python中的加權移動平均數

Question

我以基本上隨機的間隔採樣數據。我想用numpy（或其他python包）計算加權移動平均數。我有一個移動平均線的粗略實現，但我無法找到一個加權移動平均線的好方法，因此朝向中心的值的權重大於邊緣的值。

這裏我生成一些樣本數據，然後取一個移動平均值。我怎樣才能最輕鬆地實現加權移動平均線？謝謝！

import numpy as np 
import matplotlib.pyplot as plt 

#first generate some datapoint for a randomly sampled noisy sinewave 
x = np.random.random(1000)*10 
noise = np.random.normal(scale=0.3,size=len(x)) 
y = np.sin(x) + noise 

#plot the data 
plt.plot(x,y,'ro',alpha=0.3,ms=4,label='data') 
plt.xlabel('Time') 
plt.ylabel('Intensity') 

#define a moving average function 
def moving_average(x,y,step_size=.1,bin_size=1): 
    bin_centers = np.arange(np.min(x),np.max(x)-0.5*step_size,step_size)+0.5*step_size 
    bin_avg = np.zeros(len(bin_centers)) 

    for index in range(0,len(bin_centers)): 
     bin_center = bin_centers[index] 
     items_in_bin = y[(x>(bin_center-bin_size*0.5)) & (x<(bin_center+bin_size*0.5))] 
     bin_avg[index] = np.mean(items_in_bin) 

    return bin_centers,bin_avg 

#plot the moving average 
bins, average = moving_average(x,y) 
plt.plot(bins, average,label='moving average') 

plt.show() 

輸出：

使用從crs17建議在np.average功能用「權重=」，我想出了加權平均函數，它使用一個高斯函數對數據進行加權：

def weighted_moving_average(x,y,step_size=0.05,width=1): 
    bin_centers = np.arange(np.min(x),np.max(x)-0.5*step_size,step_size)+0.5*step_size 
    bin_avg = np.zeros(len(bin_centers)) 

    #We're going to weight with a Gaussian function 
    def gaussian(x,amp=1,mean=0,sigma=1): 
     return amp*np.exp(-(x-mean)**2/(2*sigma**2)) 

    for index in range(0,len(bin_centers)): 
     bin_center = bin_centers[index] 
     weights = gaussian(x,mean=bin_center,sigma=width) 
     bin_avg[index] = np.average(y,weights=weights) 

    return (bin_centers,bin_avg) 

結果看起來不錯：

Answer 1

你可以使用numpy.average它允許您指定的權重：

>>> bin_avg[index] = np.average(items_in_bin, weights=my_weights) 

所以要計算你會發現在bin每個數據點的X座標的權重，計算他們的距離區間中央。

Answer 2

這不會給出一個確切的解決方案，但它會讓您的生活更輕鬆，並且可能會足夠好...首先，將您的樣品放入小容器中。一旦你重新採樣的數據被平均分佈，可以使用步幅技巧和np.average做一個加權平均值：

from numpy.lib.stride_tricks import as_strided 

def moving_weighted_average(x, y, step_size=.1, steps_per_bin=10, 
          weights=None): 
    # This ensures that all samples are within a bin 
    number_of_bins = int(np.ceil(np.ptp(x)/step_size)) 
    bins = np.linspace(np.min(x), np.min(x) + step_size*number_of_bins, 
         num=number_of_bins+1) 
    bins -= (bins[-1] - np.max(x))/2 
    bin_centers = bins[:-steps_per_bin] + step_size*steps_per_bin/2 

    counts, _ = np.histogram(x, bins=bins) 
    vals, _ = np.histogram(x, bins=bins, weights=y) 
    bin_avgs = vals/counts 
    n = len(bin_avgs) 
    windowed_bin_avgs = as_strided(bin_avgs, 
            (n-steps_per_bin+1, steps_per_bin), 
            bin_avgs.strides*2) 

    weighted_average = np.average(windowed_bin_avgs, axis=1, weights=weights) 

    return bin_centers, weighted_average 

你現在可以做這樣的事情：

#plot the moving average with triangular weights 
weights = np.concatenate((np.arange(0, 5), np.arange(0, 5)[::-1])) 
bins, average = moving_weighted_average(x, y, steps_per_bin=len(weights), 
             weights=weights) 
plt.plot(bins, average,label='moving average') 

plt.show()