Code of plotting a function in an interval (graph result)

Question

I need your help with coding a graph result - plotting a function in an interval.

The question which I got is: "Plot the following composite function. You probably want to use 'if' statements and a loop to 'build' it. Plot the function in the interval from [-3, 5].

enter code here
f(x) = {|x|     x<0}
       {-1      0 <= x < 1}
       {+1      1 <= x < 2}
       {ln(x)   2 <= x}

Can anyone write for me please, a code in which the result shows me a GRAPH, in which the above function is shown, without consistancy in the graph's line.

Thank you very much in advance!

Sheldore · Accepted Answer · 2018-12-18 15:14:42Z

1

Using if statement would be a more involved way. You can directly make use of NumPy indexing and masking to get the task done. Below is how I would do it.

Explanation: First you create a mesh of x-data points in the interval (3, 5). Then you initialize an empty y-array of same length. Next, you use the conditions on x to get the indices of x-array. This is done by using mask. mask1 = ((x>=0) & (x<1)) defines a condition and then you use y[mask1] = -1 which means, [mask1] would return the array indices where the condition holds True and then you use those indices to assign the y-value. You do this for all 4 conditions. I just used two masks for the middle two conditions. You can also use 4 variables (masks) to do the same thing. It's a matter of personal taste.

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(-3, 5, 100)
y = np.zeros(len(x))

mask1 = ((x>=0) & (x<1))
mask2 = ((x>=1) & (x<2))

y[x<0] = np.abs(x[x<0])
y[mask1] = -1
y[mask2] = 1
y[x>=2] = np.log(x[x>=2])

plt.plot(x, y)
plt.xlabel('$x$')
plt.ylabel(r'$f(x)$')
plt.show()

edited Dec 18, 2018 at 15:14

answered Dec 18, 2018 at 10:40

Sheldore

39.2k9 gold badges63 silver badges76 bronze badges

Sign up to request clarification or add additional context in comments.

2 Comments

Adi Barel Over a year ago

Thank you very much for your help, It is really useful :) In addition, I would like to know how can I eliminate the lines connecting each step of the interval? I need to show only the graphic results on the graph, in each step, without the "continuity" of the lines that connect between them.

Sheldore Over a year ago

I can't think of a straightforward way at the moment but you can plot 4 curves separately instead of plotting them once as plt.plot(x[x<0], y[x<0], 'b'), plt.plot(x[mask1], y[mask1], 'b'), plt.plot(x[mask2], y[mask2], 'b'), plt.plot(x[x>=2], np.log(x[x>=2]), 'b')

ImportanceOfBeingErnest · Accepted Answer · 2018-12-18 21:49:14Z

1

Usually, simple composite functions can easily be written like any other function by multiplying by the respective condition(s). The only place one needs to be careful is with the logarithm, which is not defined over the complete inverval. This problem is circumvented by taking the absolute value here, because it's anyways only relevant in the range > 2.

import numpy as np
import matplotlib.pyplot as plt

f = lambda x: np.abs(x)*(x<0) - ((0<=x) & (x < 1)) + ((1<=x) & (x < 2)) + np.log(np.abs(x))*(2<=x)

x = np.linspace(-3,5,200)

plt.plot(x,f(x))
plt.show()

According to a comment below the answer, one can also evaluate the function in each of the intervals separately,

intervals = [(-3, -1e-6), (0,1-1e-6), (1, 2-1e-6), (2,5)]
for (s,e) in intervals:
    x = np.linspace(s,e,100)
    plt.plot(x,f(x), color="C0")

edited Dec 18, 2018 at 21:49

answered Dec 18, 2018 at 10:56

ImportanceOfBeingErnest

342k61 gold badges737 silver badges771 bronze badges

2 Comments

Adi Barel Over a year ago

Thank you very much for your help, It is really useful :) In addition, I would like to know how can I eliminate the lines connecting each step of the interval? I need to show only the graphic results on the graph, in each step, without the "continuity" of the lines that connect between them.

ImportanceOfBeingErnest Over a year ago

It's a bit questionable why you would first define a single function and then evaluate it independently for each interval. But I updated the answer.

Adi Barel · Accepted Answer · 2018-12-18 17:42:49Z

0

Thank you very much for your help, It is really useful :)

In addition, I would like to know how can I eliminate the lines that connecting each step of the interval to the next one?

I need to show only 4 seperate graphic results on the graph, in each step, without the "continuity" of the lines that connect between them.

answered Dec 18, 2018 at 17:42

Adi Barel

112 bronze badges

Collectives™ on Stack Overflow

Code of plotting a function in an interval (graph result)

3 Answers 3

2 Comments

2 Comments

Comments

Your Answer

Hot Network Questions

Collectives™ on Stack Overflow

3 Answers 3

2 Comments

2 Comments

Comments

Your Answer

Sign up or log in

Post as a guest

Related