Re: [Matplotlib-users] [matplotlib-users] How to plot digamma function (psi)

[Damon M. <dam...@gm...>]

On Tue, Jul 10, 2012 at 12:27:59PM +0200, Fabien Lafont wrote:
> Hello everyone,
> 
> I try to plot the digamma function of (1/2 + 1/x) but I'm not sure that I'm
> plotting the good one.
> 
> I've tried:
> 
> special.polygamma(0, (1/2 + 1/x))
> 
> and
> 
> special.polygamma(1, (1/2 + 1/x))

You want special.polygamma(0, (1/2 + 1/x)). See
http://docs.scipy.org/doc/scipy/reference/generated/scipy.special.polygamma.html

The number specifies which derivative of the digamma function you want.
Surely you want the 0th derivative?

> But It returns zero division error even when x is in ]0,1]

I think it blows up at x = 0. What is the type of x in your usecase? Is
it an array? If x contains the element 0, you will get a zero
division error. You could try plotting the points explicitly:

from numpy import linspace
from pylab import *

x = linspace(0.5, 2, num=100, endpoint=True)
y = special.polygamma(0, (1/2 + 1/x))
plot(x, y)
show()

You can compare output against this:
http://www.wolframalpha.com/input/?i=digamma%281%2F2+%2B+1%2Fx%29+between+0.5+and+2

Hope this helps.

-- 
Damon McDougall
http://damon-is-a-geek.com
B2.39
Mathematics Institute
University of Warwick
Coventry
West Midlands
CV4 7AL
United Kingdom