How can I plot the Voigt Profile function with varying values of a in Python?

[sketos]

I very new to python and this might look relatively easy to some of you. I need to write a code so that

$$H(a,u) = \frac{a}{\pi} \int_{-\infty}^{\infty} \frac{e^{-y^2}}{a^2+(u-y)^2}dy$$

it plots the above function for different values of the a parameter, so that ultimately i will have a graph of 3 or more function of the form $H(a_1,u)$, $H(a_2,u)$, $H(a_3,u)$ as functions of u. Can anyone provide a code ?

 

[Mark44]

I very new to python and this might look relatively easy to some of you. I need to write a code so that

$$H(a,u) = \frac{a}{\pi} \int_{-\infty}^{\infty} \frac{e^{-y^2}}{a^2+(u-y)^2}dy$$

it plots the above function for different values of the a parameter, so that ultimately i will have a graph of 3 or more function of the form $H(a_1,u)$, $H(a_2,u)$, $H(a_3,u)$ as functions of u. Can anyone provide a code ?

The key is

I need to write a code

We're not going to do this for you. We'll be happy to help you out on it, but you need to show us what you've tried.

 

[sketos]

import numpy as np
import pylab as pl
from math import exp
from scipy.integrate import quad

def voigt( u , a ):

def integrand( y ):

return exp(-y**2)/( a**2 + ( u - y )**2 )

return quad( integrand ,-np.inf , np.inf )x = np.linspace(-100 , 100 )

Func = voigt( x , 0.1 )

pl.plot( x , Func )

pl.show()

This is as far as i got before i posted...

 

[Fooality]

I very new to python and this might look relatively easy to some of you. I need to write a code so that

$$H(a,u) = \frac{a}{\pi} \int_{-\infty}^{\infty} \frac{e^{-y^2}}{a^2+(u-y)^2}dy$$

it plots the above function for different values of the a parameter, so that ultimately i will have a graph of 3 or more function of the form $H(a_1,u)$, $H(a_2,u)$, $H(a_3,u)$ as functions of u. Can anyone provide a code ?

Teach a man to fish he eats for a lifetime. Here's some important tools to breaking it down. I suck at calculus so I use this to calculate integrals.
http://integrals.wolfram.com/index.jsp
You would enter it in the Wolfram language, where x^y means x to the power of y, remember your parenthesis. Then take the output, and code it in the python language...its the same except x**y = x to the power of y.

 

[Daverz]

Wikipedia has some info:

http://en.wikipedia.org/wiki/Numerical_integration#Integrals_over_infinite_intervals

I googled "numerical integration of infinite integrals" to find that.