Python 如何使用NumPy/SciPy计算滚动/移动平均线？

似乎没有函数可以简单地计算numpy/scipy上的移动平均值，从而导致

我的问题有两个方面：

• 使用numpy（正确）实现移动平均线的最简单方法是什么
• 既然这看起来不琐碎且容易出错，那么在这种情况下，有没有一个很好的理由不使用该选项

---

如果您只想要一个简单的非加权移动平均值，您可以使用

np轻松实现它。cumsum

，它可能比基于FFT的方法更快：

EDIT纠正了代码中Bean发现的一个错误索引编辑

def moving_average(a, n=3) :
    ret = np.cumsum(a, dtype=float)
    ret[n:] = ret[n:] - ret[:-n]
    return ret[n - 1:] / n

>>> a = np.arange(20)
>>> moving_average(a)
array([  1.,   2.,   3.,   4.,   5.,   6.,   7.,   8.,   9.,  10.,  11.,
        12.,  13.,  14.,  15.,  16.,  17.,  18.])
>>> moving_average(a, n=4)
array([  1.5,   2.5,   3.5,   4.5,   5.5,   6.5,   7.5,   8.5,   9.5,
        10.5,  11.5,  12.5,  13.5,  14.5,  15.5,  16.5,  17.5])

---

所以我想答案是：它确实很容易实现，也许numpy已经有点过于专业化了。

numpy缺少特定领域的功能可能是因为核心团队的纪律性和对numpy的基本指令的忠实性：提供一个N维数组类型，以及用于创建和索引这些数组的函数。像许多基本目标一样，这个目标并不小，NumPy做得非常出色

（大得多的）SciPy包含大量特定于领域的库（SciPy开发人员称之为子包），例如，数值优化（optimize）、信号处理（signal）和积分（INTEGLE）

我的猜测是，您所追求的函数至少在一个SciPy子包中（可能是SciPy.signal）；但是，我会首先查看SciPy scikit集合，确定相关scikit，并在其中查找感兴趣的功能

是基于NumPy/SciPy独立开发的软件包，并针对特定的技术学科（例如，scikits image、scikits learn等）。其中一些软件包（尤其是数值优化方面的优秀软件包）在选择使用相对较新的scikits标准之前很久就受到高度重视、成熟的项目。Scikits主页喜欢在上面列出大约30个这样的Scikits，尽管其中至少有几个不再处于积极开发之中

遵循此建议将引导您使用scikits timeseries；然而，该一揽子计划不再处于积极发展之中；实际上，AFAIK已经成为事实上基于NumPy的时间序列库

熊猫有几个函数可以用来计算移动平均线；其中最简单的可能是滚动意思，您可以这样使用：

>>> # the recommended syntax to import pandas
>>> import pandas as PD
>>> import numpy as NP

>>> # prepare some fake data:
>>> # the date-time indices:
>>> t = PD.date_range('1/1/2010', '12/31/2012', freq='D')

>>> # the data:
>>> x = NP.arange(0, t.shape[0])

>>> # combine the data & index into a Pandas 'Series' object
>>> D = PD.Series(x, t)

现在，只需调用函数rolling\u mean传递序列对象和窗口大小，在我下面的示例中是10天

d_mva10 = D.rolling(10).mean()

# d_mva is the same size as the original Series
# though obviously the first w values are NaN where w is the window size
d_mva10[:11]

2010-01-01    NaN
2010-01-02    NaN
2010-01-03    NaN
2010-01-04    NaN
2010-01-05    NaN
2010-01-06    NaN
2010-01-07    NaN
2010-01-08    NaN
2010-01-09    NaN
2010-01-10    4.5
2010-01-11    5.5
Freq: D, dtype: float64

验证其是否有效——例如，将原始序列中的值10-15与使用滚动平均值平滑的新序列进行比较

>>> D[10:15]
     2010-01-11    2.041076
     2010-01-12    2.041076
     2010-01-13    2.720585
     2010-01-14    2.720585
     2010-01-15    3.656987
     Freq: D

>>> d_mva[10:20]
      2010-01-11    3.131125
      2010-01-12    3.035232
      2010-01-13    2.923144
      2010-01-14    2.811055
      2010-01-15    2.785824
      Freq: D

---

函数rolling_mean，以及十几个左右的其他函数非正式地分组在Pandas文档中的移动窗口函数标题下；熊猫中的第二组相关函数称为指数加权函数（例如，ewma，计算指数移动加权平均值）。第二组不包括在第一组（移动窗口函数）中的事实可能是因为指数加权变换不依赖于固定长度的窗口，以防您需要仔细考虑边缘条件（仅从边缘的可用元素计算平均值）），下面的函数将完成此操作

import numpy as np

def running_mean(x, N):
    out = np.zeros_like(x, dtype=np.float64)
    dim_len = x.shape[0]
    for i in range(dim_len):
        if N%2 == 0:
            a, b = i - (N-1)//2, i + (N-1)//2 + 2
        else:
            a, b = i - (N-1)//2, i + (N-1)//2 + 1

        #cap indices to min and max indices
        a = max(0, a)
        b = min(dim_len, b)
        out[i] = np.mean(x[a:b])
    return out

>>> running_mean(np.array([1,2,3,4]), 2)
array([1.5, 2.5, 3.5, 4. ])

>>> running_mean(np.array([1,2,3,4]), 3)
array([1.5, 2. , 3. , 3.5])

---

这个使用熊猫的答案是从上面改编的，因为

rolling\u意思是
不再是熊猫的一部分

# the recommended syntax to import pandas
import pandas as pd
import numpy as np

# prepare some fake data:
# the date-time indices:
t = pd.date_range('1/1/2010', '12/31/2012', freq='D')

# the data:
x = np.arange(0, t.shape[0])

# combine the data & index into a Pandas 'Series' object
D = pd.Series(x, t)

现在，只需在具有窗口大小的数据帧上调用函数
rolling
，在我下面的示例中是10天

d_mva10 = D.rolling(10).mean()

# d_mva is the same size as the original Series
# though obviously the first w values are NaN where w is the window size
d_mva10[:11]

2010-01-01    NaN
2010-01-02    NaN
2010-01-03    NaN
2010-01-04    NaN
2010-01-05    NaN
2010-01-06    NaN
2010-01-07    NaN
2010-01-08    NaN
2010-01-09    NaN
2010-01-10    4.5
2010-01-11    5.5
Freq: D, dtype: float64

我觉得这可以很容易地解决使用

见下面的基本示例：

import numpy as np
import bottleneck as bn

a = np.random.randint(4, 1000, size=(5, 7))
mm = bn.move_mean(a, window=2, min_count=1)

这将给出沿每个轴的移动平均值


“mm”是“a”的移动意思

 
窗口是移动平均值要考虑的最大数量。
＞P> >“min计数”是移动平均值（例如，对于第一个元素或如果数组具有NA值）的最小数量项。

好的方面是瓶颈有助于处理nan值，而且非常有效。
实现这一点的简单方法是使用。
这背后的想法是利用计算方法，并使用它返回滚动平均值。这可以通过卷积一个长度等于我们想要的滑动窗口长度的序列来实现

为此，我们可以定义以下函数：

def moving_average(x, w):
    return np.convolve(x, np.ones(w), 'valid') / w

此函数将对序列
x
和长度
w
的序列进行卷积。请注意，所选的
模式
是
有效的
，因此卷积积只针对序列完全重叠的点给出


一些例子：

x = np.array([5,3,8,10,2,1,5,1,0,2])

对于窗口长度
2
的移动平均线，我们将：

moving_average(x, 2)
# array([4. , 5.5, 9. , 6. , 1.5, 3. , 3. , 0.5, 1. ])

对于长度为
4
的窗口：

moving_average(x, 4)
# array([6.5 , 5.75, 5.25, 4.5 , 2.25, 1.75, 2.  ])


卷积如何工作？
让我们更深入地了解离散卷积的计算方式。
以下函数旨在复制
np.convolve
计算输出值的方式：

def mov_avg(x, w):
    for m in range(len(x)-(w-1)):
        yield sum(np.ones(w) * x[m:m+w]) / w 

对于上述同一示例，也将产生：

list(mov_avg(x, 2))
# [4.0, 5.5, 9.0, 6.0, 1.5, 3.0, 3.0, 0.5, 1.0]

因此，在每个步骤中要做的是获取1数组和当前窗口之间的内积。在这种情况下，
np.ones（w）
的乘法是多余的，因为我们直接取序列的
和

Bellow是一个如何计算第一个输出的示例，以便更清楚一点。假设我们想要一个
w=4
的窗口：

[1,1,1,1]
[5,3,8,10,2,1,5,1,0,2]
= (1*5 + 1*3 + 1*8 + 1*10) / w = 6.5

以下输出将被计算为：

  [1,1,1,1]
[5,3,8,10,2,1,5,1,0,2]
= (1*3 + 1*8 + 1*10 + 1*2) / w = 5.75

依此类推，一旦执行了所有重叠，就返回序列的移动平均值。
我实际上想要
def moving_average_col(X, n):
  z2 = np.cumsum(np.pad(X, ((n,0),(0,0)), 'constant', constant_values=0), axis=0)
  z1 = np.cumsum(np.pad(X, ((0,n),(0,0)), 'constant', constant_values=X[-1]), axis=0)
  return (z1-z2)[(n-1):-1]/n

def moving_average_array(X, n):
  z2 = np.cumsum(np.pad(X, (n,0), 'constant', constant_values=0))
  z1 = np.cumsum(np.pad(X, (0,n), 'constant', constant_values=X[-1]))
  return (z1-z2)[(n-1):-1]/n

import numpy as np
import scipy as sci
import scipy.signal as sig
import pandas as pd
import bottleneck as bn
import time as time

def rollavg_direct(a,n): 
    'Direct "for" loop'
    assert n%2==1
    b = a*0.0
    for i in range(len(a)) :
        b[i]=a[max(i-n//2,0):min(i+n//2+1,len(a))].mean()
    return b

def rollavg_comprehension(a,n):
    'List comprehension'
    assert n%2==1
    r,N = int(n/2),len(a)
    return np.array([a[max(i-r,0):min(i+r+1,N)].mean() for i in range(N)]) 

def rollavg_convolve(a,n):
    'scipy.convolve'
    assert n%2==1
    return sci.convolve(a,np.ones(n,dtype='float')/n, 'same')[n//2:-n//2+1]  

def rollavg_convolve_edges(a,n):
    'scipy.convolve, edge handling'
    assert n%2==1
    return sci.convolve(a,np.ones(n,dtype='float'), 'same')/sci.convolve(np.ones(len(a)),np.ones(n), 'same')  

def rollavg_cumsum(a,n):
    'numpy.cumsum'
    assert n%2==1
    cumsum_vec = np.cumsum(np.insert(a, 0, 0)) 
    return (cumsum_vec[n:] - cumsum_vec[:-n]) / n

def rollavg_cumsum_edges(a,n):
    'numpy.cumsum, edge handling'
    assert n%2==1
    N = len(a)
    cumsum_vec = np.cumsum(np.insert(np.pad(a,(n-1,n-1),'constant'), 0, 0)) 
    d = np.hstack((np.arange(n//2+1,n),np.ones(N-n)*n,np.arange(n,n//2,-1)))  
    return (cumsum_vec[n+n//2:-n//2+1] - cumsum_vec[n//2:-n-n//2]) / d

def rollavg_roll(a,n):
    'Numpy array rolling'
    assert n%2==1
    N = len(a)
    rolling_idx = np.mod((N-1)*np.arange(n)[:,None] + np.arange(N), N)
    return a[rolling_idx].mean(axis=0)[n-1:] 

def rollavg_roll_edges(a,n):
    # see https://stackoverflow.com/questions/42101082/fast-numpy-roll
    'Numpy array rolling, edge handling'
    assert n%2==1
    a = np.pad(a,(0,n-1-n//2), 'constant')*np.ones(n)[:,None]
    m = a.shape[1]
    idx = np.mod((m-1)*np.arange(n)[:,None] + np.arange(m), m) # Rolling index
    out = a[np.arange(-n//2,n//2)[:,None], idx]
    d = np.hstack((np.arange(1,n),np.ones(m-2*n+1+n//2)*n,np.arange(n,n//2,-1)))
    return (out.sum(axis=0)/d)[n//2:]

def rollavg_pandas(a,n):
    'Pandas rolling average'
    return pd.DataFrame(a).rolling(n, center=True, min_periods=1).mean().to_numpy()

def rollavg_bottlneck(a,n):
    'bottleneck.move_mean'
    return bn.move_mean(a, window=n, min_count=1)

N = 10**6
a = np.random.rand(N)
functions = [rollavg_direct, rollavg_comprehension, rollavg_convolve, 
        rollavg_convolve_edges, rollavg_cumsum, rollavg_cumsum_edges, 
        rollavg_pandas, rollavg_bottlneck, rollavg_roll, rollavg_roll_edges]

print('Small window (n=3)')
%load_ext memory_profiler
for f in functions : 
    print('\n'+f.__doc__+ ' : ')
    %timeit b=f(a,3)

print('\nLarge window (n=1001)')
for f in functions[0:-2] : 
    print('\n'+f.__doc__+ ' : ')
    %timeit b=f(a,1001)

print('\nMemory\n')
print('Small window (n=3)')
N = 10**7
a = np.random.rand(N)
%load_ext memory_profiler
for f in functions[2:] : 
    print('\n'+f.__doc__+ ' : ')
    %memit b=f(a,3)

print('\nLarge window (n=1001)')
for f in functions[2:-2] : 
    print('\n'+f.__doc__+ ' : ')
    %memit b=f(a,1001)

Direct "for" loop : 

4.14 s ± 23.7 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

List comprehension : 
3.96 s ± 27.9 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

scipy.convolve : 
1.07 ms ± 26.7 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

scipy.convolve, edge handling : 
4.68 ms ± 9.69 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

numpy.cumsum : 
5.31 ms ± 5.11 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

numpy.cumsum, edge handling : 
8.52 ms ± 11.1 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

Pandas rolling average : 
9.85 ms ± 9.63 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

bottleneck.move_mean : 
1.3 ms ± 12.2 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

Numpy array rolling : 
31.3 ms ± 91.9 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

Numpy array rolling, edge handling : 
61.1 ms ± 55.9 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

Direct "for" loop : 
4.67 s ± 34 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

List comprehension : 
4.46 s ± 14.6 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

scipy.convolve : 
103 ms ± 165 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

scipy.convolve, edge handling : 
272 ms ± 1.23 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

numpy.cumsum : 
5.19 ms ± 12.4 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

numpy.cumsum, edge handling : 
8.7 ms ± 11.5 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

Pandas rolling average : 
9.67 ms ± 199 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

bottleneck.move_mean : 
1.31 ms ± 15.7 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

The memory_profiler extension is already loaded. To reload it, use:
  %reload_ext memory_profiler

scipy.convolve : 
peak memory: 362.66 MiB, increment: 73.61 MiB

scipy.convolve, edge handling : 
peak memory: 510.24 MiB, increment: 221.19 MiB

numpy.cumsum : 
peak memory: 441.81 MiB, increment: 152.76 MiB

numpy.cumsum, edge handling : 
peak memory: 518.14 MiB, increment: 228.84 MiB

Pandas rolling average : 
peak memory: 449.34 MiB, increment: 160.02 MiB

bottleneck.move_mean : 
peak memory: 374.17 MiB, increment: 75.54 MiB

Numpy array rolling : 
peak memory: 661.29 MiB, increment: 362.65 MiB

Numpy array rolling, edge handling : 
peak memory: 1111.25 MiB, increment: 812.61 MiB

scipy.convolve : 
peak memory: 370.62 MiB, increment: 71.83 MiB

scipy.convolve, edge handling : 
peak memory: 521.98 MiB, increment: 223.18 MiB

numpy.cumsum : 
peak memory: 451.32 MiB, increment: 152.52 MiB

numpy.cumsum, edge handling : 
peak memory: 527.51 MiB, increment: 228.71 MiB

Pandas rolling average : 
peak memory: 451.25 MiB, increment: 152.50 MiB

bottleneck.move_mean : 
peak memory: 374.64 MiB, increment: 75.85 MiB

%timeit pd.Series(np.arange(100000)).rolling(3).mean()
2.53 ms ± 40.5 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

%timeit talib.SMA(real = np.arange(100000.), timeperiod = 3)
348 µs ± 3.5 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

%timeit moving_average(np.arange(100000))
638 µs ± 45.1 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

import numpy as np
import numba as nb

@nb.jit(nb.float64[:](nb.float64[:],nb.int64),
        fastmath=True,nopython=True)
def moving_average( array, window ):    
    ret = np.cumsum(array)
    ret[window:] = ret[window:] - ret[:-window]
    ma = ret[window - 1:] / window
    n = np.empty(window-1); n.fill(np.nan)
    return np.concatenate((n.ravel(), ma.ravel())) 

for i in range(len(Data)):
    Data[i, 1] = Data[i-lookback:i, 0].sum() / lookback

x = np.random.randint(10, size=20)

def moving_average(arr, n):
    return [ (arr[:i+1][::-1][:n]).mean() for i, ele in enumerate(arr) ]
d = 5

moving_average(x, d)

moving_average = np.convolve(x, np.ones(d)/d, mode='valid')

import numpy as np
import pandas as pd

def moving_average(a, n):
    ret = np.cumsum(a, dtype=float)
    ret[n:] = ret[n:] - ret[:-n]
    return ret / n

def moving_average_centered(a, n):
    return pd.Series(a).rolling(window=n, center=True).mean().to_numpy()

A = [0, 0, 1, 2, 4, 5, 4]
print(moving_average(A, 3))    
# [0.         0.         0.33333333 1.         2.33333333 3.66666667 4.33333333]
print(moving_average_centered(A, 3))
# [nan        0.33333333 1.         2.33333333 3.66666667 4.33333333 nan       ]

def moving_average(array_numbers, n):
    if n > len(array_numbers):
      return []
    temp_sum = sum(array_numbers[:n])
    averages = [temp_sum / float(n)]
    for first_index, item in enumerate(array_numbers[n:]):
        temp_sum += item - array_numbers[first_index]
        averages.append(temp_sum / float(n))
    return averages

from numpy.lib.stride_tricks import sliding_window_view

# values = np.array([5, 3, 8, 10, 2, 1, 5, 1, 0, 2])
np.average(sliding_window_view(values, window_shape = 4), axis=1)
# array([6.5, 5.75, 5.25, 4.5, 2.25, 1.75, 2])

# values = np.array([5, 3, 8, 10, 2, 1, 5, 1, 0, 2])
sliding_window_view(values, window_shape = 4)
# array([[ 5,  3,  8, 10],
#        [ 3,  8, 10,  2],
#        [ 8, 10,  2,  1],
#        [10,  2,  1,  5],
#        [ 2,  1,  5,  1],
#        [ 1,  5,  1,  0],
#        [ 5,  1,  0,  2]])

import numpy as np
class RunningAverage():
    def __init__(self, stack_size):
        self.stack = [0 for _ in range(stack_size)]
        self.ptr = 0
        self.full_cycle = False
    def add(self,value):
        self.stack[self.ptr] = value
        self.ptr += 1
        if self.ptr == len(self.stack):
            self.full_cycle = True
            self.ptr = 0
    def get_avg(self):
        if self.full_cycle:
            return np.mean(self.stack)
        else:
            return np.mean(self.stack[:self.ptr])

N = 50  # size of the averaging window
run_avg = RunningAverage(N)
for i in range(1000):
    value = <my computation>
    run_avg.add(value)
    if i % 20 ==0: # print once in 20 iters:
        print(f'the average value is {run_avg.get_avg()}')