Data.LinFunc

Documentation

type LinFunc = Map

LinFunc v c is a linear combination of variables of type v with coefficients from c. Formally, this is the free c-module on v.

class Module r m | m -> r where

In algebra, if r is a ring, an r-module is an additive group with a scalar multiplication operation. When r is a field, this is equivalent to a vector space.

Methods

(*^) :: r -> m -> m

zero :: m

(^+^) :: m -> m -> m

(^-^) :: m -> m -> m

neg :: m -> m

Instances

Module Double Double

Module Int Int

Module Integer Integer

Module r m => Module r (IntMap m)

(IArray UArray m, Module r m) => Module r (UArray Int m)

Module r m => Module r (Array Int m)

(Ord k, Module r m) => Module r (Map k m)

Module r m => Module r (a -> m)

Integral a => Module (Ratio a) (Ratio a)

var :: (Ord v, Num c) => v -> LinFunc v c

Given a variable v, returns the function equivalent to v.

varSum :: (Ord v, Num c) => [v] -> LinFunc v c

Equivalent to vsum . map var.

(*&) :: (Ord v, Num c) => c -> v -> LinFunc v c

c *& v is equivalent to c *^ var v.

vsum :: Module r v => [v] -> v

Returns a vector sum.

combination :: Module r m => [(r, m)] -> m

Given a collection of vectors and scaling coefficients, returns this linear combination.

linCombination :: (Ord v, Num r) => [(r, v)] -> LinFunc v r

Given a set of basic variables and coefficients, returns the linear combination obtained by summing.