Copyright	(c) Scott N. Walck 2011-2018
License	BSD3 (see LICENSE)
Maintainer	Scott N. Walck <walck@lvc.edu>
Stability	experimental
Safe Haskell	Safe
Language	Haskell98

Physics.Learn.CarrotVec

Contents

Orphan instances

Description

This module defines some basic vector functionality. It uses the same internal data representation as SimpleVec, but declares Vec to be an instance of VectorSpace. We import zeroV, negateV, sumV, ^+^, ^-^ from AdditiveGroup, and *^, ^*, ^/, <.>, magnitude from VectorSpace.

CarrotVec exports exactly the same symbols as SimpleVec; they are just defined differently.

Synopsis

data Vec
xComp :: Vec -> Double
yComp :: Vec -> Double
zComp :: Vec -> Double
vec :: Double -> Double -> Double -> Vec
(^+^) :: AdditiveGroup v => v -> v -> v
(^-^) :: AdditiveGroup v => v -> v -> v
(*^) :: VectorSpace v => Scalar v -> v -> v
(^*) :: (VectorSpace v, s ~ Scalar v) => v -> s -> v
(^/) :: (VectorSpace v, s ~ Scalar v, Fractional s) => v -> s -> v
(<.>) :: InnerSpace v => v -> v -> Scalar v
(><) :: Vec -> Vec -> Vec
magnitude :: (InnerSpace v, s ~ Scalar v, Floating s) => v -> s
zeroV :: AdditiveGroup v => v
negateV :: AdditiveGroup v => v -> v
sumV :: (Foldable f, AdditiveGroup v) => f v -> v
iHat :: Vec
jHat :: Vec
kHat :: Vec

Documentation

data Vec #

A type for vectors.

Instances

Eq Vec #
Instance details Defined in Physics.Learn.CommonVec Methods (==) :: Vec -> Vec -> Bool # (/=) :: Vec -> Vec -> Bool #
Show Vec #
Instance details Defined in Physics.Learn.CommonVec Methods showsPrec :: Int -> Vec -> ShowS # show :: Vec -> String # showList :: [Vec] -> ShowS #
VectorSpace Vec #
Instance details Defined in Physics.Learn.CarrotVec Associated Types type Scalar Vec :: * # Methods (*^) :: Scalar Vec -> Vec -> Vec #
InnerSpace Vec #
Instance details Defined in Physics.Learn.CarrotVec Methods (<.>) :: Vec -> Vec -> Scalar Vec #
AdditiveGroup Vec #
Instance details Defined in Physics.Learn.CarrotVec Methods zeroV :: Vec # (^+^) :: Vec -> Vec -> Vec # negateV :: Vec -> Vec # (^-^) :: Vec -> Vec -> Vec #
StateSpace Vec #
Instance details Defined in Physics.Learn.StateSpace Associated Types type Diff Vec :: * # Methods (.-.) :: Vec -> Vec -> Diff Vec # (.+^) :: Vec -> Diff Vec -> Vec #
type Scalar Vec #
Instance details Defined in Physics.Learn.CarrotVec type Scalar Vec = Double
type Diff Vec #
Instance details Defined in Physics.Learn.StateSpace type Diff Vec = Vec

xComp :: Vec -> Double #

x component

yComp :: Vec -> Double #

y component

zComp :: Vec -> Double #

z component

vec #

Arguments

:: Double	x component
-> Double	y component
-> Double	z component
-> Vec

Form a vector by giving its x, y, and z components.

(^+^) :: AdditiveGroup v => v -> v -> v infixl 6 #

Add vectors

(^-^) :: AdditiveGroup v => v -> v -> v infixl 6 #

Group subtraction

(*^) :: VectorSpace v => Scalar v -> v -> v infixr 7 #

Scale a vector

(^*) :: (VectorSpace v, s ~ Scalar v) => v -> s -> v infixl 7 #

Vector multiplied by scalar

(^/) :: (VectorSpace v, s ~ Scalar v, Fractional s) => v -> s -> v infixr 7 #

Vector divided by scalar

(<.>) :: InnerSpace v => v -> v -> Scalar v infixr 7 #

Inner/dot product

(><) :: Vec -> Vec -> Vec infixl 7 #

Cross product.

magnitude :: (InnerSpace v, s ~ Scalar v, Floating s) => v -> s #

Length of a vector. See also magnitudeSq.

zeroV :: AdditiveGroup v => v #

The zero element: identity for '(^+^)'

negateV :: AdditiveGroup v => v -> v #

Additive inverse

sumV :: (Foldable f, AdditiveGroup v) => f v -> v #

Sum over several vectors

iHat :: Vec #

Unit vector in the x direction.

jHat :: Vec #

Unit vector in the y direction.

kHat :: Vec #

Unit vector in the z direction.

Orphan instances

VectorSpace Vec #
Instance details Associated Types type Scalar Vec :: * # Methods (*^) :: Scalar Vec -> Vec -> Vec #
InnerSpace Vec #
Instance details Methods (<.>) :: Vec -> Vec -> Scalar Vec #
AdditiveGroup Vec #
Instance details Methods zeroV :: Vec # (^+^) :: Vec -> Vec -> Vec # negateV :: Vec -> Vec # (^-^) :: Vec -> Vec -> Vec #