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Tweak library functions to match reps

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This commit is contained in:
Kiana Sheibani 2023-09-25 23:47:58 -04:00
parent 983733f241
commit b924d960b5
Signed by: toki
GPG key ID: 6CB106C25E86A9F7
8 changed files with 123 additions and 103 deletions
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15
src/Data/NumIdr/Array/Array.idr
View file

@ -70,6 +70,7 @@ export
getRep : Array s a -> Rep
getRep (MkArray rep _ _) = rep
export
getRepC : (arr : Array s a) -> RepConstraint (getRep arr) a
getRepC (MkArray _ @{rc} _ _) = rc
@ -242,7 +243,7 @@ export
indexSetRange : (rs : CoordsRange s) -> Array (newShape rs) a ->
Array s a -> Array s a
indexSetRange rs (MkArray _ _ rpl) (MkArray rep s arr) =
MkArray rep s (PrimArray.indexSetRange {rep} rs (convertRep rpl) arr)
MkArray rep s (PrimArray.indexSetRange {rep} rs (convertRepPrim rpl) arr)
||| Update the sub-array at the given range of coordinates by applying
@ -302,7 +303,7 @@ arr !?.. rs = indexRangeNB rs arr
||| Index the array using the given coordinates.
||| WARNING: This function does not perform any bounds check on its inputs.
||| Misuse of this function can easily break memory safety.
export
export %unsafe
indexUnsafe : Vect rk Nat -> Array {rk} s a -> a
indexUnsafe is (MkArray _ _ arr) = PrimArray.indexUnsafe is arr
@ -311,7 +312,7 @@ indexUnsafe is (MkArray _ _ arr) = PrimArray.indexUnsafe is arr
||| Misuse of this function can easily break memory safety.
|||
||| This is the operator form of `indexUnsafe`.
export %inline
export %inline %unsafe
(!#) : Array {rk} s a -> Vect rk Nat -> a
arr !# is = indexUnsafe is arr
@ -371,10 +372,10 @@ reshape : (s' : Vect rk' Nat) -> (arr : Array {rk} s a) -> LinearRep (getRep arr
(0 ok : product s = product s') => Array s' a
reshape s' (MkArray rep _ arr) = MkArray rep s' (PrimArray.reshape s' arr)
||| Change the internal order of the array's elements.
||| Change the internal representation of the array's elements.
export
convertRep : (rep : Rep) -> RepConstraint rep a => Array s a -> Array s a
convertRep rep (MkArray _ s arr) = MkArray rep s (PrimArray.convertRep arr)
convertRep rep (MkArray _ s arr) = MkArray rep s (convertRepPrim arr)
||| Resize the array to a new shape, preserving the coordinates of the original
||| elements. New coordinates are filled with a default value.
@ -563,7 +564,7 @@ export
Functor (Array s) where
map f (MkArray rep @{rc} s arr) = MkArray (forceRepNC rep) @{forceRepConstraint} s
(mapPrim @{forceRepConstraint} @{forceRepConstraint} f
$ convertRep @{rc} @{forceRepConstraint} arr)
$ convertRepPrim @{rc} @{forceRepConstraint} arr)
export
{s : _} -> Applicative (Array s) where
@ -591,7 +592,7 @@ Traversable (Array s) where
map (MkArray (forceRepNC rep) @{forceRepConstraint} s)
(PrimArray.traverse {rep=forceRepNC rep}
@{%search} @{forceRepConstraint} @{forceRepConstraint} f
(PrimArray.convertRep @{rc} @{forceRepConstraint} arr))
(convertRepPrim @{rc} @{forceRepConstraint} arr))
export

32
src/Data/NumIdr/Homogeneous.idr
View file

@ -78,8 +78,7 @@ hmatrix : Num a => Matrix m n a -> Vector m a -> HMatrix m n a
hmatrix {m,n} mat tr with (viewShape mat)
_ | Shape [m,n] = indexSet [last,last] 1 $
resize [S m, S n] 0 $
mat `hconcat` reshape
{ok = sym $ multOneRightNeutral _} [m,1] tr
mat `hconcat` hstack [tr]
||| Convert a regular matrix to a homogeneous matrix.
export
@ -120,8 +119,9 @@ getTranslationVector {m,n} mat with (viewShape mat)
||| Construct a homogeneous matrix that scales a vector by the input.
export
scalingH : {n : _} -> Num a => a -> HMatrix' n a
scalingH x = indexSet [last,last] 1 $ repeatDiag x 0
scalingH : {default B rep : Rep} -> RepConstraint rep a =>
{n : _} -> Num a => a -> HMatrix' n a
scalingH x = indexSet [last,last] 1 $ repeatDiag {rep} x 0
||| Construct a homogeneous matrix that translates by the given vector.
export
@ -132,23 +132,27 @@ translationH {n} v with (viewShape v)
||| Construct a 2D homogeneous matrix that rotates by the given angle (in radians).
export
rotate2DH : Double -> HMatrix' 2 Double
rotate2DH = matrixToH . rotate2D
rotate2DH : {default B rep : Rep} -> RepConstraint rep Double =>
Double -> HMatrix' 2 Double
rotate2DH = matrixToH . rotate2D {rep}
||| Construct a 3D homogeneous matrix that rotates around the x-axis.
export
rotate3DXH : Double -> HMatrix' 3 Double
rotate3DXH = matrixToH . rotate3DX
rotate3DXH : {default B rep : Rep} -> RepConstraint rep Double =>
Double -> HMatrix' 3 Double
rotate3DXH = matrixToH . rotate3DX {rep}
||| Construct a 3D homogeneous matrix that rotates around the y-axis.
export
rotate3DYH : Double -> HMatrix' 3 Double
rotate3DYH = matrixToH . rotate3DY
rotate3DYH : {default B rep : Rep} -> RepConstraint rep Double =>
Double -> HMatrix' 3 Double
rotate3DYH = matrixToH . rotate3DY {rep}
||| Construct a 3D homogeneous matrix that rotates around the z-axis.
export
rotate3DZH : Double -> HMatrix' 3 Double
rotate3DZH = matrixToH . rotate3DZ
rotate3DZH : {default B rep : Rep} -> RepConstraint rep Double =>
Double -> HMatrix' 3 Double
rotate3DZH = matrixToH . rotate3DZ {rep}
export
@ -161,8 +165,8 @@ reflectXH = reflectH 0
export
reflectYH : {n : _} -> Neg a => HMatrix' (2 + n) a
reflectYH = reflectH 0
reflectYH = reflectH 1
export
reflectZH : {n : _} -> Neg a => HMatrix' (3 + n) a
reflectZH = reflectH 0
reflectZH = reflectH 2

97
src/Data/NumIdr/Matrix.idr
View file

@ -5,8 +5,8 @@ import Data.Vect
import Data.Permutation
import Data.NumIdr.Interfaces
import public Data.NumIdr.Array
import Data.NumIdr.PrimArray
import Data.NumIdr.Vector
import Data.NumIdr.LArray
%default total
@ -31,13 +31,9 @@ Matrix' n = Array [n,n]
||| Construct a matrix with the given order and elements.
export
matrix' : {m, n : _} -> Order -> Vect m (Vect n a) -> Matrix m n a
matrix' ord x = array' [m,n] ord x
||| Construct a matrix with the given elements.
export
matrix : {m, n : _} -> Vect m (Vect n a) -> Matrix m n a
matrix = matrix' COrder
matrix : {default B rep : Rep} -> RepConstraint rep a => {m, n : _} ->
Vect m (Vect n a) -> Matrix m n a
matrix x = array' {rep} [m,n] x
||| Construct a matrix with a specific value along the diagonal.
@ -45,8 +41,9 @@ matrix = matrix' COrder
||| @ diag The value to repeat along the diagonal
||| @ other The value to repeat elsewhere
export
repeatDiag : {m, n : _} -> (diag, other : a) -> Matrix m n a
repeatDiag d o = fromFunctionNB [m,n]
repeatDiag : {default B rep : Rep} -> RepConstraint rep a => {m, n : _} ->
(diag, other : a) -> Matrix m n a
repeatDiag d o = fromFunctionNB {rep} [m,n]
(\[i,j] => if i == j then d else o)
||| Construct a matrix given its diagonal elements.
@ -54,8 +51,9 @@ repeatDiag d o = fromFunctionNB [m,n]
||| @ diag The elements of the matrix's diagonal
||| @ other The value to repeat elsewhere
export
fromDiag : {m, n : _} -> (diag : Vect (minimum m n) a) -> (other : a) -> Matrix m n a
fromDiag ds o = fromFunction [m,n] (\[i,j] => maybe o (`index` ds) $ i `eq` j)
fromDiag : {default B rep : Rep} -> RepConstraint rep a => {m, n : _} ->
(diag : Vect (minimum m n) a) -> (other : a) -> Matrix m n a
fromDiag ds o = fromFunction {rep} [m,n] (\[i,j] => maybe o (`index` ds) $ i `eq` j)
where
eq : {0 m,n : Nat} -> Fin m -> Fin n -> Maybe (Fin (minimum m n))
eq FZ FZ = Just FZ
@ -66,52 +64,62 @@ fromDiag ds o = fromFunction [m,n] (\[i,j] => maybe o (`index` ds) $ i `eq` j)
||| Construct a permutation matrix based on the given permutation.
export
permuteM : {n : _} -> Num a => Permutation n -> Matrix' n a
permuteM p = permuteInAxis 0 p (repeatDiag 1 0)
permuteM : {default B rep : Rep} -> RepConstraint rep a => {n : _} -> Num a =>
Permutation n -> Matrix' n a
permuteM p = permuteInAxis 0 p (repeatDiag {rep} 1 0)
||| Construct the matrix that scales a vector by the given value.
export
scale : {n : _} -> Num a => a -> Matrix' n a
scale x = repeatDiag x 0
scale : {default B rep : Rep} -> RepConstraint rep a => {n : _} -> Num a =>
a -> Matrix' n a
scale x = repeatDiag {rep} x 0
||| Construct a 2D rotation matrix that rotates by the given angle (in radians).
export
rotate2D : Double -> Matrix' 2 Double
rotate2D a = matrix [[cos a, - sin a], [sin a, cos a]]
rotate2D : {default B rep : Rep} -> RepConstraint rep Double =>
Double -> Matrix' 2 Double
rotate2D a = matrix {rep} [[cos a, - sin a], [sin a, cos a]]
||| Construct a 3D rotation matrix around the x-axis.
export
rotate3DX : Double -> Matrix' 3 Double
rotate3DX a = matrix [[1,0,0], [0, cos a, - sin a], [0, sin a, cos a]]
rotate3DX : {default B rep : Rep} -> RepConstraint rep Double =>
Double -> Matrix' 3 Double
rotate3DX a = matrix {rep} [[1,0,0], [0, cos a, - sin a], [0, sin a, cos a]]
||| Construct a 3D rotation matrix around the y-axis.
export
rotate3DY : Double -> Matrix' 3 Double
rotate3DY a = matrix [[cos a, 0, sin a], [0,1,0], [- sin a, 0, cos a]]
rotate3DY : {default B rep : Rep} -> RepConstraint rep Double =>
Double -> Matrix' 3 Double
rotate3DY a = matrix {rep} [[cos a, 0, sin a], [0,1,0], [- sin a, 0, cos a]]
||| Construct a 3D rotation matrix around the z-axis.
export
rotate3DZ : Double -> Matrix' 3 Double
rotate3DZ a = matrix [[cos a, - sin a, 0], [sin a, cos a, 0], [0,0,1]]
rotate3DZ : {default B rep : Rep} -> RepConstraint rep Double =>
Double -> Matrix' 3 Double
rotate3DZ a = matrix {rep} [[cos a, - sin a, 0], [sin a, cos a, 0], [0,0,1]]
export
reflect : {n : _} -> Neg a => Fin n -> Matrix' n a
reflect i = indexSet [i, i] (-1) (repeatDiag 1 0)
reflect : {default B rep : Rep} -> RepConstraint rep a =>
{n : _} -> Neg a => Fin n -> Matrix' n a
reflect i = indexSet [i, i] (-1) (repeatDiag {rep} 1 0)
export
reflectX : {n : _} -> Neg a => Matrix' (1 + n) a
reflectX = reflect 0
reflectX : {default B rep : Rep} -> RepConstraint rep a =>
{n : _} -> Neg a => Matrix' (1 + n) a
reflectX = reflect {rep} 0
export
reflectY : {n : _} -> Neg a => Matrix' (2 + n) a
reflectY = reflect 1
reflectY : {default B rep : Rep} -> RepConstraint rep a =>
{n : _} -> Neg a => Matrix' (2 + n) a
reflectY = reflect {rep} 1
export
reflectZ : {n : _} -> Neg a => Matrix' (3 + n) a
reflectZ = reflect 2
reflectZ : {default B rep : Rep} -> RepConstraint rep a =>
{n : _} -> Neg a => Matrix' (3 + n) a
reflectZ = reflect {rep} 2
--------------------------------------------------------------------------------
@ -146,13 +154,13 @@ getColumn c mat = rewrite sym (rangeLenZ m) in mat!!..[All, One c]
export
diagonal' : Matrix m n a -> Vector (minimum m n) a
diagonal' {m,n} mat with (viewShape mat)
_ | Shape [m,n] = fromFunctionNB _ (\[i] => mat!#[i,i])
_ | Shape [m,n] = fromFunctionNB {rep=_} @{getRepC mat} _ (\[i] => mat!#[i,i])
||| Return the diagonal elements of the matrix as a vector.
export
diagonal : Matrix' n a -> Vector n a
diagonal {n} mat with (viewShape mat)
_ | Shape [n,n] = fromFunctionNB [n] (\[i] => mat!#[i,i])
_ | Shape [n,n] = fromFunctionNB {rep=_} @{getRepC mat} [n] (\[i] => mat!#[i,i])
||| Return a minor of the matrix, i.e. the matrix formed by removing a
@ -165,7 +173,8 @@ minor i j mat = believe_me $ mat!!..[Filter (/=i), Filter (/=j)]
filterInd : Num a => (Nat -> Nat -> Bool) -> Matrix m n a -> Matrix m n a
filterInd {m,n} p mat with (viewShape mat)
_ | Shape [m,n] = fromFunctionNB [m,n] (\[i,j] => if p i j then mat!#[i,j] else 0)
_ | Shape [m,n] = fromFunctionNB {rep=_} @{getRepC mat}
[m,n] (\[i,j] => if p i j then mat!#[i,j] else 0)
export
upperTriangle : Num a => Matrix m n a -> Matrix m n a
@ -259,13 +268,15 @@ reflectNormal {n} v with (viewShape v)
export
Num a => Mult (Matrix m n a) (Vector n a) (Vector m a) where
(*.) {m,n} mat v with (viewShape mat)
_ | Shape [m,n] = fromFunction [m]
_ | Shape [m,n] = fromFunction {rep=_}
@{mergeRepConstraint (getRepC mat) (getRepC v)} [m]
(\[i] => sum $ map (\j => mat!![i,j] * v!!j) range)
export
Num a => Mult (Matrix m n a) (Matrix n p a) (Matrix m p a) where
(*.) {m,n,p} m1 m2 with (viewShape m1, viewShape m2)
_ | (Shape [m,n], Shape [n,p]) = fromFunction [m,p]
_ | (Shape [m,n], Shape [n,p]) = fromFunction {rep=_}
@{mergeRepConstraint (getRepC m1) (getRepC m2)} [m,p]
(\[i,j] => sum $ map (\k => m1!![i,k] * m2!![k,j]) range)
export
@ -295,7 +306,7 @@ namespace DecompLU
export
lower : Num a => DecompLU {m,n,a} mat -> Matrix m (minimum m n) a
lower {m,n} (MkLU lu) with (viewShape lu)
_ | Shape [m,n] = fromFunctionNB _ (\[i,j] =>
_ | Shape [m,n] = fromFunctionNB {rep=_} @{getRepC lu} _ (\[i,j] =>
case compare i j of
LT => 0
EQ => 1
@ -325,7 +336,7 @@ namespace DecompLU
export
upper : Num a => DecompLU {m,n,a} mat -> Matrix (minimum m n) n a
upper {m,n} (MkLU lu) with (viewShape lu)
_ | Shape [m,n] = fromFunctionNB _ (\[i,j] =>
_ | Shape [m,n] = fromFunctionNB {rep=_} @{getRepC lu} _ (\[i,j] =>
if i <= j then lu!#[i,j] else 0)
||| The upper triangular matrix U of the LU decomposition.
@ -392,7 +403,8 @@ gaussStep i lu =
export
decompLU : Field a => (mat : Matrix m n a) -> Maybe (DecompLU mat)
decompLU {m,n} mat with (viewShape mat)
_ | Shape [m,n] = map MkLU $ iterateN (minimum m n) (\i => (>>= gaussStepMaybe i)) (Just mat)
_ | Shape [m,n] = map (MkLU . convertRep _ @{getRepC mat})
$ iterateN (minimum m n) (\i => (>>= gaussStepMaybe i)) (Just (convertRep Delayed mat))
where
gaussStepMaybe : Fin (minimum m n) -> Matrix m n a -> Maybe (Matrix m n a)
gaussStepMaybe i mat = if mat!#[cast i,cast i] == 0 then Nothing
@ -417,7 +429,7 @@ namespace DecompLUP
export
lower : Num a => DecompLUP {m,n,a} mat -> Matrix m (minimum m n) a
lower {m,n} (MkLUP lu _ _) with (viewShape lu)
_ | Shape [m,n] = fromFunctionNB _ (\[i,j] =>
_ | Shape [m,n] = fromFunctionNB {rep=_} @{getRepC lu} _ (\[i,j] =>
case compare i j of
LT => 0
EQ => 1
@ -447,7 +459,7 @@ namespace DecompLUP
export
upper : Num a => DecompLUP {m,n,a} mat -> Matrix (minimum m n) n a
upper {m,n} (MkLUP lu _ _) with (viewShape lu)
_ | Shape [m,n] = fromFunctionNB _ (\[i,j] =>
_ | Shape [m,n] = fromFunctionNB {rep=_} @{getRepC lu} _ (\[i,j] =>
if i <= j then lu!#[i,j] else 0)
||| The upper triangular matrix U of the LUP decomposition.
@ -634,4 +646,3 @@ export
{n : _} -> FieldCmp a => MultGroup (Matrix' n a) where
inverse mat = let lup = decompLUP mat in
hstack $ map (solveWithLUP' mat lup . basis) range

26
src/Data/NumIdr/PrimArray.idr
View file

@ -152,18 +152,18 @@ indexUnsafe {rep = Delayed} is arr = assert_total $ case validateCoords s is of
Just is' => arr is'
export
convertRep : {r1,r2,s : _} -> RepConstraint r1 a => RepConstraint r2 a => PrimArray r1 s a -> PrimArray r2 s a
convertRep {r1 = Bytes o, r2 = Bytes o'} @{rc} arr = reorder @{rc} arr
convertRep {r1 = Boxed o, r2 = Boxed o'} arr = reorder arr
convertRep {r1 = Linked, r2 = Linked} arr = arr
convertRep {r1 = Linked, r2 = Bytes COrder} @{_} @{rc} arr = fromList @{rc} s (collapse arr)
convertRep {r1 = Linked, r2 = Boxed COrder} arr = fromList s (collapse arr)
convertRep {r1 = Delayed, r2 = Delayed} arr = arr
convertRep {r1, r2} arr = fromFunction s (\is => PrimArray.index is arr)
convertRepPrim : {r1,r2,s : _} -> RepConstraint r1 a => RepConstraint r2 a => PrimArray r1 s a -> PrimArray r2 s a
convertRepPrim {r1 = Bytes o, r2 = Bytes o'} @{rc} arr = reorder @{rc} arr
convertRepPrim {r1 = Boxed o, r2 = Boxed o'} arr = reorder arr
convertRepPrim {r1 = Linked, r2 = Linked} arr = arr
convertRepPrim {r1 = Linked, r2 = Bytes COrder} @{_} @{rc} arr = fromList @{rc} s (collapse arr)
convertRepPrim {r1 = Linked, r2 = Boxed COrder} arr = fromList s (collapse arr)
convertRepPrim {r1 = Delayed, r2 = Delayed} arr = arr
convertRepPrim {r1, r2} arr = fromFunction s (\is => PrimArray.index is arr)
export
fromVects : {rep : Rep} -> RepConstraint rep a => (s : Vect rk Nat) -> Vects s a -> PrimArray rep s a
fromVects s v = convertRep {r1=Linked} v
fromVects s v = convertRepPrim {r1=Linked} v
export
fromList : {rep : Rep} -> LinearRep rep => RepConstraint rep a => (s : Vect rk Nat) -> List a -> PrimArray rep s a
@ -184,14 +184,14 @@ foldl : {rep,s : _} -> RepConstraint rep a => (b -> a -> b) -> b -> PrimArray re
foldl {rep = Bytes _} = Bytes.foldl
foldl {rep = Boxed _} = Boxed.foldl
foldl {rep = Linked} = Linked.foldl
foldl {rep = Delayed} = \f,z => Boxed.foldl f z . convertRep {r1=Delayed,r2=B}
foldl {rep = Delayed} = \f,z => Boxed.foldl f z . convertRepPrim {r1=Delayed,r2=B}
export
foldr : {rep,s : _} -> RepConstraint rep a => (a -> b -> b) -> b -> PrimArray rep s a -> b
foldr {rep = Bytes _} = Bytes.foldr
foldr {rep = Boxed _} = Boxed.foldr
foldr {rep = Linked} = Linked.foldr
foldr {rep = Delayed} = \f,z => Boxed.foldr f z . convertRep {r1=Delayed,r2=B}
foldr {rep = Delayed} = \f,z => Boxed.foldr f z . convertRepPrim {r1=Delayed,r2=B}
export
traverse : {rep,s : _} -> Applicative f => RepConstraint rep a => RepConstraint rep b =>
@ -199,6 +199,6 @@ traverse : {rep,s : _} -> Applicative f => RepConstraint rep a => RepConstraint
traverse {rep = Bytes o} = Bytes.traverse
traverse {rep = Boxed o} = Boxed.traverse
traverse {rep = Linked} = Linked.traverse
traverse {rep = Delayed} = \f => map (convertRep @{()} @{()} {r1=B,r2=Delayed}) .
traverse {rep = Delayed} = \f => map (convertRepPrim @{()} @{()} {r1=B,r2=Delayed}) .
Boxed.traverse f .
convertRep @{()} @{()} {r1=Delayed,r2=B}
convertRepPrim @{()} @{()} {r1=Delayed,r2=B}

2
src/Data/NumIdr/Scalar.idr
View file

@ -23,7 +23,7 @@ scalar x = fromVect _ [x]
||| Unwrap the single value from a scalar.
export
unwrap : Scalar a -> a
unwrap = index 0 . getPrim
unwrap s = s !# []
export

3
src/Data/NumIdr/Transform/Point.idr
View file

@ -176,8 +176,7 @@ Traversable (Point n) where
export
Show a => Show (Point n a) where
showPrec d (MkPoint v) = showCon d "point" $
showArg $ PrimArray.toList $ getPrim v
showPrec d (MkPoint v) = showCon d "point" $ showArg $ elements v
export
Cast a b => Cast (Point n a) (Point n b) where

4
src/Data/NumIdr/Transform/Transform.idr
View file

@ -101,6 +101,10 @@ export
getMatrix : Transform ty n a -> Matrix' n a
getMatrix (MkTrans _ mat) = getMatrix mat
export
convertRep : (rep : Rep) -> RepConstraint rep a => Transform ty n a -> Transform ty n a
convertRep rep (MkTrans _ mat) = MkTrans _ (convertRep rep mat)
||| Linearize a transform by removing its translation component.
||| If the transform is already linear, then this function does nothing.
export

47
src/Data/NumIdr/Vector.idr
View file

@ -32,43 +32,45 @@ dimEq v = cong head $ shapeEq v
||| Construct a vector from a `Vect`.
export
vector : Vect n a -> Vector n a
vector : {default B rep : Rep} -> RepConstraint rep a => Vect n a -> Vector n a
vector v = rewrite sym (lengthCorrect v)
in fromVect [length v] $ -- the order doesn't matter here, as
rewrite lengthCorrect v in -- there is only 1 axis
rewrite multOneLeftNeutral n in v
in array {rep,s=[length v]} $
rewrite lengthCorrect v in v
||| Convert a vector into a `Vect`.
export
toVect : Vector n a -> Vect n a
toVect v = believe_me $ Vect.fromList $ toList v
toVect v = believe_me $ Vect.fromList $ Prelude.toList v
||| Return the `i`-th basis vector.
export
basis : Num a => {n : _} -> (i : Fin n) -> Vector n a
basis i = fromFunction _ (\[j] => if i == j then 1 else 0)
basis : {default B rep : Rep} -> RepConstraint rep a =>
Num a => {n : _} -> (i : Fin n) -> Vector n a
basis i = fromFunction {rep} _ (\[j] => if i == j then 1 else 0)
||| The first basis vector.
export
basisX : {n : _} -> Num a => Vector (1 + n) a
basisX = basis FZ
basisX : {default B rep : Rep} -> RepConstraint rep a =>
{n : _} -> Num a => Vector (1 + n) a
basisX = basis {rep} FZ
||| The second basis vector.
export
basisY : {n : _} -> Num a => Vector (2 + n) a
basisY = basis (FS FZ)
basisY : {default B rep : Rep} -> RepConstraint rep a =>
{n : _} -> Num a => Vector (2 + n) a
basisY = basis {rep} (FS FZ)
||| The third basis vector.
export
basisZ : {n : _} -> Num a => Vector (3 + n) a
basisZ = basis (FS (FS FZ))
basisZ : {default B rep : Rep} -> RepConstraint rep a =>
{n : _} -> Num a => Vector (3 + n) a
basisZ = basis {rep} (FS (FS FZ))
||| Calculate the 2D unit vector with the given angle off the x-axis.
export
unit2D : (ang : Double) -> Vector 2 Double
unit2D ang = vector [cos ang, sin ang]
unit2D : {default B rep : Rep} -> RepConstraint rep Double =>
(ang : Double) -> Vector 2 Double
unit2D ang = vector {rep} [cos ang, sin ang]
||| Calculate the 3D unit vector corresponding to the given spherical coordinates,
||| where the polar axis is the z-axis.
@ -76,8 +78,9 @@ unit2D ang = vector [cos ang, sin ang]
||| @ pol The polar angle of the vector
||| @ az The azimuthal angle of the vector
export
unit3D : (pol, az : Double) -> Vector 3 Double
unit3D pol az = vector [cos az * sin pol, sin az * sin pol, cos pol]
unit3D : {default B rep : Rep} -> RepConstraint rep Double =>
(pol, az : Double) -> Vector 3 Double
unit3D pol az = vector {rep} [cos az * sin pol, sin az * sin pol, cos pol]
@ -142,9 +145,8 @@ export
export
swizzle : Vect n (Fin m) -> Vector m a -> Vector n a
swizzle p v = rewrite sym (lengthCorrect p)
in fromFunction [length p] (\[i] =>
index (index (rewrite sym (lengthCorrect p) in i) p) v
)
in fromFunction {rep=_} @{getRepC v} [length p] (\[i] =>
index (index (rewrite sym (lengthCorrect p) in i) p) v)
||| Swap two coordinates in a vector.
@ -168,7 +170,6 @@ export
(++) : Vector m a -> Vector n a -> Vector (m + n) a
(++) = concat 0
||| Calculate the dot product of the two vectors.
export
dot : Num a => Vector n a -> Vector n a -> a