def 函數(shù)名(形參列表):
    #可執(zhí)行語(yǔ)句
    return 返回值

# 函數(shù)定義
def myfunc(arg1, arg2, arg3=None):
    ''' 
    This is a example for python documentation.
    這是一個(gè)為python函數(shù)提供文檔的例子。
    arg1: 第一個(gè)參數(shù)的說(shuō)明
    arg2: 第二個(gè)參數(shù)的說(shuō)明
    arg3: 第三個(gè)參數(shù)的說(shuō)明（這個(gè)參數(shù)有默認(rèn)值）
    v1, v2, v3: 返回值的說(shuō)明 
    '''
    v1 = arg1 + arg2
    v2 = arg1 * arg2
    if arg3 is None:
        v3 = arg1 + arg2
    else:
        v3 = arg1 + arg2 + arg3
    return v1, v2, v3
# 函數(shù)調(diào)用
v1, v2, v3 = myfunc(5, 3, arg3=4)
print(v1, v2, v3)    #8 15 12
# 使用arg3的默認(rèn)值調(diào)用函數(shù)
v1, v2, v3 = myfunc(5, 3)
print(v1, v2, v3)    #8 15 8
# 忽略一個(gè)返回值
v1, v2, _ = myfunc(5, 3)
print(v1, v2, v3)    #8 15 8
# 看看返回值是元組tuple，在返回的過(guò)程中被自動(dòng)解包
print(type(myfunc(5,3)))    #<class 'tuple'>

#舉一個(gè)小栗子，計(jì)算紙箱子的體積
def cube_volume(length, width, height = 0.25):
    '''
    計(jì)算紙箱子的體積(單位：m)
    length: 長(zhǎng)；    width: 寬
    height: 高（默認(rèn)參數(shù)0.25）
    v: 返回值，紙箱的體積，單位m**3
    '''
    if length <= 0:
        print('length must larger than 0!')
        return 0
    if width <= 0:
        print('width must larger than 0!')
        return 0
    if height <= 0:
        print('height must larger than 0!')
        return 0
    v = length*width*height
    print('length = %.2f; width = %.2f; height = %.2f; cube volume = %.2f' % \
          (length, width, height, v))
    return v
# 使用位置參數(shù)調(diào)用
v = cube_volume(1, 2, 3)
# 使用關(guān)鍵字參數(shù)調(diào)用
v = cube_volume(width = 1, height = 2, length = 3)
# 位置參數(shù)和關(guān)鍵字參數(shù)混用
v = cube_volume(1, height = 2, width = 3)
# 關(guān)鍵字參數(shù)在位置參數(shù)之前會(huì)報(bào)錯(cuò)
# v = cube_volume(width = 1, 2, 3)

# 對(duì)列表的乘方運(yùn)算
def pow_list(x, p):
    '''
    power of a list
    x: list
    p: power
    not return value
    '''
    for i in range(len(x)):
        x[i] **= p
    #這樣會(huì)輸出乘方后的值，但不會(huì)改變x列表里的值
    #因?yàn)樵谟?jì)算時(shí)將x中的值傳入了新的參數(shù)進(jìn)行計(jì)算
    #for i in x:
    #    i **= p
    #    print(i)
    #print(x)
x = [1,2,3,5,7,9,10,12]
pow_list(x,2)
print(x)
# 可見(jiàn)函數(shù)內(nèi)部對(duì)列表x中元素的更改，當(dāng)函數(shù)退出之后依然有效

# 隱藏的參數(shù)記錄器
def growing_list(x, y=[]):
    y.append(x)
    print(y)
# 重復(fù)執(zhí)行g(shù)rowing_list(‘a(chǎn)')會(huì)發(fā)生什么結(jié)果？
growing_list(2)         #[2]
growing_list('張三')    #[2, '張三']
growing_list(22333)     #[2, '張三', 22333]

# 不定個(gè)數(shù)的數(shù)字求和
def my_sum(*t):
    # 帶星號(hào)的輸入?yún)?shù)被當(dāng)作元組處理
    print(t, type(t))
    sum = 0
    for s in t:
        sum += s
    return sum
# 事實(shí)上該函數(shù)接受了不定個(gè)數(shù)的輸入?yún)?shù)
my_sum(1,2,3,4,2233)

# 不定個(gè)數(shù)的數(shù)字乘方后求和
def pow_sum(*t, p):
    # 帶星號(hào)的輸入?yún)?shù)被當(dāng)作元組處理
    print(t, type(t))
    sum = 0
    for s in t:
        sum += s**p
    return sum
# 最后一個(gè)參數(shù)p，需要指定關(guān)鍵字傳遞
pow_sum(1,2,3,4,2233,p=2)
# 如果不指定關(guān)鍵字傳遞呢？會(huì)報(bào)錯(cuò)
# pow_sum(1,2,3,4,2233,2)

# 不定個(gè)數(shù)的數(shù)字加權(quán)求和
# 權(quán)重隨著數(shù)字的個(gè)數(shù)而發(fā)生變化
def weighted_sum(x1,x2,*y):
    sum = 0
    n = len(y)
    weight = 1/3/n
    for i in y:
        sum += weight*i
    return sum+1/3*x1+1/3*x2
weighted_sum(1,2,3)
weighted_sum(1,2,3,22,44,55)
weighted_sum(1,2,3,4,5,6)

# 測(cè)試一星參數(shù)和兩星參數(shù)
def test_star(a, b, c, *onestar, **twostar):
    print('a = %d; b = %d; c = %d' % (a, b, c))
    print(onestar, type(onestar))
    print(twostar, type(twostar))
test_star(1, 2, 3, 4, 5, 6, s1 = 7, s2 = 8, s3 = 9)
# 換個(gè)順序呢？
# test_star(1, 2, 3, 4, 5, 6, s1 = 7, s2 = 8, s3 = 9, a = 10, b = 11, c = 12)
# 報(bào)錯(cuò)了，二星參數(shù)后面不能再傳遞關(guān)鍵字參數(shù)了（當(dāng)然位置參數(shù)也不行）

# 如果有默認(rèn)參數(shù)，要注意可能引起的bug
def test_star(a, b, c, p = 5, *onestar, **twostar):
    print('a = %d; b = %d; c = %d; p = %d' % (a, b, c, p))    #a = 1; b = 2; c = 3; p = 4
    print(onestar, type(onestar))            #(5, 6) <class 'tuple'>
    print(twostar, type(twostar))            #{'s1': 7, 's2': 8, 's3': 9} <class 'dict'>
# 會(huì)傳遞一個(gè)p=4進(jìn)去，而不是設(shè)想的，onestar=(4,5,6)
test_star(1, 2, 3, 4, 5, 6, s1 = 7, s2 = 8, s3 = 9)

# 炸參數(shù)例子
def zha(a,b,c):
    print(a,b,c)
# 炸元組
z = (1,2,3)            #1 2 3
zha(*z)
# 炸列表
z = [4,5,6]            #4 5 6
zha(*z)
# 炸字典
z = {'a':7,'b':8,'c':9}    #7 8 9
zha(**z)
# 炸字典
z = {'c':7,'a':8,'b':9}    #8 9 7
zha(**z)
# 如果炸開(kāi)后參數(shù)個(gè)數(shù)或Key不匹配，會(huì)報(bào)錯(cuò)
# z = {'c':7,'a':8}
# zha(**z)

# 傳遞數(shù)值類(lèi)型參數(shù)
# 在函數(shù)內(nèi)修改，在函數(shù)外面不受影響
def mod_para1(a,b):
    print('In mod_para1, before modification: a = %d; b = %d' % (a,b))    #a = 2; b = 8
    a *= 2
    b += 4
    print('In mod_para1, after modification: a = %d; b = %d' % (a,b))    #a = 4; b = 12
a = 2
b = 8
print('Out of mod_para1, before modification: a = %d; b = %d' % (a,b))    #a = 2; b = 8
mod_para1(a,b)
print('Out of mod_para1, after modification: a = %d; b = %d' % (a,b))    #a = 2; b = 8

# 列表通過(guò)函數(shù)傳參時(shí)，被改動(dòng)了數(shù)據(jù)
def mod_para2(x):
    print('In mod_para2, before modification: x = ' + str(x))
    for i in range(len(x)):
        x[i] *= 2
    print('In mod_para2, after modification: x = ' + str(x))
x = [i for i in range(10)]
print('Out of mod_para2, before modification: x = ' + str(x))
mod_para2(x)
print('Out of mod_para2, after modification: x = ' + str(x))
import copy
A = [1,2,3]; B = copy.copy(A)
mod_para2(B); print(A,B)

gv1 = 1
def test():
    # gv1=2
    print('在函數(shù)內(nèi)部訪問(wèn)全局變量：gv1 = %d' % gv1)    #1
    # gv1=2
test()
print('在函數(shù)外部訪問(wèn)全局變量：gv1 = %d' % gv1)    #1

# 訪問(wèn)被遮蔽的全局變量
gv1 = 1
def test():
    # 用globals函數(shù)訪問(wèn)被遮蔽的全局變量
    print('在函數(shù)內(nèi)部訪問(wèn)全局變量：gv1 = %d' % globals()['gv1'])
    gv1 = 2 
    print('在函數(shù)內(nèi)部訪問(wèn)修改后的全局變量：gv1 = %d' % gv1)
test()
print('在函數(shù)外部訪問(wèn)全局變量：gv1 = %d' % gv1) # 函數(shù)內(nèi)部修改的其實(shí)是同名局部變量，全局變量沒(méi)有被修改。

# 測(cè)試全局變量
gv1 = 1
def test():
    global gv1 #全局變量我來(lái)?yè)慰?
    print('在函數(shù)內(nèi)部訪問(wèn)全局變量：gv1 = %d' % gv1)    #1
    gv1+=1
test()
print('在函數(shù)外部訪問(wèn)全局變量：gv1 = %d' % gv1)    #2

# 利用局部函數(shù)實(shí)現(xiàn)多種平均值的切換
def mymean(x, mtype = 'arithmetic'):
    '''計(jì)算列表x的平均值，用mtype定義計(jì)算哪種平均值，默認(rèn)為算術(shù)平均值（arithmetic mean）    '''
    def arithmetic(x): 
        ''' 算術(shù)平均值（arithmetic mean)  '''
        m = sum(x)/len(x);    return m
    def geometric(x): 
        '''幾何平均值（geometric mean） '''
        p = 1.;  n = len(x)
        for i in range(n):      p *= x[i]
        m = p ** (1/n);       return m
    def harmonic(x): 
        ''' 調(diào)和平均值（harmonic mean) '''
        s = 0.;      n = len(x)
        for i in range(n):        s += 1/x[i]
        m = 1/(s/n);        return m
    if mtype == 'arithmetic':    return arithmetic
    elif mtype == 'geometric':    return geometric
    elif mtype == 'harmonic':     return harmonic
    else:        return arithmetic

# 局部函數(shù)內(nèi)的變量與函數(shù)內(nèi)的局部變量相沖突，這個(gè)程序會(huì)報(bào)錯(cuò)
def test1():
    fv = 1
    def test2():
        # print('局部函數(shù)內(nèi)打印上層函數(shù)中的局部變量：%d' % fv) # 會(huì)在這里報(bào)錯(cuò)
        fv = 2
        print('局部函數(shù)內(nèi)打印上層函數(shù)中的局部變量（更改后）：%d' % fv)    #2        
    test2()
    print('上層函數(shù)內(nèi)打印局部變量（更改后）：%d' % fv)    #1        
    return fv
print('上層函數(shù)外打印局部變量（更改后）：%d' % test1())    #1

# 局部函數(shù)內(nèi)的變量與函數(shù)內(nèi)的局部變量相沖突，應(yīng)該改成這樣就不報(bào)錯(cuò)了
def test1():
    fv = 1
    def test2():
        nonlocal fv # 用nonlocal聲明，把fv聲明為上一層函數(shù)的變量
        print('局部函數(shù)內(nèi)打印上層函數(shù)中的局部變量：%d' % fv)    #1
        fv = 2
        print('局部函數(shù)內(nèi)打印上層函數(shù)中的局部變量（更改后）：%d' % fv)    #2    
    test2()
    print('上層函數(shù)內(nèi)打印局部變量（更改后）：%d' % fv)    #2
    return fv
print('上層函數(shù)外打印局部變量（更改后）：%d' % test1())    #2

# 以第三章栗子中mymean函數(shù)為例
# 將函數(shù)賦值給變量f
f = mymean2('arithmetic')
# 打印出來(lái)看看
print(f)
# 測(cè)試一下
x = list(range(1,10))
m = f(x)
print(m)
# 也可以像上面的例子一樣，連起來(lái)寫(xiě)
print(mymean2('geometric')(x))

# 以第三章栗子中mymean函數(shù)為例
# 編寫(xiě)另一個(gè)程序，對(duì)列表中的數(shù)字進(jìn)行變換，變成均值為1的另一個(gè)列表
# 均值，可以是算術(shù)平均值、幾何平均值、調(diào)和平均值
def mynormalize(x, mtype):
    f = mymean(mtype)
    m = f(x)
    return [i/m for i in x]
x = list(range(1,10))
mtype = 'geometric'
print(mymean(mtype)(x))
print(mynormalize(x, mtype))

# 斐波那契數(shù)列（Fibonacci sequence）
# 在現(xiàn)代物理、準(zhǔn)晶體結(jié)構(gòu)、化學(xué)等領(lǐng)域，斐波納契數(shù)列都有直接的應(yīng)用
def Fibonacci(n):
    '''    Fibonacci sequence
    f(0)=1, f(1) = 1, f(n) = f(n-1)+f(n-2)    '''
    if n == 0 or n == 1:        return 1
    else:      return Fibonacci(n-1) + Fibonacci(n-2)
# 測(cè)試一下，注意n不要設(shè)的太大，python的遞歸效率是比較低的，太大會(huì)死機(jī)
print(Fibonacci(5))
# 斐波那契數(shù)列，前20位
print('Fibonacci sequence:')
for i in range(20):
    print('%d: %d' % (i,Fibonacci(i)))

# 一行中的hello world
greeting = lambda: print('Hello lambda!')
greeting()
# lambda表達(dá)式可以放在數(shù)組里面，批量運(yùn)行
L = [lambda x: x**2, lambda x: x**3, lambda x: x**4]
for p in L:
    print(p(3))

# 用lambda表達(dá)式代替局部函數(shù)
def mymean2(mtype = 'arithmetic'):
    '''    返回計(jì)算平均值所用的函數(shù)，用mtype定義計(jì)算哪種平均值，默認(rèn)為算術(shù)平均值（arithmetic mean）    '''
    # 由于lambda表達(dá)式只能寫(xiě)一行，這里用numpy和scipy的現(xiàn)成的函數(shù)來(lái)實(shí)現(xiàn)
    import numpy as np
    import scipy.stats as st
    a = np.array(x)
    if mtype == 'arithmetic': # 算術(shù)平均值（arithmetic mean）
        return lambda a: np.mean(a)
    elif mtype == 'geometric':# 幾何平均值（geometric mean）
        return lambda a: st.gmean(a)
    elif mtype == 'harmonic': # 調(diào)和平均值（harmonic mean）
        return lambda a: st.hmean(a)
    else:        # 默認(rèn)：算術(shù)平均值（arithmetic mean）
        return lambda a: np.mean(a)
x = list(range(1,10))
print(x)
print(mymean2('arithmetic')(x))
print(mymean2('geometric')(x))
print(mymean2('harmonic')(x))

# 判斷所有元素是否為T(mén)rue，相當(dāng)于多重的and
help(all)
print(all([3>2,6<9]))
# 任意一個(gè)元素是否為T(mén)rue，相當(dāng)于多重的or
help(any)
print(any([3>2,6<9]))
# 最大值和最小值
help(max)
help(min)
print(max([1,2,5,3]))
print(min([1,2,5,3]))
# 四舍五入(到小數(shù)點(diǎn)后第n位)
help(round)
print(round(3.1415926,3))
# 所有元素相加 
help(sum)
print(sum([1,2,3]))
print(sum([1,2,3],5))
# 乘冪
help(pow)
print(pow(6,2))
print(pow(6,2,5))
# 帶余除法
help(divmod)
print(divmod(6,2))
# 絕對(duì)值
help(abs)
print(abs(-2.56))