在Python中为概率密度函数生成随机数

Question

I'm currently working on a project relating to brownian motion, and trying to simulate some of it using Python (a language I'm admittedly very new at). Currently, my goal is to generate random numbers following a given probability density function. I've been trying to use the scipy library for it.

My current code looks like this:

>>> import scipy.stats as st
>>> class my_pdf(st.rv_continuous):
        def _pdf(self,x,y):
            return (1/math.sqrt(4*t*D*math.pi))*(math.exp(-((x^2)/(4*D*t))))*(1/math.sqrt(4*t*D*math.pi))*(math.exp(-((y^2)/(4*D*t))))
>>> def get_brown(a,b):
        D,t = a,b
        return my_pdf()
>>> get_brown(1,1)
<__main__.my_pdf object at 0x000000A66400A320>

All attempts at launching the get_brown function end up giving me these hexadecimals (always starting at 0x000000A66400A with only the last three digits changing, no matter what parameters I give for D and t). I'm not sure how to interpret that. All I want is to get random numbers following the given PDF; what do these hexadecimals mean?

Answer 1

The result you see is the memory address of the object you have created. Now you might ask: which object? Your method get_brown(int, int) calls return my_pdf() which creates an object of the class my_pdf and returns it. If you want to access the _pdf function of your class now and calculate the value of the pdf you can use this code:

get_brown(1,1)._pdf(x, y)

On the object you have just created you can also use all methods of the scipy.stats.rv_continous class, which you can find here .

For your situation you could also discard your current code and just use the normal distribution included in scipy as Brownian motion is mainly a Normal random process.

Answer 2

As noted, this is a memory location. Your function get_brown gets an instance of the my_pdf class, but doesn't evaluate the method inside that class.

What you probably want to do is call the _pdf method on that instance, rather than return the class itself.

def get_brown(a,b):
    D,t = a,b  #  what is D,t for?
    return my_pdf()_pdf(a,b)

I expect that the code you've posted is a simplification of what you're really doing, but functions don't need to be inside classes - so the _pdf function could live on it's own. Alternatively, you don't need to use the get_brown function - just instantiate the my_pdf class and call the calculation method.