python - 如何使用numpy获取没有对角线的三角形上矩阵

Question

可以说我有以下矩阵:

A = np.array([
     [1,2,3],
     [4,5,6],
     [7,8,9]])

如何在没有对角线的情况下有效地提取上三角矩阵？
输出将是以下数组:

B = np.array([2,3,6])

Answer 1

一种掩盖的方法-

def upper_tri_masking(A):
    m = A.shape[0]
    r = np.arange(m)
    mask = r[:,None] < r
    return A[mask]

另一个与 np.triu_indices -

def upper_tri_indexing(A):
    m = A.shape[0]
    r,c = np.triu_indices(m,1)
    return A[r,c]

sample 运行-

In [403]: A
Out[403]: 
array([[79, 17, 79, 58, 14],
       [87, 63, 89, 26, 31],
       [69, 34, 90, 24, 96],
       [59, 60, 80, 52, 46],
       [75, 80, 11, 61, 47]])

In [404]: upper_tri_masking(A)
Out[404]: array([17, 79, 58, 14, 89, 26, 31, 24, 96, 46])

运行时测试-

In [415]: A = np.random.randint(0,9,(5000,5000))

In [416]: %timeit upper_tri_masking(A)
10 loops, best of 3: 64.2 ms per loop

In [417]: %timeit upper_tri_indexing(A)
1 loop, best of 3: 252 ms per loop