为什么Numpy在矢量化之后也显得很慢？

Question

作为练习的一部分，我在Numpy中实现了一个多项式类。我还使用标准Python列表和循环创建了另一个类，我在下面添加了这个类。

class Polynomial: # Implemented with Numpy
  '''
  This class is implementing a polynomial.

  Instance variable --> coefficients which contains the coeff of the polynomial.

  Methods:
  __init__ initializes the class.
  __call__ returns value of the polynomial given value of x
  derivative takes derivative of the polynomial and returns the new coefficients.
  '''
  def __init__(self, coefficients):
    self.coefficients = coefficients

  def __call__(self, x):
    polynomial_value = 0
    X = np.ones(len(self.coefficients))
    X[1:] = x
    return np.cumprod(X) @ self.coefficients

  def derivative(self):
    n = len(self.coefficients)
    new_coeff = self.coefficients[1:] * np.cumsum(np.ones(n-1))
    self.coefficients = new_coeff
    return self.coefficients 

class Polynomial: # Implemented without Numpy
  def __init__(self, coefficients):
    self.coefficients = coefficients

  def __call__(self, x):
    polynomial_value = 0
    for i in range(len(self.coefficients)):
      polynomial_value += self.coefficients[i]*(x**i)
    return polynomial_value

  def derivative(self):
    n = len(self.coefficients)
    new_coeff=[]
    for i in range(1,n):                  # Note we are dropping a0 and thus we
      new_coeff.append(self.coefficients[i]*i)  # are starting from 1
    self.coefficients = new_coeff
    return self.coefficients 

我使用以下例程测试了这2段代码：

1. Numpy

%%timeit
import random
#Runtime on polynomial class
N = 10000
for i in range(1,N):
  coeff = np.random.randint(0, 100, size = 10)
  my_poly = Polynomial(coeff)
  x = random.randint(0,100)
  my_poly(x)

1. 标准Python列表&用于循环

%%timeit
import random
#Runtime on polynomial class
N = 10000
for i in range(1,N):
  coeff = random.sample(range(0, 100), 10)
  my_poly = Polynomial(coeff)
  x = random.randint(0,100)
  my_poly(x)

第一次实施时间(Numpy)为249 ms，第二次实施时间为153 ms。

为什么是这种情况？在定义类或测试类时，我是否错误地实现了矢量化？还是还发生了什么事？

Answer 1

这是因为你这样做的小方程，只有10个系数。我运行了100个系数的代码(即一个99度的方程)，而numpy的运行时间是250 ms，而Python列表的运行时间是8.23秒。希望这能消除你的疑虑