入门级计算
1、算数平均值
#样本：
S = [s1, s2, s3, …, sn]
#算术平均值：
m = (s1 + s2 + s3 + … + sn)/n
Numpy中的写法
m = numpy.mean(样本数组)
2、加权平均值
#样本：
S = [s1, s2, s3, …, sn]
#权重：
W = [w1, w2, w3, …, wn]
#加权平均值：
a = (s1w1 + s2w2 + s3w3 + … + snwn)/(w1 + w2 + w3 + … + wn)
3、Numpy中的格式
首先是数据源：需要求加权平均值的数据列表和对应的权值列表
elements = []
weights = []
使用numpy直接求：
import numpy as np
np.average(elements, weights=weights)
附纯python写法：
# 不使用numpy写法1
round(sum([elements[i]*weights[i] for i in range(n)])/sum(weights), 1)
# 不使用numpy写法2
round(sum([j[0]*j[1] for j in zip(elements, weights)])/sum(weights), 1)
定义函数计算一个序列的平均值的方法
def average(seq, total=0.0):
num = 0
for item in seq:
total += item
num += 1
return total / num
如果序列是数组或者元祖可以简单使用下面的代码
def average(seq):
return float(sum(seq)) / len(seq)
3、最大值与最小值
1、最大值、最小值
max：获取一个数组中最大元素
min：获取一个数组中最小元素
2、比较出最值数组
maximum：在两个数组的对应元素之间构造最大值数组
minimum：在两个数组的对应元素之间构造最小值数组
例：numpy.maximum(a, b)：在a数组与b数组中的各个元素对应比较，每次取出较大的那个数构成一个新数组
3、练习
import numpy as np
# 最大值最小值
a = np.random.randint(10, 100, 9).reshape(3, 3)
print(a)
# print('最大值：', np.max(a), a.max()) # 最大值
# print('最小值：', np.min(a), a.min()) # 最小值
# print('最大值索引：', np.argmax(a), a.argmax()) # 数组扁平为一维后的最大值索引
# maximum最大值，minimum最小值
b = np.random.randint(10, 100, 9).reshape(3, 3)
print(b)
print('构造最大值数组：
', np.maximum(a, b))
print('构造最小值数组：
', np.minimum(a, b))
精通级学习
例一
有一个df：
ID wt value
Date
01/01/2012 100 0.50 60
01/01/2012 101 0.75 80
01/01/2012 102 1.00 100
01/02/2012 201 0.50 100
01/02/2012 202 1.00 80
相关代码如下：
import numpy as np
import pandas as pd
index = pd.Index(['01/01/2012','01/01/2012','01/01/2012','01/02/2012','01/02/2012'], name='Date')
df = pd.DataFrame({'ID':[100,101,102,201,202],'wt':[.5,.75,1,.5,1],'value':[60,80,100,100,80]},index=index)
按“值”加权并按指数分组的“wt”的平均值为：
Date
01/01/2012 0.791667
01/02/2012 0.722222
dtype: float64
或者，也可以定义函数：
def grouped_weighted_avg(values, weights, by):
return (values * weights).groupby(by).sum() / weights.groupby(by).sum()
grouped_weighted_avg(values=df.wt, weights=df.value, by=df.index)
Date
01/01/2012 0.791667
01/02/2012 0.722222
dtype: float64
更复杂的：
grouped = df.groupby('Date')
def wavg(group):
d = group['value']
w = group['wt']
return (d * w).sum() / w.sum()
grouped.apply(wavg)
例二
ind dist diff cas
0 la 10.0 0.54 1.0
1 p 5.0 3.20 2.0
2 la 7.0 8.60 3.0
3 la 8.0 7.20 4.0
4 p 7.0 2.10 5.0
5 g 2.0 1.00 6.0
6 g 5.0 3.50 7.0
7 la 3.0 4.50 8.0
df = pd.DataFrame({'ind':['la','p','la','la','p','g','g','la'],
'dist':[10.,5.,7.,8.,7.,2.,5.,3.],
'diff':[0.54,3.2,8.6,7.2,2.1,1.,3.5,4.5],
'cas':[1.,2.,3.,4.,5.,6.,7.,8.]})
生成一列（使用 transform在组内获得标准化权重）weight
df['weight'] = df['dist'] / df.groupby('ind')['dist'].transform('sum')
df
ind dist diff cas weight
0 la 10.0 0.54 1.0 0.357143
1 p 5.0 3.20 2.0 0.416667
2 la 7.0 8.60 3.0 0.250000
3 la 8.0 7.20 4.0 0.285714
4 p 7.0 2.10 5.0 0.583333
5 g 2.0 1.00 6.0 0.285714
6 g 5.0 3.50 7.0 0.714286
7 la 3.0 4.50 8.0 0.107143
将这些权重乘以这些值,并取总和：
df['wcas'], df['wdiff'] = (df[n] * df['weight'] for n in ('cas', 'diff'))
df.groupby('ind')[['wcas', 'wdiff']].sum()
wcas wdiff
ind
g 6.714286 2.785714
la 3.107143 4.882143
p 3.750000 2.558333
变异的写法：
backup = df.copy() # make a backup copy to mutate in place
cols = df.columns[:2] # cas, diff
df[cols] = df['weight'].values[:, None] * df[cols]
df.groupby('ind')[cols].sum()
cas diff
ind
g 6.714286 2.785714
la 3.107143 4.882143
p 3.750000 2.558333
例四（比较直观）
df = pd.DataFrame([('bird', 'Falconiformes', 389.0),
...: ('bird', 'Psittaciformes', 24.0),
...: ('mammal', 'Carnivora', 80.2),
...: ('mammal', 'Primates', np.nan),
...: ('mammal', 'Carnivora', 58)],
...: index=['falcon', 'parrot', 'lion', 'monkey', 'leopard'],
...: columns=('class', 'order', 'max_speed'))
df:
class order max_speed
falcon bird Falconiformes 389.0
parrot bird Psittaciformes 24.0
lion mammal Carnivora 80.2
monkey mammal Primates NaN
leopard mammal Carnivora 58.0
grouped = df.groupby('class')
grouped.sum()
Out:
max_speed
class
bird 413.0
mammal 138.2
例五
df = pd.DataFrame({'animal': 'cat dog cat fish dog cat cat'.split(),
'size': list('SSMMMLL'),
'weight': [8, 10, 11, 1, 20, 12, 12],
'adult': [False] * 5 + [True] * 2})
df:
animal size weight adult
0 cat S 8 False
1 dog S 10 False
2 cat M 11 False
3 fish M 1 False
4 dog M 20 False
5 cat L 12 True
6 cat L 12 True
List the size of the animals with the highest weight.
df.groupby('animal').apply(lambda subf: subf['size'][subf['weight'].idxmax()])
Out:
animal
cat L
dog M
fish M
dtype: object
其它参考文档：
理解Pandas的Transform
https://www.jianshu.com/p/20f15354aedd
https://www.jianshu.com/p/509d7b97088c
https://zhuanlan.zhihu.com/p/86350553
http://www.zyiz.net/tech/detail-136539.html
pandas：apply和transform方法的性能比较
https://www.cnblogs.com/wkang/p/9794678.html
https://www.jianshu.com/p/20f15354aedd
https://zhuanlan.zhihu.com/p/101284491?utm_source=wechat_session
https://www.cnblogs.com/bjwu/p/8970818.html
https://www.jianshu.com/p/42f1d2909bb6
官网的例子
https://pandas.pydata.org/pandas-docs/dev/user_guide/groupby.html
https://pandas.pydata.org/pandas-docs/stable/user_guide/cookbook.html#cookbook-grouping
https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.Series.transform.html
获得Pandas中几列的加权平均值和标准差
https://xbuba.com/questions/48307663
Pandas里面的加权平均，我猜你不会用！
https://blog.csdn.net/ddxygq/article/details/101351686