#! /usr/bin/env python3
# -*- coding:utf8 -*-

import matplotlib.pyplot as plt
import numpy as np
from math import *


def shepp_logan(x):
    return 2. / (pi * pi * (1 - 4. * x * x))

N = 18
xlim = -8, 8
xd = np.arange(-8, 9)
kernel = shepp_logan(xd)

plt.figure(figsize=(5, 3.5))

xa = np.linspace(*xlim, 801)
ys = (0.5 / pi**2) * (1 - 2 * xa * np.sin(pi*xa)) / (0.25 - xa * xa)
ys[xa*xa==0.25] = 1. / (pi * pi)

plt.plot(xd, kernel, "o-", label="discrete")
ya = shepp_logan(xa)
ya[xa==0] = float(nan)
plt.plot(xa, ya, "--", color="#bbbbbb", zorder=1.8, label=r"$2/(\pi^2 (1 - 4x^2))$")

annotate_args = {"va":"center", "ha":"left", "xytext":(12, 0), "zorder":1.7,
    "textcoords":"offset points", "fontsize":14,
    "bbox":{"fc":"white", "ec":"none"} }
plt.annotate(r"$\frac{2}{\pi^2}$", (0, shepp_logan(0)), **annotate_args)
plt.annotate(r"$\frac{-2}{3\pi^2}$", (1, shepp_logan(1)), **annotate_args)

plt.grid(True)
plt.xlim(*xlim)
plt.ylim(-0.1, 0.23)
plt.legend(loc="upper left", framealpha=1, borderaxespad=1.0, borderpad=0.6)
plt.tight_layout()
plt.savefig("Shepp-logan kernel.svg")