Copyright	(c) Alexey Kuleshevich 2018
License	BSD3
Maintainer	Alexey Kuleshevich <lehins@yandex.ru>
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Data.Massiv.Array.Stencil

Contents

Stencil
Convolution

Description

Synopsis

data Stencil ix e a
data Value e
makeStencil :: (Index ix, Default e) => ix -> ix -> ((ix -> Value e) -> Value a) -> Stencil ix e a
mapStencil :: (Source r ix e, Manifest r ix e) => Border e -> Stencil ix e a -> Array r ix e -> Array DW ix a
makeConvolutionStencil :: (Index ix, Num e) => ix -> ix -> ((ix -> Value e -> Value e -> Value e) -> Value e -> Value e) -> Stencil ix e e
makeConvolutionStencilFromKernel :: (Manifest r ix e, Num e) => Array r ix e -> Stencil ix e e
makeCorrelationStencil :: (Index ix, Num e) => ix -> ix -> ((ix -> Value e -> Value e -> Value e) -> Value e -> Value e) -> Stencil ix e e
makeCorrelationStencilFromKernel :: (Manifest r ix e, Num e) => Array r ix e -> Stencil ix e e

Stencil

data Stencil ix e a Source #

Stencil is abstract description of how to handle elements in the neighborhood of every array cell in order to compute a value for the cells in the new array. Use makeStencil and makeConvolutionStencil in order to create a stencil.

Instances

Functor (Stencil ix e) Source #
Instance details Defined in Data.Massiv.Array.Stencil.Internal Methods fmap :: (a -> b) -> Stencil ix e a -> Stencil ix e b # (<$) :: a -> Stencil ix e b -> Stencil ix e a #
(Default e, Index ix) => Applicative (Stencil ix e) Source #
Instance details Defined in Data.Massiv.Array.Stencil.Internal Methods pure :: a -> Stencil ix e a # (<>) :: Stencil ix e (a -> b) -> Stencil ix e a -> Stencil ix e b # liftA2 :: (a -> b -> c) -> Stencil ix e a -> Stencil ix e b -> Stencil ix e c # (>) :: Stencil ix e a -> Stencil ix e b -> Stencil ix e b # (<*) :: Stencil ix e a -> Stencil ix e b -> Stencil ix e a #
(Index ix, Default e, Floating a) => Floating (Stencil ix e a) Source #
Instance details Defined in Data.Massiv.Array.Stencil.Internal Methods pi :: Stencil ix e a # exp :: Stencil ix e a -> Stencil ix e a # log :: Stencil ix e a -> Stencil ix e a # sqrt :: Stencil ix e a -> Stencil ix e a # (**) :: Stencil ix e a -> Stencil ix e a -> Stencil ix e a # logBase :: Stencil ix e a -> Stencil ix e a -> Stencil ix e a # sin :: Stencil ix e a -> Stencil ix e a # cos :: Stencil ix e a -> Stencil ix e a # tan :: Stencil ix e a -> Stencil ix e a # asin :: Stencil ix e a -> Stencil ix e a # acos :: Stencil ix e a -> Stencil ix e a # atan :: Stencil ix e a -> Stencil ix e a # sinh :: Stencil ix e a -> Stencil ix e a # cosh :: Stencil ix e a -> Stencil ix e a # tanh :: Stencil ix e a -> Stencil ix e a # asinh :: Stencil ix e a -> Stencil ix e a # acosh :: Stencil ix e a -> Stencil ix e a # atanh :: Stencil ix e a -> Stencil ix e a # log1p :: Stencil ix e a -> Stencil ix e a # expm1 :: Stencil ix e a -> Stencil ix e a # log1pexp :: Stencil ix e a -> Stencil ix e a # log1mexp :: Stencil ix e a -> Stencil ix e a #
(Index ix, Default e, Fractional a) => Fractional (Stencil ix e a) Source #
Instance details Defined in Data.Massiv.Array.Stencil.Internal Methods (/) :: Stencil ix e a -> Stencil ix e a -> Stencil ix e a # recip :: Stencil ix e a -> Stencil ix e a # fromRational :: Rational -> Stencil ix e a #
(Index ix, Default e, Num a) => Num (Stencil ix e a) Source #
Instance details Defined in Data.Massiv.Array.Stencil.Internal Methods (+) :: Stencil ix e a -> Stencil ix e a -> Stencil ix e a # (-) :: Stencil ix e a -> Stencil ix e a -> Stencil ix e a # (*) :: Stencil ix e a -> Stencil ix e a -> Stencil ix e a # negate :: Stencil ix e a -> Stencil ix e a # abs :: Stencil ix e a -> Stencil ix e a # signum :: Stencil ix e a -> Stencil ix e a # fromInteger :: Integer -> Stencil ix e a #
Index ix => NFData (Stencil ix e a) Source #
Instance details Defined in Data.Massiv.Array.Stencil.Internal Methods rnf :: Stencil ix e a -> () #

data Value e Source #

This is a simple wrapper for value of an array cell. It is used in order to improve safety of Stencil mapping. Using various class instances, such as Num and Functor for example, make it possible to manipulate the value, without having direct access to it.

Instances

Functor Value Source #
Instance details Defined in Data.Massiv.Array.Stencil.Internal Methods fmap :: (a -> b) -> Value a -> Value b # (<$) :: a -> Value b -> Value a #
Applicative Value Source #
Instance details Defined in Data.Massiv.Array.Stencil.Internal Methods pure :: a -> Value a # (<>) :: Value (a -> b) -> Value a -> Value b # liftA2 :: (a -> b -> c) -> Value a -> Value b -> Value c # (>) :: Value a -> Value b -> Value b # (<*) :: Value a -> Value b -> Value a #
Bounded e => Bounded (Value e) Source #
Instance details Defined in Data.Massiv.Array.Stencil.Internal Methods minBound :: Value e # maxBound :: Value e #
Floating e => Floating (Value e) Source #
Instance details Defined in Data.Massiv.Array.Stencil.Internal Methods pi :: Value e # exp :: Value e -> Value e # log :: Value e -> Value e # sqrt :: Value e -> Value e # (**) :: Value e -> Value e -> Value e # logBase :: Value e -> Value e -> Value e # sin :: Value e -> Value e # cos :: Value e -> Value e # tan :: Value e -> Value e # asin :: Value e -> Value e # acos :: Value e -> Value e # atan :: Value e -> Value e # sinh :: Value e -> Value e # cosh :: Value e -> Value e # tanh :: Value e -> Value e # asinh :: Value e -> Value e # acosh :: Value e -> Value e # atanh :: Value e -> Value e # log1p :: Value e -> Value e # expm1 :: Value e -> Value e # log1pexp :: Value e -> Value e # log1mexp :: Value e -> Value e #
Fractional e => Fractional (Value e) Source #
Instance details Defined in Data.Massiv.Array.Stencil.Internal Methods (/) :: Value e -> Value e -> Value e # recip :: Value e -> Value e # fromRational :: Rational -> Value e #
Num e => Num (Value e) Source #
Instance details Defined in Data.Massiv.Array.Stencil.Internal Methods (+) :: Value e -> Value e -> Value e # (-) :: Value e -> Value e -> Value e # (*) :: Value e -> Value e -> Value e # negate :: Value e -> Value e # abs :: Value e -> Value e # signum :: Value e -> Value e # fromInteger :: Integer -> Value e #
Show e => Show (Value e) Source #
Instance details Defined in Data.Massiv.Array.Stencil.Internal Methods showsPrec :: Int -> Value e -> ShowS # show :: Value e -> String # showList :: [Value e] -> ShowS #
Semigroup a => Semigroup (Value a) Source #	Since: massiv-0.1.5
Instance details Defined in Data.Massiv.Array.Stencil.Internal Methods (<>) :: Value a -> Value a -> Value a # sconcat :: NonEmpty (Value a) -> Value a # stimes :: Integral b => b -> Value a -> Value a #
Monoid a => Monoid (Value a) Source #	Since: massiv-0.1.5
Instance details Defined in Data.Massiv.Array.Stencil.Internal Methods mempty :: Value a # mappend :: Value a -> Value a -> Value a # mconcat :: [Value a] -> Value a #

makeStencil Source #

Arguments

:: (Index ix, Default e)
=> ix	Size of the stencil
-> ix	Center of the stencil
-> ((ix -> Value e) -> Value a)	Stencil function that receives a "get" function as it's argument that can retrieve values of cells in the source array with respect to the center of the stencil. Stencil function must return a value that will be assigned to the cell in the result array. Offset supplied to the "get" function cannot go outside the boundaries of the stencil, otherwise an error will be raised during stencil creation.
-> Stencil ix e a

Construct a stencil from a function, which describes how to calculate the value at a point while having access to neighboring elements with a function that accepts idices relative to the center of stencil. Trying to index outside the stencil box will result in a runtime error upon stencil creation.

Example

Expand

Below is an example of creating a Stencil, which, when mapped over a 2-dimensional array, will compute an average of all elements in a 3x3 square for each element in that array. Note: Make sure to add INLINE pragma, otherwise performance will be terrible.

average3x3Stencil :: (Default a, Fractional a) => Stencil Ix2 a a
average3x3Stencil = makeStencil (3 :. 3) (1 :. 1) $ \ get ->
  (  get (-1 :. -1) + get (-1 :. 0) + get (-1 :. 1) +
     get ( 0 :. -1) + get ( 0 :. 0) + get ( 0 :. 1) +
     get ( 1 :. -1) + get ( 1 :. 0) + get ( 1 :. 1)   ) / 9
{-# INLINE average3x3Stencil #-}

mapStencil Source #

Arguments

:: (Source r ix e, Manifest r ix e)
=> Border e	Border resolution technique
-> Stencil ix e a	Stencil to map over the array
-> Array r ix e	Source array
-> Array DW ix a

Map a constructed stencil over an array. Resulting array must be computed in order to be useful.

Convolution

makeConvolutionStencil :: (Index ix, Num e) => ix -> ix -> ((ix -> Value e -> Value e -> Value e) -> Value e -> Value e) -> Stencil ix e e Source #

Create a convolution stencil by specifying border resolution technique and an accumulator function.

Examples

Expand

Here is how to create a 2D horizontal Sobel Stencil:

sobelX :: Num e => Stencil Ix2 e e
sobelX = makeConvolutionStencil (3 :. 3) (1 :. 1) $
           \f -> f (-1 :. -1) 1 . f (-1 :. 1) (-1) .
                 f ( 0 :. -1) 2 . f ( 0 :. 1) (-2) .
                 f ( 1 :. -1) 1 . f ( 1 :. 1) (-1)
{-# INLINE sobelX #-}

makeConvolutionStencilFromKernel :: (Manifest r ix e, Num e) => Array r ix e -> Stencil ix e e Source #

Make a stencil out of a Kernel Array. This Stencil will be slower than if makeConvolutionStencil is used, but sometimes we just really don't know the kernel at compile time.

makeCorrelationStencil :: (Index ix, Num e) => ix -> ix -> ((ix -> Value e -> Value e -> Value e) -> Value e -> Value e) -> Stencil ix e e Source #

Make a cross-correlation stencil.

makeCorrelationStencilFromKernel :: (Manifest r ix e, Num e) => Array r ix e -> Stencil ix e e Source #

Make a stencil out of a Kernel Array. This Stencil will be slower than if makeCorrelationStencil is used, but sometimes we just really don't know the kernel at compile time.