Beginners python, easy function

Question

Make a function gaussian(x, m=0, s=1) for computing the gaussian function. Write out a nicely formatted table of x and f(x) values for n uniformly spaced x values in [m-5s, m+5s]. (Choose s, m, n as you like)

Here's what I did so far:

from math import *
from numpy import linspace

def gaussian(x, m=0, s=1):
    fx=(1/((sqrt(2*pi))*s)*exp(-0.5*(((x - m)/s))**2))
    return fx

I want to make the variables s and m global,

xmin=m-5s
xmax=m+5s
x=linspace(xmin, xmax, 10)

Then call the function from a for loop where I loop over x

My first attempt was to try everything within the function, but my tutor said its a better idea to define x outside the function. If s and m only exist inside the function, how can I reach them -- or should I go about this in another way? Any help is apreciated and keep in mind I've only been learning this for a couple of weeks.

XRR · Answer 1 · 2017-09-14T16:30:49.143

0

How about this:

from numpy import linspace
from math import *

def gaussian(x, m, s):
   fx=(1/((sqrt(2*pi))*s)*exp(-0.5*(((x - m)/s))**2))
   return fx

m = 0
s = 1
xmin = m-5*s
xmax = m+5*s
x = linspace(xmin, xmax, 10)

for val in x:
   print "f(",val,") = ",gaussian(val,m,s)

edited Sep 14 '17 at 16:30

answered Sep 14 '17 at 16:03

XRR

418
4
16

Why cheating? I don't get you. You have a function that computes the gaussian probability, and you use it for the X values as you mentioned! If this works, do you mind accepting this as your answer? – XRR Sep 14 '17 at 16:28

Brad Solomon · Answer 2 · 2017-09-14T16:10:57.660

Vectorize this with NumPy to avoid the need to loop:

import numpy as np
def gaussian(x, m, s):
    fx = (1/((np.sqrt(2*np.pi))*s)*np.exp(-0.5*(((x - m)/s))**2))
    return fx

m=0; s=1    
x = np.linspace(m-5*s, m+5*s, num=100)

print(gaussian(x))
[  1.48671951e-06   2.45106104e-06   3.99989037e-06   6.46116639e-06
   1.03310066e-05   1.63509589e-05   2.56160812e-05   3.97238224e-05
   6.09759040e-05   9.26476353e-05   1.39341123e-04   2.07440309e-04
   3.05686225e-04   4.45889725e-04   6.43795498e-04   9.20104770e-04
   1.30165384e-03   1.82273110e-03   2.52649578e-03   3.46643792e-03
   4.70779076e-03   6.32877643e-03   8.42153448e-03   1.10925548e-02
   1.44624148e-02   1.86646099e-02   2.38432745e-02   3.01496139e-02
   3.77369231e-02   4.67541424e-02   5.73380051e-02   6.96039584e-02
   8.36361772e-02   9.94771388e-02   1.17117360e-01   1.36486009e-01
   1.57443188e-01   1.79774665e-01   2.03189836e-01   2.27323506e-01
   2.51741947e-01   2.75953371e-01   2.99422683e-01   3.21590023e-01
   3.41892294e-01   3.59786558e-01   3.74773979e-01   3.86422853e-01
   3.94389234e-01   3.98433802e-01   3.98433802e-01   3.94389234e-01
   3.86422853e-01   3.74773979e-01   3.59786558e-01   3.41892294e-01
   3.21590023e-01   2.99422683e-01   2.75953371e-01   2.51741947e-01
   2.27323506e-01   2.03189836e-01   1.79774665e-01   1.57443188e-01
   1.36486009e-01   1.17117360e-01   9.94771388e-02   8.36361772e-02
   6.96039584e-02   5.73380051e-02   4.67541424e-02   3.77369231e-02
   3.01496139e-02   2.38432745e-02   1.86646099e-02   1.44624148e-02
   1.10925548e-02   8.42153448e-03   6.32877643e-03   4.70779076e-03
   3.46643792e-03   2.52649578e-03   1.82273110e-03   1.30165384e-03
   9.20104770e-04   6.43795498e-04   4.45889725e-04   3.05686225e-04
   2.07440309e-04   1.39341123e-04   9.26476353e-05   6.09759040e-05
   3.97238224e-05   2.56160812e-05   1.63509589e-05   1.03310066e-05
   6.46116639e-06   3.99989037e-06   2.45106104e-06   1.48671951e-06]

For a table:

import pandas as pd
pd.DataFrame({'x' : x, 'gauss' : gaussian(x)})

As for your comment:

my tutor said its a better idea to define x outside the function. If s and m only exist inside the function, how can I reach them -- or should I go about this in another way?

This depends mainly on whether you want x to be a function of m and s. If that's always the case, then it is x that you should incorporate into your function (defining x locally in the function body):

def gaussian(m, s, num):
    x = np.linspace(m-5*s, m+5*s, num=num)
    fx = (1/((np.sqrt(2*np.pi))*s)*np.exp(-0.5*(((x - m)/s))**2))
    return fx

Either way there is no need to deal with global here and that's something you should probably avoid unless you have a very good reason for it.

The way things are set up in my first definition of gaussian above, you are treating x, m, and s as independent variables. That is, you could specify some other x that doesn't depend on m or s. If you want x to always be a function of m and s, then incorporate that directly into your function to avoid having to specify it outside of the function.

score 0 · Answer 3 · answered Sep 14 '17 at 16:11

I'm gonna try and replicate what I think you're going for. Python does have a global keyword, but I'm not sure that's what you need here (here's a pretty good explanation of when you need globals).

from numpy import linspace, sqrt, pi, exp

def gaussian(x, m=0, s=1):
    fx=(1/((sqrt(2*pi))*s)*exp(-0.5*(((x - m)/s))**2))
    return fx

#we must define m and s in order to calculate our bounds for linspace
m = 5 
s = 1

#you must have a '*' with multiplication. 5s is not equivelent to 5*s
xmin = m - 5 * s 
xmax = m + 5 * s

x = linspace(xmin, xmax, 10)

#apply your gaussian to every value in x
fx = [gaussian(a, m=m, s=s) for a in x]

print(fx)

Beginners python, easy function

3 Answers3