vecs

a python implementation of real-valued vectors with a custom inner product

Installation

1. clone this repository:

   git clone https://github.com/sygmoyd/vecs.git

Useage

create an vector

to create an n-dimensional vector

vector = vec([1,2,...,n])

print the entries of an vector

print(vector.value)

add/subtract vectors

both vectors must have the same length

vector1 + vector2
vector1 - vector2

this returns an new vector

scale an vector by scalar

vector.scale(3)

calculate the dotProduct

both vectors must have the same length

vector1.dotP(vector2)

#this also works with an list
vector1.dotP([1,2,...,n])

calculate l1 / l2 norm

vector.l1Norm()
vector.l2Norm()

create an inner product

to create the inner product you first must create an calculation blueprint, here is an example for the dotProduct

def dotPCalc(v1,v2):
    s = 0
    for a,b in zip(v1.value, v2.value):
        s += a*b
    return s

with this you can create an inner product via the InnerProduct-Class

dotP = InnerProduct(dotPCalc)

and use it with the func-method

dotP.func(vector1, vector2)

both vectors must have the same length
you can also use the func-method with lists

dotP.func([1,2,3],[4,5,6])

in general this means

InnerProduct(innerProductCalc).func(vector1, vector2)

calculate the norm of an vector

to calculate the norm of an vector with respect to an specific inner product you can use the Norm-method,
where you pass an inner product calculation blueprint

vector.Norm(innerProductCalc)

if you dont pass an inner product, this method will be using the dotProduct

calculate the angle between 2 vectors

to calculate the angle between two vectors with respect to an specific inner product you can use the Angle-method,
where you pass an inner product calculation blueprint

vector1.Angle(vector2, innerProductCalc=innerProductCalc, deg=True)

if you dont pass an inner product, this method will be using the dotProduct

calculate the distance between 2 vectors

to calculate the distance between two vectors with respect to an specific inner product you can use the dist-method,
where you pass an inner product calculation blueprint

vector1.dist(vector2, innerProductCalc=innerProductCalc)

if you dont pass an inner product, this method will be using the dotProduct

Example

#create 3-dimensional vectors
v1 = vec([1,2,3])
v2 = vec([3,2,2])

#create inner product calculation blueprint for an weighted dotProduct
def weightedDotPCalc(v1,v2):
    s = 0
    for a,b in zip(v1.value, v2.value):
        s += a*b*5
    return s

#calculate the distance between v1 and v2 with respect to this weighted dotProduct
v1.dist(v2, innerProductCalc=weightedDotPCalc)

#calculate the l2Norm of the sum of v1 and v2
(v1+v2).l2Norm()