Python 使用for循环和if语句的根查找迭代

我正在使用python进行根查找迭代

我首先定义了F（x）

我还定义了dFdx

def dFdx(x):
    return -0.4+2*x/((1+x**2)**2)

下面是我的根查找代码

def Testing_Root(x, F, dFdx):
    # store the values of x_n in a list, xstore
    # first, make an initial list with an initial guess x_0
    xstore = [x]
    # calculate differences in each iteration and store in a list, difference
    # first, make an empty list
    difference = []
    print('n=0, x[0] =', x)
    for i in range(50):
        x = x - F(x)/dFdx(x)
        xstore.append(x)
    for j in range(50):
        d = xstore[j+1] - xstore[j]
        difference.append(d)
    for k in range(50):
        print('n=', k+1, 'x[', k+1, ']=', xstore[k+1], 'difference is', difference[k])
        for j in range(k, 50):
            if all(abs(difference[j]) < 0.000000000001):
                break
        break 
    return print('so the root is', round(x, 4), 'to 4dp')

---

在我的函数中，我想检查它是否收敛到根。另外，我不想打印所有的迭代。我希望它在某个点停止打印迭代，如果该点上所有k>=的差值小于0.000000000001。所以我在for循环中使用了if循环（范围（50）中的'for k）：if all（abs（difference[j]）三个简单的问题需要解决：

• all

  设计用于一个iterable（想想：“在列表上”）。通过将

  for

  循环置于

  all

  调用之外，您正在欺骗

  all

  的能力。相反，将感兴趣的整个列表传递给

  all

  并且根本不循环

---

• abs

  和

  三件简单的事情需要解决：
  
  
  all
  设计用于一个iterable（想想：“在列表上”）。通过将
  for
  循环置于
  all
  调用之外，您正在欺骗
  all
  的能力。相反，将感兴趣的整个列表传递给
  all
  并且根本不循环
  abs
  和
  
  def Testing_Root(x, F, dFdx):
      # store the values of x_n in a list, xstore
      # first, make an initial list with an initial guess x_0
      xstore = [x]
      # calculate differences in each iteration and store in a list, difference
      # first, make an empty list
      difference = []
      print('n=0, x[0] =', x)
      for i in range(50):
          x = x - F(x)/dFdx(x)
          xstore.append(x)
      for j in range(50):
          d = xstore[j+1] - xstore[j]
          difference.append(d)
      for k in range(50):
          print('n=', k+1, 'x[', k+1, ']=', xstore[k+1], 'difference is', difference[k])
          for j in range(k, 50):
              if all(abs(difference[j]) < 0.000000000001):
                  break
          break 
      return print('so the root is', round(x, 4), 'to 4dp')
  
  In [38]: Testing_Root(-0.1, F, dFdx)
  n=0, x[0] = -0.1
  n= 1 x[ 1 ]= 0.0004950332214986031 difference is 0.10049503322149861
  so the root is 0.0268 to 4dp
  
  for k in range(50):
      print('n=', k+1, 'x[', k+1, ']=', xstore[k+1], 'difference is', difference[k])
      if all([abs(n)<0.000000000001 for n in difference[k:]]):
          break
  
  n=0, x[0] = -0.1
  n= 1 x[ 1 ]= 0.0004950332214986031 difference is 0.10049503322149861
  n= 2 x[ 2 ]= 0.025061418498996398 difference is 0.024566385277497795
  n= 3 x[ 3 ]= 0.0267848938218123 difference is 0.001723475322815901
  n= 4 x[ 4 ]= 0.02679343238175541 difference is 8.538559943111618e-06
  n= 5 x[ 5 ]= 0.026793432591266996 difference is 2.0951158516413493e-10
  n= 6 x[ 6 ]= 0.026793432591266996 difference is 0.0
  so the root is 0.0268 to 4dp