Vector

A module for Vectors

Types

type Vector a

= Vector (List a)

Vector type

type Vector3 a

= Vector3 a a a

3 Dimensional Vector type

type Scalar a

= Scalar a

Type to represent a scalar value

type alias AbelianGroup a =

{ field : Field a

, addVects : Vector a -> Vector a -> Vector a

, subtractVects : Vector a -> Vector a -> Vector a

}

Type to represent a Abelian Group

type alias VectorSpace a =

{ abelianGroup : AbelianGroup a

, vectorScalarMultiplication : a -> Vector a -> Vector a

}

Type to represent a Vector Space

type alias InnerProductSpace a =

{ vectorSpace : VectorSpace a

, innerProduct : Vector a -> Vector a -> a

}

Type to represent an Inner Product Space

Values

realVectorSpace : VectorSpace Float

Real Numbered Vector Space

realVectorAbelianGroup : AbelianGroup Float

Real Numbered Abelian Group

realInnerProductSpace : InnerProductSpace Float

Real Numbered Inner Product Space

complexVectorSpace : VectorSpace (ComplexNumber Float)

Complex Numbered Vector Space

complexVectorAbelianGroup : AbelianGroup (ComplexNumber Float)

Complex Numbered Abelian Group

complexInnerProductSpace : InnerProductSpace (ComplexNumber Float)

Complex Numbered Inner Product Space

zeros : Field a -> Int -> Vector a

Zero vector given a Field and dimension

Unitary Operations

scalarMultiplication : Field a -> a -> Vector a -> Vector a

Scalar multiplication over a Vector

length : Field a -> Vector a -> a

Calculate the length of a Vector

normalise : Field a -> Vector a -> Vector a

Adjust a vector so that its length is exactly one

sum : Field a -> Vector a -> a

Calculate the sum of a Vector

Binary Operations

addVectors : Field a -> Vector a -> Vector a -> Vector a

Add two Vectors

subtractVectors : Field a -> Vector a -> Vector a -> Vector a

Subtract Vectors

hadamardMultiplication : Field a -> Vector a -> Vector a -> Vector a

Hadamard Multiplication Vectors

dotProduct : Field a -> Vector a -> Vector a -> a

Calculate the dot product of two Vectors

angleBetween : Vector Float -> Vector Float -> Float

Calculate the angle between two vectors

cross : Field a -> Vector3 a -> Vector3 a -> Vector3 a

Take the cross product of two 3D vectors

distance : AbelianGroup a -> Vector a -> Vector a -> a

Calculate distance between two vectors

tensorProduct : Field a -> Vector a -> Vector a -> Vector a

Calculate the tensor product of two vectors

Vector Properties

dimension : Vector a -> Int

Count of number of elements in a vector

vectorSubspace : AbelianGroup a -> Scalar a -> List (Vector a) -> List (a -> Bool) -> Bool

Determine whether a list of Vectors makes a Subspace

all : (a -> Bool) -> Vector a -> Bool

Determine if all elements in a vector satisfy some test

Monoid

empty : Vector a

Monoid empty for Vector

append : Vector a -> Vector a -> Vector a

Append Vectors together

concat : Monoid (Vector a)

Monoidally append Vectors together

Functor, Applicative, Monad, Foldable

map : (a -> b) -> Vector a -> Vector b

Map over a vector

pure : a -> Vector a

Place a value in minimal Vector context

andMap : Vector a -> Vector (a -> b) -> Vector b

Apply for Vector

map2 : (a -> b -> c) -> Vector a -> Vector b -> Vector c

Lift a binary function to work with Vectors

andThen : (a -> Vector b) -> Vector a -> Vector b

andThen for Vector

foldl : (a -> b -> b) -> b -> Vector a -> b

Left fold over a Vector

Equality

equal : (a -> a -> Bool) -> Vector a -> Vector a -> Bool

Compare two vectors for equality using a comparator

Manipulation

findIndex : (a -> Bool) -> Vector a -> Maybe Int

Find index of a value in a Vector

getAt : Int -> Vector a -> Maybe a

Get the value in a Vector at the specified index

setAt : Int -> a -> Vector a -> Vector a

Set the value in a Vector at the specified index

parseVector : Parser a -> Parser (Vector a)

Parse a Vector

printRealVector : Vector Float -> String

Print a Real Vector as a string

printComplexVector : Vector (ComplexNumber Float) -> String

Print a Complex Vector as a string

readRealVector : String -> Result (List DeadEnd) (Vector Float)

Try to read a string into a Real Vector

readComplexVector : String -> Result (List DeadEnd) (Vector (ComplexNumber Float))

Try to read a string into a Complex Vector

vector3ToVector : Vector3 a -> Vector a

Convert a Vector3 type to a Vector type

negativeOrPositiveFloat : Parser Float

Parse a Float that can be negative or positive

jonathanfishbein1/linear-algebra/9.0.0