Numpy的有效求和面积表计算

Question

我正在尝试使用python和numpy 计算特征计数矩阵的求和区域表.目前我正在使用以下代码:

def summed_area_table(img):

    table = np.zeros_like(img).astype(int)

    for row in range(img.shape[0]):
        for col in range(img.shape[1]):

            if (row > 0) and (col > 0):
                table[row, col] = (img[row, col] +
                                   table[row, col - 1] +
                                   table[row - 1, col] -
                                   table[row - 1, col - 1])
            elif row > 0:   
                table[row, col] = img[row, col] + table[row - 1, col]
            elif col > 0:
                table[row, col] = img[row, col] + table[row, col - 1]
            else:
                table[row, col] = img[row, col]

    return table

上面的代码大约需要35秒才能在3200 x 1400阵列上执行计算.有没有办法使用Numpy技巧来加速计算？我意识到基本的速度问题在于嵌套的python循环,但我不知道如何避免它们.

Answer 1

有cumsum累积和的NumPy函数.应用它两次会产生所需的表格:

import numpy as np

A = np.random.randint(0, 10, (3, 4))

print A
print A.cumsum(axis=0).cumsum(axis=1)

输出:

[[7 4 7 2]
 [6 9 9 5]
 [6 6 7 6]]
[[ 7 11 18 20]
 [13 26 42 49]
 [19 38 61 74]]

性能分析:(/sf/answers/1774594111/)

import numpy as np
import time

A = np.random.randint(0, 10, (3200, 1400))

t = time.time()
S = A.cumsum(axis=0).cumsum(axis=1)
print np.round_(time.time() - t, 3), 'sec elapsed'

输出:

0.15 sec elapsed