Copyright	(c) Nils Alex 2020
License	MIT
Maintainer	nils.alex@fau.de
Safe Haskell	Safe
Language	Haskell2010

Math.Tensor.LinearAlgebra.Scalar

Description

Scalar types for usage as Tensor values.

Synopsis

newtype Lin a = Lin (IntMap a)
data Poly a
- = Const !a
- | Affine !a !(Lin a)
- | NotSupported
singletonPoly :: a -> Int -> a -> Poly a
polyMap :: (a -> b) -> Poly a -> Poly b
getVars :: Poly a -> [Int]
shiftVars :: Int -> Poly a -> Poly a
normalize :: (Fractional a, Eq a) => Poly a -> Poly a

Documentation

newtype Lin a Source #

Linear combination represented as mapping from variable number to prefactor.

Constructors

Lin (IntMap a)

Instances

Instances details

Eq a => Eq (Lin a) Source #
Instance details Defined in Math.Tensor.LinearAlgebra.Scalar Methods (==) :: Lin a -> Lin a -> Bool # (/=) :: Lin a -> Lin a -> Bool #
Ord a => Ord (Lin a) Source #
Instance details Defined in Math.Tensor.LinearAlgebra.Scalar Methods compare :: Lin a -> Lin a -> Ordering # (<) :: Lin a -> Lin a -> Bool # (<=) :: Lin a -> Lin a -> Bool # (>) :: Lin a -> Lin a -> Bool # (>=) :: Lin a -> Lin a -> Bool # max :: Lin a -> Lin a -> Lin a # min :: Lin a -> Lin a -> Lin a #
Show a => Show (Lin a) Source #
Instance details Defined in Math.Tensor.LinearAlgebra.Scalar Methods showsPrec :: Int -> Lin a -> ShowS # show :: Lin a -> String # showList :: [Lin a] -> ShowS #
Generic (Lin a) Source #
Instance details Defined in Math.Tensor.LinearAlgebra.Scalar Associated Types type Rep (Lin a) :: Type -> Type # Methods from :: Lin a -> Rep (Lin a) x # to :: Rep (Lin a) x -> Lin a #
NFData a => NFData (Lin a) Source #
Instance details Defined in Math.Tensor.LinearAlgebra.Scalar Methods rnf :: Lin a -> () #
type Rep (Lin a) Source #
Instance details Defined in Math.Tensor.LinearAlgebra.Scalar type Rep (Lin a) = D1 ('MetaData "Lin" "Math.Tensor.LinearAlgebra.Scalar" "safe-tensor-0.2.1.0-inplace" 'True) (C1 ('MetaCons "Lin" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (IntMap a))))

data Poly a Source #

Polynomial: Can be constant, affine, or something of higher rank which is not yet implemented.

Constructors

Const !a	constant value
Affine !a !(Lin a)	constant value plus linear term
NotSupported	higher rank

Instances

Instances details

Eq a => Eq (Poly a) Source #
Instance details Defined in Math.Tensor.LinearAlgebra.Scalar Methods (==) :: Poly a -> Poly a -> Bool # (/=) :: Poly a -> Poly a -> Bool #
(Num a, Eq a) => Num (Poly a) Source #
Instance details Defined in Math.Tensor.LinearAlgebra.Scalar Methods (+) :: Poly a -> Poly a -> Poly a # (-) :: Poly a -> Poly a -> Poly a # (*) :: Poly a -> Poly a -> Poly a # negate :: Poly a -> Poly a # abs :: Poly a -> Poly a # signum :: Poly a -> Poly a # fromInteger :: Integer -> Poly a #
Ord a => Ord (Poly a) Source #
Instance details Defined in Math.Tensor.LinearAlgebra.Scalar Methods compare :: Poly a -> Poly a -> Ordering # (<) :: Poly a -> Poly a -> Bool # (<=) :: Poly a -> Poly a -> Bool # (>) :: Poly a -> Poly a -> Bool # (>=) :: Poly a -> Poly a -> Bool # max :: Poly a -> Poly a -> Poly a # min :: Poly a -> Poly a -> Poly a #
Show a => Show (Poly a) Source #
Instance details Defined in Math.Tensor.LinearAlgebra.Scalar Methods showsPrec :: Int -> Poly a -> ShowS # show :: Poly a -> String # showList :: [Poly a] -> ShowS #
Generic (Poly a) Source #
Instance details Defined in Math.Tensor.LinearAlgebra.Scalar Associated Types type Rep (Poly a) :: Type -> Type # Methods from :: Poly a -> Rep (Poly a) x # to :: Rep (Poly a) x -> Poly a #
NFData a => NFData (Poly a) Source #
Instance details Defined in Math.Tensor.LinearAlgebra.Scalar Methods rnf :: Poly a -> () #
type Rep (Poly a) Source #
Instance details Defined in Math.Tensor.LinearAlgebra.Scalar type Rep (Poly a) = D1 ('MetaData "Poly" "Math.Tensor.LinearAlgebra.Scalar" "safe-tensor-0.2.1.0-inplace" 'False) (C1 ('MetaCons "Const" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)) :+: (C1 ('MetaCons "Affine" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (Lin a))) :+: C1 ('MetaCons "NotSupported" 'PrefixI 'False) (U1 :: Type -> Type)))

singletonPoly Source #

Arguments

:: a	constant
-> Int	variable number
-> a	prefactor
-> Poly a

Produces an affine value \(c + a\cdot x_i\)

polyMap :: (a -> b) -> Poly a -> Poly b Source #

Maps over Poly

getVars :: Poly a -> [Int] Source #

Returns list of variable numbers present in the polynomial.

shiftVars :: Int -> Poly a -> Poly a Source #

Shifts variable numbers in the polynomial by a constant value.

normalize :: (Fractional a, Eq a) => Poly a -> Poly a Source #

Normalizes a polynomial: \[ \mathrm{normalize}(c) = 1 \\ \mathrm{normalize}(c + a_1\cdot x_1 + a_2\cdot x_2 + \dots + a_n\cdot x_n) = \frac{c}{a_1} + 1\cdot x_1 + \frac{a_2}{a_1}\cdot x_2 + \dots + \frac{a_n}{a_1}\cdot x_n \]