在另一个函数中编写 lambda 函数

Question

我有一个函数，area_approximator()，它计算图形下方的面积。我希望用户定义一个函数（例如，f = 2*x），然后定义限制（a，b），以及函数将计算的梯形数量，N。函数area_approximator（）应该然后计算用户定义的函数追踪的总面积。

目前，我已经能够通过使用用户输入来使area_approximator()工作，以允许用户定义函数f。

def area_approximator(a, b, N, f):

    # The width of each trapezium, w
    w = abs((b - a) / N)

    # A list containing the heights, or y values, of each trapezium's left and right sides, is created
    heights = np.linspace(a, b, N+1)
    realheights = [f(h) for h in heights]

    # The total area is found by summing the area of of all trapeziums
    area = 0
    for i in range(N):
        area += 0.5 * (realheights[i] + realheights[i+1]) * w

    return area

area_approximator(a, b, N, f)

function = input('Define the function for x: ')
f = lambda x: eval(function)

但是，我希望 area_approximator() 无需用户输入即可工作。我的尝试如下。

def area_approximator(a, b, N, f):

    g = lambda x: eval(f)

    # The width of each trapezium, w
    w = abs((b - a) / N)

    # A list containing the heights, or y values, of each trapezium's left and right sides, is created
    heights = np.linspace(a, b, N+1)
    realheights = [g(h) for h in heights]

    # The total area is found by summing the area of of all trapeziums
    area = 0
    for i in range(N):
        area += 0.5 * (realheights[i] + realheights[i+1]) * w

    return area

area_approximator(a, b, N, f)

但是，当我尝试使用它时，它会为我使用的任何 f 值给出一个 NameError （例如 f = 5*x）

Answer 1

您应该将函数直接传递给 g，而不使用

eval()

。

试试这个：

def area_approximator(a, b, N, f):

# The width of each trapezium, w
w = abs((b - a) / N)

# A list containing the heights, or y values, of each trapezium's left and right sides, is created
heights = np.linspace(a, b, N+1)
realheights = [f(h) for h in heights]

# The total area is found by summing the area of all trapeziums
area = 0
for i in range(N):
    area += 0.5 * (realheights[i] + realheights[i+1]) * w

return area

# Example usage:

import numpy as np

f = lambda x: 2 * x  # Example function: f(x) = 2x

# Define limits and number of trapeziums
a = 0
b = 1
N = 100

# Calculate the area using the defined function
result = area_approximator(a, b, N, f)
print("Approximated area:", result)

输出：

Approximated Area: 1.0