Math.Tensor.LinearAlgebra.Scalar

Scalar types for usage as Tensor values.

Documentation

newtype Lin a

Linear combination represented as mapping from variable number to prefactor.

Constructors

Lin (IntMap a)

Instances

Eq a => Eq (Lin a)

Defined in Math.Tensor.LinearAlgebra.Scalar

Methods

(==) :: Lin a -> Lin a -> Bool

(/=) :: Lin a -> Lin a -> Bool

Ord a => Ord (Lin a)

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)

Defined in Math.Tensor.LinearAlgebra.Scalar

Methods

showsPrec :: Int -> Lin a -> ShowS

show :: Lin a -> String

showList :: [Lin a] -> ShowS

Generic (Lin a)

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)

Defined in Math.Tensor.LinearAlgebra.Scalar

Methods

rnf :: Lin a -> ()

type Rep (Lin a)

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

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

Eq a => Eq (Poly a)

Defined in Math.Tensor.LinearAlgebra.Scalar

Methods

(==) :: Poly a -> Poly a -> Bool

(/=) :: Poly a -> Poly a -> Bool

(Num a, Eq a) => Num (Poly a)

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)

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)

Defined in Math.Tensor.LinearAlgebra.Scalar

Methods

showsPrec :: Int -> Poly a -> ShowS

show :: Poly a -> String

showList :: [Poly a] -> ShowS

Generic (Poly a)

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)

Defined in Math.Tensor.LinearAlgebra.Scalar

Methods

rnf :: Poly a -> ()

type Rep (Poly a)

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

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

Maps over Poly

getVars :: Poly a -> [Int]

Returns list of variable numbers present in the polynomial.

shiftVars :: Int -> Poly a -> Poly a

Shifts variable numbers in the polynomial by a constant value.

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

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