Python not computing equation correctly

Question

I'm trying to write a simple program to plot x vs y. However, it does not seem to be computing the correct value ofy.

For instance in the first case when x = -1 the value of e^(x^2/2 - x) -1 should be 3.48, but instead it is returning 1.

The other error I have is it doesn't seem to be plotting x vs y, but instead a separate line for each value of x.

import numpy as np
import math
import matplotlib.pyplot as plt

x = np.arange(-2, 2)
y = np.arange(-2, 2)

for i in range(-3, 3):
    y[i] = math.exp(( x[i]^2/2 ) - x[i])-1

print x, y
plt.plot([x, y])
plt.show()

A couple points: (1) exponentiation is **, not ^; (2) x is an integer array, so x[i]**2/2 uses integer arithmetic in Python 2. You can fix that by using x[i]**2/2.0. — Warren Weckesser
– Warren Weckesser, Commented Sep 30, 2015 at 14:56

Waylon Flinn · Accepted Answer · 2015-09-30 15:31:16Z

3

The built in numpy array operations are perfect for this.

This is the line you want:

 y = np.exp(np.power(x, 2)/2 - x) - 1

Full code then becomes

import numpy as np
import math
import matplotlib.pyplot as plt

x = np.arange(-2, 2)

y = np.exp(np.power(x, 2)/2 - x) - 1


print(x, y)
plt.plot(x, y)
plt.show()

(Note, the plot statement is also changed here)

Details

If you start to write a loop when working with numpy, look for another way. Vector operations can be much faster (sometimes several orders of magnitude) than the corresponding python code, that's why people love it. Many of the basic operations (+, -, *, /, **) are even overloaded. Check the last item in the References section for more info.

References

edited Sep 30, 2015 at 15:31

answered Sep 30, 2015 at 15:13

Waylon Flinn

20.3k15 gold badges73 silver badges73 bronze badges

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

Comments

taleinat · Accepted Answer · 2015-09-30 15:17:04Z

2

The problems in your code:

you used the xor operator ^ instead of the exponentiation operator **
you didn't pass the lists of values to plt.plot() properly
by dividing an integer by an integer, you were actually doing integer division, i.e. 3/2 -> 1
you accidentally rounded all of the results into integers by assigning to y[i], because y was made as an array of integers (as @efirvida explained, this is because np.arange() infers the type from the given values)
the range of indexes you were iterating over was very unclear, lots of room for mistakes there... (not actually a bug)

This works on Python 3.4:

import numpy as np
import math
import matplotlib.pyplot as plt

x = np.arange(-2, 2)
y = np.ndarray(len(x), float)

for i in range(len(x)):
    y[i] = math.exp(( (x[i]**2)/2.0 ) - x[i])-1
print(x, y)
plt.plot(x, y)
plt.show()

edited Sep 30, 2015 at 15:17

answered Sep 30, 2015 at 15:01

taleinat

8,7411 gold badge36 silver badges47 bronze badges

4 Comments

Jstuff Over a year ago

I didn't realize that python would do integer division. Cool trick to get around it. Any advice on how to plot my points using a higher order degree polynomial?

Jstuff Over a year ago

Never mind realized I could just create more points with the arange command.

taleinat Over a year ago

Advice: 1) use IPython and work interactively 2) just write any formula you want in Python, it will just work, e.g. x ** 3.5 - 6.7 3) make sure to use floats instead of integers 4) define each formula as a function and then map that on the range of inputs (read about the map() function)

taleinat Over a year ago

If this answered your question and you think it is the best of the given answers, please accept it.

efirvida · Accepted Answer · 2015-09-30 15:09:15Z

0

As @xnx answer my question few days ago "NumPy arrays have a fixed datatype (dtype) which is inferred from the initialization data if you don't specify it yourself. It won't change unless you tell it to"

And this is what happening here, you are using a range of int np.arange(-2, 2), and then the number has no floating point division.

import numpy as np
import math
import matplotlib.pyplot as plt

x = np.arange(-2., 2.)  #<-- use dots to define a float array
y = []

for i in range(-3, 3):
    y.append(math.exp(( x[i]**2/2 ) - x[i])-1)

y = np.array(y)
print x, y

# x = array([-2., -1.,  0.,  1.])    
# y = array([ 3.48168907, 0. , 0.39346934,  53.59815003, 3.48168907, 0.])

edited Sep 30, 2015 at 15:09

answered Sep 30, 2015 at 14:58

efirvida

4,8855 gold badges50 silver badges76 bronze badges

Comments

tzaman · Accepted Answer · 2015-09-30 15:12:22Z

0

^ isn't the exponentiation operator in Python, it's bitwise-XOR. You need to use ** instead. Also, if you're plotting functions over arrays, it's much cleaner to write your function directly and apply it via vectorize.

Also, if you're using Python2.7 you should add from __future__ import division to get true (floating point) division, otherwise x/2 will use integer division instead.

from __future__ import division
import math
import numpy as np    
import matplotlib.pyplot as plt

f = np.vectorize(lambda x: math.exp((x**2/2) - x) - 1)
x = np.arange(-2, 2)
y = f(x)

Finally, you need to pass x and y as separate arguments to plot, not put them in a list:

plt.plot(x, y)

edited Sep 30, 2015 at 15:12

answered Sep 30, 2015 at 14:56

tzaman

48k11 gold badges93 silver badges118 bronze badges

Collectives™ on Stack Overflow

Python not computing equation correctly

4 Answers 4

Details

References

Comments

4 Comments

Comments

Comments

Your Answer

Linked

Hot Network Questions

Collectives™ on Stack Overflow

4 Answers 4

Details

References

Comments

4 Comments

Comments

Comments

Your Answer

Sign up or log in

Post as a guest

Linked

Related