Yampa-0.11: Library for programming hybrid systems.

Copyright (c) Antony Courtney and Henrik Nilsson Yale University 2003 BSD-style (see the LICENSE file in the distribution) nilsson@cs.yale.edu provisional non-portable (GHC extensions) Safe Haskell98

FRP.Yampa.VectorSpace

Description

Vector space type relation and basic instances.

Synopsis

# Documentation

class (Eq a, Floating a) => VectorSpace v a | v -> a where Source #

Vector space type relation.

A vector space is a set (type) closed under addition and multiplication by a scalar. The type of the scalar is the field of the vector space, and it is said that v is a vector space over a.

The encoding uses a type class |VectorSpace| v a, where v represents the type of the vectors and a represents the types of the scalars.

Minimal complete definition

Methods

Vector with no magnitude (unit for addition).

(*^) :: a -> v -> v infixr 9 Source #

Multiplication by a scalar.

(^/) :: v -> a -> v infixl 9 Source #

Division by a scalar.

(^+^) :: v -> v -> v infixl 6 Source #

(^-^) :: v -> v -> v infixl 6 Source #

Vector subtraction

negateVector :: v -> v Source #

Vector negation. Addition with a negated vector should be same as subtraction.

dot :: v -> v -> a infix 7 Source #

Dot product (also known as scalar or inner product).

For two vectors, mathematically represented as a = a1,a2,...,an and b = b1,b2,...,bn, the dot product is a . b = a1*b1 + a2*b2 + ... + an*bn.

Some properties are derived from this. The dot product of a vector with itself is the square of its magnitude (norm), and the dot product of two orthogonal vectors is zero.

norm :: v -> a Source #

Vector's norm (also known as magnitude).

For a vector represented mathematically as a = a1,a2,...,an, the norm is the square root of a1^2 + a2^2 + ... + an^2.

normalize :: v -> v Source #

Return a vector with the same origin and orientation (angle), but such that the norm is one (the unit for multiplication by a scalar).

Instances

 Source # Vector space instance for Doubles, with Double scalars. Methods Source # Vector space instance for Floats, with Float scalars. Methods RealFloat a => VectorSpace (Vector3 a) a Source # Methods(*^) :: a -> Vector3 a -> Vector3 a Source #(^/) :: Vector3 a -> a -> Vector3 a Source #(^+^) :: Vector3 a -> Vector3 a -> Vector3 a Source #(^-^) :: Vector3 a -> Vector3 a -> Vector3 a Source #dot :: Vector3 a -> Vector3 a -> a Source #norm :: Vector3 a -> a Source # RealFloat a => VectorSpace (Vector2 a) a Source # Methods(*^) :: a -> Vector2 a -> Vector2 a Source #(^/) :: Vector2 a -> a -> Vector2 a Source #(^+^) :: Vector2 a -> Vector2 a -> Vector2 a Source #(^-^) :: Vector2 a -> Vector2 a -> Vector2 a Source #dot :: Vector2 a -> Vector2 a -> a Source #norm :: Vector2 a -> a Source # (Eq a, Floating a) => VectorSpace (a, a) a Source # Vector space instance for pairs of Floating point numbers. MethodszeroVector :: (a, a) Source #(*^) :: a -> (a, a) -> (a, a) Source #(^/) :: (a, a) -> a -> (a, a) Source #(^+^) :: (a, a) -> (a, a) -> (a, a) Source #(^-^) :: (a, a) -> (a, a) -> (a, a) Source #negateVector :: (a, a) -> (a, a) Source #dot :: (a, a) -> (a, a) -> a Source #norm :: (a, a) -> a Source #normalize :: (a, a) -> (a, a) Source # (Eq a, Floating a) => VectorSpace (a, a, a) a Source # Vector space instance for triplets of Floating point numbers. MethodszeroVector :: (a, a, a) Source #(*^) :: a -> (a, a, a) -> (a, a, a) Source #(^/) :: (a, a, a) -> a -> (a, a, a) Source #(^+^) :: (a, a, a) -> (a, a, a) -> (a, a, a) Source #(^-^) :: (a, a, a) -> (a, a, a) -> (a, a, a) Source #negateVector :: (a, a, a) -> (a, a, a) Source #dot :: (a, a, a) -> (a, a, a) -> a Source #norm :: (a, a, a) -> a Source #normalize :: (a, a, a) -> (a, a, a) Source # (Eq a, Floating a) => VectorSpace (a, a, a, a) a Source # Vector space instance for tuples with four Floating point numbers. MethodszeroVector :: (a, a, a, a) Source #(*^) :: a -> (a, a, a, a) -> (a, a, a, a) Source #(^/) :: (a, a, a, a) -> a -> (a, a, a, a) Source #(^+^) :: (a, a, a, a) -> (a, a, a, a) -> (a, a, a, a) Source #(^-^) :: (a, a, a, a) -> (a, a, a, a) -> (a, a, a, a) Source #negateVector :: (a, a, a, a) -> (a, a, a, a) Source #dot :: (a, a, a, a) -> (a, a, a, a) -> a Source #norm :: (a, a, a, a) -> a Source #normalize :: (a, a, a, a) -> (a, a, a, a) Source # (Eq a, Floating a) => VectorSpace (a, a, a, a, a) a Source # Vector space instance for tuples with five Floating point numbers. MethodszeroVector :: (a, a, a, a, a) Source #(*^) :: a -> (a, a, a, a, a) -> (a, a, a, a, a) Source #(^/) :: (a, a, a, a, a) -> a -> (a, a, a, a, a) Source #(^+^) :: (a, a, a, a, a) -> (a, a, a, a, a) -> (a, a, a, a, a) Source #(^-^) :: (a, a, a, a, a) -> (a, a, a, a, a) -> (a, a, a, a, a) Source #negateVector :: (a, a, a, a, a) -> (a, a, a, a, a) Source #dot :: (a, a, a, a, a) -> (a, a, a, a, a) -> a Source #norm :: (a, a, a, a, a) -> a Source #normalize :: (a, a, a, a, a) -> (a, a, a, a, a) Source #