Demonstrates vector convolution

convolution.py

"""
This code shows how to perform convolution between two vectors.

Danushka Bollegala.
14-04-2016
"""


import numpy


def conv(u, v):
    d = u.shape[0]
    p = numpy.zeros(d, dtype=float)
    for i in range(0, d):
        #print i
        for j in range(0, d):
            #print j, i-j , u[j], v[i-j]
            p[i] += u[j] * v[i-j]
    return p


def pconv(u, v):
    d = u.shape[0]
    p = numpy.zeros(d, dtype=float)
    for i in range(0, d):
        for j in range(0, d):
            p[i] += u[j] * v[j-i]
    return p


def main():
    # Lets first compute the convolution between two vectors u and v.
    u = numpy.array([0, 6, 2, 10, 4])
    v = numpy.array([1, 8, 4,  4, 0])
    p = conv(u, v)
    print p
    p = conv(v, u)
    print p
    # This shows that vector convolution is commutative
    # (which is bad because word order is ignored during composition)

    # To overcome this, lets involute the second vector, before
    # we compute its convolution with the first vector.
    # This is known as periodic convolution (http://ltfat.sourceforge.net/doc/fourier/pconv.php)
    p = pconv(u, v)
    print p
    p = pconv(v, u)
    print p
    pass


if __name__ == '__main__':
    main()