Python 中有一种特殊的机制,称为生成器函数。它返回一个对象,该对象记住最后一个状态,并使用前一次调用(迭代器)中的值执行函数体。
它在语法上与普通函数的不同之处仅在于使用yield
命令而不是return
. 您通常可以在需要迭代器的地方使用这样的生成器函数,即 for-loop、容器构造函数等。参见代码:
def f(x, c, n=5):
while n > 0:
yield x # returns x0 as first value
x = x * x + c # this value is to be returned next time
n -= 1 # decrement the sequence counter
# Using the generator function in a for loop.
for value in f(1/2, 1, 14): # I want 14 members of the sequence
print(value)
# Using the generator function to build a list of the values.
print('----------------------------------')
lst = list(f(1/2, 1, 10)) # 10 members wanted here
print(lst)
# Using the standard module called fractions for the same function.
print('==================================')
from fractions import Fraction as frac
# Using the generator function in a for loop.
for value in f(frac(1, 2), 1): # default number of loop used here
print(value)
# Using the generator function to build a list of the values.
print('----------------------------------')
lst = list(f(frac(1, 2), 1, 10)) # 10 members wanted here
print(lst)
# Generating Mandelbrot set values.
print('==================================')
# Using the generator function in a for loop.
for value in f(complex(0), complex(0, 1)): # default number of loop used here
print(value)
Python 不像 matlab 那样以符号方式计算表达式。但是,它具有标准模块 fractions,该模块具有 Fraction 类来表示分数。您也可以对该类型使用相同的生成器函数,因为它定义了自己的乘法和加法。由于 Python 整数的限制小于浮点数,因此使用分数可能会得到更大的结果(如果它有意义的话)。但是您可能想要生成一个 Mandelbrot 集,对吗?
它显示在我的控制台上(换行):
0.5
1.25
2.5625
7.56640625
58.25050354003906
3394.1211626681034
11520059.466871478
132711770120256.16
1.7612413928451715e+28
3.1019712438712e+56
9.62222559780384e+112
9.258722545503146e+225
inf
inf
----------------------------------
[0.5, 1.25, 2.5625, 7.56640625, 58.25050354003906, 3394.1211626681034, 11520059.
466871478, 132711770120256.16, 1.7612413928451715e+28, 3.1019712438712e+56]
==================================
1/2
5/4
41/16
1937/256
3817505/65536
----------------------------------
[Fraction(1, 2), Fraction(5, 4), Fraction(41, 16), Fraction(1937, 256), Fraction
(3817505, 65536), Fraction(14577639392321, 4294967296), Fraction(212507588699293
047863318657, 18446744073709551616), Fraction(4515947525478824258458249067737177
3490882293292495105, 340282366920938463463374607431768211456), Fraction(20393782
05287831607501825305820853979646214602081433287459323242821411496740800167480972
336912829578600961, 115792089237316195423570985008687907853269984665640564039457
584007913129639936), Fraction(41590634642030170391815210870941032988232016881852
69467060076200306147021769623813726880369383179868466442311933392597163786089664
61843166606956164602440721448188927878363156181727061624343416854647005907620761
7, 13407807929942597099574024998205846127479365820592393377723561443721764030073
546976801874298166903427690031858186486050853753882811946569946433649006084096)]
==================================
0j
1j
(-1+1j)
-1j
(-1+1j)