Vec-0.9.0: 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 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', n v' -> v where take :: n -> v -> v' class Drop n v v' | 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 where snoc :: v -> a -> v' 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) PackedVec Vec4D (Vec4 Double) PackedVec Vec3D (Vec3 Double) PackedVec Vec2D (Vec2 Double) PackedVec Vec4F (Vec4 Float) PackedVec Vec3F (Vec3 Float) PackedVec Vec2F (Vec2 Float) PackedVec Vec4I (Vec4 Int) PackedVec Vec3I (Vec3 Int) PackedVec Vec2I (Vec2 Int) 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) 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)) 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 :. ()) (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) (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 (a :. as) a

class Tail v v_ | v -> v_ where Source

All but the first element. Methods tail :: v -> v_ Source Instances 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 (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 (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 (a' :. u) => Fold a (a :. (a' :. u)) Fold a (a :. ())

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

Methods reverse' :: p -> v -> v' Source Instances Reverse' p () p 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', 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 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', 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 (Tail v' v'', Drop n v v') => Drop (Succ n) 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 (a' :. v) a => Last (a :. (a' :. v)) a Last (a :. ()) a

class Snoc v a v' | v a -> v', v' -> 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 (a :. v) => Snoc (a :. v) a (a :. (a :. v))

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)

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