Copyright | (c) Antony Courtney and Henrik Nilsson Yale University 2003 |
---|---|
License | BSD-style (see the LICENSE file in the distribution) |
Maintainer | nilsson@cs.yale.edu |
Stability | provisional |
Portability | non-portable (GHC extensions) |
Safe Haskell | Safe |
Language | Haskell98 |
Vector space type relation and basic instances.
- class (Eq a, Floating a) => VectorSpace v a | v -> a where
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.
zeroVector, (*^), (^+^), dot
zeroVector :: v Source #
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 #
Vector addition
(^-^) :: 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.
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
.
Return a vector with the same origin and orientation (angle), but such that the norm is one (the unit for multiplication by a scalar).
VectorSpace Double Double Source # | |
VectorSpace Float Float Source # | |
RealFloat a => VectorSpace (Vector3 a) a Source # | |
RealFloat a => VectorSpace (Vector2 a) a Source # | |
(Eq a, Floating a) => VectorSpace (a, a) a Source # | Vector space instance for pairs of |
(Eq a, Floating a) => VectorSpace (a, a, a) a Source # | Vector space instance for triplets of |
(Eq a, Floating a) => VectorSpace (a, a, a, a) a Source # | Vector space instance for tuples with four |
(Eq a, Floating a) => VectorSpace (a, a, a, a, a) a Source # | Vector space instance for tuples with five |