Data.VectorSpace

Definitions

interface VectorSpace : Type -> Type

Parameters: v
Methods:

zeroVector : v

  Vector with no magnitude (unit for addition).

(*^) : Double -> v -> v

  Multiplication by a scalar.

Fixity Declaration: infixr operator, level 9

(^/) : v -> Double -> v

  Division by a scalar.

Fixity Declaration: infixl operator, level 9

(^+^) : v -> v -> v

  Vector addition

Fixity Declaration: infixl operator, level 6

(^-^) : v -> v -> v

  Vector subtraction

Fixity Declaration: infixl operator, level 6

negateVector : v -> v

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

dot : v -> v -> Double

  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.

Fixity Declaration: infix operator, level 7

norm : v -> Double

  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

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

Implementations:

VectorSpace Double

VectorSpace (Vect n Double)

zeroVector : VectorSpace v => v

  Vector with no magnitude (unit for addition).

Visibility: public export

(*^) : VectorSpace v => Double -> v -> v

  Multiplication by a scalar.

Visibility: public export
Fixity Declaration: infixr operator, level 9

(^/) : VectorSpace v => v -> Double -> v

  Division by a scalar.

Visibility: public export
Fixity Declaration: infixl operator, level 9

(^+^) : VectorSpace v => v -> v -> v

  Vector addition

Visibility: public export
Fixity Declaration: infixl operator, level 6

(^-^) : VectorSpace v => v -> v -> v

  Vector subtraction

Visibility: public export
Fixity Declaration: infixl operator, level 6

negateVector : VectorSpace v => v -> v

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

Visibility: public export

dot : VectorSpace v => v -> v -> Double

  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.

Visibility: public export
Fixity Declaration: infix operator, level 7

norm : VectorSpace v => v -> Double

  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.

Visibility: public export

normalize : VectorSpace v => v -> v

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

Visibility: public export