## How to define periodic function in python?

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how can you define a periodic function in python, e.g. 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?

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

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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

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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)

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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

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##### Comments

- plz explain
`2-pi periodically continued on IR`

- probably would be tricky with a lambda but I'd be tempted to use fmod from the mathmodule
- 2-pi periodically continued on IR (the set of all real numbers) means f(x) is defined for all real numbers x, and furthermore f(x) is identically equal to f(x + 2pi)
- @AhsanulHaque: I believe "IR" is serving as an ASCII approximation to "ℝ" here.
- docs.scipy.org/doc/scipy-0.13.0/reference/generated/…
- +1 Nice idea!
`expense`

is an odd word to use, though. Did you mean`expanse`

?`extent`

? (I'd probably just call it`periodic`

, or perhaps`periodic_on`

.) - You also want to replace
`x % interval`

with`(x - a) % interval`

, I think. - @MarkDickinson Thanks for correction. Oh my poor English skill >_<
- oha, now there is a missing ly :D But nice use of decorators!
- You don't need the Python 3 disclaimer:
`%`

works for floating-point numbers in both Python 2 and Python 3. And I think you want`(x + pi) % (2*pi) - pi`

to get the right result. - @Mark Dickinson: you are right. just made a quick plot... thanks & updated.
- What is the offset?