Plot an equation with matplotlib and numpy

Question

I want to plot an equation where the x axis represents time t and the y axis represents a variable n. Now the formula for n is n =((np.log(t)*10**6)/np.log(2)) + 1 and the maximum time on my graph is the time since big bang theory in seconds which is 4.35 x 10**17 seconds.

I tried this:

import matplotlib.pyplot as plt
import numpy as np

def graph(formula, x_range):  
    y = np.array(x_range)  
    x = eval(formula)
    plt.plot(x,y)  
    plt.show() 

graph(((np.log(x)*10**6)/np.log(2)) + 1, range(0, 4.35*10**17 ))

which doesn't seem to work. Any ideas on how I can achieve this?

eval works on a string. Nevertheless it is not seen as very elegant anyway. — willeM_ Van Onsem
– willeM_ Van Onsem, Commented Feb 1, 2017 at 21:39
Time since big bang theory is maximum 90000 seconds nowadays. Time since big bang may be considerably larger. — ImportanceOfBeingErnest
– ImportanceOfBeingErnest, Commented Feb 1, 2017 at 21:43

willeM_ Van Onsem · Accepted Answer · 2017-02-01 22:01:28Z

3

There are several problems here:

The range is supposed to be defined over integers;
The number of items the range would generate is too large, you have to take huge steps;
The formula takes x as a variable, but you seem to define a np.array(x_range) in y; and more importantly
you use eval(..), but eval(..) usually a string or another object that can be parsed;
you do not give graph(..) a formula as first element: before Python calls graph(..) it first evaluates the operands.

In my opinion, the best way to achieve this is using a lambda-expression:

import matplotlib.pyplot as plt
import numpy as np

def graph(formula, x_range):  
    x = np.array(x_range)
    #^ use x as range variable
    y = formula(x)
    #^          ^call the lambda expression with x
    #| use y as function result
    plt.plot(x,y)  
    plt.show() 

graph(lambda x : ((np.log(x)*10**6)/np.log(2)) + 1, range(0, 435*10**15,10**12))
#     ^use a lambda expression                               ^range over integers
#                                                             take huge steps

This generates the following image:

EDIT:

based on your comment you want time on the y-axis and the function on the x-axis, this can simply be achieved by assigning to the other variables like:

import matplotlib.pyplot as plt
import numpy as np

def graph(formula, x_range):  
    y = np.array(x_range)
    x = formula(y)
    plt.plot(x,y)  
    plt.show() 

graph(lambda x : ((np.log(x)*10**6)/np.log(2)) + 1, range(0,435*10**15,10**12))

Note that you do not need to change the name of the variable in the lambda-expression: indeed when you call the lambda expression, the local x will simply be the y of the caller.

edited Feb 1, 2017 at 22:01

answered Feb 1, 2017 at 21:44

willeM_ Van Onsem

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2 Comments

Wasswa Samuel Over a year ago

I realise that maybe time t being on the y axis makes more sense. How would you flip it such that time is on y axis and n is on the x axis.

willeM_ Van Onsem Over a year ago

@WasswaSamuel: simply rename x, y and y x in the assignment in the function. Will edit the answer.

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