Physics.Learn.SimpleVec

Basic operations on the vector type Vec, such as vector addition and scalar multiplication. This module is simple in the sense that the operations on vectors all have simple, concrete types, without the need for type classes. This makes using and reasoning about vector operations easier for a person just learning Haskell.

Documentation

data Vec

A type for vectors.

Instances

Eq Vec

Defined in Physics.Learn.CommonVec

Methods

(==) :: Vec -> Vec -> Bool

(/=) :: Vec -> Vec -> Bool

Show Vec

Defined in Physics.Learn.CommonVec

Methods

showsPrec :: Int -> Vec -> ShowS

show :: Vec -> String

showList :: [Vec] -> ShowS

VectorSpace Vec

Defined in Physics.Learn.CarrotVec

Associated Types

type Scalar Vec :: *

Methods

(*^) :: Scalar Vec -> Vec -> Vec

InnerSpace Vec

Defined in Physics.Learn.CarrotVec

Methods

(<.>) :: Vec -> Vec -> Scalar Vec

AdditiveGroup Vec

Defined in Physics.Learn.CarrotVec

Methods

zeroV :: Vec

(^+^) :: Vec -> Vec -> Vec

negateV :: Vec -> Vec

(^-^) :: Vec -> Vec -> Vec

StateSpace Vec

Defined in Physics.Learn.StateSpace

Associated Types

type Diff Vec :: *

Methods

(.-.) :: Vec -> Vec -> Diff Vec

(.+^) :: Vec -> Diff Vec -> Vec

type Scalar Vec

Defined in Physics.Learn.CarrotVec

type Scalar Vec = Double

type Diff Vec

Defined in Physics.Learn.StateSpace

type Diff Vec = Vec

type R = Double

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.

(^+^) :: Vec -> Vec -> Vec infixl 6

Vector addition.

(^-^) :: Vec -> Vec -> Vec infixl 6

Vector subtraction.

(*^) :: R -> Vec -> Vec infixl 7

Scalar multiplication, where the scalar is on the left and the vector is on the right.

(^*) :: Vec -> R -> Vec infixl 7

Scalar multiplication, where the scalar is on the right and the vector is on the left.

(^/) :: Vec -> R -> Vec infixl 7

Division of a vector by a scalar.

(<.>) :: Vec -> Vec -> R infixl 7

Dot product of two vectors.

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

Cross product.

magnitude :: Vec -> R

Magnitude of a vector.

zeroV :: Vec

The zero vector.

negateV :: Vec -> Vec

The additive inverse of a vector.

sumV :: [Vec] -> Vec

Sum of a list of 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.