Vec-0.9.2: Fixed-length lists and low-dimensional linear algebra. Source code Contents Index

Data.Vec.Base

Contents Vector Types List-like functions Matrix Types

Synopsis

data a :. b = !a :. !b class ShowVec v where showVec :: v -> String type Vec2 a = a :. (a :. ()) type Vec3 a = a :. Vec2 a type Vec4 a = a :. Vec3 a type Vec5 a = a :. Vec4 a type Vec6 a = a :. Vec5 a type Vec7 a = a :. Vec6 a type Vec8 a = a :. Vec7 a type Vec9 a = a :. Vec8 a type Vec10 a = a :. Vec9 a type Vec11 a = a :. Vec10 a type Vec12 a = a :. Vec11 a type Vec13 a = a :. Vec12 a type Vec14 a = a :. Vec13 a type Vec15 a = a :. Vec14 a type Vec16 a = a :. Vec15 a type Vec17 a = a :. Vec16 a type Vec18 a = a :. Vec17 a type Vec19 a = a :. Vec18 a class Vec n a v | n a -> v, v -> n a where mkVec :: n -> a -> v fromList :: [a] -> v getElem :: Int -> v -> a setElem :: Int -> a -> v -> v vec :: Vec n a v => a -> v class Access n a v | v -> a where get :: n -> v -> a set :: n -> a -> v -> v class Head v a | v -> a where head :: v -> a class Tail v v_ | v -> v_ where tail :: v -> v_ class Map a b u v | u -> a, v -> b, b u -> v, a v -> u where map :: (a -> b) -> u -> v class ZipWith a b c u v w | u -> a, v -> b, w -> c, u v c -> w where zipWith :: (a -> b -> c) -> u -> v -> w class Fold a v | v -> a where fold :: (a -> a -> a) -> v -> a foldl :: (b -> a -> b) -> b -> v -> b foldr :: (a -> b -> b) -> b -> v -> b reverse :: Reverse' () v v' => v -> v' class Reverse' p v v' | p v -> v' where reverse' :: p -> v -> v' class Append v1 v2 v3 | v1 v2 -> v3, v1 v3 -> v2 where append :: v1 -> v2 -> v3 class Take n v v' | n v -> v' where take :: n -> v -> v' class Drop n v v' | n v -> v' where drop :: n -> v -> v' class Last v a | v -> a where last :: v -> a class Snoc v a v' | v a -> v', v' -> v a, v -> a where snoc :: v -> a -> v' class Length v n | v -> n where length :: v -> Int sum :: (Fold a v, Num a) => v -> a product :: (Fold a v, Num a) => v -> a maximum :: (Fold a v, Ord a) => v -> a minimum :: (Fold a v, Ord a) => v -> a toList :: Fold a v => v -> [a] type Mat22 a = Vec2 (Vec2 a) type Mat23 a = Vec2 (Vec3 a) type Mat24 a = Vec2 (Vec4 a) type Mat32 a = Vec3 (Vec2 a) type Mat33 a = Vec3 (Vec3 a) type Mat34 a = Vec3 (Vec4 a) type Mat35 a = Vec3 (Vec5 a) type Mat36 a = Vec3 (Vec6 a) type Mat42 a = Vec4 (Vec2 a) type Mat43 a = Vec4 (Vec3 a) type Mat44 a = Vec4 (Vec4 a) type Mat45 a = Vec4 (Vec5 a) type Mat46 a = Vec4 (Vec6 a) type Mat47 a = Vec4 (Vec7 a) type Mat48 a = Vec4 (Vec8 a) matToLists :: (Fold a v, Fold v m) => m -> [[a]] matToList :: (Fold a v, Fold v m) => m -> [a] matFromLists :: (Vec j a v, Vec i v m) => [[a]] -> m matFromList :: forall i j v m a. (Vec i v m, Vec j a v, Nat i) => [a] -> m

Documentation

data a :. b Source

The vector constructor. (:.) for vectors is like (:) for lists, and () takes the place of []. (The list of instances here is not meant to be readable.) Constructors !a :. !b Instances ZipWith a b c (a' :. u) (b' :. v) (c' :. w) => ZipWith a b c (a :. (a' :. u)) (b :. (b' :. v)) (c :. (c' :. w)) ZipWith a b c (a :. (a :. as)) (b :. ()) (c :. ()) ZipWith a b c (a :. ()) (b :. (b :. bs)) (c :. ()) ZipWith a b c (a :. ()) (b :. ()) (c :. ()) Snoc () a (a :. ()) Access N0 a (a :. v) Vec N1 a (a :. ()) Alternating N1 a (a :. ()) (Access n a r, Append p (a :. ()) p', GetDiagonal' (Succ n) p' (r :. m) v) => GetDiagonal' n p (r :. (r :. m)) v Map a b (a' :. u) (b' :. v) => Map a b (a :. (a' :. u)) (b :. (b' :. v)) Map a b (a :. ()) (b :. ()) (Append p (a :. v) x, Append p (a :. ()) y, ReplConsec' a y v z) => ReplConsec' a p (a :. v) (x :. z) (Access n a r, Append p (a :. ()) (a :. p)) => GetDiagonal' n p (r :. ()) (a :. p) Fold a (a' :. u) => Fold a (a :. (a' :. u)) Fold a (a :. ()) (Fractional a, Map (a :. r) r ((a :. r) :. rs) rs_, Map r (a :. r) rs_ ((a :. r) :. rs), Pivot a ((a :. r) :. ((a :. r) :. rs)), GaussElim a rs_) => GaussElim a ((a :. r) :. ((a :. r) :. rs)) (Num a, Pivot a (r :. ())) => GaussElim a (r :. ()) (Fractional a, NearZero a, Pivot1 a rs, Tail (a :. r) r, Map (a :. r) r ((a :. r) :. rs) (r :. rs'), Map r (a :. r) (r :. rs') ((a :. r) :. rs), Pivot1 a ((a :. r) :. rs), Pivot a (r :. rs')) => Pivot a ((a :. r) :. rs) Pivot a (() :. v) (Fractional a, NearZero a, Map a a (a :. r) (a :. r), ZipWith a a a (a :. r) (a :. r) (a :. r), Map (a :. r) (a :. r) ((a :. r) :. rs) ((a :. r) :. rs), Pivot1 a ((a :. r) :. rs)) => Pivot1 a ((a :. r) :. ((a :. r) :. rs)) (Fractional a, NearZero a, Map a a (a :. r) (a :. r)) => Pivot1 a ((a :. (a :. r)) :. ()) (Fractional a, NearZero a) => Pivot1 a ((a :. ()) :. ()) (Num a, Num (a :. (a :. (a :. v))), Fold a (a :. (a :. (a :. v))), Alternating (Succ (Succ (Succ n))) a (a :. (a :. (a :. v))), DropConsec (a :. (a :. (a :. v))) vv, Map (a :. (a :. (a :. v))) vv ((a :. (a :. (a :. v))) :. ((a :. (a :. (a :. v))) :. m)) vmt, Transpose vmt vm, Map ((a :. (a :. v)) :. ((a :. (a :. v)) :. m_)) a vm (a :. (a :. (a :. v))), Det' a ((a :. (a :. v)) :. ((a :. (a :. v)) :. m_)), Vec (Succ (Succ (Succ n))) a (a :. (a :. (a :. v))), Vec (Succ (Succ (Succ n))) (a :. (a :. (a :. v))) ((a :. (a :. (a :. v))) :. ((a :. (a :. (a :. v))) :. ((a :. (a :. (a :. v))) :. m)))) => Det' a ((a :. (a :. (a :. v))) :. ((a :. (a :. (a :. v))) :. ((a :. (a :. (a :. v))) :. m))) Num a => Det' a ((a :. (a :. ())) :. ((a :. (a :. ())) :. ())) Reverse' (a :. p) v v' => Reverse' p (a :. v) v' (Append p (a :. v) x, Append p (a :. ()) y, DropConsec' y (a :. v) z) => DropConsec' p (a :. (a :. v)) (x :. z) DropConsec' p (a :. ()) (p :. ()) (SetDiagonal' (Succ n) v m, Access n a r) => SetDiagonal' n (a :. v) (r :. m) PackedVec (Vec4 Double) PackedVec (Vec4 Float) PackedVec (Vec4 Int) PackedVec (Vec3 Double) PackedVec (Vec3 Float) PackedVec (Vec3 Int) PackedVec (Vec2 Double) PackedVec (Vec2 Float) PackedVec (Vec2 Int) Access n a v => Access (Succ n) a (a :. v) Vec (Succ n) a (a' :. v) => Vec (Succ (Succ n)) a (a :. (a' :. v)) (Num a, Alternating n a (a :. v)) => Alternating (Succ n) a (a :. (a :. v)) Drop n (a :. v) v' => Drop (Succ n) (a :. (a :. v)) v' Take n v v' => Take (Succ n) (a :. v) (a :. v') (Eq a, Eq b) => Eq (a :. b) (Fractional a, Ord (a :. u), ZipWith a a a (a :. u) (a :. u) (a :. u), Map a a (a :. u) (a :. u), Vec (Succ l) a (a :. u), Show (a :. u)) => Fractional (a :. u) (Eq (a :. u), Show (a :. u), Num a, Map a a (a :. u) (a :. u), ZipWith a a a (a :. u) (a :. u) (a :. u), Vec (Succ l) a (a :. u)) => Num (a :. u) (Ord a, Ord b) => Ord (a :. b) (Read a, Read b) => Read (a :. b) (Show a, ShowVec v) => Show (a :. v) (Vec (Succ (Succ n)) a (a :. (a :. v)), Storable a, Storable (a :. v)) => Storable (a :. (a :. v)) Storable a => Storable (a :. ()) (Length (a :. v) (Succ n), Arbitrary a', Arbitrary (a :. v)) => Arbitrary (a' :. (a :. v)) Arbitrary a => Arbitrary (a :. ()) (Show a, ShowVec v) => ShowVec (a :. v) (Map (a :. r) r ((a :. r) :. rs) rs_, Map r (a :. r) rs_ ((a :. r) :. rs), Fold ((,) a (a :. r)) aas, ZipWith a a a (a :. r) (a :. r) (a :. r), Map a a (a :. r) (a :. r), ZipWith a (a :. r) ((,) a (a :. r)) r ((a :. r) :. rs) aas, Num a, BackSubstitute' rs_) => BackSubstitute' ((a :. r) :. ((a :. r) :. rs)) BackSubstitute' ((a :. r) :. ()) (Map (a :. r) r ((a :. r) :. rs) rs_, Map r (a :. r) rs_ ((a :. r) :. rs), Fold ((,) a (a :. r)) aas, ZipWith a a a (a :. r) (a :. r) (a :. r), Map a a (a :. r) (a :. r), ZipWith a (a :. r) ((,) a (a :. r)) r ((a :. r) :. rs) aas, Num a, NearZero a, BackSubstitute rs_) => BackSubstitute ((a :. r) :. ((a :. r) :. rs)) BackSubstitute ((a :. r) :. ()) Last (a' :. v) a => Last (a :. (a' :. v)) a Last (a :. ()) a Tail (a :. as) as Head (a :. as) a Transpose' vs vs' => Transpose' (() :. vs) vs' Snoc v a (a :. v) => Snoc (a :. v) a (a :. (a :. v)) Append (a' :. v1) v2 v3 => Append (a :. (a' :. v1)) v2 (a :. v3) Append (a :. ()) v (a :. v) Length v n => Length (a :. v) (Succ n) (Head xss_h xss_hh, Map xss_h xss_hh (xss_h :. xss_t) xs', Tail xss_h xss_ht, Map xss_h xss_ht (xss_h :. xss_t) xss_, Transpose' (xs :. xss_) xss') => Transpose' ((x :. xs) :. (xss_h :. xss_t)) ((x :. xs') :. xss') Transpose' ((x :. ()) :. ()) ((x :. ()) :. ()) (Vec (Succ n) s (s :. ra), Vec (Succ m) (s :. ra) ((s :. ra) :. a), Vec (Succ m) s (s :. rb), Vec (Succ n) (s :. rb) ((s :. rb) :. b), Transpose' ((s :. ra) :. a) ((s :. rb) :. b)) => Transpose ((s :. ra) :. a) ((s :. rb) :. b)

class ShowVec v where Source

Helper to keep parentheses at bay. Just use show as usual. Methods showVec :: v -> String Source Instances ShowVec () (Show a, ShowVec v) => ShowVec (a :. v)

Vector Types

type Vec2 a = a :. (a :. ()) Source

type Vec3 a = a :. Vec2 a Source

type Vec4 a = a :. Vec3 a Source

type Vec5 a = a :. Vec4 a Source

type Vec6 a = a :. Vec5 a Source

type Vec7 a = a :. Vec6 a Source

type Vec8 a = a :. Vec7 a Source

type Vec9 a = a :. Vec8 a Source

type Vec10 a = a :. Vec9 a Source

type Vec11 a = a :. Vec10 a Source

type Vec12 a = a :. Vec11 a Source

type Vec13 a = a :. Vec12 a Source

type Vec14 a = a :. Vec13 a Source

type Vec15 a = a :. Vec14 a Source

type Vec16 a = a :. Vec15 a Source

type Vec17 a = a :. Vec16 a Source

type Vec18 a = a :. Vec17 a Source

type Vec19 a = a :. Vec18 a Source

class Vec n a v | n a -> v, v -> n a where Source

The type constraint Vec n a v infers the vector type v from the length n, a type-level natural, and underlying component type a. So x :: Vec N4 a v => v declares x to be a 4-vector of as. Methods mkVec :: n -> a -> v Source Make a uniform vector of a given length. n is a type-level natural. Use vec when the length can be inferred. fromList :: [a] -> v Source turn a list into a vector of inferred length getElem :: Int -> v -> a Source get a vector element, which one is determined at runtime setElem :: Int -> a -> v -> v Source set a vector element, which one is determined at runtime Instances Vec N1 a (a :. ()) Vec N1 a (a :. ()) Vec (Succ n) a (a' :. v) => Vec (Succ (Succ n)) a (a :. (a' :. v)) Vec (Succ n) a (a' :. v) => Vec (Succ (Succ n)) a (a :. (a' :. v))

vec :: Vec n a v => a -> v Source

Make a uniform vector. The length is inferred.

class Access n a v | v -> a where Source

get or set a vector element, known at compile time. Use the Nat types to access vector components. For instance, get n0 gets the x component, set n2 44 sets the z component to 44. Methods get :: n -> v -> a Source set :: n -> a -> v -> v Source Instances Access N0 a (a :. v) Access N0 a (a :. v) Access n a v => Access (Succ n) a (a :. v) Access n a v => Access (Succ n) a (a :. v)

List-like functions

class Head v a | v -> a where Source

The first element. Methods head :: v -> a Source Instances (Head v h, PackedVec v) => Head (Packed v) h Head (a :. as) a

class Tail v v_ | v -> v_ where Source

All but the first element. Methods tail :: v -> v_ Source Instances (Tail v t, PackedVec v, PackedVec t) => Tail (Packed v) (Packed t) Tail (a :. as) as

class Map a b u v | u -> a, v -> b, b u -> v, a v -> u where Source

Apply a function over each element in a vector. Constraint Map a b u v states that u is a vector of as, v is a vector of bs with the same length as u, and the function is of type a -> b. Methods map :: (a -> b) -> u -> v Source Instances (Map a b u v, PackedVec u, PackedVec v) => Map a b (Packed u) (Packed v) Map a b (a' :. u) (b' :. v) => Map a b (a :. (a' :. u)) (b :. (b' :. v)) Map a b (a :. ()) (b :. ())

class ZipWith a b c u v w | u -> a, v -> b, w -> c, u v c -> w where Source

Combine two vectors using a binary function. The length of the result is the min of the lengths of the arguments. The constraint ZipWith a b c u v w states that u is a vector of as, v is a vector of bs, w is a vector of cs, and the binary function is of type a -> b -> c. Methods zipWith :: (a -> b -> c) -> u -> v -> w Source Instances (ZipWith a b c u v w, PackedVec u, PackedVec v, PackedVec w) => ZipWith a b c (Packed u) (Packed v) (Packed w) ZipWith a b c (a' :. u) (b' :. v) (c' :. w) => ZipWith a b c (a :. (a' :. u)) (b :. (b' :. v)) (c :. (c' :. w)) ZipWith a b c (a :. (a :. as)) (b :. ()) (c :. ()) ZipWith a b c (a :. ()) (b :. (b :. bs)) (c :. ()) ZipWith a b c (a :. ()) (b :. ()) (c :. ())

class Fold a v | v -> a where Source

Fold a function over a vector. Methods fold :: (a -> a -> a) -> v -> a Source foldl :: (b -> a -> b) -> b -> v -> b Source foldr :: (a -> b -> b) -> b -> v -> b Source Instances (Fold a v, PackedVec v) => Fold a (Packed v) Fold a (a' :. u) => Fold a (a :. (a' :. u)) Fold a (a :. ())

reverse :: Reverse' () v v' => v -> v' Source

Reverse a vector

class Reverse' p v v' | p v -> v' where Source

Reverse helper function : accumulates the reversed list in its first argument Methods reverse' :: p -> v -> v' Source Instances Reverse' p () p (Reverse' () v v', PackedVec v, PackedVec v') => Reverse' () (Packed v) (Packed v') (Reverse' () v v', PackedVec v, PackedVec v') => Reverse' () (Packed v) (Packed v') Reverse' (a :. p) v v' => Reverse' p (a :. v) v'

class Append v1 v2 v3 | v1 v2 -> v3, v1 v3 -> v2 where Source

Append two vectors Methods append :: v1 -> v2 -> v3 Source Instances Append () v v Append (a' :. v1) v2 v3 => Append (a :. (a' :. v1)) v2 (a :. v3) Append (a :. ()) v (a :. v)

class Take n v v' | n v -> v' where Source

take n v constructs a vector from the first n elements of v. n is a type-level natural. For example take n3 v makes a 3-vector of the first three elements of v. Methods take :: n -> v -> v' Source Instances Take N0 v () Take N0 v () (Take (Succ n) v v', PackedVec v, PackedVec v') => Take (Succ n) (Packed v) (Packed v') (Take (Succ n) v v', PackedVec v, PackedVec v') => Take (Succ n) (Packed v) (Packed v') Take n v v' => Take (Succ n) (a :. v) (a :. v') Take n v v' => Take (Succ n) (a :. v) (a :. v')

class Drop n v v' | n v -> v' where Source

drop n v strips the first n elements from v. n is a type-level natural. For example drop n2 v drops the first two elements. Methods drop :: n -> v -> v' Source Instances Drop N0 v v (Drop n v v', PackedVec v, PackedVec v') => Drop n (Packed v) (Packed v') Drop n (a :. v) v' => Drop (Succ n) (a :. (a :. v)) v' Drop n (a :. v) v' => Drop (Succ n) (a :. (a :. v)) v'

class Last v a | v -> a where Source

Get the last element, usually significant for some reason (quaternions, homogenous coordinates, whatever) Methods last :: v -> a Source Instances (Last v l, PackedVec v) => Last (Packed v) l Last (a' :. v) a => Last (a :. (a' :. v)) a Last (a :. ()) a

class Snoc v a v' | v a -> v', v' -> v a, v -> a where Source

snoc v a appends the element a to the end of v. Methods snoc :: v -> a -> v' Source Instances Snoc () a (a :. ()) Snoc () a (a :. ()) (Snoc v a v', PackedVec v, PackedVec v') => Snoc (Packed v) a (Packed v') Snoc v a (a :. v) => Snoc (a :. v) a (a :. (a :. v))

class Length v n | v -> n where Source

The length of a vector Methods length :: v -> Int Source Instances Length () N0 Length () N0 (Length v n, PackedVec v) => Length (Packed v) n Length v n => Length (a :. v) (Succ n) Length v n => Length (a :. v) (Succ n)

sum :: (Fold a v, Num a) => v -> a Source

sum of vector elements

product :: (Fold a v, Num a) => v -> a Source

product of vector elements

maximum :: (Fold a v, Ord a) => v -> a Source

maximum vector element

minimum :: (Fold a v, Ord a) => v -> a Source

minimum vector element

toList :: Fold a v => v -> [a] Source

Matrix Types

type Mat22 a = Vec2 (Vec2 a) Source

type Mat23 a = Vec2 (Vec3 a) Source

type Mat24 a = Vec2 (Vec4 a) Source

type Mat32 a = Vec3 (Vec2 a) Source

type Mat33 a = Vec3 (Vec3 a) Source

type Mat34 a = Vec3 (Vec4 a) Source

type Mat35 a = Vec3 (Vec5 a) Source

type Mat36 a = Vec3 (Vec6 a) Source

type Mat42 a = Vec4 (Vec2 a) Source

type Mat43 a = Vec4 (Vec3 a) Source

type Mat44 a = Vec4 (Vec4 a) Source

type Mat45 a = Vec4 (Vec5 a) Source

type Mat46 a = Vec4 (Vec6 a) Source

type Mat47 a = Vec4 (Vec7 a) Source

type Mat48 a = Vec4 (Vec8 a) Source

matToLists :: (Fold a v, Fold v m) => m -> [[a]] Source

convert a matrix to a list-of-lists

matToList :: (Fold a v, Fold v m) => m -> [a] Source

convert a matrix to a list in row-major order

matFromLists :: (Vec j a v, Vec i v m) => [[a]] -> m Source

convert a list-of-lists into a matrix

matFromList :: forall i j v m a. (Vec i v m, Vec j a v, Nat i) => [a] -> m Source

convert a list into a matrix. (row-major order)

Produced by Haddock version 2.3.0