使用python解释结果 [英] Using python to interpret results

问题描述

我正在尝试解决以下问题.

I am trying to solve the following question.

这是我编写的代码

import numpy as np
import math
sum = 4
while sum <= 13:
    b = 10**(-sum)
    x = (math.sqrt(9+b)-3)/(b)
    print(x)
    sum +=1

给出以下结果

0.16666620370475727
0.1666666203714584
0.1666666618049817
0.1666666671340522
0.1666666804567285
0.1666666804567285
0.1666666804567285
0.1666666804567285
0.16653345369377348
0.16431300764452317

我不确定我的代码是否正确.当我在Wolfram的原始方程式中将 n 的13插入时，我得到了一些不同的东西.我认为随着距离13越来越近，它将接近0.1666666.

I am not sure if my code is correct or not. When I plug in 13 for n into the original equation in wolfram I am getting something different. I figured as it got closer to 13 it would approach 0.1666666.

我又如何从中制作图表?我想这是观察结果的最好方法.

Also how would I make a graph from this? I guess this would be the best way to observe my results.

推荐答案

下面是与情节一起的完整解决方案.说明: np.logspace(4，13，10)将 x 的值创建为10 ^(4)，10 ^(5)，10 ^(6)... 10 ^(13).您将其输出取反值，以得到所需的x点为10 ^(-4)，10 ^(-5)，10 ^(-6)... 10 ^(-13).然后，您可以遍历这些x值并求解方程式.将每个x的输出值保存在列表中，然后将其绘制出来.

Here is a complete solution together with the plot. Explanation: np.logspace(4, 13, 10) creates the values of x as 10^(4), 10^(5), 10^(6)... 10^(13). You take the inverse of its output to get your desired x-points as 10^(-4), 10^(-5), 10^(-6)... 10^(-13). You then loop over these x-values and solve for your equation. You save the output value for each x in a list and then plot it.

还有其他矢量化方法，而无需创建循环.但这应该可以帮助您入门.

There are other vectorized approaches without having to create a loop. But this should get you started.

import numpy as np
import math
import matplotlib.pyplot as plt
xmesh = 1./np.logspace(4, 13, 10)
result = []

for x in xmesh:
    elem = (math.sqrt(9+x)-3)/(x) # removed 'b' because xmesh is already inverse
    result.append(elem) # Adds each element to the list for later plotting

plt.semilogx(xmesh, result, '-bo') # Uses a logarithmic x-axis
plt.gca().invert_xaxis() # Inverts the x-axis because you want it so as per comments
plt.xlabel('1/x', fontsize=16)
plt.ylabel('y', fontsize=16)
plt.show()

输出

使用您的代码

以下是如何在无需大量修改的情况下使用您的代码使其工作

Following is how to make it work using your code without much modification

import numpy as np
import math
import matplotlib.pyplot as plt
sum = 4
xmesh = 1./np.logspace(4, 13, 10)
result = []
while sum <= 13:
    b = 10**(-sum)
    x = (math.sqrt(9+b)-3)/(b)
    result.append(x)
    sum +=1
plt.semilogx(xmesh, result, '-bo')    
plt.gca().invert_xaxis()
plt.xlabel('1/x', fontsize=16)
plt.ylabel('y', fontsize=16)
plt.show()

矢量化方法

import numpy as np

xmesh = 1./np.logspace(4, 13, 10)
result = (np.sqrt(9+xmesh)-3)/(xmesh) # No need to loop. Used `np.sqrt`

plt.semilogx(xmesh, result, '-bo')
plt.gca().invert_xaxis()

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