如何在python中定义周期函数？

Question

how can you define a periodic function in python, eg the "sawtooth" function?

f(x) = x, for –π < x < π and 2-pi periodically continued on IR

Can you do this with a lambda function?

Answer 1

as a normal function you can use modulo ( % ) also with float:

from math import pi

def f(x):
    return (x+pi) % (2*pi) - pi

this easily translates to a lambda expression:

lambda x: (x+pi) % (2*pi) - pi

Answer 2

You can make use of decorators:

def periodically_continued(a, b):
    interval = b - a
    return lambda f: lambda x: f((x - a) % interval + a)

@periodically_continued(-1, 1)
def f(x):
    return x

g = periodically_continued(0, 1)(lambda x: -x)

assert f(2.5) == 0.5
assert g(2.5) == -0.5

Answer 3

You could write a function that takes a function and a period, and returns a function:

import math

def periodic_function(func, period, offset):
    return lambda x: func( ((x - offset) % period ) + offset )

and use that then:

sawtooth = periodic_function(lambda x: x, 2*math.pi, math.pi)

Answer 4

A very simple way is to limit the inputs to the first period. Iteratively remove one period until the input falls within the defined values. For example the following example gives a square wave with period 2*pi.

def f(t):
    while t>2*np.pi:
            t=t-2*np.pi
    if 0.0 <= t <=np.pi:
        return 1.0
    else:
        return -1.0