Copyright	(c) Andrew Lelechenko 2014-2015
License	GPL-3
Maintainer	andrew.lelechenko@gmail.com
Stability	experimental
Portability	POSIX
Safe Haskell	None
Language	Haskell2010

Math.ExpPairs.ProcessMatrix

Description

Provides types for sequences of A- and B-processes of van der Corput. A good account on this topic can be found in Graham S. W., Kolesnik G. A. Van Der Corput's Method of Exponential Sums, Cambridge University Press, 1991, especially Ch. 5.

Synopsis

data Process
- = A
- | BA
data ProcessMatrix
aMatrix :: ProcessMatrix
baMatrix :: ProcessMatrix
evalMatrix :: Num t => ProcessMatrix -> (t, t, t) -> (t, t, t)

Documentation

data Process #

Since B^2 = id, B Corput16 = Corput16, B Hux05 = Hux05 and B HuxW87b1 = ???, the sequence of A- and B-processes, applied to initPairs can be rewritten as a sequence of A and BA.

Constructors

A	A-process
BA	BA-process

Instances

Enum Process #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods succ :: Process -> Process # pred :: Process -> Process # toEnum :: Int -> Process # fromEnum :: Process -> Int # enumFrom :: Process -> [Process] # enumFromThen :: Process -> Process -> [Process] # enumFromTo :: Process -> Process -> [Process] # enumFromThenTo :: Process -> Process -> Process -> [Process] #
Eq Process #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods (==) :: Process -> Process -> Bool # (/=) :: Process -> Process -> Bool #
Ord Process #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods compare :: Process -> Process -> Ordering # (<) :: Process -> Process -> Bool # (<=) :: Process -> Process -> Bool # (>) :: Process -> Process -> Bool # (>=) :: Process -> Process -> Bool # max :: Process -> Process -> Process # min :: Process -> Process -> Process #
Read Process #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods readsPrec :: Int -> ReadS Process # readList :: ReadS [Process] # readPrec :: ReadPrec Process # readListPrec :: ReadPrec [Process] #
Show Process #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods showsPrec :: Int -> Process -> ShowS # show :: Process -> String # showList :: [Process] -> ShowS #
Generic Process #
Instance details Defined in Math.ExpPairs.ProcessMatrix Associated Types type Rep Process :: Type -> Type # Methods from :: Process -> Rep Process x # to :: Rep Process x -> Process #
Pretty Process #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods pretty :: Process -> Doc ann # prettyList :: [Process] -> Doc ann #
type Rep Process #
Instance details Defined in Math.ExpPairs.ProcessMatrix type Rep Process = D1 (MetaData "Process" "Math.ExpPairs.ProcessMatrix" "exp-pairs-0.2.0.0-KY4XJcXJO7x3kwZICxZQLJ" False) (C1 (MetaCons "A" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "BA" PrefixI False) (U1 :: Type -> Type))

data ProcessMatrix #

Sequence of processes, represented as a matrix 3x3.

Instances

Eq ProcessMatrix #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods (==) :: ProcessMatrix -> ProcessMatrix -> Bool # (/=) :: ProcessMatrix -> ProcessMatrix -> Bool #
Num ProcessMatrix #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods (+) :: ProcessMatrix -> ProcessMatrix -> ProcessMatrix # (-) :: ProcessMatrix -> ProcessMatrix -> ProcessMatrix # (*) :: ProcessMatrix -> ProcessMatrix -> ProcessMatrix # negate :: ProcessMatrix -> ProcessMatrix # abs :: ProcessMatrix -> ProcessMatrix # signum :: ProcessMatrix -> ProcessMatrix # fromInteger :: Integer -> ProcessMatrix #
Show ProcessMatrix #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods showsPrec :: Int -> ProcessMatrix -> ShowS # show :: ProcessMatrix -> String # showList :: [ProcessMatrix] -> ShowS #
Semigroup ProcessMatrix #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods (<>) :: ProcessMatrix -> ProcessMatrix -> ProcessMatrix # sconcat :: NonEmpty ProcessMatrix -> ProcessMatrix # stimes :: Integral b => b -> ProcessMatrix -> ProcessMatrix #
Monoid ProcessMatrix #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods mempty :: ProcessMatrix # mappend :: ProcessMatrix -> ProcessMatrix -> ProcessMatrix # mconcat :: [ProcessMatrix] -> ProcessMatrix #
Pretty ProcessMatrix #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods pretty :: ProcessMatrix -> Doc ann # prettyList :: [ProcessMatrix] -> Doc ann #

aMatrix :: ProcessMatrix #

Return process matrix for A-process.

baMatrix :: ProcessMatrix #

Return process matrix for BA-process.

evalMatrix :: Num t => ProcessMatrix -> (t, t, t) -> (t, t, t) #

Apply a projective transformation, defined by Path, to a given point in two-dimensional projective space.