在没有库的python中给定y的x，找到x

Question

enter image description here对于我的练习薄，我需要编写一个函数，该函数在没有任何库函数的情况下为给定y值的函数（称为Maxwell_Boltzmann）找到x值。因此，我尝试定义一个函数（称为most_probable_speed），该函数首先查找Maxwell_Boltzmann的y值的最大值，然后查找为其x（在我的代码中定义为v）的最大值。我使用for和if循环尝试打印v，但是它并没有打印出达到最大值的参数v，但给了我整个矢量v。有人知道我如何打印参数v，为此y已到达？

我的代码是：

import numpy as np
import matplotlib.pyplot as plt
import scipy
import scipy.constants as cs

v= np.linspace(-100,10000,1000) #this are my x values


#this is my function, which prints y value in fonction of x
def Maxwell_Boltzmann(v, m, T):
      ''' calculate the Maxwell-Boltzmann  distribution
      for the speed of the chemical elements

      3 parameters: -the speed of the particle
              -its masse
              -its temperature'''
      y = np.sqrt(2/np.pi) * (m /( cs.k * T))**(3/2) * v**2 * np.exp(-m*v**2/(2 * cs.k * T)) 
      return y;




# this is the function which is suppose to find the x value given the y value
def most_probable_speed(v,m,T):
       '''determine the most probable speed of a given mass and temperature'''

       x = Maxwell_Boltzmann(v, m, T) #put the y values of Maxwel_B for all x in an array named x
       highest_probability = np.amax(x) #Return the maximum value of y


       # I want to print the value of v for whcih Maxwell_Boltzmann(v, m, T)= highest_probability
       for a in Maxwell_Boltzmann(v, m, T):
           if a == highest_probability:
               print(v)
           else:
               continue

return highest_probability;


m_oxy = 15.99 * cs.u 
most_probable_speed(v, m = m_oxy, T = 273)  

Answer 1

由于y的每个元素对应于同一索引中v的元素（这是您想要的x值），因此您可以使用enumerate为您提供每个值的索引并打印出相应的x比整个矢量：

def most_probable_speed(v,m,T):
       '''determine the most probable speed of a given mass and temperature'''

       x = Maxwell_Boltzmann(v, m, T) #put the y values of Maxwel_B for all x in an array named x
       highest_probability = np.amax(x) #Return the maximum value of y


       # I want to print the value of v for whcih Maxwell_Boltzmann(v, m, T)= highest_probability
       for idx, a in enumerate(Maxwell_Boltzmann(v, m, T)):
           if a == highest_probability:
               print(v[idx])
           else:
               continue