随着时间的推移将多维多索引数据帧与单索引数据帧相乘

Question

我是 Python 新手，正在寻求帮助以随着时间的推移将 2 个数据帧相乘。任何帮助理解错误将不胜感激。

第一个数据帧（cov）

Date                                 NoDur         Durbl           Manuf
2018-12-27     NoDur                 0.000109      0.000112        0.000118
               Durbl                 0.000112      0.000339        0.000238
               Manuf                 0.000118      0.000238        0.000246
2018-12-28     NoDur                 0.000109      0.000113        0.000117
               Durbl                 0.000113      0.000339        0.000239
               Manuf                 0.000117      0.000239        0.000242
2018-12-31     NoDur                 0.000109      0.000113        0.000118
               Durbl                 0.000113      0.000339        0.000239
               Manuf                 0.000118      0.000239        0.000245

第二个数据帧（w）

Date           NoDur         Durbl           Manuf
2018-12-27     -69.190732    -96.316224      -324.058486    
2018-12-28     -113.831750   30.426696       -410.055587
2018-12-31     -101.365016   -16.613136      -362.232014

代码：

std = np.dot(np.transpose(w) , np.matmul(cov , w)) 

错误：

ValueError: matmul: Input operand 1 has a mismatch in its core dimension 0, with gufunc signature (n?,k),(k,m?)->(n?,m?) (size 12361 is different from 10)

我只展示了数据框中的小片段。原始 cov 数据帧为 123610 行 × 10 列，w 数据帧为 12361 行 × 10 列。

预期输出：

Date           
2018-12-27     44.45574103083
2018-12-28     46.593367859
2018-12-31     45.282932300

提前非常感谢！！

Answer 1

我认为您可以在'Date' 级别上使用groupby，然后将w 中与组中日期对应的权重相乘：

cov.groupby(level='Date').apply(lambda g: w.loc[g.name].dot(g.values@(w.loc[g.name])))

由于您的数据确实可以更好地由 3 维数组表示，您还可以避免 apply 中组的隐式循环并使用 np.einsum：

reshaped = cov.values.reshape(cov.index.levels[0].nunique(), cov.index.levels[1].nunique(), cov.shape[-1])
np.einsum('ik,ik->i', w.values, np.einsum('ijk,ik->ij', reshaped, w.values))

在性能方面，第二种解决方案看起来更好：

%timeit cov.groupby(level='Date').apply(lambda g: w.loc[g.name].dot(g.values@(w.loc[g.name])))
4.74 ms ± 614 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

%timeit np.einsum('ik,ik->i', w.values, np.einsum('ijk,ik->ij', reshaped, w.values))
35.6 µs ± 5.19 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)

数据：

cov = pd.DataFrame.from_dict({'NoDur': {('2018-12-27', 'NoDur'): 0.000109,
  ('2018-12-27', 'Durbl'): 0.000112,
  ('2018-12-27', 'Manuf'): 0.000118,
  ('2018-12-28', 'NoDur'): 0.000109,
  ('2018-12-28', 'Durbl'): 0.000113,
  ('2018-12-28', 'Manuf'): 0.000117,
  ('2018-12-31', 'NoDur'): 0.000109,
  ('2018-12-31', 'Durbl'): 0.000113,
  ('2018-12-31', 'Manuf'): 0.000118},
 'Durbl': {('2018-12-27', 'NoDur'): 0.000112,
  ('2018-12-27', 'Durbl'): 0.000339,
  ('2018-12-27', 'Manuf'): 0.000238,
  ('2018-12-28', 'NoDur'): 0.000113,
  ('2018-12-28', 'Durbl'): 0.000339,
  ('2018-12-28', 'Manuf'): 0.000239,
  ('2018-12-31', 'NoDur'): 0.000113,
  ('2018-12-31', 'Durbl'): 0.000339,
  ('2018-12-31', 'Manuf'): 0.000239},
 'Manuf': {('2018-12-27', 'NoDur'): 0.000118,
  ('2018-12-27', 'Durbl'): 0.000238,
  ('2018-12-27', 'Manuf'): 0.000246,
  ('2018-12-28', 'NoDur'): 0.000117,
  ('2018-12-28', 'Durbl'): 0.000239,
  ('2018-12-28', 'Manuf'): 0.000242,
  ('2018-12-31', 'NoDur'): 0.000118,
  ('2018-12-31', 'Durbl'): 0.000239,
  ('2018-12-31', 'Manuf'): 0.000245}})

 w = pd.DataFrame.from_dict({'NoDur': {'2018-12-27': -69.190732,
  '2018-12-28': -113.83175,
  '2018-12-31': -101.365016},
 'Durbl': {'2018-12-27': -96.316224,
  '2018-12-28': 30.426696,
  '2018-12-31': -16.613136},
 'Manuf': {'2018-12-27': -324.058486,
  '2018-12-28': -410.055587,
  '2018-12-31': -362.232014}})