plotting multiple functions in different intervals (python) in log-log axes

Question

I am trying to plot 3 different functions on a log-log scale in python for three intervals of the x-range. Attaching the image of the kind of plot that I want to create and which functions, y, for what intervals of x.

My code attempt is as follows. Maybe I am overcomplicating it.

import math as m
import numpy as np
import pylab as pl 
import matplotlib.pyplot as plt
x = np.arange(100)  # this gives `array([0, 1, 2, ..., 9])`
y = np.arange(100)

for i in range (-50,20):
   if x[i] < -43:
      y[i] = m.log10((10**x[i])/(10**-43))**(1/2)
   if x[i] >  -43 and x[i] < -40:
      y[i] = m.log10(np.exp((10**36)((10**x[i])-(10**-43))))
   if x[i] >-40:
      y[i] = m.log10((np.exp((10**36)((10**-40) - (10**-43)))(((10**x[i])/(10**-43))**(1/2)))
   #i+=1


pl.plot(x,y)
#pl.xlim([-100.,100.])
#pl.ylim([-100.,100.]) 
pl.xlabel('log x')
pl.ylabel('log y')
pl.show()

PLEASE NOTE: updated code with help from @Sembei which works but there's further question on colours below:

import matplotlib.pyplot as plt
x = np.linspace(-50,23,500)
y = []

for xval in x:
    if xval < -36:
        y.append(m.log10(((10**xval)/(10**-36))**(1/2)))
    elif -36 <= xval <= -34:
        y.append(m.log10(np.exp((10**36)*((10**xval)-(10**-36)))))
    else:
        y.append(m.log10((np.exp((10**36)*((10**-34) - (10**-36)))*(((10**xval)/(10**-36))**(1/2)))))
       
plt.plot(x,y)
pl.xlim([-44.,-30.])
#pl.ylim([-10.,20.]) 
pl.xlabel('log x')
pl.ylabel('log y')
plt.show()

FURTHER QUESTION: how to set 3 different colours for the different y functions for the 3 x-intervals? Any help is appreciated. Thanks!

Answer 1

you can do something like this:

x = range(-50,23)
y = []

for xval in x:
   if xval < -43:
       y.append(-43) #your function in this interval
   elif -43 <= xval <= -40:
       y.append(xval) #your function in this interval)
   else:
       y.append(-40) #your function in this interval)

plt.plot(x,y, '.-')
plt.xlabel('log x')
plt.ylabel('log y')
plt.show()

You just need to fill the #your function in this interval with a correct syntax (note that in your syntax you are missing product operators *)

Here I have used y as a list and I'm appending values. You can also initialize y to all zeros and assign values based on indexes. For that you will need to include an enumerate in the loop that will give you the index of y where you have to put the value.

Note: here, range steps one by one. if you want more resolution you might want to use np.linspace so you can control the resolution of your function.

Edit: I put some toy definitions of the function so you can see how it works. Now just change my function definitions for your own