numhask 0.3.1 → 0.4.0

raw patch · 16 files changed

+57/−201 lines, 16 files

Files

• numhask.cabal +1/−4
• other/field.svg +3/−0
• other/ring.svg +0/−3
• src/NumHask/Algebra/Abstract.hs +0/−2
• src/NumHask/Algebra/Abstract/Additive.hs +14/−0
• src/NumHask/Algebra/Abstract/Field.hs +6/−6
• src/NumHask/Algebra/Abstract/Homomorphism.hs +0/−43
• src/NumHask/Algebra/Abstract/Module.hs +1/−1
• src/NumHask/Algebra/Abstract/Multiplicative.hs +15/−1
• src/NumHask/Algebra/Abstract/Ring.hs +10/−11
• src/NumHask/Algebra/Abstract/TensorProduct.hs +0/−81
• src/NumHask/Algebra/Linear/Hadamard.hs +0/−4
• src/NumHask/Analysis/Banach.hs +0/−38
• src/NumHask/Analysis/Metric.hs +1/−1
• src/NumHask/Data/LogField.hs +4/−4
• src/NumHask/Data/Positive.hs +2/−2

@@ -1,5 +1,5 @@ name: numhask-version: 0.3.1+version: 0.4.0 synopsis:   numeric classes description:@@ -56,14 +56,11 @@     NumHask.Algebra.Abstract.Additive     NumHask.Algebra.Abstract.Field     NumHask.Algebra.Abstract.Group-    NumHask.Algebra.Abstract.Homomorphism     NumHask.Algebra.Abstract.Lattice     NumHask.Algebra.Abstract.Module     NumHask.Algebra.Abstract.Multiplicative     NumHask.Algebra.Abstract.Ring-    NumHask.Algebra.Abstract.TensorProduct     NumHask.Algebra.Linear.Hadamard-    NumHask.Analysis.Banach     NumHask.Analysis.Metric     NumHask.Data.Complex     NumHask.Data.Integral

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@@ -14,7 +14,6 @@   , module NumHask.Algebra.Abstract.Module   , module NumHask.Algebra.Abstract.Action   , module NumHask.Algebra.Abstract.Lattice-  , module NumHask.Algebra.Abstract.Homomorphism   ) where @@ -26,7 +25,6 @@ import NumHask.Algebra.Abstract.Module import NumHask.Algebra.Abstract.Action import NumHask.Algebra.Abstract.Lattice-import NumHask.Algebra.Abstract.Homomorphism  -- $numMap --

@@ -14,15 +14,29 @@ import Prelude (Int, Integer, Float, Double, Bool) import qualified Prelude as P +-- | For practical reasons, 'Additive' has no super classes. Using `Associative` and 'Unital' from this library, or using 'Semigroup' and 'Monoid' from base tends to complexify the interface once you start having to disinguish between (say) monoidal addition and monoidal multiplication.+--+-- > zero + a == a+-- > a + zero == a+-- > (a + b) + c == a + (b + c)+-- > a + b == b + a+--+-- By convention, (+) is regarded as commutative, but this is not universal, and the introduction of another symbol which means non-commutative multiplication seems a bit dogmatic. class Additive a where   infixl 6 +   (+) :: a -> a -> a    zero :: a +-- | Compute the sum of a 'Foldable'. sum :: (Additive a, P.Foldable f) => f a -> a sum = P.foldr (+) zero +-- |+-- > a - a = zero+-- > negate a = zero - a+-- > negate a + a = zero+-- > a + negate a = zero class (Additive a) => Subtractive a where   negate :: a -> a 

@@ -27,11 +27,10 @@ import qualified Prelude as P import Prelude ((.)) --- | A <https://en.wikipedia.org/wiki/Field_(mathematics) Field> is an---   Integral domain in which every non-zero element has a multiplicative---   inverse.+-- | A <https://en.wikipedia.org/wiki/Field_(mathematics) Field> is a set+--   on which addition, subtraction, multiplication, and division are defined. It is also assumed that multiplication is distributive over addition. ----- A summary of the rules inherited from super-classes of Field+-- A summary of the rules thus inherited from super-classes of Field -- -- > zero + a == a -- > a + zero == a@@ -53,7 +52,7 @@ -- > recip a = one / a -- > recip a * a = one -- > a * recip a = one-class (IntegralDomain a) =>+class (Distributive a, Subtractive a, Divisive a) =>       Field a  instance Field P.Double@@ -156,7 +155,7 @@ -- > zero / zero != nan -- -- Note the tricky law that, although nan is assigned to zero/zero, they are never-the-less not equal. A committee decided this.-class (IntegralDomain a) =>+class (Field a) =>       UpperBoundedField a where    infinity :: a@@ -244,5 +243,6 @@   acosh f = acosh . f   atanh f = atanh . f +-- | A 'half' is a 'Field' because it requires addition, multiplication and division to be computed. half :: (Field a) => a half = one / two

@@ -1,43 +0,0 @@-{-# LANGUAGE FlexibleInstances #-}-{-# LANGUAGE MultiParamTypeClasses #-}-{-# LANGUAGE UndecidableInstances #-}-{-# OPTIONS_GHC -Wall #-}---- | The Homomorphism Hierarchy-module NumHask.Algebra.Abstract.Homomorphism-  ( Hom(..)-  , End-  , Iso-  , iso-  , invIso-  , Automorphism-  )-where--import NumHask.Algebra.Abstract.Group---- | A Homomorphism between two magmas--- law: forall a b. hom(a `magma` b) = hom(a) `magma` hom(b)-class (Magma a, Magma b) => Hom a b where-  hom :: a -> b--instance Hom b c => Hom (a -> b) (a -> c) where-  hom f = hom . f--class (Hom a a) => End a-instance (Hom a a) => End a---- | A Isomorphism between two magmas--- an Isomorphism is a bijective Homomorphism-class (Hom a b, Hom b a) => Iso a b--iso :: Iso a b => a -> b-iso = hom--invIso :: Iso a b => b -> a-invIso = hom--instance Iso b c => Iso (a -> b) (a -> c)--class (Iso a a) => Automorphism a-instance (Iso a a) => Automorphism a

@@ -12,7 +12,7 @@ import NumHask.Algebra.Abstract.Action  -- | A <https://en.wikipedia.org/wiki/Module_(mathematics) Module> over r a is---   a (Ring a), an abelian (Group r a) and an scalar-mult. (.*, *.) with the+--   a (Ring a), an abelian (Group r a) and a scalar multiplier (.*, *.) with the --   laws: -- -- > a .* one == a

@@ -14,6 +14,14 @@ import Prelude (Int, Integer, Float, Double) import qualified Prelude as P +-- | For practical reasons, 'Multiplicative' has no super classes. Using 'Associative' and 'Unital' from this library, or using 'Semigroup' and 'Monoid' from base tends to complexify the interface once you start having to disinguish between (say) monoidal addition and monoidal multiplication.+--+-- > one * a == a+-- > a * one == a+-- > (a * b) * c == a * (b * c)+-- > a * b == b * a+--+-- By convention, (*) is regarded as commutative, but this is not universal, and the introduction of another symbol which means non-commutative multiplication seems a bit dogmatic. class Multiplicative a where    infixl 7 *@@ -21,9 +29,16 @@    one :: a +-- | Compute the product of a 'Foldable'. product :: (Multiplicative a, P.Foldable f) => f a -> a product = P.foldr (*) one +-- |+--+-- > a / a = one+-- > recip a = one / a+-- > recip a * a = one+-- > a * recip a = one class (Multiplicative a) => Divisive a where   recip :: a -> a @@ -102,4 +117,3 @@  instance Divisive b => Divisive (a -> b) where   recip f = recip P.. f-

@@ -28,6 +28,10 @@ -- -- > a * (b + c) == a * b + a * c -- > (a * b) * c == a * c + b * c+-- > zero * a == zero+-- > a * zero == zero+--+-- The sneaking in of the <https://en.wikipedia.org/wiki/Absorbing_element annihilation> laws here glosses over the possibility that the multiplicative zero element does not have to correspond with the additive unital zero. class (Additive a, Multiplicative a) =>   Distributive a @@ -48,27 +52,22 @@ instance Distributive P.Bool instance Distributive b => Distributive (a -> b) --- | A <https://en.wikipedia.org/wiki/Semiring Semiring> is a ring without,---   necessarily, negative elements.------ FIXME: rule zero' = zero. Is this somehow expressible in haskell?+-- | A <https://en.wikipedia.org/wiki/Semiring Semiring> is commutative monoidal under addition, has a monoidal multiplication operator (not necessarily commutative), and where multiplication distributes over addition. class (Distributive a) =>   Semiring a where instance (Distributive a) =>   Semiring a  -- | A <https://en.wikipedia.org/wiki/Ring_(mathematics) Ring> is an abelian---   group under addition and monoid under multiplication where multiplication---   distributes over addition. Alternatively, a ring is semiring where additive---   inverses exist+--   group under addition and monoidal under multiplication, and where multiplication+--   distributes over addition. class (Distributive a, Subtractive a) =>   Ring a instance (Distributive a, Subtractive a) =>   Ring a  -- | A <https://en.wikipedia.org/wiki/Commutative_ring Commutative Ring> is a---   ring with a Commutative Multiplication operation. Recall that Addition is---   Commutative in all Rings+--   ring with commutative multiplication. class (Distributive a, Subtractive a) =>   CommutativeRing a instance (Distributive a, Subtractive a) =>@@ -78,9 +77,8 @@ --   generalizes a ring of integers by requiring the product of any two nonzero --   elements to be nonzero. This means that if a ≠ 0, an equality ab = ac --   implies b = c.--- FIXME: write a rule for this ---class (Distributive a, Divisive a) =>+class (Distributive a) =>   IntegralDomain a  instance IntegralDomain P.Double@@ -142,5 +140,6 @@ instance InvolutiveRing Word64 instance InvolutiveRing b => InvolutiveRing (a -> b) +-- | Defining 'two' requires adding the multiplicative unital to itself. two :: (Multiplicative a, Additive a) => a two = one + one

@@ -1,81 +0,0 @@-{-# LANGUAGE PolyKinds #-}-{-# LANGUAGE TypeFamilies #-}-{-# LANGUAGE TypeOperators #-}-{-# LANGUAGE MultiParamTypeClasses #-}-{-# OPTIONS_GHC -Wall #-}---- | TensorProduct-module NumHask.Algebra.Abstract.TensorProduct-  ( TensorProduct(..)-  , TensorProduct'(..)-  , type (><)-  ) where--import Data.Int (Int8, Int16, Int32, Int64)-import Data.Word (Word, Word8, Word16, Word32, Word64)-import GHC.Natural-import Prelude (Double, Float, Int, Integer)---- | tensorial type-type family (><) (a :: k1) (b :: k2) :: *--type instance Int >< Int = Int--type instance Integer >< Integer = Integer--type instance Double >< Double = Double--type instance Float >< Float = Float--type instance Natural >< Natural = Natural--type instance Int8 >< Int8 = Int8--type instance Int16 >< Int16 = Int16--type instance Int32 >< Int32 = Int32--type instance Int64 >< Int64 = Int64--type instance Word >< Word = Word--type instance Word8 >< Word8 = Word8--type instance Word16 >< Word16 = Word16--type instance Word32 >< Word32 = Word32--type instance Word64 >< Word64 = Word64---- | representation synthesis-type family TensorRep k1 k2 where-  TensorRep (r a) (r a) = r (r a)-  TensorRep (r a) (s a) = r (s a)-  TensorRep (r a) a = r a--type instance r a >< b = TensorRep (r a) b---- | generalised outer product------ > a><b + c><b == (a+c) >< b--- > a><b + a><c == a >< (b+c)--- > a *. (b><c) == (a><b) .* c--- > (a><b) .* c == a *. (b><c)-class TensorProduct a where-  infix 8 ><-  (><) :: a -> a -> (a >< a)-  outer :: a -> a -> (a >< a)-  outer = (><)-  timesleft :: a -> (a >< a) -> a-  timesright :: (a >< a) -> a -> a---- | generalised outer product------ > a><b + c><b == (a+c) >< b--- > a><b + a><c == a >< (b+c)--- > a *. (b><c) == (a><b) .* c--- > (a><b) .* c == a *. (b><c)-class TensorProduct' a b where-  outer' :: a -> b -> (a >< b)-  timesleft' :: a -> (a >< b) -> b-  timesright' :: (a >< b) -> a -> b

@@ -1,7 +1,6 @@ {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE UndecidableInstances #-}-{-# LANGUAGE TypeApplications #-} {-# LANGUAGE ScopedTypeVariables #-} {-# OPTIONS_GHC -Wall #-} @@ -14,7 +13,6 @@ where  import NumHask.Algebra.Abstract.Multiplicative-import Data.Coerce  -- | element by element multiplication --@@ -26,7 +24,6 @@   HadamardMultiplication m a where   infixl 7 .*.   (.*.) :: m a -> m a -> m a-  -- (.*.) = coerce ((.*.) @m @a)   -- | element by element division@@ -36,7 +33,6 @@   HadamardDivision m a where   infixl 7 ./.   (./.) :: m a -> m a -> m a-  (./.) = coerce ((./.) @m @a)  class (HadamardMultiplication m a, HadamardDivision m a) => Hadamard m a instance (HadamardMultiplication m a, HadamardDivision m a) => Hadamard m a

@@ -1,38 +0,0 @@-{-# LANGUAGE FlexibleContexts #-}-{-# LANGUAGE RankNTypes #-}-{-# LANGUAGE MultiParamTypeClasses #-}-{-# OPTIONS_GHC -Wall #-}---- | Metric classes-module NumHask.Analysis.Banach-  ( Banach(..)-  , Hilbert(..)-  )-where--import NumHask.Algebra.Abstract.Action-import NumHask.Algebra.Abstract.Ring-import NumHask.Algebra.Abstract.Field-import NumHask.Analysis.Metric---- | Banach (with Norm) laws form rules around size and direction of a number, with a potential crossing into another codomain.------ > a == singleton zero || normalizeL2 a *. normL2 a == a-class (ExpField (Actor h), Normed h (Actor h), DivisiveAction h) =>-  Banach h where-  normalizeL1 :: h -> h-  normalizeL1 a = a ./ normL1 a --  normalizeL2 :: h -> h-  normalizeL2 a = a ./ normL2 a---- | the inner product: a distributive fold------ > a <.> b == b <.> a--- > a <.> (b +c) == a <.> b + a <.> c--- > a <.> (s *. b + c) == s * (a <.> b) + a <.> c--- (s0 *. a) <.> (s1 *. b) == s0 * s1 * (a <.> b)-class (Distributive (Actor h)) =>-  Hilbert h where-  infix 8 <.>-  (<.>) :: h -> h -> Actor h

@@ -27,7 +27,7 @@ import NumHask.Algebra.Abstract.Multiplicative import NumHask.Algebra.Abstract.Lattice --- | 'signum' from base is not an operator replicated in numhask, being such a very silly name, and preferred is the much more obvious 'sign'.  Compare with 'Norm' and 'Banach' where there is a change in codomain+-- | 'signum' from base is not an operator replicated in numhask, being such a very silly name, and preferred is the much more obvious 'sign'.  Compare with 'Norm' where there is a change in codomain -- -- > abs a * sign a == a --

@@ -160,7 +160,7 @@ {-# INLINE [0] log1p #-} log1p x = log (one + x) -expm1 :: (ExpField a, Subtractive a) => a -> a+expm1 :: (ExpField a) => a -> a {-# INLINE [0] expm1 #-} expm1 x = exp x - one @@ -230,7 +230,7 @@   nearZero (LogField x) = nearZero $ exp x   aboutEqual (LogField x) (LogField y) = aboutEqual (exp x) (exp y) -instance (Ord a, ExpField a, LowerBoundedField a) => Field (LogField a)+instance (Ord a, ExpField a, LowerBoundedField a, UpperBoundedField a) => Field (LogField a)  instance (Ord a, ExpField a, LowerBoundedField a, UpperBoundedField a) =>   LowerBoundedField (LogField a)@@ -281,7 +281,7 @@ -- it is not amenable to list fusion, and hence will use a lot of -- memory when summing long lists. {-# INLINE accurateSum #-}-accurateSum :: (ExpField a, Subtractive a, Foldable f, Ord a) => f (LogField a) -> LogField a+accurateSum :: (ExpField a, Foldable f, Ord a) => f (LogField a) -> LogField a accurateSum xs = LogField (theMax + log theSum)  where   LogField theMax = maximum xs@@ -295,7 +295,7 @@ -- -- > LogField . accurateProduct == accurateProduct . map LogField {-# INLINE accurateProduct #-}-accurateProduct :: (ExpField a, Subtractive a, Foldable f) => f (LogField a) -> LogField a+accurateProduct :: (ExpField a, Foldable f) => f (LogField a) -> LogField a accurateProduct = LogField . fst . F.foldr kahanPlus (zero, zero)  where   kahanPlus (LogField x) (t, c) =

@@ -63,11 +63,11 @@   QuotientField (Positive a) (Positive P.Integer) where   properFraction (Positive a) = let (i,r) = properFraction a in (Positive i, Positive r) -instance (UpperBoundedField a) =>+instance (P.Ord a, UpperBoundedField a) =>   UpperBoundedField (Positive a) where   infinity = Positive infinity -instance (UpperBoundedField a) => P.Bounded (Positive a) where+instance (P.Ord a, UpperBoundedField a) => P.Bounded (Positive a) where   minBound = zero   maxBound = infinity