Python基础学习（五）：函数

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前言

一、Lambda函数

提示：本章介绍lambda函数，感觉用处与列表表达式重合

1.语法

lambda函数（匿名函数）的语法只包含一个语句：

lambda [arg1 [,arg2,.....argn]]:expression

2.常见用法

（1）将lambda函数赋值给一个变量，通过变量直接调用lambda函数

jisuan = lambda x, y: x+y
for i in range(5):
    print(jisuan(i, i+1))

（2）与map函数连用

result = list(map(lambda x: x ** 2, [1, 2, 3, 4, 5]))
print(result)

（3）与filter函数连用

newlist = filter(lambda x: x % 3 == 0, [1, 2, 3])
print(list(newlist))

3、例题

（1）与map函数连用

spells = ["protego", "accio", "expecto patronum", "legilimens"]
shout_spells_list = list(map(lambda x: x+'!!!', spells))
print(shout_spells_list)

二、函数

The following notation will be used throughout

• $Y$: Output
• $L$: Total labor units
• $K$: Physical capital

We write a production function $F$, that transforms labor ($L$) and capital ($K$) into output ($Y$) as

$$Y=F(K,L)=z{K}^{\alpha }{L}^{1-\alpha }$$

1.函数定义

def cobb_douglas(K, L):

    # Create alpha and z
    z = 1
    alpha = 0.33

    return z * K**alpha * L**(1 - alpha)

If, for any $K,L$, we multiply $K,L$ by a value $\gamma$
then

• If $\frac{Y_2}{Y_1}<\gamma$ then we say the production function has
  decreasing returns to scale.
• If $\frac{Y_2}{Y_1}=\gamma$ then we say the production function has
  constant returns to scale.
• If $\frac{Y_2}{Y_1}>\gamma$ then we say the production function has
  increasing returns to scale.

  def returns_to_scale(K, L, gamma):
    y1 = cobb_douglas(K, L)
    y2 = cobb_douglas(gamma*K, gamma*L)
    y_ratio = y2 / y1
    return y_ratio / gamma

2.函数注释

有了函数注释后，cobb_douglas?即可显示

def cobb_douglas(K, L):
    """
    Computes the production F(K, L) for a Cobb-Douglas production function

    Takes the form F(K, L) = z K^{\alpha} L^{1 - \alpha}

    We restrict z = 1 and alpha = 0.33 
    """
    return 1.0 * K**(0.33) * L**(1.0 - 0.33)