3 r4 r5 r6) = do
let p = castPtr q :: Ptr a
k = sizeOf (undefined :: a)
poke p r1
pokeByteOff p (k ) r2
pokeByteOff p (k+k) r3
pokeByteOff p (3*k) r4
pokeByteOff p (4*k) r5
pokeByteOff p (5*k) r6
instance Storable a => Storable (M3x4 a) where
sizeOf _ = 12 * sizeOf (undefined :: a)
alignment _ = alignment (undefined :: a)
peek q = do
let p = castPtr q :: Ptr a
k = sizeOf (undefined :: a)
r1 <- peek p
r2 <- peekByteOff p (k )
r3 <- peekByteOff p (k+k)
r4 <- peekByteOff p (3*k)
r5 <- peekByteOff p (4*k)
r6 <- peekByteOff p (5*k)
r7 <- peekByteOff p (6*k)
r8 <- peekByteOff p (7*k)
r9 <- peekByteOff p (8*k)
ra <- peekByteOff p (9*k)
rb <- peekByteOff p (10*k)
rc <- peekByteOff p (11*k)
return (M3x4 r1 r2 r3 r4 r5 r6 r7 r8 r9 ra rb rc)
poke q (M3x4 r1 r2 r3 r4 r5 r6 r7 r8 r9 ra rb rc) = do
let p = castPtr q :: Ptr a
k = sizeOf (undefined :: a)
poke p r1
pokeByteOff p (k ) r2
pokeByteOff p (k+k) r3
pokeByteOff p (3*k) r4
pokeByteOff p (4*k) r5
pokeByteOff p (5*k) r6
pokeByteOff p (6*k) r7
pokeByteOff p (7*k) r8
pokeByteOff p (8*k) r9
pokeByteOff p (9*k) ra
pokeByteOff p (10*k) rb
pokeByteOff p (11*k) rc
instance Storable a => Storable (M4x2 a) where
sizeOf _ = 8 * sizeOf (undefined :: a)
alignment _ = alignment (undefined :: a)
peek q = do
let p = castPtr q :: Ptr a
k = sizeOf (undefined :: a)
r1 <- peek p
r2 <- peekByteOff p (k )
r3 <- peekByteOff p (k+k)
r4 <- peekByteOff p (3*k)
r5 <- peekByteOff p (4*k)
r6 <- peekByteOff p (5*k)
r7 <- peekByteOff p (6*k)
r8 <- peekByteOff p (7*k)
return (M4x2 r1 r2 r3 r4 r5 r6 r7 r8)
poke q (M4x2 r1 r2 r3 r4 r5 r6 r7 r8) = do
let p = castPtr q :: Ptr a
k = sizeOf (undefined :: a)
poke p r1
pokeByteOff p (k ) r2
pokeByteOff p (k+k) r3
pokeByteOff p (3*k) r4
pokeByteOff p (4*k) r5
pokeByteOff p (5*k) r6
pokeByteOff p (6*k) r7
pokeByteOff p (7*k) r8
instance Storable a => Storable (M4x3 a) where
sizeOf _ = 12 * sizeOf (undefined :: a)
alignment _ = alignment (undefined :: a)
peek q = do
let p = castPtr q :: Ptr a
k = sizeOf (undefined :: a)
r1 <- peek p
r2 <- peekByteOff p (k )
r3 <- peekByteOff p (k+k)
r4 <- peekByteOff p (3*k)
r5 <- peekByteOff p (4*k)
r6 <- peekByteOff p (5*k)
r7 <- peekByteOff p (6*k)
r8 <- peekByteOff p (7*k)
r9 <- peekByteOff p (8*k)
ra <- peekByteOff p (9*k)
rb <- peekByteOff p (10*k)
rc <- peekByteOff p (11*k)
return (M4x3 r1 r2 r3 r4 r5 r6 r7 r8 r9 ra rb rc)
poke q (M4x3 r1 r2 r3 r4 r5 r6 r7 r8 r9 ra rb rc) = do
let p = castPtr q :: Ptr a
k = sizeOf (undefined :: a)
poke p r1
pokeByteOff p (k ) r2
pokeByteOff p (k+k) r3
pokeByteOff p (3*k) r4
pokeByteOff p (4*k) r5
pokeByteOff p (5*k) r6
pokeByteOff p (6*k) r7
pokeByteOff p (7*k) r8
pokeByteOff p (8*k) r9
pokeByteOff p (9*k) ra
pokeByteOff p (10*k) rb
pokeByteOff p (11*k) rc