Question

我有一个形状为（A，B，C）的数组input_data，以及一个形状为（B，）的数组ind。我想循环通过B轴并取元素C [B [i]]和C [B [i] +1]的总和。期望的输出具有形状（A，B）。我有以下代码可以使用，但由于通过B轴进行基于索引的循环，我觉得效率很低。有更有效的方法吗？

import numpy as np

input_data = np.random.rand(2, 6, 10)
ind = [ 2, 3, 5, 6, 5, 4 ]

out = np.zeros( ( input_data.shape[0], input_data.shape[1] ) )

for i in range( len(ind) ):
    d = input_data[:, i, ind[i]:ind[i]+2]
    out[:, i] = np.sum(d, axis = 1)

根据Divakar的回答编辑：

import timeit
import numpy as np

N = 1000

input_data = np.random.rand(10, N, 5000)
ind = ( 4999 * np.random.rand(N) ).astype(np.int)

def test_1(): # Old loop-based method
    out = np.zeros( ( input_data.shape[0], input_data.shape[1] ) )

    for i in range( len(ind) ):
        d = input_data[:, i, ind[i]:ind[i]+2]
        out[:, i] = np.sum(d, axis = 1)
    return out

def test_2(): 
    extent = 2 # Comes from 2 in "ind[i]:ind[i]+2"

    m,n,r = input_data.shape
    idx = (np.arange(n)*r + ind)[:,None] + np.arange(extent)
    out1 = input_data.reshape(m,-1)[:,idx].reshape(m,n,-1).sum(2)
    return out1

print timeit.timeit(stmt = test_1, number = 1000)
print timeit.timeit(stmt = test_2, number = 1000)

print np.all( test_1() == test_2(), keepdims = True )

>> 7.70429363482
>> 0.392034666757
>> [[ True]]

Answer 1

这是使用linear indexing的矢量化方法，并在broadcasting的帮助下使用Static and global variable in memory。我们合并输入数组的最后两个轴，计算与最后两个轴对应的线性索引，执行切片并重新整形回3D形状。最后，我们沿最后一个轴进行求和以获得所需的输出。实现看起来像这样 -

extent = 2 # Comes from 2 in "ind[i]:ind[i]+2"

m,n,r = input_data.shape
idx = (np.arange(n)*r + ind)[:,None] + np.arange(extent)
out1 = input_data.reshape(m,-1)[:,idx].reshape(m,n,-1).sum(2)

如果问题extent中所述的2总是"... sum of elements C[B[i]] and C[B[i]+1]"，那么您可以这样做 -

m,n,r = input_data.shape
ind_arr = np.array(ind)
axis1_r = np.arange(n)
out2 = input_data[:,axis1_r,ind_arr] + input_data[:,axis1_r,ind_arr+1]

Answer 2

您还可以将integer array indexing与basic slicing结合使用：

import numpy as np

m,n,r = 2, 6, 10
input_data = np.arange(2*6*10).reshape(m, n, r)
ind = np.array([ 2, 3, 5, 6, 5, 4 ])
out = np.zeros( ( input_data.shape[0], input_data.shape[1] ) )
for i in range( len(ind) ):
    d = input_data[:, i, ind[i]:ind[i]+2]
    out[:, i] = np.sum(d, axis = 1)


out2 = input_data[:, np.arange(n)[:,None], np.add.outer(ind,range(2))].sum(axis=-1)
print(out2)
# array([[  5,  27,  51,  73,  91, 109],
#        [125, 147, 171, 193, 211, 229]])

assert np.allclose(out, out2)

NumPy索引具有不同的位置

2 个答案: