numpy - Implementing Discrete Gaussian Kernel in Python? -

i'm looking implement discrete gaussian kernel defined lindeberg in work scale space theory.

it defined t(n,t) = exp(-t)*i_n(t) i_n modified bessel function of first kind.

i trying implement in python using numpy , scipy running trouble.

def discrete_gaussian_kernel(t, n):     return math.exp(-t) * scipy.special.iv(n, t) 

i try plotting with:

import math import numpy np import scipy matplotlib import pyplot plt  def kernel(t, n):     return math.exp(-t) * scipy.special.iv(n, t) ns = np.linspace(-5, 5, 1000) y0 = discrete_gaussian_kernel(0.5, ns) y1 = discrete_gaussian_kernel(1, ns) y2 = discrete_gaussian_kernel(2, ns) y3 = discrete_gaussian_kernel(4, ns) plt.plot(ns, y0, ns, y1, ns, y2, ns, y3) plt.xlim([-4, 4]) plt.ylim([0, 0.7]) 

the output looks like:

from wikipedia article, should like:

i assume i'm making trivial mistake. :/ thoughts? thanks!

edit: wrote equivalent scipy.special.ive(n, t). i'm pretty sure it's supposed modified bessel function of first kind, not second, can confirm?

if want wikipedia plot, replace

ns = np.linspace(-5, 5, 1000) 

with

ns = np.arange(-5, 5+1) 

namely, formula use makes sense @ integer points. bessel function function of negative order oscillating function, http://dlmf.nist.gov/10.27#e2 plot looks fine me.