Cumulative sum of vectors from a point

Question

I have a list of vectors, a list of scalars and a start point represented by a tuple.

vecs = [(1,1), (2,3), (-1,1)]
scalars = [2, 3, 2]
start = (-5,0)

I have a function to add "k times" a vector to a point.

def add_vector(point, k, vec):
    return (point[0]+k*vec[0], point[1]+k*vec[1])

I would like to get the list of the points on the polyline such that :

result[0] = start
result[n+1] = add_vector(result[n], scalars[n], vecs[n])

I thought of using itertools.accumulate but the func argument must be a function of two arguments. Any ideas ?

Is it possible to accumulate x and then y? Combine x and y to become vector — Striker, May 09 '16 at 14:10
@strike: that wouldn't be ideal since my points are actually a subclass of a tuple with added properties `point.x` and `point.y`, same for the vectors. — Jacques Gaudin, May 09 '16 at 14:18
If your points are a subclass of tuple, why does your `add_vector` function not return an instance of that class? — holdenweb, May 09 '16 at 14:20
@holdenweb: Good point. In the actual code it returns an instance of my `Point` class. I didn't show this in the question as I thought it would make it less clear. I can create an instance of `Point` from a `tuple` and a `tuple` from an instance of `Point` though. The list of vecs is already created as instances of `Point`. — Jacques Gaudin, May 09 '16 at 14:27

Jacques Gaudin · Accepted Answer · 2016-05-09T14:52:42.450

1

Just figured out I could create a generator function instead of using itertools.accumulate...

def accumulate_vector(start, scalars, vecs):
    prev = start
    yield start
    for k, vec in zip(scalars, vecs):
        prev = add_vector(prev, k, vec)
        yield prev

edited May 09 '16 at 14:52

answered May 09 '16 at 14:38

Jacques Gaudin

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score 0 · Answer 2 · answered May 09 '16 at 14:43

How about adding a helper function for add_vector (func() in the following code) :

from itertools import accumulate

def add_vector(point, k, vec):
    return (point[0]+k*vec[0], point[1]+k*vec[1])

def func(data1, data2): # data : a tuple (vector, scalar)
    vec1, k1 = data1
    vec2, k2 = data2
    return (add_vector(vec1, k2, vec2), k2)

vecs = [(1,1), (2,3), (-1,1)]
scalars = [2, 3, 2]
start = (-5,0)

temp = zip([start]+vecs, [1]+scalars)
result = [data[0] for data in accumulate(temp, func)]

print(result) # [(-5, 0), (-3, 2), (3, 11), (1, 13)]

Thanks for your suggestion. The line `temp = zip([start]+vecs, [1]+scalars)` creates two lists which can potentially be quite long (1E5) though. — Jacques Gaudin, May 09 '16 at 15:17

score 0 · Answer 3 · answered May 09 '16 at 18:06

0

You could use numpy for vector calculations. Use numpy.dot function to multiply your scalars with your matrix of vectors. Finally add the start vector to the .dot product.

answered May 09 '16 at 18:06

raptisth

62
3

Cumulative sum of vectors from a point

3 Answers3