-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/
-- | Tensors of statically known size
--
-- This library provides a toolkit for working with tensors of statically
-- known size and element's type. See README.md
@package static-tensor
@version 0.2.0.0
module Data.Function.NAry
-- | N-ary function from n arguments of type t to value
-- of type r.
-- | Apply list of params to N-ary function.
class ApplyNAry (n :: Nat) (t :: Type) (r :: Type)
applyNAry :: ApplyNAry n t r => NAry n t r -> [t] -> r
instance Data.Function.NAry.ApplyNAry 0 t r
instance (Data.Function.NAry.ApplyNAry (n GHC.TypeNats.- 1) t r, Data.Function.NAry.NAry n t r ~ (t -> Data.Function.NAry.NAry (n GHC.TypeNats.- 1) t r), GHC.TypeNats.KnownNat n) => Data.Function.NAry.ApplyNAry n t r
-- | This module provides unrollable versions of functions on lists.
--
-- Classes in this module are assumed to be closed. You should not
-- create new instances for them.
module Data.List.Unrolled
-- | Append two lists. Type param l is the length of the left
-- list.
class Append (n :: Nat)
append :: Append n => [a] -> [a] -> [a]
-- | Drop n elements from a list.
class Drop (n :: Nat)
drop :: Drop n => [a] -> [a]
-- | Take n elements from a list
class Take (n :: Nat)
take :: Take n => [a] -> [a]
-- | Split list at n-th element.
splitAt :: forall (n :: Nat) a. (Take n, Drop n) => [a] -> ([a], [a])
-- | Split list into chunks of the given length c. n is
-- length of the list.
class ChunksOf (n :: Nat) (c :: Nat)
chunksOf :: ChunksOf n c => [a] -> [[a]]
-- | Number of resulting chunks when list of length len split by
-- chunks of length clen.
-- | Zip 2 lists together. Type param n is the length of the first
-- list.
class Zip (n :: Nat)
zip :: Zip n => [a] -> [b] -> [(a, b)]
-- | Zip 3 lists together. Type param n is the length of the first
-- list.
class Zip3 (n :: Nat)
zip3 :: Zip3 n => [a] -> [b] -> [c] -> [(a, b, c)]
-- | Zip 2 lists together using given function. Type param n is
-- the length of the first list.
class ZipWith (n :: Nat)
zipWith :: ZipWith n => (a -> b -> c) -> [a] -> [b] -> [c]
-- | Unzip a list. Type param n is the length of the list.
class Unzip (n :: Nat)
unzip :: Unzip n => [(a, b)] -> ([a], [b])
-- | Filter list with given predicate. Type param n is the length
-- of the list.
class Filter (n :: Nat)
filter :: Filter n => (a -> Bool) -> [a] -> [a]
-- | Apply function to all elements of a list. Type param n is the
-- length of the list.
class Map (n :: Nat)
map :: Map n => (a -> b) -> [a] -> [b]
-- | Check if all elements of the list satisfy the predicate. Type param
-- n is the length of the list.
class All (n :: Nat)
all :: All n => (a -> Bool) -> [a] -> Bool
-- | Right fold of a list of length n.
class Foldr (n :: Nat)
foldr :: Foldr n => (a -> b -> b) -> b -> [a] -> b
-- | Right fold of a list of length n with no base element.
class Foldr1 (n :: Nat)
foldr1 :: Foldr1 n => (a -> a -> a) -> [a] -> a
-- | Left fold of a list of length n.
class Foldl (n :: Nat)
foldl :: Foldl n => (b -> a -> b) -> b -> [a] -> b
-- | Right fold of a list of length n with no base element.
class Foldl1 (n :: Nat)
foldl1 :: Foldl1 n => (a -> a -> a) -> [a] -> a
-- | Map each element of the list of length n to a monoid, and
-- combine the results.
foldMap :: forall (n :: Nat) m a. (FoldMap n m) => (a -> m) -> [a] -> m
-- | Constraint of the foldMap function.
type FoldMap (n :: Nat) m = (Monoid m, Foldr n)
-- | Sum of the elements of the list of length n.
sum :: forall (n :: Nat) a. (Sum n a) => [a] -> a
-- | Constraint of the sum function.
type Sum (n :: Nat) a = (Foldr n, Num a)
-- | Fill the list of length n with the same values.
class Replicate (n :: Nat)
replicate :: Replicate n => a -> [a]
-- | Enumeration of length n starting from given value.
class EnumFromN (n :: Nat)
enumFromN :: (EnumFromN n, (Num a)) => a -> [a]
-- | Enumeration of length n starting from given value with given
-- step.
class EnumFromStepN (n :: Nat)
enumFromStepN :: (EnumFromStepN n, (Num a)) => a -> a -> [a]
instance Data.List.Unrolled.EnumFromStepN 0
instance Data.List.Unrolled.EnumFromStepN (n GHC.TypeNats.- 1) => Data.List.Unrolled.EnumFromStepN n
instance Data.List.Unrolled.EnumFromN 0
instance Data.List.Unrolled.EnumFromN (n GHC.TypeNats.- 1) => Data.List.Unrolled.EnumFromN n
instance Data.List.Unrolled.Replicate 0
instance Data.List.Unrolled.Replicate (n GHC.TypeNats.- 1) => Data.List.Unrolled.Replicate n
instance Data.List.Unrolled.Foldl1 1
instance Data.List.Unrolled.Foldl1 (n GHC.TypeNats.- 1) => Data.List.Unrolled.Foldl1 n
instance Data.List.Unrolled.Foldl 0
instance Data.List.Unrolled.Foldl (n GHC.TypeNats.- 1) => Data.List.Unrolled.Foldl n
instance Data.List.Unrolled.Foldr1 1
instance Data.List.Unrolled.Foldr1 (n GHC.TypeNats.- 1) => Data.List.Unrolled.Foldr1 n
instance Data.List.Unrolled.Foldr 0
instance Data.List.Unrolled.Foldr (n GHC.TypeNats.- 1) => Data.List.Unrolled.Foldr n
instance Data.List.Unrolled.All 0
instance Data.List.Unrolled.All (n GHC.TypeNats.- 1) => Data.List.Unrolled.All n
instance Data.List.Unrolled.Map 0
instance Data.List.Unrolled.Map (n GHC.TypeNats.- 1) => Data.List.Unrolled.Map n
instance Data.List.Unrolled.Filter 0
instance Data.List.Unrolled.Filter (n GHC.TypeNats.- 1) => Data.List.Unrolled.Filter n
instance Data.List.Unrolled.ZipWith 0
instance Data.List.Unrolled.ZipWith (n GHC.TypeNats.- 1) => Data.List.Unrolled.ZipWith n
instance Data.List.Unrolled.Unzip 0
instance Data.List.Unrolled.Unzip (n GHC.TypeNats.- 1) => Data.List.Unrolled.Unzip n
instance Data.List.Unrolled.Zip3 0
instance Data.List.Unrolled.Zip3 (n GHC.TypeNats.- 1) => Data.List.Unrolled.Zip3 n
instance Data.List.Unrolled.Zip 0
instance Data.List.Unrolled.Zip (n GHC.TypeNats.- 1) => Data.List.Unrolled.Zip n
instance Data.List.Unrolled.ChunksOf 0 0
instance Data.List.Unrolled.ChunksOf 0 c
instance Data.List.Unrolled.ChunksOf n 0
instance (Data.List.Unrolled.Take c, Data.List.Unrolled.Drop c, Data.List.Unrolled.ChunksOf (n GHC.TypeNats.- 1) c) => Data.List.Unrolled.ChunksOf n c
instance Data.List.Unrolled.Take 0
instance Data.List.Unrolled.Take (n GHC.TypeNats.- 1) => Data.List.Unrolled.Take n
instance Data.List.Unrolled.Drop 0
instance Data.List.Unrolled.Drop (n GHC.TypeNats.- 1) => Data.List.Unrolled.Drop n
instance Data.List.Unrolled.Append 0
instance Data.List.Unrolled.Append (n GHC.TypeNats.- 1) => Data.List.Unrolled.Append n
module Type.List
-- | Demote type-level list of Nat.
class KnownNats (ns :: [Nat])
natsVal :: KnownNats ns => [Int]
-- | Make a constraint for type x :: kx from TyFun, or
-- partially applied constraint, or make an empty constraint.
-- | Demote a type-level list to value-level list with a type-indexed
-- function. The function takes list element as type parameter x
-- and applies constraints ctx for that element.
class DemoteWith (kx :: Type) (kctx :: Type) (ctx :: kctx) (xs :: [kx])
demoteWith :: DemoteWith kx kctx ctx xs => (forall (x :: kx). (MkCtx kx kctx ctx x) => Proxy x -> a) -> [a]
instance forall kx kctx (ctxs :: kctx). Type.List.DemoteWith kx kctx ctxs '[]
instance forall kx kctx (ctx :: kctx) (xs :: [kx]) (x :: kx). (Type.List.DemoteWith kx kctx ctx xs, Type.List.MkCtx kx kctx ctx x) => Type.List.DemoteWith kx kctx ctx (x : xs)
instance Type.List.KnownNats '[]
instance (GHC.TypeNats.KnownNat n, Type.List.KnownNats ns) => Type.List.KnownNats (n : ns)
module Data.Tensor.Static
-- | Data family of unboxed tensors. Dimensions of a tensor are represented
-- as type-level list of naturals. For instance, Tensor [3]
-- Float is a vector of 3 Float elements; Tensor [4,3]
-- Double is a matrix with 4 rows 3 columns of Double and so
-- on.
class (PositiveDims dims, KnownNats dims) => IsTensor (dims :: [Nat]) e where {
data family Tensor dims e :: Type;
}
-- | Alias for a concrete tensor data constructor.
--
--
-- >>> tensor @[2,2] @Int 0 1 2 3
-- Tensor'2'2 [[0,1],[2,3]]
--
tensor :: IsTensor dims e => TensorConstructor dims e
-- | Build tensor from the list. The list must contain at least
-- length elements or method will throw an exception.
unsafeFromList :: IsTensor dims e => [e] -> Tensor dims e
-- | Convert tensor to list.
toList :: IsTensor dims e => Tensor dims e -> [] e
-- | Type of a tensor data constructor.
--
--
-- >>> :kind! TensorConstructor '[2,2] Float
-- TensorConstructor '[2,2] Float :: *
-- = Float -> Float -> Float -> Float -> Tensor '[2, 2] Float
--
type TensorConstructor (dims :: [Nat]) (e :: Type) = NAry (ElemsNumber dims) e (Tensor dims e)
-- | Check if all dimensions are greater than 0.
-- | Tensor filled with given elements.
fill :: forall (dims :: [Nat]) e. (Fill dims e) => e -> Tensor dims e
-- | Tensor filled with zeros.
zero :: (Fill dims e, Num e) => Tensor dims e
-- | Tensor which elements are enumeration starting from given value.
enumFromN :: forall (dims :: [Nat]) e. (EnumFromN dims e) => e -> Tensor dims e
-- | Constraints for enumFromN function.
type EnumFromN (dims :: [Nat]) e = (IsTensor dims e, EnumFromN (ElemsNumber dims), Num e)
-- | Tensor which elements are enumeration starting from given value with
-- given step.
enumFromStepN :: forall (dims :: [Nat]) e. (EnumFromStepN dims e) => e -> e -> Tensor dims e
-- | Constraints for enumFromStepN function.
type EnumFromStepN (dims :: [Nat]) e = (IsTensor dims e, EnumFromStepN (ElemsNumber dims), Num e)
-- | Generate a tensor by applying the function to each index. ctx
-- type parameter is a producer of constraint of kind kctx for
-- each index. See MkCtx for more info.
--
--
-- >>> import Data.Singletons
--
-- >>> type Ctx (dims :: [Nat]) (index :: [Nat]) = KnownNat (FlattenIndex index dims); $(genDefunSymbols [''Ctx])
--
-- >>> generate @[2,3,4] @Int @([Nat] ~> Constraint) @(CtxSym1 [2,3,4]) $ \(Proxy :: Proxy index) -> fromIntegral $ natVal (Proxy @(FlattenIndex index [2,3,4]))
-- Tensor'2'3'4 [[[0,1,2,3],[4,5,6,7],[8,9,10,11]],[[12,13,14,15],[16,17,18,19],[20,21,22,23]]]
--
generate :: forall (dims :: [Nat]) (e :: Type) (kctx :: Type) (ctx :: kctx). (Generate dims e kctx ctx) => (forall (index :: [Nat]). (MkCtx [Nat] kctx ctx index) => Proxy index -> e) -> Tensor dims e
-- | Constraints for generate function.
type Generate (dims :: [Nat]) (e :: Type) (kctx :: Type) (ctx :: kctx) = (IsTensor dims e, DemoteWith [Nat] kctx ctx (AllIndexes dims))
-- | Dimensions of a tensor.
dimensions :: forall (dims :: [Nat]). (KnownNats dims) => [Int]
-- | Number of elements in a tensor.
elemsNumber :: forall (dims :: [Nat]). (KnownNat (ElemsNumber dims)) => Int
-- | Number of elements of all subtensors of a tensor.
--
--
-- >>> subtensorsElemsNumbers @[2,3,4]
-- [12,4,1]
--
--
--
-- >>> subtensorsElemsNumbers @[4,4]
-- [4,1]
--
subtensorsElemsNumbers :: forall (dims :: [Nat]). (KnownNats (SubtensorsElemsNumbers dims)) => [Int]
-- | Number of elements in a tensor.
-- | Number of elements of all subtensors of a tensor with given shape
-- dims.
--
--
-- >>> :kind! SubtensorsElemsNumbers '[2,3,4]
-- SubtensorsElemsNumbers '[2,3,4] :: [Nat]
-- = '[12, 4, 1]
--
--
--
-- >>> :kind! SubtensorsElemsNumbers '[4,4]
-- SubtensorsElemsNumbers '[4,4] :: [Nat]
-- = '[4, 1]
--
type SubtensorsElemsNumbers (dims :: [Nat]) = Tail (SubtensorsElemsNumbers' dims)
-- | Convert multidimentional index in tensor of shape
-- dims to flat index. index parameter must have the
-- same length as dims.
--
--
-- >>> :kind! FlattenIndex '[1,1,1] '[2,3,4]
-- FlattenIndex '[1,1,1] '[2,3,4] :: Nat
-- = 17
--
type FlattenIndex (index :: [Nat]) (dims :: [Nat]) = FlattenIndex' index (SubtensorsElemsNumbers dims)
-- | Sequence of all indexes in a tensor of shape dims.
--
--
-- >>> :kind! AllIndexes '[2,3,4]
-- AllIndexes '[2,3,4] :: [[Nat]]
-- = '['[0, 0, 0], '[0, 0, 1], '[0, 0, 2], '[0, 0, 3], '[0, 1, 0],
-- '[0, 1, 1], '[0, 1, 2], '[0, 1, 3], '[0, 2, 0], '[0, 2, 1],
-- '[0, 2, 2], '[0, 2, 3], '[1, 0, 0], '[1, 0, 1], '[1, 0, 2],
-- '[1, 0, 3], '[1, 1, 0], '[1, 1, 1], '[1, 1, 2], '[1, 1, 3],
-- '[1, 2, 0], '[1, 2, 1], '[1, 2, 2], '[1, 2, 3]]
--
type AllIndexes (dims :: [Nat]) = Sequence (IndexesRanges dims)
-- | Generate range of naturals starting from from param inclusive
-- and up to to param inclusive.
type NatsFromTo (from :: Nat) (to :: Nat) = NatsFromTo' from to (from <=? to)
-- | Remove unit dimentions, i.e. dimensions with size 1.
--
--
-- >>> :kind! NormalizeDims '[2, 1, 3]
-- '[2, 3]
--
-- | Pass tensor elements to a function.
--
--
-- >>> withTensor (matrix @2 @2 @Float 0 1 2 3) (\a b c d -> a * d - b * c)
-- -2.0
--
--
--
-- >>> withTensor (vector @2 @Float 3 4) (\x y -> sqrt $ x * x + y * y)
-- 5.0
--
withTensor :: forall dims e r. (IsTensor dims e, ApplyNAry (ElemsNumber dims) e r) => Tensor dims e -> (NAry (ElemsNumber dims) e r) -> r
-- | Add two tensors element-wise.
add :: (Add dims e) => Tensor dims e -> Tensor dims e -> Tensor dims e
-- | Constraints for add.
type Add (dims :: [Nat]) e = (IsTensor dims e, Num e, ZipWith (ElemsNumber dims), Zip (ElemsNumber dims), Unzip (ElemsNumber dims), Map (ElemsNumber dims))
-- | Substract two tensors element-wise.
diff :: (Diff dims e) => Tensor dims e -> Tensor dims e -> Tensor dims e
-- | Constraints for diff.
type Diff (dims :: [Nat]) e = (IsTensor dims e, Num e, ZipWith (ElemsNumber dims), Zip (ElemsNumber dims), Unzip (ElemsNumber dims), Map (ElemsNumber dims))
-- | Multiply every element of a tensor by given value.
scale :: (Scale dims e) => Tensor dims e -> e -> Tensor dims e
-- | Constraints for scale.
type Scale (dims :: [Nat]) e = (IsTensor dims e, Num e, Map (ElemsNumber dims))
-- | Prepend a subtensor along axis to the tensor with shape
-- dims
--
--
-- >>> cons @0 (enumFromStepN @[3,4] @Int (-1) (-1)) (enumFromN @[2,3,4] 0)
-- Tensor'3'3'4 [[[ -1, -2, -3, -4]
-- ,[ -5, -6, -7, -8]
-- ,[ -9, -10, -11, -12]]
-- ,[[ 0, 1, 2, 3]
-- ,[ 4, 5, 6, 7]
-- ,[ 8, 9, 10, 11]]
-- ,[[ 12, 13, 14, 15]
-- ,[ 16, 17, 18, 19]
-- ,[ 20, 21, 22, 23]]]
--
--
--
-- >>> cons @1 (enumFromStepN @[2,4] @Int (-1) (-1)) (enumFromN @[2,3,4] 0)
-- Tensor'2'4'4 [[[ -1, -2, -3, -4]
-- ,[ 0, 1, 2, 3]
-- ,[ 4, 5, 6, 7]
-- ,[ 8, 9, 10, 11]]
-- ,[[ -5, -6, -7, -8]
-- ,[ 12, 13, 14, 15]
-- ,[ 16, 17, 18, 19]
-- ,[ 20, 21, 22, 23]]]
--
--
--
-- >>> cons @2 (enumFromStepN @[2,3] @Int (-1) (-1)) (enumFromN @[2,3,4] 0)
-- Tensor'2'3'5 [[[ -1, 0, 1, 2, 3]
-- ,[ -2, 4, 5, 6, 7]
-- ,[ -3, 8, 9, 10, 11]]
-- ,[[ -4, 12, 13, 14, 15]
-- ,[ -5, 16, 17, 18, 19]
-- ,[ -6, 20, 21, 22, 23]]]
--
cons :: forall (axis :: Nat) (dims :: [Nat]) e. (Cons axis dims e) => Tensor (NormalizeDims (ConsSubtensorDims axis dims)) e -> Tensor dims e -> Tensor (DimsAfterCons axis dims) e
-- | Constraints for cons.
type Cons (axis :: Nat) (dims :: [Nat]) e = (SetSlice (ConsSubtensorStartingIndex dims) (ConsSubtensorDims axis dims) (DimsAfterCons axis dims) e, SetSlice (ConsTensorStartingIndex axis dims) dims (DimsAfterCons axis dims) e, dims ~ NormalizeDims dims, Fill (DimsAfterCons axis dims) e)
-- | Shape of subtensor being cons'ed to the tensor dims.
--
--
-- >>> :kind! ConsSubtensorDims 0 [2,3,4]
-- ConsSubtensorDims 0 [2,3,4] :: [Nat]
-- = '[1, 3, 4]
--
--
--
-- >>> :kind! ConsSubtensorDims 1 [2,3,4]
-- ConsSubtensorDims 1 [2,3,4] :: [Nat]
-- = '[2, 1, 4]
--
--
--
-- >>> :kind! ConsSubtensorDims 2 [2,3,4]
-- ConsSubtensorDims 2 [2,3,4] :: [Nat]
-- = '[2, 3, 1]
--
type ConsSubtensorDims (axis :: Nat) (dims :: [Nat]) = ConsSubtensorDims' axis dims 0
-- | Shape of the tensor after cons'ing
--
--
-- >>> :kind! DimsAfterCons 0 [2,3,4]
-- DimsAfterCons 0 [2,3,4] :: [Nat]
-- = '[3, 3, 4]
--
--
--
-- >>> :kind! DimsAfterCons 1 [2,3,4]
-- DimsAfterCons 1 [2,3,4] :: [Nat]
-- = '[2, 4, 4]
--
--
--
-- >>> :kind! DimsAfterCons 2 [2,3,4]
-- DimsAfterCons 2 [2,3,4] :: [Nat]
-- = '[2, 3, 5]
--
-- | Append a subtensor along axis to the tensor with shape
-- dims
--
--
-- >>> snoc @0 (enumFromN @[2,3,4] 0) (enumFromStepN @[3,4] @Int (-1) (-1))
-- Tensor'3'3'4 [[[ 0, 1, 2, 3]
-- ,[ 4, 5, 6, 7]
-- ,[ 8, 9, 10, 11]]
-- ,[[ 12, 13, 14, 15]
-- ,[ 16, 17, 18, 19]
-- ,[ 20, 21, 22, 23]]
-- ,[[ -1, -2, -3, -4]
-- ,[ -5, -6, -7, -8]
-- ,[ -9, -10, -11, -12]]]
--
--
--
-- >>> snoc @1 (enumFromN @[2,3,4] 0) (enumFromStepN @[2,4] @Int (-1) (-1))
-- Tensor'2'4'4 [[[ 0, 1, 2, 3]
-- ,[ 4, 5, 6, 7]
-- ,[ 8, 9, 10, 11]
-- ,[ -1, -2, -3, -4]]
-- ,[[ 12, 13, 14, 15]
-- ,[ 16, 17, 18, 19]
-- ,[ 20, 21, 22, 23]
-- ,[ -5, -6, -7, -8]]]
--
--
--
-- >>> snoc @2 (enumFromN @[2,3,4] 0) (enumFromStepN @[2,3] @Int (-1) (-1))
-- Tensor'2'3'5 [[[ 0, 1, 2, 3, -1]
-- ,[ 4, 5, 6, 7, -2]
-- ,[ 8, 9, 10, 11, -3]]
-- ,[[ 12, 13, 14, 15, -4]
-- ,[ 16, 17, 18, 19, -5]
-- ,[ 20, 21, 22, 23, -6]]]
--
snoc :: forall (axis :: Nat) (dims :: [Nat]) e. (Snoc axis dims e) => Tensor dims e -> Tensor (NormalizeDims (SnocSubtensorDims axis dims)) e -> Tensor (DimsAfterSnoc axis dims) e
-- | Constraints for snoc.
type Snoc (axis :: Nat) (dims :: [Nat]) e = (SetSlice (SnocSubtensorStartingIndex axis dims) (SnocSubtensorDims axis dims) (DimsAfterSnoc axis dims) e, SetSlice (SnocTensorStartingIndex dims) dims (DimsAfterSnoc axis dims) e, dims ~ NormalizeDims dims, Fill (DimsAfterSnoc axis dims) e)
-- | Shape of subtensor being snoc'ed to the tensor dims.
--
--
-- >>> :kind! SnocSubtensorDims 0 [2,3,4]
-- SnocSubtensorDims 0 [2,3,4] :: [Nat]
-- = '[1, 3, 4]
--
--
--
-- >>> :kind! SnocSubtensorDims 1 [2,3,4]
-- SnocSubtensorDims 1 [2,3,4] :: [Nat]
-- = '[2, 1, 4]
--
--
--
-- >>> :kind! SnocSubtensorDims 2 [2,3,4]
-- SnocSubtensorDims 2 [2,3,4] :: [Nat]
-- = '[2, 3, 1]
--
type SnocSubtensorDims (axis :: Nat) (dims :: [Nat]) = SnocSubtensorDims' axis dims 0
-- | Shape of the tensor after snoc'ing
--
--
-- >>> :kind! DimsAfterSnoc 0 [2,3,4]
-- DimsAfterSnoc 0 [2,3,4] :: [Nat]
-- = '[3, 3, 4]
--
--
--
-- >>> :kind! DimsAfterSnoc 1 [2,3,4]
-- DimsAfterSnoc 1 [2,3,4] :: [Nat]
-- = '[2, 4, 4]
--
--
--
-- >>> :kind! DimsAfterSnoc 2 [2,3,4]
-- DimsAfterSnoc 2 [2,3,4] :: [Nat]
-- = '[2, 3, 5]
--
-- | Append the second tensor dims1 to the first tensor
-- dims0 along axis.
--
--
-- >>> append @0 (enumFromN @[2,3,4] 0) (enumFromStepN @[2,3,4] @Int (-1) (-1))
-- Tensor'4'3'4 [[[ 0, 1, 2, 3]
-- ,[ 4, 5, 6, 7]
-- ,[ 8, 9, 10, 11]]
-- ,[[ 12, 13, 14, 15]
-- ,[ 16, 17, 18, 19]
-- ,[ 20, 21, 22, 23]]
-- ,[[ -1, -2, -3, -4]
-- ,[ -5, -6, -7, -8]
-- ,[ -9, -10, -11, -12]]
-- ,[[ -13, -14, -15, -16]
-- ,[ -17, -18, -19, -20]
-- ,[ -21, -22, -23, -24]]]
--
--
--
-- >>> append @1 (enumFromN @[2,3,4] 0) (enumFromStepN @[2,3,4] @Int (-1) (-1))
-- Tensor'2'6'4 [[[ 0, 1, 2, 3]
-- ,[ 4, 5, 6, 7]
-- ,[ 8, 9, 10, 11]
-- ,[ -1, -2, -3, -4]
-- ,[ -5, -6, -7, -8]
-- ,[ -9, -10, -11, -12]]
-- ,[[ 12, 13, 14, 15]
-- ,[ 16, 17, 18, 19]
-- ,[ 20, 21, 22, 23]
-- ,[ -13, -14, -15, -16]
-- ,[ -17, -18, -19, -20]
-- ,[ -21, -22, -23, -24]]]
--
-- >>> append @2 (enumFromN @[2,3,4] 0) (enumFromStepN @[2,3,4] @Int (-1) (-1))
-- Tensor'2'3'8 [[[ 0, 1, 2, 3, -1, -2, -3, -4]
-- ,[ 4, 5, 6, 7, -5, -6, -7, -8]
-- ,[ 8, 9, 10, 11, -9, -10, -11, -12]]
-- ,[[ 12, 13, 14, 15, -13, -14, -15, -16]
-- ,[ 16, 17, 18, 19, -17, -18, -19, -20]
-- ,[ 20, 21, 22, 23, -21, -22, -23, -24]]]
--
append :: forall (axis :: Nat) (dims0 :: [Nat]) (dims1 :: [Nat]) e. (Append axis dims0 dims1 e) => Tensor dims0 e -> Tensor dims1 e -> Tensor (DimsAfterAppend axis dims0 dims1) e
-- | Constraints for append.
type Append (axis :: Nat) (dims0 :: [Nat]) (dims1 :: [Nat]) e = (SetSlice (AppendFstTensorStartingIndex dims0) dims0 (DimsAfterAppend axis dims0 dims1) e, SetSlice (AppendSndTensorStartingIndex axis dims1) dims1 (DimsAfterAppend axis dims0 dims1) e, dims0 ~ NormalizeDims dims0, dims1 ~ NormalizeDims dims1, Fill (DimsAfterAppend axis dims0 dims1) e)
-- | Shape of the tensor after appending
--
--
-- >>> :kind! DimsAfterAppend 0 [2,3,4] [5,3,4]
-- DimsAfterAppend 0 [2,3,4] [5,3,4] :: [Nat]
-- = '[7, 3, 4]
--
--
--
-- >>> :kind! DimsAfterAppend 1 [2,3,4] [2,5,4]
-- DimsAfterAppend 1 [2,3,4] [2,5,4] :: [Nat]
-- = '[2, 8, 4]
--
--
--
-- >>> :kind! DimsAfterAppend 2 [2,3,4] [2,3,5]
-- DimsAfterAppend 2 [2,3,4] [2,3,5] :: [Nat]
-- = '[2, 3, 9]
--
type DimsAfterAppend (axis :: Nat) (dims0 :: [Nat]) (dims1 :: [Nat]) = DimsAfterAppend' axis dims0 dims1 0
-- | Remove a slice from the tensor. We can only remove slices which have
-- one dimension fewer than the tensor, and which span from borders of
-- the tensor to opposite borders of the tensor (i.e. contain all
-- elements of the tensor in their dimensions).
--
-- axis is the index of dimension in dims
-- indexOnAxis is offset along axis that points to the
-- slice to be removed.
--
-- For example, suppose we have tensor t :: Tensor '[2,3,4]
-- Float that is, tensor made of two matrices of 3*4 elements.
--
-- If we want to remove first matrix we write remove @0 @0 t, if
-- second - remove @0 @1 t.
--
-- If we want to remove n-th row in all matrices we write remove @1
-- @n t.
--
-- If we want to remove n-th column in all matrices we write remove
-- @2 @n t.
--
--
-- >>> let t = enumFromN @[2,3,4] @Int 0
--
-- >>> t
-- Tensor'2'3'4 [[[ 0, 1, 2, 3]
-- ,[ 4, 5, 6, 7]
-- ,[ 8, 9,10,11]]
-- ,[[12,13,14,15]
-- ,[16,17,18,19]
-- ,[20,21,22,23]]]
--
-- >>> remove @0 @0 t
-- Tensor'1'3'4 [[[12,13,14,15]
-- ,[16,17,18,19]
-- ,[20,21,22,23]]]
--
-- >>> remove @1 @0 t
-- Tensor'2'2'4 [[[ 4, 5, 6, 7]
-- ,[ 8, 9,10,11]]
-- ,[[16,17,18,19]
-- ,[20,21,22,23]]]
--
-- >>> remove @2 @0 t
-- Tensor'2'3'3 [[[ 1, 2, 3]
-- ,[ 5, 6, 7]
-- ,[ 9,10,11]]
-- ,[[13,14,15]
-- ,[17,18,19]
-- ,[21,22,23]]]
--
remove :: forall (axis :: Nat) (indexOnAxis :: Nat) (dims :: [Nat]) e. (Remove axis indexOnAxis dims e) => Tensor dims e -> Tensor (DimsAfterRemove axis indexOnAxis dims) e
-- | Constraints for remove.
type Remove (axis :: Nat) (indexOnAxis :: Nat) (dims :: [Nat]) e = (IsTensor dims e, IsTensor (DimsAfterRemove axis indexOnAxis dims) e, RemoveWrk (ElemsInSlice (RemoveSliceStartIndex axis indexOnAxis dims) (RemoveSliceDims axis indexOnAxis dims) dims))
-- | Shape of a tensor dims after removing a slice at
-- index along axis.
--
--
-- >>> :kind! DimsAfterRemove 0 0 [2,3,4]
-- DimsAfterRemove 0 0 [2,3,4] :: [Nat]
-- = '[1, 3, 4]
--
--
--
-- >>> :kind! DimsAfterRemove 1 0 [2,3,4]
-- DimsAfterRemove 1 0 [2,3,4] :: [Nat]
-- = '[2, 2, 4]
--
--
--
-- >>> :kind! DimsAfterRemove 2 0 [2,3,4]
-- DimsAfterRemove 2 0 [2,3,4] :: [Nat]
-- = '[2, 3, 3]
--
-- | Nested list of given depth.
--
--
-- >>> :kind! NestedList 3 Float
-- [[[Float]]]
--
--
--
-- >>> :kind! NestedList 2 Float
-- [[Float]]
--
-- | Convert tensor to nested list.
toNestedList :: forall dims e. (ToNestedList dims e) => Tensor dims e -> NestedList (Length dims) e
-- | Constraints for toNestedList function.
type ToNestedList (dims :: [Nat]) e = (IsTensor dims e, ToNestedListWrk dims e)
-- | Lens for an element of a tensor.
--
--
-- >>> let t = enumFromN @[2,3,4] @Int 0
--
-- >>> t
-- Tensor'2'3'4 [[[ 0, 1, 2, 3]
-- ,[ 4, 5, 6, 7]
-- ,[ 8, 9, 10, 11]]
-- ,[[ 12, 13, 14, 15]
-- ,[ 16, 17, 18, 19]
-- ,[ 20, 21, 22, 23]]]
--
-- >>> t ^. tensorElem @[1,1,1]
-- 17
--
-- >>> set (tensorElem @[1,1,1]) 0 t
-- Tensor'2'3'4 [[[ 0, 1, 2, 3]
-- ,[ 4, 5, 6, 7]
-- ,[ 8, 9, 10, 11]]
-- ,[[ 12, 13, 14, 15]
-- ,[ 16, 0, 18, 19]
-- ,[ 20, 21, 22, 23]]]
--
tensorElem :: forall (index :: [Nat]) (dims :: [Nat]) e. (TensorElem index dims e) => Lens' (Tensor dims e) e
-- | Constraint for tensorElem function.
type TensorElem index dims e = (SubtensorCtx index dims e, NormalizeDims (SubtensorDims index dims) ~ '[])
-- | Subtensor at index of a tensor of shape dims.
--
--
-- >>> :kind! Subtensor '[] '[2,3,4] Float
-- Subtensor '[] '[2,3,4] Float :: *
-- = Tensor '[2, 3, 4] Float
--
--
--
-- >>> :kind! Subtensor '[0] '[2,3,4] Float
-- Subtensor '[0] '[2,3,4] Float :: *
-- = Tensor '[3, 4] Float
--
--
--
-- >>> :kind! Subtensor '[0,0] '[2,3,4] Float
-- Subtensor '[0,0] '[2,3,4] Float :: *
-- = Tensor '[4] Float
--
--
--
-- >>> :kind! Subtensor '[0,0,0] '[2,3,4] Float
-- Subtensor '[0,0,0] '[2,3,4] Float :: *
-- = Tensor '[] Float
--
type Subtensor index dims e = Tensor (NormalizeDims (SubtensorDims index dims)) e
-- | Index of the first element of the subtensor of the tensor of shape
-- dims at index. This function returns index with
-- number of dimensions equal to number of dimensions of the tensor.
--
--
-- >>> :kind! SubtensorStartIndex '[1] '[2,3,4]
-- SubtensorStartIndex '[1] '[2,3,4] :: [Nat]
-- = '[1, 0, 0]
--
--
--
-- >>> :kind! SubtensorStartIndex '[0,1] '[2,3,4]
-- SubtensorStartIndex '[0,1] '[2,3,4] :: [Nat]
-- = '[0, 1, 0]
--
--
--
-- >>> :kind! SubtensorStartIndex '[1,1] '[2,3,4]
-- SubtensorStartIndex '[1,1] '[2,3,4] :: [Nat]
-- = '[1, 1, 0]
--
-- | Shape of a subtensor of tensor of shape dims located at
-- index. Resulting shape is not normalized.
--
--
-- >>> :kind! SubtensorDims '[0] '[2,3,4]
-- SubtensorDims '[0] '[2,3,4] :: [Nat]
-- = '[1, 3, 4]
--
--
--
-- >>> :kind! SubtensorDims '[0,0] '[2,3,4]
-- SubtensorDims '[0,0] '[2,3,4] :: [Nat]
-- = '[1, 1, 4]
--
-- | Lens for subtensor at given index.
--
--
-- >>> let t = enumFromN @[2,3,4] @Int 0
--
-- >>> t
-- Tensor'2'3'4 [[[ 0, 1, 2, 3]
-- ,[ 4, 5, 6, 7]
-- ,[ 8, 9, 10, 11]]
-- ,[[ 12, 13, 14, 15]
-- ,[ 16, 17, 18, 19]
-- ,[ 20, 21, 22, 23]]]
--
-- >>> t ^. subtensor @'[0]
-- Tensor'3'4 [[ 0, 1, 2, 3]
-- ,[ 4, 5, 6, 7]
-- ,[ 8, 9, 10, 11]]
--
-- >>> t ^. subtensor @'[1]
-- Tensor'3'4 [[ 12, 13, 14, 15]
-- ,[ 16, 17, 18, 19]
-- ,[ 20, 21, 22, 23]]
--
-- >>> t ^. subtensor @'[0,0]
-- Tensor'4 [ 0, 1, 2, 3]
--
-- >>> t ^. subtensor @'[1,0]
-- Tensor'4 [ 12, 13, 14, 15]
--
subtensor :: forall (index :: [Nat]) (dims :: [Nat]) e. (SubtensorCtx index dims e) => Lens' (Tensor dims e) (Subtensor index dims e)
-- | Constraint for subtensor function.
type SubtensorCtx index dims e = (GetSubtensor index dims e, SetSubtensor index dims e)
-- | Extract subtensor at given index.
getSubtensor :: forall (index :: [Nat]) (dims :: [Nat]) e. (GetSubtensor index dims e) => Tensor dims e -> Subtensor index dims e
-- | Constraint for getSubtensor function.
type GetSubtensor index dims e = (GetSlice (SubtensorStartIndex index dims) (SubtensorDims index dims) dims e)
-- | Extract elements of subtensor at given index. Like
-- getSubtensor, but without building actual subtensor.
getSubtensorElems :: forall (index :: [Nat]) (dims :: [Nat]) e. (GetSubtensorElems index dims e) => Tensor dims e -> [e]
-- | Constraint for getSubtensorElems function.
type GetSubtensorElems index dims e = GetSliceElems (SubtensorStartIndex index dims) (SubtensorDims index dims) dims e
-- | Set subtensor at given index.
setSubtensor :: forall (index :: [Nat]) (dims :: [Nat]) e. (SetSubtensor index dims e) => Tensor dims e -> Subtensor index dims e -> Tensor dims e
-- | Constraint for setSubtensor function.
type SetSubtensor index dims e = SetSlice (SubtensorStartIndex index dims) (SubtensorDims index dims) dims e
-- | Like setSubtensor but takes a list of elements instead of a
-- tensor. Returns Nothing if list has not enough elements.
setSubtensorElems :: forall (index :: [Nat]) (dims :: [Nat]) e. (SetSubtensorElems index dims e) => Tensor dims e -> [e] -> Maybe (Tensor dims e)
-- | Constraint for setSubtensorElems function.
type SetSubtensorElems index dims e = SetSliceElems (SubtensorStartIndex index dims) (SubtensorDims index dims) dims e
-- | Modify subtensor elements with a function.
mapSubtensorElems :: forall (index :: [Nat]) (dims :: [Nat]) e. (MapSubtensorElems index dims e) => Tensor dims e -> (e -> e) -> Tensor dims e
-- | Constraints for mapSubtensorElems.
type MapSubtensorElems index dims e = MapSliceElems (SubtensorStartIndex index dims) (SubtensorDims index dims) dims e
-- | Index of the end of the slice of the tensor. startIndex
-- parameter is the starting index of the slice, sliceDims is
-- the shape of the slice, dims is the shape of the tensor. The
-- slice must be contained inside the tensor. All dimensions of the slice
-- must be positive. startIndex, sliceDims and
-- dims must have the same length. If you want to get slice of
-- lower rank than the tensor's, set one or more dimensions in
-- sliceDims to 1.
--
--
-- >>> :kind! SliceEndIndex '[0,0,0] '[2,2,2] '[2,3,4]
-- SliceEndIndex '[0,0,0] '[2,2,2] '[2,3,4] :: [Nat]
-- = '[1, 1, 1]
--
--
--
-- >>> :kind! SliceEndIndex '[1,1,0] '[1,2,4] '[2,3,4]
-- SliceEndIndex '[1,1,0] '[1,2,4] '[2,3,4] :: [Nat]
-- = '[1, 2, 3]
--
-- | Check each element of the tensor of shape dims if it is
-- inside the slice from startIndex of shape sliceDims.
-- The slice must be contained inside the tensor. All dimensions of the
-- slice must be positive. startIndex, sliceDims and
-- dims must have the same length.
--
--
-- >>> :kind! ElemsInSlice '[0,0,0] '[2,2,2] '[2,3,4]
-- ElemsInSlice '[0,0,0] '[2,2,2] '[2,3,4] :: [Bool]
-- = '['True, 'True, 'False, 'False, 'True, 'True, 'False, 'False,
-- 'False, 'False, 'False, 'False, 'True, 'True, 'False, 'False,
-- 'True, 'True, 'False, 'False, 'False, 'False, 'False, 'False]
--
--
--
-- >>> :kind! ElemsInSlice '[1,1,0] '[1,2,4] '[2,3,4]
-- ElemsInSlice '[1,1,0] '[1,2,4] '[2,3,4] :: [Bool]
-- = '['False, 'False, 'False, 'False, 'False, 'False, 'False, 'False,
-- 'False, 'False, 'False, 'False, 'False, 'False, 'False, 'False,
-- 'True, 'True, 'True, 'True, 'True, 'True, 'True, 'True]
--
type ElemsInSlice (startIndex :: [Nat]) (sliceDims :: [Nat]) (dims :: [Nat]) = ElemsInSlice' startIndex (SliceEndIndex startIndex sliceDims dims) (AllIndexes dims)
-- | Lens for the slice starting from startIndex of shape
-- sliceDims of the tensor of shape dims.
--
--
-- >>> let t = (enumFromN @[2,3,4] @Int 0)
--
-- >>> t
-- Tensor'2'3'4 [[[ 0, 1, 2, 3]
-- ,[ 4, 5, 6, 7]
-- ,[ 8, 9, 10, 11]]
-- ,[[ 12, 13, 14, 15]
-- ,[ 16, 17, 18, 19]
-- ,[ 20, 21, 22, 23]]]
--
-- >>> t ^. slice @[0,0,0] @[2,2,2]
-- Tensor'2'2'2 [[[ 0, 1]
-- ,[ 4, 5]]
-- ,[[ 12, 13]
-- ,[ 16, 17]]]
--
-- >>> set (slice @[0,0,0] @[2,2,2]) zero t
-- Tensor'2'3'4 [[[ 0, 0, 2, 3]
-- ,[ 0, 0, 6, 7]
-- ,[ 8, 9, 10, 11]]
-- ,[[ 0, 0, 14, 15]
-- ,[ 0, 0, 18, 19]
-- ,[ 20, 21, 22, 23]]]
--
slice :: forall startIndex sliceDims dims e. (Slice startIndex sliceDims dims e) => Lens' (Tensor dims e) (Tensor (NormalizeDims sliceDims) e)
-- | Constraints for slice function.
type Slice startIndex sliceDims dims e = (IsTensor dims e, IsTensor (NormalizeDims sliceDims) e, GetSliceElemsWrk (ElemsInSlice startIndex sliceDims dims), SetSliceElemsWrk (ElemsInSlice startIndex sliceDims dims))
-- | Extract slice of shape sliceDims from a tensor of shape
-- dims starting at startIndex for each axis.
getSlice :: forall startIndex sliceDims dims e. (GetSlice startIndex sliceDims dims e) => Tensor dims e -> Tensor (NormalizeDims sliceDims) e
-- | Constraints for getSlice.
type GetSlice startIndex sliceDims dims e = (IsTensor dims e, IsTensor (NormalizeDims sliceDims) e, GetSliceElemsWrk (ElemsInSlice startIndex sliceDims dims))
-- | Same as slice but returns list of elements instead of tensor data
-- type.
getSliceElems :: forall startIndex sliceDims dims e. (GetSliceElems startIndex sliceDims dims e) => Tensor dims e -> [e]
-- | Constraints for getSliceElems.
type GetSliceElems startIndex sliceDims dims e = (IsTensor dims e, GetSliceElemsWrk (ElemsInSlice startIndex sliceDims dims))
-- | Set elements of the slice.
setSlice :: forall startIndex sliceDims dims e. (SetSlice startIndex sliceDims dims e) => Tensor dims e -> Tensor (NormalizeDims sliceDims) e -> Tensor dims e
-- | Constraints for setSlice.
type SetSlice startIndex sliceDims dims e = (IsTensor dims e, IsTensor (NormalizeDims sliceDims) e, SetSliceElemsWrk (ElemsInSlice startIndex sliceDims dims))
-- | Like setSlice but takes a list of elements instead of a tensor.
-- Returns Nothing if list has less than ElemsNumber
-- sliceDims elements.
setSliceElems :: forall startIndex sliceDims dims e. (SetSliceElems startIndex sliceDims dims e) => Tensor dims e -> [e] -> Maybe (Tensor dims e)
-- | Constraints for setSliceElems.
type SetSliceElems startIndex sliceDims dims e = (IsTensor dims e, SetSliceElemsWrk (ElemsInSlice startIndex sliceDims dims))
-- | Modify slice elements with a function.
mapSliceElems :: forall startIndex sliceDims dims e. (MapSliceElems startIndex sliceDims dims e) => Tensor dims e -> (e -> e) -> Tensor dims e
-- | Constraints for mapSliceElems.
type MapSliceElems startIndex sliceDims dims e = (IsTensor dims e, GetSliceElemsWrk (ElemsInSlice startIndex sliceDims dims), SetSliceElemsWrk (ElemsInSlice startIndex sliceDims dims), Map (ElemsNumber sliceDims))
-- | Constraints for MonoFunctor instance for Tensor dims
-- e.
type MonoFunctorCtx (dims :: [Nat]) e = (IsTensor dims e, Map (ElemsNumber dims))
-- | Constraints for MonoFoldable instance for Tensor
-- dims e.
type MonoFoldableCtx (dims :: [Nat]) e = (IsTensor dims e, Foldr (ElemsNumber dims), Foldl (ElemsNumber dims), Foldr1 (ElemsNumber dims), Foldl1 (ElemsNumber dims))
-- | Constraints for MonoTraversable instance for Tensor
-- dims e.
type MonoTraversableCtx (dims :: [Nat]) e = (IsTensor dims e, Map (ElemsNumber dims), Foldr (ElemsNumber dims), Foldl (ElemsNumber dims), Foldr1 (ElemsNumber dims), Foldl1 (ElemsNumber dims))
-- | Constraints for MonoZip instance for Tensor dims
-- e.
type MonoZipCtx (dims :: [Nat]) e = (IsTensor dims e, Map (ElemsNumber dims), ZipWith (ElemsNumber dims), Zip (ElemsNumber dims), Unzip (ElemsNumber dims))
-- | Pass a pointer to the tensor's data to the IO action. The data may not
-- be modified through the 'Ptr. Pointer may not be used after action is
-- complete.
unsafeWithTensorPtr :: (IsTensor dims e, Storable e, KnownNat (ElemsNumber dims)) => Tensor dims e -> (Ptr e -> IO a) -> IO a
instance Data.Tensor.Static.MonoZipCtx dims e => Data.Containers.MonoZip (Data.Tensor.Static.Tensor dims e)
instance Data.Tensor.Static.MonoTraversableCtx dims e => Data.MonoTraversable.MonoTraversable (Data.Tensor.Static.Tensor dims e)
instance Data.Tensor.Static.MonoFoldableCtx dims e => Data.MonoTraversable.MonoFoldable (Data.Tensor.Static.Tensor dims e)
instance Data.Tensor.Static.MonoFunctorCtx dims e => Data.MonoTraversable.MonoFunctor (Data.Tensor.Static.Tensor dims e)
instance Data.Tensor.Static.RemoveWrk '[]
instance Data.Tensor.Static.RemoveWrk xs => Data.Tensor.Static.RemoveWrk ('GHC.Types.False : xs)
instance Data.Tensor.Static.RemoveWrk xs => Data.Tensor.Static.RemoveWrk ('GHC.Types.True : xs)
instance Data.Tensor.Static.SetSliceElemsWrk '[]
instance Data.Tensor.Static.SetSliceElemsWrk xs => Data.Tensor.Static.SetSliceElemsWrk ('GHC.Types.True : xs)
instance Data.Tensor.Static.SetSliceElemsWrk xs => Data.Tensor.Static.SetSliceElemsWrk ('GHC.Types.False : xs)
instance Data.Tensor.Static.GetSliceElemsWrk '[]
instance Data.Tensor.Static.GetSliceElemsWrk xs => Data.Tensor.Static.GetSliceElemsWrk ('GHC.Types.True : xs)
instance Data.Tensor.Static.GetSliceElemsWrk xs => Data.Tensor.Static.GetSliceElemsWrk ('GHC.Types.False : xs)
instance (GHC.Show.Show (Data.Tensor.Static.NestedList (Data.Singletons.Prelude.List.Length dims) e), Data.Tensor.Static.IsTensor dims e, Data.Tensor.Static.ToNestedListWrk dims e, Type.List.KnownNats dims) => GHC.Show.Show (Data.Tensor.Static.Tensor dims e)
instance Data.Tensor.Static.ToNestedListWrk '[] e
instance Data.Tensor.Static.ToNestedListWrk '[x] e
instance (Data.Tensor.Static.ToNestedListWrk (xx : xs) e, GHC.TypeNats.KnownNat (Data.Singletons.Prelude.List.Product (xx : xs)), Data.Tensor.Static.NestedList (Data.Singletons.Prelude.List.Length (x : xx : xs)) e ~ [Data.Tensor.Static.NestedList (Data.Singletons.Prelude.List.Length (xx : xs)) e]) => Data.Tensor.Static.ToNestedListWrk (x : xx : xs) e
instance Data.Tensor.Static.IsTensor '[] e
instance GHC.Show.Show e => GHC.Show.Show (Data.Tensor.Static.Tensor '[] e)
instance (Data.Tensor.Static.IsTensor dims a, Data.Tensor.Static.IsTensor dims b) => Control.Lens.Each.Each (Data.Tensor.Static.Tensor dims a) (Data.Tensor.Static.Tensor dims b) a b
instance (Data.Tensor.Static.IsTensor dims e, Foreign.Storable.Storable e, GHC.TypeNats.KnownNat (Data.Tensor.Static.ElemsNumber dims)) => Foreign.Storable.Storable (Data.Tensor.Static.Tensor dims e)
module Data.Tensor.Static.TH
-- | Generate instance for tensor and lenses for its elements.
genTensorInstance :: NonEmpty Int -> Name -> Q [Dec]
module Data.Vector.Static
-- | N-dimensional vector.
type Vector n e = Tensor '[n] e
-- | Type of vector data constructor.
type VectorConstructor n e = TensorConstructor '[n] e
-- | Vector constraint.
type IsVector n e = IsTensor '[n] e
-- | Alias for a conrete vector data constructor.
vector :: forall n e. (IsVector n e) => VectorConstructor n e
-- | Normalize vector.
normalize :: (Normalize n e) => Vector n e -> NormalizedVector n e
-- | Normalized vector.
data NormalizedVector n e
-- | Constraints for normalize function.
type Normalize (n :: Nat) e = (VectorLen n e, Scale '[n] e)
-- | unwrap NormalizedVector. Note: this does not give you original
-- vector back.
--
--
-- unNormalizedVector . normalize /= id
--
unNormalizedVector :: NormalizedVector n e -> Vector n e
-- | Get square of length of a vector.
vectorLenSquare :: (VectorLenSquare n e) => Vector n e -> e
-- | Constraints for vectorLenSquare function.
type VectorLenSquare (n :: Nat) e = (Num e, IsVector n e, MonoFunctorCtx '[n] e, MonoFoldableCtx '[n] e)
-- | Get length of a vector.
vectorLen :: (VectorLen n e) => Vector n e -> e
-- | Constraints for vectorLen function.
type VectorLen (n :: Nat) e = (Floating e, VectorLenSquare n e)
-- | Dot product of two vectors.
dot :: (Dot n e) => Vector n e -> Vector n e -> e
-- | Constraints for dot function.
type Dot (n :: Nat) e = (Num e, IsVector n e, MonoFunctorCtx '[n] e, MonoFoldableCtx '[n] e, MonoZipCtx '[n] e)
-- | Cross product is only defined for 3-dimensional vectors.
cross :: (Num e, IsVector 3 e) => Vector 3 e -> Vector 3 e -> Vector 3 e
-- | Generate instance of a vector.
genVectorInstance :: Int -> Name -> Q [Dec]
instance GHC.Generics.Generic (Data.Vector.Static.NormalizedVector n e)
instance GHC.Classes.Eq (Data.Vector.Static.Vector n e) => GHC.Classes.Eq (Data.Vector.Static.NormalizedVector n e)
instance GHC.Show.Show (Data.Vector.Static.Vector n e) => GHC.Show.Show (Data.Vector.Static.NormalizedVector n e)
module Data.Matrix.Static
-- | Matrix with m rows, n columns
type Matrix m n e = Tensor '[m, n] e
-- | Type of matrix data constructor.
type MatrixConstructor m n e = TensorConstructor '[m, n] e
-- | Matrix constraint.
type IsMatrix m n e = IsTensor '[m, n] e
-- | Alias for a conrete matrix data constructor.
matrix :: forall m n e. (IsMatrix m n e) => MatrixConstructor m n e
-- | Identity matrix of size m*m
identity :: forall m e. (IsMatrix m m e, Generate '[m, m] e ([Nat] -> Constraint) (IdentityWrk e), Num e) => Matrix m m e
-- | Constraints for identity function.
type Identity m e = (IsMatrix m m e, Generate '[m, m] e ([Nat] -> Constraint) (IdentityWrk e), Num e)
-- | Lens for the row number r of the matrix
-- mxn.
--
--
-- >>> matrix @2 @2 @Float 0 1 2 3 ^. row @0
-- Tensor'2 [0.0,1.0]
--
--
--
-- >>> set (row @1) (vector @2 @Float 20 30) (matrix @2 @2 @Float 0 1 2 3)
-- Tensor'2'2 [[0.0,1.0],[20.0,30.0]]
--
row :: forall (r :: Nat) (m :: Nat) (n :: Nat) e. (Row r m n e) => Lens' (Matrix m n e) (Vector n e)
-- | Constraints for row function.
type Row (r :: Nat) (m :: Nat) (n :: Nat) e = (SubtensorCtx '[r] '[m, n] e, r <= (m - 1), NormalizeDims '[n] ~ '[n])
-- | List of elements of the row number r of the matrix
-- mxn.
--
--
-- >>> getRowElems @0 (matrix @2 @2 @Float 0 1 2 3)
-- [0.0,1.0]
--
getRowElems :: forall (r :: Nat) (m :: Nat) (n :: Nat) e. (GetRowElems r m n e) => Matrix m n e -> [e]
-- | Constraints for getRowElems function.
type GetRowElems (r :: Nat) (m :: Nat) (n :: Nat) e = GetSubtensorElems '[r] '[m, n] e
-- | Put elements of the list into row number r. The list must
-- have enough elements.
--
--
-- >>> setRowElems @1 (matrix @2 @2 @Float 0 1 2 3) [20, 30]
-- Just Tensor'2'2 [[0.0,1.0],[20.0,30.0]]
--
--
--
-- >>> setRowElems @1 (matrix @2 @2 @Float 0 1 2 3) [20]
-- Nothing
--
setRowElems :: forall (r :: Nat) (m :: Nat) (n :: Nat) e. (SetRowElems r m n e) => Matrix m n e -> [e] -> Maybe (Matrix m n e)
-- | Constraints for setRowElems function.
type SetRowElems (r :: Nat) (m :: Nat) (n :: Nat) e = SetSubtensorElems '[r] '[m, n] e
-- | Apply a function to all elements of the row number r.
--
--
-- >>> mapRowElems @1 (matrix @2 @2 @Float 0 1 2 3) (* 100)
-- Tensor'2'2 [[0.0,1.0],[200.0,300.0]]
--
mapRowElems :: forall (r :: Nat) (m :: Nat) (n :: Nat) e. (MapRowElems r m n e) => Matrix m n e -> (e -> e) -> Matrix m n e
-- | Constraints for mapRowElems function.
type MapRowElems (r :: Nat) (m :: Nat) (n :: Nat) e = MapSubtensorElems '[r] '[m, n] e
-- | Lens for the column number c of the matrix
-- mxn.
--
--
-- >>> matrix @2 @2 @Float 0 1 2 3 ^. col @0
-- Tensor'2 [0.0,2.0]
--
--
--
-- >>> set (col @1) (vector @2 @Float 10 30) (matrix @2 @2 @Float 0 1 2 3)
-- Tensor'2'2 [[0.0,10.0],[2.0,30.0]]
--
col :: forall (c :: Nat) (m :: Nat) (n :: Nat) e. (Col c m n e) => Lens' (Matrix m n e) (Vector m e)
-- | Constraints for col function.
type Col (c :: Nat) (m :: Nat) (n :: Nat) e = (Slice '[0, c] '[m, 1] '[m, n] e, NormalizeDims '[m, 1] ~ '[m])
-- | List of elements of the column number c of the matrix
-- mxn.
--
--
-- >>> getColElems @0 (matrix @2 @2 @Float 0 1 2 3)
-- [0.0,2.0]
--
getColElems :: forall (c :: Nat) (m :: Nat) (n :: Nat) e. (GetColElems c m n e) => Matrix m n e -> [e]
-- | Constraints for getColElems function.
type GetColElems (c :: Nat) (m :: Nat) (n :: Nat) e = GetSliceElems '[0, c] '[m, 1] '[m, n] e
-- | Put elements of the list into column number r. The list must
-- have enough elements.
--
--
-- >>> setColElems @1 (matrix @2 @2 @Float 0 1 2 3) [10, 30]
-- Just Tensor'2'2 [[0.0,10.0],[2.0,30.0]]
--
--
--
-- >>> setColElems @1 (matrix @2 @2 @Float 0 1 2 3) [10]
-- Nothing
--
setColElems :: forall (c :: Nat) (m :: Nat) (n :: Nat) e. (SetColElems c m n e) => Matrix m n e -> [e] -> Maybe (Matrix m n e)
-- | Constraints for setColElems function.
type SetColElems (c :: Nat) (m :: Nat) (n :: Nat) e = SetSliceElems '[0, c] '[m, 1] '[m, n] e
-- | Apply a function to all elements of the column number c.
--
--
-- >>> mapColElems @1 (matrix @2 @2 @Float 0 1 2 3) (* 100)
-- Tensor'2'2 [[0.0,100.0],[2.0,300.0]]
--
mapColElems :: forall (c :: Nat) (m :: Nat) (n :: Nat) e. (MapColElems c m n e) => Matrix m n e -> (e -> e) -> Matrix m n e
-- | Constraints for mapColElems function.
type MapColElems (c :: Nat) (m :: Nat) (n :: Nat) e = MapSliceElems '[0, c] '[m, 1] '[m, n] e
-- | Shape of the result of matrix multiplication.
-- | Matrix multiplication.
class MatrixMult (dims0 :: [Nat]) (dims1 :: [Nat]) e
-- | Multiply two matrices, or matrix and vector. Matrices (or matrix and
-- vector) must have compatible dimensions.
mult :: (MatrixMult dims0 dims1 e, IsTensor dims0 e, IsTensor dims1 e, IsTensor (MatrixMultDims dims0 dims1) e) => Tensor dims0 e -> Tensor dims1 e -> Tensor (MatrixMultDims dims0 dims1) e
-- | Transpose a matrix.
transpose :: forall m n e. (Transpose m n e) => Matrix m n e -> Matrix n m e
-- | Constraints for transpose function.
type Transpose m n e = (IsMatrix m n e, IsMatrix n m e, Generate '[n, m] e ([Nat] ~> Constraint) (TransposeGoSym3 m n e))
-- | Minor matrix is a matrix made by deleting i-th row and
-- j-th column from given square matrix.
minorMatrix :: forall (i :: Nat) (j :: Nat) (n :: Nat) e. (Generate ([n - 1, n - 1]) e ([Nat] ~> Constraint) (MinorMatrixGoSym4 i j n e)) => Matrix n n e -> Matrix (n - 1) (n - 1) e
-- | Constraint for minorMatrix function.
type MinorMatrix (i :: Nat) (j :: Nat) (n :: Nat) e = Generate ([n - 1, n - 1]) e ([Nat] ~> Constraint) (MinorMatrixGoSym4 i j n e)
-- | Determinant of a matrix.
class Determinant (n :: Nat) e
determinant :: (Determinant n e, (Num e)) => Matrix n n e -> e
-- | Minor is the determinant of minor matrix.
minor :: forall (i :: Nat) (j :: Nat) (n :: Nat) e. (Minor i j n e) => Matrix n n e -> e
-- | Constraint for minor function.
type Minor (i :: Nat) (j :: Nat) (n :: Nat) e = (MinorMatrix i j n e, Determinant (n - 1) e, Num e)
-- | cofactor @i @j is the minor @i @j
-- multiplied by (-1) ^ (i + j).
cofactor :: forall (i :: Nat) (j :: Nat) (n :: Nat) e. (Cofactor i j n e) => Matrix n n e -> e
-- | Constraint for cofactor function.
type Cofactor (i :: Nat) (j :: Nat) (n :: Nat) e = (Minor i j n e, Sign (i + j))
-- | The matrix formed by all of the cofactors of given square matrix.
cofactorMatrix :: forall (n :: Nat) e. (CofactorMatrix n e) => Matrix n n e -> Matrix n n e
-- | Constraint for cofactorMatrix function.
type CofactorMatrix (n :: Nat) e = Generate [n, n] e ([Nat] ~> Constraint) (CofactorMatrixGoSym2 n e)
-- | Adjugate matrix of given square matrix is the transpose of its
-- cofactor matrix.
--
--
-- adjugateMatrix = transpose . cofactorMatrix
--
adjugateMatrix :: forall (n :: Nat) e. (AdjugateMatrix n e) => Matrix n n e -> Matrix n n e
-- | Constraint for adjugateMatrix function.
type AdjugateMatrix (n :: Nat) e = (CofactorMatrix n e, Transpose n n e)
-- | Inverse of the matrix.
inverse :: forall (n :: Nat) e. (Inverse n e) => Matrix n n e -> Matrix n n e
-- | Constraint for inverse function.
type Inverse (n :: Nat) e = (AdjugateMatrix n e, Determinant n e, Fractional e, Scale '[n, n] e)
-- | Generate instance of a matrix.
genMatrixInstance :: Int -> Int -> Name -> Q [Dec]
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.CofactorMatrixGoSym0
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.CofactorMatrixGoSym1
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.CofactorMatrixGoSym2
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.DeterminantGoSym0
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.DeterminantGoSym1
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.DeterminantGoSym2
instance (GHC.Num.Num e, Data.Matrix.Static.IsMatrix n n e, Type.List.DemoteWith GHC.Types.Nat (GHC.Types.Nat Data.Singletons.~> GHC.Types.Constraint) (Data.Matrix.Static.DeterminantGoSym2 n e) (Data.Tensor.Static.NatsFromTo 0 (n GHC.TypeNats.- 1)), Data.List.Unrolled.Sum n e) => Data.Matrix.Static.Determinant n e
instance Data.Matrix.Static.Sign 0
instance Data.Matrix.Static.Sign (n GHC.TypeNats.- 1) => Data.Matrix.Static.Sign n
instance (GHC.Num.Num e, Data.Matrix.Static.IsMatrix 2 2 e) => Data.Matrix.Static.Determinant 2 e
instance (GHC.Num.Num e, Data.Matrix.Static.IsMatrix 3 3 e) => Data.Matrix.Static.Determinant 3 e
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.MinorMatrixGoSym0
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.MinorMatrixGoSym1
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.MinorMatrixGoSym2
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.MinorMatrixGoSym3
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.MinorMatrixGoSym4
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.MultMatVecGoSym0
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.MultMatVecGoSym1
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.MultMatVecGoSym2
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.MultMatVecGoSym3
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.MultMatVecGoSym4
instance (GHC.Num.Num e, Data.Tensor.Static.Generate (Data.Matrix.Static.MatrixMultDims '[m, n] '[n]) e ([GHC.Types.Nat] Data.Singletons.~> GHC.Types.Constraint) (Data.Matrix.Static.MultMatVecGoSym4 m n o e)) => Data.Matrix.Static.MatrixMult '[m, n] '[n] e
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.MultVecMatGoSym0
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.MultVecMatGoSym1
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.MultVecMatGoSym2
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.MultVecMatGoSym3
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.MultVecMatGoSym4
instance (GHC.Num.Num e, Data.Tensor.Static.Generate (Data.Matrix.Static.MatrixMultDims '[n] '[n, o]) e ([GHC.Types.Nat] Data.Singletons.~> GHC.Types.Constraint) (Data.Matrix.Static.MultVecMatGoSym4 m n o e)) => Data.Matrix.Static.MatrixMult '[n] '[n, o] e
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.MultMatMatGoSym0
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.MultMatMatGoSym1
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.MultMatMatGoSym2
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.MultMatMatGoSym3
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.MultMatMatGoSym4
instance (GHC.Num.Num e, Data.Tensor.Static.Generate (Data.Matrix.Static.MatrixMultDims '[m, n] '[n, o]) e ([GHC.Types.Nat] Data.Singletons.~> GHC.Types.Constraint) (Data.Matrix.Static.MultMatMatGoSym4 m n o e)) => Data.Matrix.Static.MatrixMult '[m, n] '[n, o] e
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.TransposeGoSym0
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.TransposeGoSym1
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.TransposeGoSym2
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Matrix.Static.TransposeGoSym3
instance GHC.Num.Num e => Data.Matrix.Static.IdentityWrk e '[i, j]
instance GHC.Num.Num e => Data.Matrix.Static.IdentityWrk e '[i, i]