实现这一点的一个简单方法是使用np.卷积。 这背后的思想是利用离散卷积的计算方式，并使用它来返回滚动平均值。这可以通过与np序列进行卷积来实现。长度等于我们想要的滑动窗口长度。

为了做到这一点，我们可以定义以下函数:

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

该函数将对序列x和长度为w的序列进行卷积。注意，所选模式是有效的，因此卷积积只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])

对于窗口长度为2的移动平均线，我们有:

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.  ])

卷积是怎么工作的?

让我们更深入地看看离散卷积是如何计算的。 下面的函数旨在复制np。卷积计算输出值:

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

对于上面的同一个例子，也会得到:

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

所以每一步要做的就是求1数组和当前窗口之间的内积。在这种情况下，乘以np.ones(w)是多余的，因为我们直接取序列的和。

下面是一个计算第一个输出的例子，这样会更清楚一些。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

下面的输出将被计算为:

  [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，在所有重叠完成后返回序列的移动平均值。

如果你只想要一个简单的非加权移动平均，你可以很容易地用np实现它。cumsum，可能比基于FFT的方法更快:

修正了Bean在代码中发现的偏离一的错误索引。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])

所以我猜答案是:它真的很容易实现，也许numpy已经有了一些专门的功能。

我觉得使用瓶颈可以很容易地解决这个问题

参见下面的基本示例:

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)

这就给出了每个轴上的移动平均值。

“mm”是“a”的移动平均值。 “窗口”是考虑移动均值的最大条目数。 "min_count"是考虑移动平均值的最小条目数(例如，对于第一个元素或如果数组有nan值)。

好在瓶颈有助于处理nan值，而且非常高效。

移动平均线 迭代器方法 在i处反转数组，简单地求i到n的均值。 使用列表推导式在运行中生成迷你数组。

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)

张量卷积

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

您也可以编写自己的Python C扩展。

这当然不是最简单的方法，但与使用np相比，这将使您运行得更快，内存效率更高。堆积:作为建筑块的堆积

// moving_average.c
#define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION
#include <Python.h>
#include <numpy/arrayobject.h>

static PyObject *moving_average(PyObject *self, PyObject *args) {
    PyObject *input;
    int64_t window_size;
    PyArg_ParseTuple(args, "Ol", &input, &window_size);
    if (PyErr_Occurred()) return NULL;
    if (!PyArray_Check(input) || !PyArray_ISNUMBER((PyArrayObject *)input)) {
        PyErr_SetString(PyExc_TypeError, "First argument must be a numpy array with numeric dtype");
        return NULL;
    }
    
    int64_t input_size = PyObject_Size(input);
    double *input_data;
    if (PyArray_AsCArray(&input, &input_data, (npy_intp[]){ [0] = input_size }, 1, PyArray_DescrFromType(NPY_DOUBLE)) != 0) {
        PyErr_SetString(PyExc_TypeError, "Failed to simulate C array of type double");
        return NULL;
    }
    
    int64_t output_size = input_size - window_size + 1;
    PyObject *output = PyArray_SimpleNew(1, (npy_intp[]){ [0] = output_size }, NPY_DOUBLE);
    double *output_data = PyArray_DATA((PyArrayObject *)output);
    
    double cumsum_before = 0;
    double cumsum_after = 0;
    for (int i = 0; i < window_size; ++i) {
        cumsum_after += input_data[i];
    }
    for (int i = 0; i < output_size - 1; ++i) {
        output_data[i] = (cumsum_after - cumsum_before) / window_size;
        cumsum_after += input_data[i + window_size];
        cumsum_before += input_data[i];
    }
    output_data[output_size - 1] = (cumsum_after - cumsum_before) / window_size;

    return output;
}

static PyMethodDef methods[] = {
    {
        "moving_average", 
        moving_average, 
        METH_VARARGS, 
        "Rolling mean of numpy array with specified window size"
    },
    {NULL, NULL, 0, NULL}
};

static struct PyModuleDef moduledef = {
    PyModuleDef_HEAD_INIT,
    "moving_average",
    "C extension for finding the rolling mean of a numpy array",
    -1,
    methods
};

PyMODINIT_FUNC PyInit_moving_average(void) {
    PyObject *module = PyModule_Create(&moduledef);
    import_array();
    return module;
}

METH_VARARGS specifies that the method only takes positional arguments. PyArg_ParseTuple allows you to parse these positional arguments. By using PyErr_SetString and returning NULL from the method, you can signal that an exception has occurred to the Python interpreter from the C extension. PyArray_AsCArray allows your method to be polymorphic when it comes to input array dtype, alignment, whether the array is C-contiguous (See "Can a numpy 1d array not be contiguous?") etc. without needing to create a copy of the array. If you instead used PyArray_DATA, you'd need to deal with this yourself. PyArray_SimpleNew allows you to create a new numpy array. This is similar to using np.empty. The array will not be initialized, and might contain non-deterministic junk which could surprise you if you forget to overwrite it.

构建C扩展

# setup.py
from setuptools import setup, Extension
import numpy

setup(
  ext_modules=[
    Extension(
      'moving_average',
      ['moving_average.c'],
      include_dirs=[numpy.get_include()]
    )
  ]
)

# python setup.py build_ext --build-lib=.

基准

import numpy as np

# Our compiled C extension:
from moving_average import moving_average as moving_average_c

# Answer by Jaime using npcumsum
def moving_average_cumsum(a, n) :
    ret = np.cumsum(a, dtype=float)
    ret[n:] = ret[n:] - ret[:-n]
    return ret[n - 1:] / n

# Answer by yatu using np.convolve
def moving_average_convolve(a, n):
    return np.convolve(a, np.ones(n), 'valid') / n

a = np.random.rand(1_000_000)
print('window_size = 3')
%timeit moving_average_c(a, 3)
%timeit moving_average_cumsum(a, 3)
%timeit moving_average_convolve(a, 3)

print('\nwindow_size = 100')
%timeit moving_average_c(a, 100)
%timeit moving_average_cumsum(a, 100)
%timeit moving_average_convolve(a, 100)

window_size = 3
958 µs ± 4.68 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)
4.52 ms ± 15.4 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
809 µs ± 463 ns per loop (mean ± std. dev. of 7 runs, 1,000 loops each)

window_size = 100
977 µs ± 937 ns per loop (mean ± std. dev. of 7 runs, 1,000 loops each)
6.16 ms ± 19.1 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
14.2 ms ± 12.4 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

Talib包含一个简单的移动平均工具，以及其他类似的平均工具(即指数移动平均)。下面将该方法与其他一些解决方案进行比较。

%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)

需要注意的是，real必须有dtype = float的元素。否则将引发以下错误

例外:实不是双的