python 图中的大舍入误差

Question

I try to plot the following simple sequence

a_n=\frac{3^n+1}{7^n+8}

which should tend to 0, but the plot shows a weird effect for values of $n$ near 20....

I use the code

import numpy as np
import matplotlib.pyplot as plt

def f(n):
    return (3**n+1)/(7**n+8)

n=np.arange(0,25, 1)

plt.plot(n,f(n),'bo-')

On the other hand, computing numerically the above sequence one does not find such large values

for i in range(0,25):
    print([i,f(i)])

[0, 0.2222222222222222]
[1, 0.26666666666666666]
[2, 0.17543859649122806]
[3, 0.07977207977207977]
[4, 0.034039020340390205]
[5, 0.014510853404698185]
[6, 0.0062044757218015075]
[7, 0.0026567874970706124]
[8, 0.0011382857610720493]
[9, 0.00048778777316480816]
[10, 0.00020904485804220367]
[11, 8.958964415487241e-05]
[12, 3.8395417418579486e-05]
[13, 1.6455158259653074e-05]
[14, 7.05220773432529e-06]
[15, 3.022374322043928e-06]
[16, 1.295303220696569e-06]
[17, 5.551299431298911e-07]
[18, 2.3791283154177113e-07]
[19, 1.0196264191387531e-07]
[20, 4.3698275080881505e-08]
[21, 1.872783217393992e-08]
[22, 8.026213788319863e-09]
[23, 3.439805909206865e-09]
[24, 1.4742025325067883e-09]

Why is this happening?

Answer 1

The issue is not with matplotlib , but with the datatype of the numbers that arange is producing. You are not specifying the dtype , because in the docs for arange , it states that is inferred from the input. Your inputs are integers, so it must assume they are 32-bit integers since the dtype is unmodified so that when I check the type:

print(type(n[0]))
<class 'numpy.int32'>

If I change the dtype to single precision floats, we get the behavior you expect:

n = np.arange(0,25,1, dtype=np.float32)

print(type(n[0]))
<class 'numpy.float32'>

plt.plot(n,f(n),'bo-')

Alternatively, you could just put a period behind the 1 -> 1. to imply you want double-precision floats (even if the resulting array contains integer-esque numbers [0., 1., 2., ...])