递归计算 DataFrame 值

Question

我正在尝试“递归”计算熊猫数据框的列值。

假设有两个不同天的数据，每个天有 10 个观测值，并且您想要计算一些变量 r，其中仅给出 r 的第一个值（在每一天），并且您想要计算剩余的 2*9 个条目，而每个后续值取决于 r 的前一个条目和一个额外的“同时期”变量“x”。

第一个问题是我想单独执行每一天的计算，即我想使用 pandas.groupby() 函数进行所有计算...但是当我尝试对数据进行子集化并使用 @987654325 @函数，我只得到“NaN”条目

data.groupby(data.index)['r'] =   ( (1+data.groupby(data.index)['x']*0.25) * (1+data.groupby(data.index)['r'].shift(1)))

对于我的第二种方法，我使用了一个 for 循环来遍历索引（日期）：

for i in range(2,21):
    data[data['rank'] == i]['r'] =  ( (1+data[data['rank'] == i]['x']*0.25) * (1+data[data['rank'] == i]['r'].shift(1))

但是，这对我不起作用。有没有办法在 DataFrames 上执行这样的计算？也许像滚动应用之类的东西？

数据：

df = pd.DataFrame({
  'rank' : [1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10],
  'x' : [0.00275,0.00285,0.0031,0.0036,0.0043,0.0052,0.0063,0.00755,0.00895,0.0105,0.0027,0.00285,0.0031,0.00355,0.00425,0.0051,0.00615,0.00735,0.00875,0.0103],
  'r' : [0.00158,'NaN','NaN','NaN','NaN','NaN','NaN','NaN','NaN','NaN',0.001485,'NaN','NaN','NaN','NaN','NaN','NaN','NaN','NaN','NaN']
  },index=['2014-01-02', '2014-01-02', '2014-01-02', '2014-01-02',
           '2014-01-02', '2014-01-02', '2014-01-02', '2014-01-02',
           '2014-01-02', '2014-01-02', '2014-01-03', '2014-01-03',
           '2014-01-03', '2014-01-03', '2014-01-03', '2014-01-03',
           '2014-01-03', '2014-01-03', '2014-01-03', '2014-01-03'])

Answer 1

要进行滚动申请，您可以使用pandas.groupby().apply()。在 apply 内部，您可以使用循环来进行每组的计算。内部循环也可以使用scipy.lfilter 完成，但我无法理解您所追求的确切公式，所以我只是跳过了那部分。

代码：

def rolling_apply(group):
    r = [group.r.iloc[0]]
    for x in group.x:
        r.append((1 + r[-1]) * (1 + x * 0.25))
    group.r = r[1:]
    return group

df['R'] = df.groupby(df.index).apply(rolling_apply).r

结果：

                   r  rank        x          R
2014-01-02   0.00158     1  0.00275   1.002269
2014-01-02       NaN     2  0.00285   2.003695
2014-01-02       NaN     3  0.00310   3.006023
2014-01-02       NaN     4  0.00360   4.009628
2014-01-02       NaN     5  0.00430   5.015014
2014-01-02       NaN     6  0.00520   6.022833
2014-01-02       NaN     7  0.00630   7.033894
2014-01-02       NaN     8  0.00755   8.049058
2014-01-02       NaN     9  0.00895   9.069306
2014-01-02       NaN    10  0.01050  10.095737
2014-01-03  0.001485     1  0.00270   1.002161
2014-01-03       NaN     2  0.00285   2.003588
2014-01-03       NaN     3  0.00310   3.005915
2014-01-03       NaN     4  0.00355   4.009471
2014-01-03       NaN     5  0.00425   5.014793
2014-01-03       NaN     6  0.00510   6.022462
2014-01-03       NaN     7  0.00615   7.033259
2014-01-03       NaN     8  0.00735   8.048020
2014-01-03       NaN     9  0.00875   9.067813
2014-01-03       NaN    10  0.01030  10.093737

测试数据：

df = pd.DataFrame({
    'rank': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
    'x': [0.00275, 0.00285, 0.0031, 0.0036, 0.0043, 0.0052, 0.0063, 0.00755,
          0.00895, 0.0105, 0.0027, 0.00285, 0.0031, 0.00355, 0.00425,
          0.0051, 0.00615, 0.00735, 0.00875, 0.0103],
    'r': [0.00158, 'NaN', 'NaN', 'NaN', 'NaN', 'NaN', 'NaN', 'NaN', 'NaN',
          'NaN', 0.001485, 'NaN', 'NaN', 'NaN', 'NaN', 'NaN', 'NaN', 'NaN',
          'NaN', 'NaN']
}, index=['2014-01-02', '2014-01-02', '2014-01-02', '2014-01-02',
          '2014-01-02', '2014-01-02', '2014-01-02', '2014-01-02',
          '2014-01-02', '2014-01-02', '2014-01-03', '2014-01-03',
          '2014-01-03', '2014-01-03', '2014-01-03', '2014-01-03',
          '2014-01-03', '2014-01-03', '2014-01-03', '2014-01-03'])

更新：

既然已知所需的实际递归方程，以下是 apply 函数的更新：

def rolling_apply(group):
    r = [group.r.iloc[0]]
    for x in group.x[:-1]:
        r.append((1 + r[-1]) * (1 + x * 0.25) - 1)
    group.r = r
    return group

df.r = df.groupby(df.index).apply(rolling_apply).r

Answer 2

Stephen Rauch 的回答非常有帮助。由于我正在寻找一列“r”，其中仅计算每天的连续值而初始值（0.00158，0.001485）保持不变，因此我将另外发布最终解决方案（以防万一有人遇到类似问题）。 在 Stephen Rauch 的解决方案中，R[0] 的值属于 r[1] 等。因此，除了 1 之外，必须移动所有“等级”的数据。

测试数据

df = pd.DataFrame({
'rank': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
'x': [0.00275, 0.00285, 0.0031, 0.0036, 0.0043, 0.0052, 0.0063, 0.00755,
      0.00895, 0.0105, 0.0027, 0.00285, 0.0031, 0.00355, 0.00425,
      0.0051, 0.00615, 0.00735, 0.00875, 0.0103],
'r': [0.00158, 'NaN', 'NaN', 'NaN', 'NaN', 'NaN', 'NaN', 'NaN', 'NaN',
      'NaN', 0.001485, 'NaN', 'NaN', 'NaN', 'NaN', 'NaN', 'NaN', 'NaN',
      'NaN', 'NaN'] }, index=['2014-01-02', '2014-01-02', '2014-01-02', '2014-01-02',
      '2014-01-02', '2014-01-02', '2014-01-02', '2014-01-02',
      '2014-01-02', '2014-01-02', '2014-01-03', '2014-01-03',
      '2014-01-03', '2014-01-03', '2014-01-03', '2014-01-03',
      '2014-01-03', '2014-01-03', '2014-01-03', '2014-01-03'])

代码

 def rolling_apply(group):
     r = [group.r.iloc[0]]
     for x in group.x:
         r.append((1 + r[-1]) * (1 + x * 0.25) -1)
     group.r = r[1:]
     return group

df['R'] = df.groupby(df.index).apply(rolling_apply).r

df['r'] = np.where(df['rank']==1,df['r'],df['R'].shift(1) )

df = df.drop('R',1)

结果

                     r  rank        x
2014-01-02     0.00158     1  0.00275
2014-01-02  0.00226859     2  0.00285
2014-01-02   0.0029827     3  0.00310
2014-01-02  0.00376001     4  0.00360
2014-01-02   0.0046634     5  0.00430
2014-01-02  0.00574341     6  0.00520
2014-01-02  0.00705088     7  0.00630
2014-01-02  0.00863698     8  0.00755
2014-01-02   0.0105408     9  0.00895
2014-01-02   0.0128019    10  0.01050
2014-01-03    0.001485     1  0.00270
2014-01-03    0.002161     2  0.00285
2014-01-03  0.00287504     3  0.00310
2014-01-03  0.00365227     4  0.00355
2014-01-03  0.00454301     5  0.00425
2014-01-03  0.00561034     6  0.00510
2014-01-03  0.00689249     7  0.00615
2014-01-03  0.00844059     8  0.00735
2014-01-03   0.0102936     9  0.00875
2014-01-03   0.0125036    10  0.01030