Produce random wavefunction

Question

I need to produce a random curve in matplotlib.

My x values are from say 1 to 1000 for example. I don't want to generate scattered random y values, I need a smooth curve. Like some kind of very distorted sin curve with varying amplitude and wavelength.

Does something already exist to allow me to easily do this?

Answer 1

Try this code:

import matplotlib.pyplot as pl
import numpy as np

x = np.linspace(1, 10)

def f(x):
    return np.sin(x) + np.random.normal(scale=0.1, size=len(x))

pl.plot(x, f(x))

It will give you a sin wave with some noise added to it:

Edit:

It seems like some kind of random walk is what you're looking for. This function will do that for you:

def f(x):
    y = 0
    result = []
    for _ in x:
        result.append(y)
        y += np.random.normal(scale=1)
    return np.array(result)

This is an example of what it can look like (with x = np.linspace(0, 1000, 1000)):

It's not a function of x any longer though, so the code should probably be refactored to generate a random walk with n steps instead. I'll leave that to you :)

Edit 2:

If you want a smoother curve, you can apply a running mean (stolen from this question):

def runningMean(x, N):
    return np.convolve(x, np.ones((N,))/N)[(N-1):]

pl.plot(x, runningMean(f(x), 10))

The bigger window (the N parameter) you use, the smoother the result.

Example: