Question

我正在尝试编写一个程序，以x _{n + 1} = x _n ² + c的形式为我迭代。我该怎么做？

例如，对于c = 1且x ₀ = 1/2

（1/2）² + 1 = 5/4，
（5/4）² + 1 = 25/16 + 1 = 41/16
......等等。

我的代码在这里不起作用：

def main():
   import math
   print("This program iterates a function of the form x^2 + c:")
   x=complex(input("Enter a seed value:"))
   c=complex(input("Enter a value for c"))

for i in range(50):
   f(0) = x*x + c
   f(i) = f(i-1)*f(i-1) + c
   print(f(i))
main()

Python不允许我像matlab一样使用f(0)或f(i)，还有什么替代方案？

Answer 1

Tabbing在python中至关重要，请尝试下面的代码。这是一个很长的镜头来猜测你的意图是什么，但它会让你更接近最终结果

def main(x):
    import math
    print("This program iterates a function of the form x^2 + c:")
    c = complex(input("Enter a value for c"))

    print "C : %s" % c

    f = [x * x + c]

    for i in range(1, 50):
        f.append(f[i - 1] * f[i - 1] + c)

    print f

main(2)

Answer 2

如果您对保留所有部分结果不感兴趣，可以这样迭代：

import math
print("This program iterates a function of the form x^2 + c:")
x = complex(input("Enter a seed value:"))
c = complex(input("Enter a value for c"))

f = x * x + c
for _ in range(50):
   f = f * f + c
   print(f)

Answer 3

让我们调用你的函数f：

def f(x, c):
    return x * x + c

然后在main()中你可以这样称呼它：

def main():
    n = complex(input("Enter a seed value: "))
    c = complex(input("Enter a value for c: "))

    print n
    for term in range(50):
        n = f(n, c)
        print n

每次迭代时，n都会重新分配给f的返回值，前值为n。

Answer 4

Python中有一种称为生成器函数的特殊机制。它返回一个记住最后一个状态的对象，并使用前一个调用的值（迭代器）执行函数体。

仅通过使用yield命令而不是return在语法上与正常功能不同。您通常可以在期望迭代器的位置使用这样的生成器函数，即for-loop，容器构造函数等。请参阅代码：

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不会像matlab那样以符号方式计算表达式。但是，它具有标准模块分数，其具有Fraction类来表示分数。您也可以为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整数的限制不如浮点数，因此使用分数可能会获得更大的结果（如果它完全有意义的话）。但你可能想要生成一个Mandelbrot集，对吗？

它显示在我的控制台上（包裹的线条）：

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)

Answer 5

美好的一天。

# x_(n+1) = x_(n)^2 + c

def f(n,c):
    a=0
    while a < n:
        a +=1
        yield a * a + c

现在你可以使用f作为生成器

if __name__ == '__main__':
    for element in f(100, 0):
        print element

Python：一个迭代函数

5 个答案: