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

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

plt.rcParams['font.sans-serif'] = 'DejaVu Sans'
np.random.seed(2)

"""
red noise is identical to a Wiener process, that can be approximated by a
random walk
"""

nsamples = 501
sigma = 1. # diffusion
t0 = 1.
t = np.linspace(0, t0, nsamples)

dt = t[1:] - t[:-1]
randnorm = np.random.normal(0, 1, nsamples)
X = np.zeros_like(t)
X[1:] = X[0] + np.cumsum(sigma * np.sqrt(dt) * randnorm[1:])
X -= np.mean(X)
X /= np.std(X)

fig = plt.figure(figsize=(520 / 90.0, 340 / 90.0), dpi=72)
plt.plot(t, X)
plt.grid(True)
plt.xlim(t[0], t[-1])
plt.ylim(-2.6, 2.6)
plt.xlabel('t')
plt.ylabel('X')
plt.tight_layout()
plt.savefig('Red-noise-trace.svg')