Vektor operations (basic) in python - always need it - always reprogram it - until now ;)

vector_util.py

import math
from math import sin, cos, pi
from numpy import dot, matrix, array
from numpy.linalg import norm
#import numpy as np

# author Jasper Buesch

def rotate_vector(angle=0, vector=(0,0)):
    rot_mat = matrix( ((cos(angle),-sin(angle)), (sin(angle), cos(angle))) )
    vector = array(vector)
    result = vector * rot_mat
    return result.tolist()[0]


def sub_vectors(a, b):
    """Subtracts b from a. 
    E.g. if the vector pointing from b to a is to be calculated. sub_vectors(a, b)"""
    diff = array(a) - array(b)
    return diff.tolist()


def angle_between(a,b):
    """Returns the angle between two vectors - a is the reference.
    The return value lies between 0 an pi."""
    na, nb = norm(a), norm(b)
    assert na > 0 and nb > 0
    arccosInput = dot(a,b)/na/nb
    arccosInput = 1.0 if arccosInput > 1.0 else arccosInput
    arccosInput = -1.0 if arccosInput < -1.0 else arccosInput
    return math.acos(arccosInput)


def angle_between_s(a, b):
    """Returns the angle between a and b. a is the reference. 
    If the angle is between 0 and pi in math-positive direction
    and between 0 and -pi in the clockwise direction."""
    angle = angle_between(a,b)
    if angle < angle_between(a, rotate_vector(angle=0.001, vector=b)):
        return - angle
    else:
        return angle


if __name__ == "__main__":
    print
    print "subtracting b=(1, 1) from a=(2, 1): ", sub_vectors( (2,1), (1,1))
    print "###"
    print "angle_between_s( (0,1), (1,0) ): ", angle_between_s( (0,1), (1,0) )  # math negative
    print "angle_between_s( (1,0), (0,1) ): ", angle_between_s( (1,0), (0,1) )  # math positive
    print "###"
    print "(1,0) rotated by 90 degrees in math pos dir: ", rotate_vector(angle=pi/2, vector=(1,0))
    print