| Copyright | (c) Scott N. Walck 2011-2019 |
|---|---|
| License | BSD3 (see LICENSE) |
| Maintainer | Scott N. Walck <walck@lvc.edu> |
| Stability | experimental |
| Safe Haskell | Safe |
| Language | Haskell2010 |
Physics.Learn.CarrotVec
Contents
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
- type R = Double
- xComp :: Vec -> R
- yComp :: Vec -> R
- zComp :: Vec -> R
- vec :: R -> R -> R -> 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
A type for vectors.
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
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