How do I find the area under a function in matplotlib?
I am new to python and matplotlib library, I am trying to get the area under my function line in my plot. I have a variable a
and b
that moves a rectangle in my plot. I could probably use the original math to solve this problem, but I wanted to know if there was an easier way to achieve what I am trying to do with matplotlib.
My plot looks like this
I want to get the area of this zone
If there is also an easy way to color this area, I would love to hear it too.
Here's my code to display this graph:
plt.clf()
plt.draw()
plt.axis(xmin = 0, xmax = 80, ymin = 0, ymax = 5)
plt.plot(-np.cbrt(np.power(t, 2) - 16 * t + 63) +4)
currentAxis = plt.gca()
line = currentAxis.lines[0]
for x, y in zip(line.get_xdata(), line.get_ydata()):
if x == 0 or y == 0:
if b > a:
currentAxis.add_patch(patches.Rectangle(((a * 80 / 11), y), (b * 80 / 11) - (a * 80 / 11), 5, fill=False))
else:
currentAxis.add_patch(patches.Rectangle((-(b * 80 / 11) + 80, y), -(a * 80 / 11) + (b * 80 / 11), 5, fill=False))
plt.show()
Thanks for the help, sorry for the lack of embedded images.
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Scipy can calculate integrals for you , which seems to be the easiest way to get what you are looking for. I think your picture and your function are not consistent with each other. Here's what I get to create your copy / paste of your function:
t = pd.Series(range(0,80)) plt.plot(-np.cbrt(np.power(t, 2) - 16 * t + 63) +4)
In any case, how to get the integral, taking into account the function and the boundaries of integration.
import scipy.integrate as integrate
# define components for integral calculation
lower_bound = 22
upper_bound = 36
f = lambda t: -np.cbrt(np.power(t, 2) - 16 * t + 63) +4
# calculate integral
integral, error = integrate.quad(f, lower_bound, upper_bound)
print(integral)
-50.03118191324093
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Since Max Power will answer the integration part of your question, that's really good, I'll just be looking at the problem of drawing an area below / above the curve. You can use fill_between
:
import numpy as np
from matplotlib import pyplot as plt
def f(t):
return -np.cbrt(np.power(t, 2) - 16 * t + 63) +4
t = np.arange(0,80,1/40.)
plt.plot(t,f(t))
section = np.arange(22, 36, 1/20.)
plt.fill_between(section,f(section))
plt.axhline(0, color='k')
plt.axvline(0, color='k')
plt.show()
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