pandas层次化索引¶

1. 创建多层行索引¶

1) 隐式构造¶

最常见的方法是给DataFrame构造函数的index参数传递两个或更多的数组

Series也可以创建多层索引

In [4]:

s = Series(data = np.random.randint(0,150,size = 6),
           index =[['张三','张三','李四','李四','Michael','Michael'],['期中','期末','期中','期末','期中','期末']] )
s

Out[4]:

张三       期中     40
         期末     79
李四       期中     88
         期末    109
Michael  期中    146
         期末     51
dtype: int64

In [1]:

import numpy as np
import pandas as pd
from pandas import Series,DataFrame

In [3]:

df = DataFrame(data = np.random.randint(0,150,size = (6,3)),
               columns = ['Python','Java','PHP'],
              index = [['张三','张三','李四','李四','Michael','Michael'],['期中','期末','期中','期末','期中','期末']])
#隐式创建
df

Out[3]:

		Python	Java	PHP
张三	期中	87	65	129
张三	期末	147	31	120
李四	期中	38	31	74
李四	期末	38	86	99
Michael	期中	107	123	46
Michael	期末	21	149	72

2) 显示构造pd.MultiIndex¶

使用数组

In [5]:

df2 = DataFrame(data = np.random.randint(0,150,size = (6,4)),
               columns = ["Spring",'Summer','Autumn','Winter'],
               index = pd.MultiIndex.from_arrays([['张三','张三','李四','李四','Michael','Michael'],['期中','期末','期中','期末','期中','期末']]))

df2

Out[5]:

		Spring	Summer	Autumn	Winter
张三	期中	33	61	104	117
张三	期末	45	20	94	61
李四	期中	39	94	144	4
李四	期末	38	67	113	111
Michael	期中	33	5	39	135
Michael	期末	117	87	5	118

使用tuple

In [6]:

df3 = DataFrame(data = np.random.randint(0,150,size = (6,4)),
               columns = ["Spring",'Summer','Autumn','Winter'],
               index = pd.MultiIndex.from_tuples([('张三','期中'),('张三','期末'),('李四','期中'),('李四','期末'),('Sara','期中'),('Sara','期末')]))

df3

Out[6]:

		Spring	Summer	Autumn	Winter
张三	期中	31	57	124	34
张三	期末	134	20	60	55
李四	期中	33	70	128	47
李四	期末	9	55	101	117
Sara	期中	14	114	146	147
Sara	期末	108	114	73	86

使用product

最简单，推荐使用

In [8]:

df4 = DataFrame(data = np.random.randint(0,150,size = (12,4)),
               columns = ["Spring",'Summer','Autumn','Winter'],
               index = pd.MultiIndex.from_product([['张三','Sara','Lisa'],['middle','end'],list('AB')]))

df4

Out[8]:

			Spring	Summer	Autumn	Winter
张三	middle	A	61	58	64	105
	middle	B	118	121	8	81
	end	A	135	147	141	107
	end	B	97	29	31	56
Sara	middle	A	111	90	9	128
	middle	B	40	95	149	44
	end	A	9	8	97	0
	end	B	70	16	60	10
Lisa	middle	A	23	142	65	67
	middle	B	75	113	122	0
	end	A	126	15	138	28
	end	B	125	118	1	110

============================================

练习8：

创建一个DataFrame，表示出张三李四期中期末各科成绩

============================================

2. 多层列索引¶

除了行索引index，列索引columns也能用同样的方法创建多层索引

In [9]:

df5 = DataFrame(data = np.random.randint(0,150,size = (4,12)),
               columns = pd.MultiIndex.from_product([['张三','Sara','Lisa'],['middle','end'],list('AB')]),
               index = ["Spring",'Summer','Autumn','Winter'])

df5

Out[9]:

	张三				Sara				Lisa
	middle		end		middle		end		middle		end
	A	B	A	B	A	B	A	B	A	B	A	B
Spring	131	7	14	21	119	72	92	139	132	63	142	56
Summer	105	118	122	19	17	133	100	36	120	20	129	136
Autumn	100	121	32	53	109	57	104	125	96	68	76	89
Winter	73	16	54	42	74	48	129	25	56	39	28	113

3. 多层索引对象的索引与切片操作¶

1）Series的操作¶

【重要】对于Series来说，直接中括号[]与使用.loc()完全一样，因此，推荐使用中括号索引和切片。

In [10]:

Out[10]:

张三       期中     40
         期末     79
李四       期中     88
         期末    109
Michael  期中    146
         期末     51
dtype: int64

In [33]:

#多层索引进行切片时，有些汉字，或者英文，不识别，运行异常，并不是代码的问题，自身的bug

s.index = pd.MultiIndex.from_product([['张三','李四','静静'],['期中','期末']])
s

Out[33]:

张三  期中     40
    期末     79
李四  期中     88
    期末    109
静静  期中    146
    期末     51
dtype: int64

In [34]:

s['张三':'李四']

Out[34]:

张三  期中     40
    期末     79
李四  期中     88
    期末    109
dtype: int64

(1) 索引

In [13]:

s['张三']

Out[13]:

期中    40
期末    79
dtype: int64

In [12]:

s['张三','期中']

Out[12]:

In [14]:

#多层索引，有层的概念
s.loc['期中']

---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
/usr/local/lib/python3.5/dist-packages/pandas/core/indexing.py in _has_valid_type(self, key, axis)
   1433                 if not ax.contains(key):
-> 1434                     error()
   1435             except TypeError as e:

/usr/local/lib/python3.5/dist-packages/pandas/core/indexing.py in error()
   1428                 raise KeyError("the label [%s] is not in the [%s]" %
-> 1429                                (key, self.obj._get_axis_name(axis)))
   1430 

KeyError: 'the label [期中] is not in the [index]'

During handling of the above exception, another exception occurred:

KeyError                                  Traceback (most recent call last)
<ipython-input-14-52a5135a3116> in <module>()
----> 1 s.loc['期中']

/usr/local/lib/python3.5/dist-packages/pandas/core/indexing.py in __getitem__(self, key)
   1326         else:
   1327             key = com._apply_if_callable(key, self.obj)
-> 1328             return self._getitem_axis(key, axis=0)
   1329 
   1330     def _is_scalar_access(self, key):

/usr/local/lib/python3.5/dist-packages/pandas/core/indexing.py in _getitem_axis(self, key, axis)
   1549 
   1550         # fall thru to straight lookup
-> 1551         self._has_valid_type(key, axis)
   1552         return self._get_label(key, axis=axis)
   1553 

/usr/local/lib/python3.5/dist-packages/pandas/core/indexing.py in _has_valid_type(self, key, axis)
   1440                 raise
   1441             except:
-> 1442                 error()
   1443 
   1444         return True

/usr/local/lib/python3.5/dist-packages/pandas/core/indexing.py in error()
   1427                                     "key")
   1428                 raise KeyError("the label [%s] is not in the [%s]" %
-> 1429                                (key, self.obj._get_axis_name(axis)))
   1430 
   1431             try:

KeyError: 'the label [期中] is not in the [index]'

In [15]:

s.loc['李四','期末']

Out[15]:

(2) 切片

In [19]:

s.iloc[0:3]

Out[19]:

张三  期中    40
    期末    79
李四  期中    88
dtype: int64

In [20]:

s['张三':'Michael']

---------------------------------------------------------------------------
UnsortedIndexError                        Traceback (most recent call last)
<ipython-input-20-bc2dcaf84d2d> in <module>()
----> 1 s['张三':'Michael']

/usr/local/lib/python3.5/dist-packages/pandas/core/series.py in __getitem__(self, key)
    640             key = check_bool_indexer(self.index, key)
    641 
--> 642         return self._get_with(key)
    643 
    644     def _get_with(self, key):

/usr/local/lib/python3.5/dist-packages/pandas/core/series.py in _get_with(self, key)
    645         # other: fancy integer or otherwise
    646         if isinstance(key, slice):
--> 647             indexer = self.index._convert_slice_indexer(key, kind='getitem')
    648             return self._get_values(indexer)
    649         elif isinstance(key, ABCDataFrame):

/usr/local/lib/python3.5/dist-packages/pandas/core/indexes/base.py in _convert_slice_indexer(self, key, kind)
   1405         else:
   1406             try:
-> 1407                 indexer = self.slice_indexer(start, stop, step, kind=kind)
   1408             except Exception:
   1409                 if is_index_slice:

/usr/local/lib/python3.5/dist-packages/pandas/core/indexes/base.py in slice_indexer(self, start, end, step, kind)
   3348         """
   3349         start_slice, end_slice = self.slice_locs(start, end, step=step,
-> 3350                                                  kind=kind)
   3351 
   3352         # return a slice

/usr/local/lib/python3.5/dist-packages/pandas/core/indexes/multi.py in slice_locs(self, start, end, step, kind)
   1908         # This function adds nothing to its parent implementation (the magic
   1909         # happens in get_slice_bound method), but it adds meaningful doc.
-> 1910         return super(MultiIndex, self).slice_locs(start, end, step, kind=kind)
   1911 
   1912     def _partial_tup_index(self, tup, side='left'):

/usr/local/lib/python3.5/dist-packages/pandas/core/indexes/base.py in slice_locs(self, start, end, step, kind)
   3536         start_slice = None
   3537         if start is not None:
-> 3538             start_slice = self.get_slice_bound(start, 'left', kind)
   3539         if start_slice is None:
   3540             start_slice = 0

/usr/local/lib/python3.5/dist-packages/pandas/core/indexes/multi.py in get_slice_bound(self, label, side, kind)
   1879         if not isinstance(label, tuple):
   1880             label = label,
-> 1881         return self._partial_tup_index(label, side=side)
   1882 
   1883     def slice_locs(self, start=None, end=None, step=None, kind=None):

/usr/local/lib/python3.5/dist-packages/pandas/core/indexes/multi.py in _partial_tup_index(self, tup, side)
   1915                 'Key length (%d) was greater than MultiIndex'
   1916                 ' lexsort depth (%d)' %
-> 1917                 (len(tup), self.lexsort_depth))
   1918 
   1919         n = len(tup)

UnsortedIndexError: 'Key length (1) was greater than MultiIndex lexsort depth (0)'

In [21]:

s.loc['张三':'Michael']

---------------------------------------------------------------------------
UnsortedIndexError                        Traceback (most recent call last)
<ipython-input-21-c37724b918c9> in <module>()
----> 1 s.loc['张三':'Michael']

/usr/local/lib/python3.5/dist-packages/pandas/core/indexing.py in __getitem__(self, key)
   1326         else:
   1327             key = com._apply_if_callable(key, self.obj)
-> 1328             return self._getitem_axis(key, axis=0)
   1329 
   1330     def _is_scalar_access(self, key):

/usr/local/lib/python3.5/dist-packages/pandas/core/indexing.py in _getitem_axis(self, key, axis)
   1504         if isinstance(key, slice):
   1505             self._has_valid_type(key, axis)
-> 1506             return self._get_slice_axis(key, axis=axis)
   1507         elif is_bool_indexer(key):
   1508             return self._getbool_axis(key, axis=axis)

/usr/local/lib/python3.5/dist-packages/pandas/core/indexing.py in _get_slice_axis(self, slice_obj, axis)
   1354         labels = obj._get_axis(axis)
   1355         indexer = labels.slice_indexer(slice_obj.start, slice_obj.stop,
-> 1356                                        slice_obj.step, kind=self.name)
   1357 
   1358         if isinstance(indexer, slice):

/usr/local/lib/python3.5/dist-packages/pandas/core/indexes/base.py in slice_indexer(self, start, end, step, kind)
   3348         """
   3349         start_slice, end_slice = self.slice_locs(start, end, step=step,
-> 3350                                                  kind=kind)
   3351 
   3352         # return a slice

/usr/local/lib/python3.5/dist-packages/pandas/core/indexes/multi.py in slice_locs(self, start, end, step, kind)
   1908         # This function adds nothing to its parent implementation (the magic
   1909         # happens in get_slice_bound method), but it adds meaningful doc.
-> 1910         return super(MultiIndex, self).slice_locs(start, end, step, kind=kind)
   1911 
   1912     def _partial_tup_index(self, tup, side='left'):

/usr/local/lib/python3.5/dist-packages/pandas/core/indexes/base.py in slice_locs(self, start, end, step, kind)
   3536         start_slice = None
   3537         if start is not None:
-> 3538             start_slice = self.get_slice_bound(start, 'left', kind)
   3539         if start_slice is None:
   3540             start_slice = 0

/usr/local/lib/python3.5/dist-packages/pandas/core/indexes/multi.py in get_slice_bound(self, label, side, kind)
   1879         if not isinstance(label, tuple):
   1880             label = label,
-> 1881         return self._partial_tup_index(label, side=side)
   1882 
   1883     def slice_locs(self, start=None, end=None, step=None, kind=None):

/usr/local/lib/python3.5/dist-packages/pandas/core/indexes/multi.py in _partial_tup_index(self, tup, side)
   1915                 'Key length (%d) was greater than MultiIndex'
   1916                 ' lexsort depth (%d)' %
-> 1917                 (len(tup), self.lexsort_depth))
   1918 
   1919         n = len(tup)

UnsortedIndexError: 'Key length (1) was greater than MultiIndex lexsort depth (0)'

In [23]:

s2 = Series(data = np.random.randint(0,150,size = 6),index = pd.MultiIndex.from_product([list('ABC'),['e','f']]))
s2

Out[23]:

A  e     46
   f     93
B  e     76
   f     77
C  e     61
   f    125
dtype: int64

In [24]:

s2['A':'C']

Out[24]:

A  e     46
   f     93
B  e     76
   f     77
C  e     61
   f    125
dtype: int64

In [25]:

s2.loc['A':'B']

Out[25]:

A  e    46
   f    93
B  e    76
   f    77
dtype: int64

2）DataFrame的操作¶

(1) 可以直接使用列名称来进行列索引

In [36]:

df3

Out[36]:

		Spring	Summer	Autumn	Winter
张三	期中	31	57	124	34
张三	期末	134	20	60	55
李四	期中	33	70	128	47
李四	期末	9	55	101	117
Sara	期中	14	114	146	147
Sara	期末	108	114	73	86

In [41]:

df3['Spring']['张三','期中']

Out[41]:

In [42]:

#DataFrame多层索引和之前索引类似
#df [] 代表着列索引
df3['Spring','李四']

---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
/usr/local/lib/python3.5/dist-packages/pandas/core/indexes/base.py in get_loc(self, key, method, tolerance)
   2441             try:
-> 2442                 return self._engine.get_loc(key)
   2443             except KeyError:

pandas/_libs/index.pyx in pandas._libs.index.IndexEngine.get_loc (pandas/_libs/index.c:5280)()

pandas/_libs/index.pyx in pandas._libs.index.IndexEngine.get_loc (pandas/_libs/index.c:5126)()

pandas/_libs/hashtable_class_helper.pxi in pandas._libs.hashtable.PyObjectHashTable.get_item (pandas/_libs/hashtable.c:20523)()

pandas/_libs/hashtable_class_helper.pxi in pandas._libs.hashtable.PyObjectHashTable.get_item (pandas/_libs/hashtable.c:20477)()

KeyError: ('Spring', '李四')

During handling of the above exception, another exception occurred:

KeyError                                  Traceback (most recent call last)
<ipython-input-42-fa2185c7b00c> in <module>()
----> 1 df3['Spring','李四']

/usr/local/lib/python3.5/dist-packages/pandas/core/frame.py in __getitem__(self, key)
   1962             return self._getitem_multilevel(key)
   1963         else:
-> 1964             return self._getitem_column(key)
   1965 
   1966     def _getitem_column(self, key):

/usr/local/lib/python3.5/dist-packages/pandas/core/frame.py in _getitem_column(self, key)
   1969         # get column
   1970         if self.columns.is_unique:
-> 1971             return self._get_item_cache(key)
   1972 
   1973         # duplicate columns & possible reduce dimensionality

/usr/local/lib/python3.5/dist-packages/pandas/core/generic.py in _get_item_cache(self, item)
   1643         res = cache.get(item)
   1644         if res is None:
-> 1645             values = self._data.get(item)
   1646             res = self._box_item_values(item, values)
   1647             cache[item] = res

/usr/local/lib/python3.5/dist-packages/pandas/core/internals.py in get(self, item, fastpath)
   3588 
   3589             if not isnull(item):
-> 3590                 loc = self.items.get_loc(item)
   3591             else:
   3592                 indexer = np.arange(len(self.items))[isnull(self.items)]

/usr/local/lib/python3.5/dist-packages/pandas/core/indexes/base.py in get_loc(self, key, method, tolerance)
   2442                 return self._engine.get_loc(key)
   2443             except KeyError:
-> 2444                 return self._engine.get_loc(self._maybe_cast_indexer(key))
   2445 
   2446         indexer = self.get_indexer([key], method=method, tolerance=tolerance)

pandas/_libs/index.pyx in pandas._libs.index.IndexEngine.get_loc (pandas/_libs/index.c:5280)()

pandas/_libs/index.pyx in pandas._libs.index.IndexEngine.get_loc (pandas/_libs/index.c:5126)()

pandas/_libs/hashtable_class_helper.pxi in pandas._libs.hashtable.PyObjectHashTable.get_item (pandas/_libs/hashtable.c:20523)()

pandas/_libs/hashtable_class_helper.pxi in pandas._libs.hashtable.PyObjectHashTable.get_item (pandas/_libs/hashtable.c:20477)()

KeyError: ('Spring', '李四')

In [44]:

df3.index = pd.MultiIndex.from_product([list('ABC'),list('ab')])
df3

Out[44]:

		Spring	Summer	Autumn	Winter
A	a	31	57	124	34
A	b	134	20	60	55
B	a	33	70	128	47
B	b	9	55	101	117
C	a	14	114	146	147
C	b	108	114	73	86

In [45]:

#使用切片
df3['A':'B']

Out[45]:

		Spring	Summer	Autumn	Winter
A	a	31	57	124	34
A	b	134	20	60	55
B	a	33	70	128	47
B	b	9	55	101	117

(2) 使用行索引需要用loc()等函数

【极其重要】推荐使用loc()函数

注意在对行索引的时候，若一级行索引还有多个，对二级行索引会遇到问题！也就是说，无法直接对二级索引进行索引，必须让二级索引变成一级索引后才能对其进行索引！

In [46]:

df3.loc['A']

Out[46]:

	Spring	Summer	Autumn	Winter
a	31	57	124	34
b	134	20	60	55

In [47]:

df3.loc['B','a']

Out[47]:

Spring     33
Summer     70
Autumn    128
Winter     47
Name: (B, a), dtype: int64

In [51]:

df3.loc['a']

---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
/usr/local/lib/python3.5/dist-packages/pandas/core/indexing.py in _has_valid_type(self, key, axis)
   1433                 if not ax.contains(key):
-> 1434                     error()
   1435             except TypeError as e:

/usr/local/lib/python3.5/dist-packages/pandas/core/indexing.py in error()
   1428                 raise KeyError("the label [%s] is not in the [%s]" %
-> 1429                                (key, self.obj._get_axis_name(axis)))
   1430 

KeyError: 'the label [a] is not in the [index]'

During handling of the above exception, another exception occurred:

KeyError                                  Traceback (most recent call last)
<ipython-input-51-178fc9e30662> in <module>()
----> 1 df3.loc['a']

/usr/local/lib/python3.5/dist-packages/pandas/core/indexing.py in __getitem__(self, key)
   1326         else:
   1327             key = com._apply_if_callable(key, self.obj)
-> 1328             return self._getitem_axis(key, axis=0)
   1329 
   1330     def _is_scalar_access(self, key):

/usr/local/lib/python3.5/dist-packages/pandas/core/indexing.py in _getitem_axis(self, key, axis)
   1549 
   1550         # fall thru to straight lookup
-> 1551         self._has_valid_type(key, axis)
   1552         return self._get_label(key, axis=axis)
   1553 

/usr/local/lib/python3.5/dist-packages/pandas/core/indexing.py in _has_valid_type(self, key, axis)
   1440                 raise
   1441             except:
-> 1442                 error()
   1443 
   1444         return True

/usr/local/lib/python3.5/dist-packages/pandas/core/indexing.py in error()
   1427                                     "key")
   1428                 raise KeyError("the label [%s] is not in the [%s]" %
-> 1429                                (key, self.obj._get_axis_name(axis)))
   1430 
   1431             try:

KeyError: 'the label [a] is not in the [index]'

In [50]:

df3.loc[['A','B']]

Out[50]:

		Spring	Summer	Autumn	Winter
A	a	31	57	124	34
A	b	134	20	60	55
B	a	33	70	128	47
B	b	9	55	101	117

In [ ]:

In [52]:

df3.loc['A':'B']

Out[52]:

		Spring	Summer	Autumn	Winter
A	a	31	57	124	34
A	b	134	20	60	55
B	a	33	70	128	47
B	b	9	55	101	117

In [54]:

df3.iloc[0:3]

Out[54]:

		Spring	Summer	Autumn	Winter
A	a	31	57	124	34
A	b	134	20	60	55
B	a	33	70	128	47

============================================

练习9：

分析比较Series和DataFrame各种索引的方式，熟练掌握.loc()方法
假设张三再一次在期中考试的时候因为特殊原因放弃英语考试，如何实现？

============================================

4. 索引的堆（stack）¶

stack()
unstack()

小技巧】使用stack()的时候，level等于哪一个，哪一个就消失，出现在行里。

In [55]:

df5

Out[55]:

	张三				Sara				Lisa
	middle		end		middle		end		middle		end
	A	B	A	B	A	B	A	B	A	B	A	B
Spring	131	7	14	21	119	72	92	139	132	63	142	56
Summer	105	118	122	19	17	133	100	36	120	20	129	136
Autumn	100	121	32	53	109	57	104	125	96	68	76	89
Winter	73	16	54	42	74	48	129	25	56	39	28	113

In [58]:

df5.stack(level = 0)

Out[58]:

		end		middle
		A	B	A	B
Spring	Lisa	142	56	132	63
	Sara	92	139	119	72
	张三	14	21	131	7
Summer	Lisa	129	136	120	20
	Sara	100	36	17	133
	张三	122	19	105	118
Autumn	Lisa	76	89	96	68
	Sara	104	125	109	57
	张三	32	53	100	121
Winter	Lisa	28	113	56	39
	Sara	129	25	74	48
	张三	54	42	73	16

In [61]:

df4.unstack(level=1)

Out[61]:

		Spring		Summer		Autumn		Winter
		end	middle	end	middle	end	middle	end	middle
Lisa	A	126	23	15	142	138	65	28	67
Lisa	B	125	75	118	113	1	122	110	0
Sara	A	9	111	8	90	97	9	0	128
Sara	B	70	40	16	95	60	149	10	44
张三	A	135	61	147	58	141	64	107	105
张三	B	97	118	29	121	31	8	56	81

【小技巧】使用unstack()的时候，level等于哪一个，哪一个就消失，出现在列里。

============================================

练习10：

使用unstack()将ddd变为两行，分别为期中期末
使用unstack()将ddd变为四行，分别为四个科目

============================================

5. 聚合操作¶

【注意】

需要指定axis
【小技巧】和unstack()相反，聚合的时候，axis等于哪一个，哪一个就会进行计算。

所谓的聚合操作：平均数，方差，最大值，最小值……

In [64]:

df3

Out[64]:

		Spring	Summer	Autumn	Winter
A	a	31	57	124	34
A	b	134	20	60	55
B	a	33	70	128	47
B	b	9	55	101	117
C	a	14	114	146	147
C	b	108	114	73	86

In [67]:

df3.mean(axis = 'columns')

Out[67]:

A  a     61.50
   b     67.25
B  a     69.50
   b     70.50
C  a    105.25
   b     95.25
dtype: float64

In [69]:

df3

Out[69]:

		Spring	Summer	Autumn	Winter
A	a	31	57	124	34
A	b	134	20	60	55
B	a	33	70	128	47
B	b	9	55	101	117
C	a	14	114	146	147
C	b	108	114	73	86

In [68]:

#数据离散的程度，
df3.std()

Out[68]:

Spring    52.738664
Summer    36.740532
Autumn    33.571814
Winter    44.086279
dtype: float64

In [ ]:

============================================

练习11：

计算各个科目期中期末平均成绩
计算各科目张三李四的最高分

============================================

		Spring	Summer	Autumn	Winter
A	a	31	57	124	34
A	b	134	20	60	55
B	a	33	70	128	47
B	b	9	55	101	117
C	a	14	114	146	147
C	b	108	114	73	86

		Spring	Summer	Autumn	Winter
A	a	31	57	124	34
A	b	134	20	60	55
B	a	33	70	128	47
B	b	9	55	101	117
C	a	14	114	146	147
C	b	108	114	73	86

		Spring	Summer	Autumn	Winter
A	a	31	57	124	34
A	b	134	20	60	55
B	a	33	70	128	47
B	b	9	55	101	117
C	a	14	114	146	147
C	b	108	114	73	86

		Spring	Summer	Autumn	Winter
A	a	31	57	124	34
A	b	134	20	60	55
B	a	33	70	128	47
B	b	9	55	101	117
C	a	14	114	146	147
C	b	108	114	73	86

		Spring	Summer	Autumn	Winter
A	a	31	57	124	34
A	b	134	20	60	55
B	a	33	70	128	47
B	b	9	55	101	117
C	a	14	114	146	147
C	b	108	114	73	86

		Spring	Summer	Autumn	Winter
A	a	31	57	124	34
A	b	134	20	60	55
B	a	33	70	128	47
B	b	9	55	101	117
C	a	14	114	146	147
C	b	108	114	73	86

		Spring	Summer	Autumn	Winter
A	a	31	57	124	34
A	b	134	20	60	55
B	a	33	70	128	47
B	b	9	55	101	117
C	a	14	114	146	147
C	b	108	114	73	86

		Spring	Summer	Autumn	Winter
A	a	31	57	124	34
A	b	134	20	60	55
B	a	33	70	128	47
B	b	9	55	101	117
C	a	14	114	146	147
C	b	108	114	73	86

		Spring	Summer	Autumn	Winter
A	a	31	57	124	34
A	b	134	20	60	55
B	a	33	70	128	47
B	b	9	55	101	117
C	a	14	114	146	147
C	b	108	114	73	86