"volumes"

Author: brunjlar

.gitignore

@@ -2,3 +2,5 @@
 .stack-work/
 dist/
 tags
+src/highlight.js
+src/style.css

neural.cabal

@@ -67,6 +67,7 @@ library
                      , Data.Utils.Statistics
                      , Data.Utils.Traversable
                      , Data.Utils.Vector
+                     , Data.Utils.Volume
   other-modules:
   ghc-options:         -Wall -fexcess-precision -optc-O3 -optc-ffast-math
   build-depends:       base >= 4.7 && < 5

src/Data/Utils.hs

@@ -23,6 +23,7 @@ module Data.Utils
     , module Data.Utils.Statistics
     , module Data.Utils.Traversable
     , module Data.Utils.Vector
+    , module Data.Utils.Volume
     ) where
 
 import Data.Utils.Analytic
@@ -35,3 +36,4 @@ import Data.Utils.Stack
 import Data.Utils.Statistics
 import Data.Utils.Traversable
 import Data.Utils.Vector
+import Data.Utils.Volume

src/Data/Utils/Matrix.hs

@@ -82,7 +82,7 @@ row (Matrix rows) = (rows !?)
 column :: Matrix m n a -> Int -> Maybe (Vector m a)
 column (Matrix rows) j = sequenceA $ (!? j) <$> rows
 
--- | Generates a matrix by applying the given function to each index (row, column).
+-- | Generates a 'Matrix' by applying the given function to each index (row, column).
 --
 -- >>> :set -XDataKinds
 -- >>> mgenerate id :: Matrix 3 2 (Int, Int)

src/Data/Utils/Vector.hs

@@ -109,7 +109,7 @@ nil = Vector V.empty
 cons :: forall a n. a -> Vector n a -> Vector (n + 1) a
 cons x (Vector xs) = withNatOp (%+) (Proxy :: Proxy n) (Proxy :: Proxy 1) $ Vector $ V.cons x xs
 
--- | Generates a vector by applying the given function to each index.
+-- | Generates a 'Vector' by applying the given function to each index.
 --
 -- >>> :set -XDataKinds
 -- >>> generate id :: Vector 3 Int

src/Data/Utils/Volume.hs

@@ -0,0 +1,66 @@
+{-# OPTIONS_HADDOCK show-extensions #-}
+
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE KindSignatures #-}
+{-# LANGUAGE DeriveFunctor #-}
+{-# LANGUAGE DeriveFoldable #-}
+{-# LANGUAGE DeriveTraversable #-}
+{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE GeneralizedNewtypeDeriving #-}
+
+{-|
+Module      : Data.Utils.Volume
+Description : fixed-size volumes
+Copyright   : (c) Lars Brünjes, 2016
+License     : MIT
+Maintainer  : brunjlar@gmail.com
+Stability   : experimental
+Portability : portable
+
+This module defines fixed-size /volumes/ and some basic typeclass instances and operations for them.
+A 'Volume' is a 'Matrix' with 'Vector' entries, i.e. a three-dimensional array.
+-}
+
+module Data.Utils.Volume
+    ( Volume(..) 
+    , slice
+    , vgenerate
+    ) where
+
+import GHC.TypeLits
+import Data.MyPrelude
+import Data.Utils.Matrix
+import Data.Utils.Vector
+
+-- | @'Volume' m n d a@ is the type of /volumes/ with @m@ rows, @n@ columns, depth @d@ and entries of type @a@.
+--
+newtype Volume (m :: Nat) (n :: Nat) (d :: Nat) a = Volume (Matrix m n (Vector d a))
+    deriving (Eq, Show, Functor, Foldable, Traversable, NFData)
+
+instance (KnownNat m, KnownNat n, KnownNat d) => Applicative (Volume m n d) where
+
+    pure x = Volume $ pure (pure x)
+
+    Volume fs <*> Volume xs = Volume $ (<*>) <$> fs <*> xs
+
+-- | @'slice' v i@ gives the matrix "at depth @i@" of volume @v@ (or 'Nothing' if @i@ is invalid).
+--
+-- >>> :set -XDataKinds
+-- >>> slice (pure True :: Volume 2 2 3 Bool) 2
+-- Just (Matrix [[True,True],[True,True]])
+--
+-- >>> slice (pure True :: Volume 2 2 3 Bool) 3
+-- Nothing
+--
+slice :: Volume m n d a -> Int -> Maybe (Matrix m n a)
+slice (Volume m) i = sequenceA $ (!? i) <$> m 
+
+-- | Generates a 'Volume' by applying the given function to each index (row, column, slice).
+--
+-- >>> :set -XDataKinds
+-- >>> vgenerate id :: Volume 1 2 3 (Int, Int, Int)
+-- Volume (Matrix [[[(0,0,0),(0,0,1),(0,0,2)],[(0,1,0),(0,1,1),(0,1,2)]]])
+--
+vgenerate :: (KnownNat m, KnownNat n, KnownNat d) => ((Int, Int, Int) -> a) -> Volume m n d a
+vgenerate f = Volume $ mgenerate (\(i, j) -> generate (\k -> f (i, j, k)))