Arnaud Legoux移動平均值和numpy

Question

我想編寫使用NumPy（或Pandas）計算Arnaud Legoux移動平均值的向量版代碼。你能幫我解決這個問題嗎？謝謝。

非向量版本看起來像下面（見下文）。

def NPALMA(pnp_array, **kwargs) : 
    ''' 
    ALMA - Arnaud Legoux Moving Average, 
    http://www.financial-hacker.com/trend-delusion-or-reality/ 
    https://github.com/darwinsys/Trading_Strategies/blob/master/ML/Features.py 
    ''' 
    length = kwargs['length'] 
    # just some number (6.0 is useful) 
    sigma = kwargs['sigma'] 
    # sensisitivity (close to 1) or smoothness (close to 0) 
    offset = kwargs['offset'] 

    asize = length - 1 
    m = offset * asize 
    s = length/sigma 
    dss = 2 * s * s 

    alma = np.zeros(pnp_array.shape) 
    wtd_sum = np.zeros(pnp_array.shape) 

    for l in range(len(pnp_array)): 
     if l >= asize: 
      for i in range(length): 
       im = i - m 
       wtd = np.exp(-(im * im)/dss) 
       alma[l] += pnp_array[l - length + i] * wtd 
       wtd_sum[l] += wtd 
      alma[l] = alma[l]/wtd_sum[l] 

    return alma 

Answer 1

啓動方法

我們可以創建沿第一軸滑動窗口，然後用張量乘以wtd值的總和，減少的範圍。

的實施將是這個樣子 -

# Get all wtd values in an array 
wtds = np.exp(-(np.arange(length) - m)**2/dss) 

# Get the sliding windows for input array along first axis 
pnp_array3D = strided_axis0(pnp_array,len(wtds)) 

# Initialize o/p array 
out = np.zeros(pnp_array.shape) 

# Get sum-reductions for the windows which don't need wrapping over 
out[length:] = np.tensordot(pnp_array3D,wtds,axes=((1),(0)))[:-1] 

# Last element of the output needed wrapping. So, do it separately. 
out[length-1] = wtds.dot(pnp_array[np.r_[-1,range(length-1)]]) 

# Finally perform the divisions 
out /= wtds.sum() 

函數來獲取滑動窗口：strided_axis0是從here。

升壓用1D卷積

那些乘法與wtds值，然後它們的總和，減少是基本上沿該第一軸線卷積。因此，我們可以沿着axis=0使用scipy.ndimage.convolve1d。考慮到內存效率，這會更快，因爲我們不會創建巨大的滑動窗口。

實施將是 -

from scipy.ndimage import convolve1d as conv 

avgs = conv(pnp_array, weights=wtds/wtds.sum(),axis=0, mode='wrap') 

因此，out[length-1:]，這是非零行。將相同avgs[:-length+1]。

如果我們使用來自wtds的非常小的內核號碼，可能會有一些精度差異。所以，請記住，如果使用這種方法convolution。

運行測試

途徑 -

def original_app(pnp_array, length, m, dss): 
    alma = np.zeros(pnp_array.shape) 
    wtd_sum = np.zeros(pnp_array.shape) 

    for l in range(len(pnp_array)): 
     if l >= asize: 
      for i in range(length): 
       im = i - m 
       wtd = np.exp(-(im * im)/dss) 
       alma[l] += pnp_array[l - length + i] * wtd 
       wtd_sum[l] += wtd 
      alma[l] = alma[l]/wtd_sum[l] 
    return alma 

def vectorized_app1(pnp_array, length, m, dss): 
    wtds = np.exp(-(np.arange(length) - m)**2/dss) 
    pnp_array3D = strided_axis0(pnp_array,len(wtds)) 
    out = np.zeros(pnp_array.shape) 
    out[length:] = np.tensordot(pnp_array3D,wtds,axes=((1),(0)))[:-1] 
    out[length-1] = wtds.dot(pnp_array[np.r_[-1,range(length-1)]]) 
    out /= wtds.sum() 
    return out 

def vectorized_app2(pnp_array, length, m, dss): 
    wtds = np.exp(-(np.arange(length) - m)**2/dss) 
    return conv(pnp_array, weights=wtds/wtds.sum(),axis=0, mode='wrap') 

計時 -

In [470]: np.random.seed(0) 
    ...: m,n = 1000,100 
    ...: pnp_array = np.random.rand(m,n) 
    ...: 
    ...: length = 6 
    ...: sigma = 0.3 
    ...: offset = 0.5 
    ...: 
    ...: asize = length - 1 
    ...: m = np.floor(offset * asize) 
    ...: s = length/sigma 
    ...: dss = 2 * s * s 
    ...: 

In [471]: %timeit original_app(pnp_array, length, m, dss) 
    ...: %timeit vectorized_app1(pnp_array, length, m, dss) 
    ...: %timeit vectorized_app2(pnp_array, length, m, dss) 
    ...: 
10 loops, best of 3: 36.1 ms per loop 
1000 loops, best of 3: 1.84 ms per loop 
1000 loops, best of 3: 684 µs per loop 

In [472]: np.random.seed(0) 
    ...: m,n = 10000,1000 # rest same as previous one 

In [473]: %timeit original_app(pnp_array, length, m, dss) 
    ...: %timeit vectorized_app1(pnp_array, length, m, dss) 
    ...: %timeit vectorized_app2(pnp_array, length, m, dss) 
    ...: 
1 loop, best of 3: 503 ms per loop 
1 loop, best of 3: 222 ms per loop 
10 loops, best of 3: 106 ms per loop