沿着下三角numpy数组的每一行翻转非零值



我有一个较低的三角形数组,如B:

B = np.array([[1,0,0,0],[.25,.75,0,0], [.1,.2,.7,0],[.2,.3,.4,.1]])
>>> B
array([[ 1.  ,  0.  ,  0.  ,  0.  ],
       [ 0.25,  0.75,  0.  ,  0.  ],
       [ 0.1 ,  0.2 ,  0.7 ,  0.  ],
       [ 0.2 ,  0.3 ,  0.4 ,  0.1 ]])

我想把它翻转成这样:

array([[ 1.  ,  0.  ,  0.  ,  0.  ],
       [ 0.75,  0.25,  0.  ,  0.  ],
       [ 0.7 ,  0.2 ,  0.1 ,  0.  ],
       [ 0.1 ,  0.4 ,  0.3 ,  0.2 ]])

也就是说,我想取所有的正值,并在正值内反转,留下后面的零。这不是fliplr所做的:

>>> np.fliplr(B)
array([[ 0.  ,  0.  ,  0.  ,  1.  ],
       [ 0.  ,  0.  ,  0.75,  0.25],
       [ 0.  ,  0.7 ,  0.2 ,  0.1 ],
       [ 0.1 ,  0.4 ,  0.3 ,  0.2 ]])

有什么建议吗?此外,我正在使用的实际数组将类似于B.shape = (200,20,4,4),而不是(4,4)。每个(4,4)块看起来像上面的例子(在200、20个不同的条目中具有不同的数字)。

这个怎么样:

# row, column indices of the lower triangle of B
r, c = np.tril_indices_from(B)
# flip the column indices by subtracting them from r, which is equal to the number
# of nonzero elements in each row minus one
B[r, c] = B[r, r - c]
print(repr(B))
# array([[ 1.  ,  0.  ,  0.  ,  0.  ],
#        [ 0.75,  0.25,  0.  ,  0.  ],
#        [ 0.7 ,  0.2 ,  0.1 ,  0.  ],
#        [ 0.1 ,  0.4 ,  0.3 ,  0.2 ]])

同样的方法将推广到任何由多个下三角子矩阵组成的任意N维阵列:

# creates a (200, 20, 4, 4) array consisting of tiled copies of B
B2 = np.tile(B[None, None, ...], (200, 20, 1, 1))
print(repr(B2[100, 10]))
# array([[ 1.  ,  0.  ,  0.  ,  0.  ],
#        [ 0.25,  0.75,  0.  ,  0.  ],
#        [ 0.1 ,  0.2 ,  0.7 ,  0.  ],
#        [ 0.2 ,  0.3 ,  0.4 ,  0.1 ]])
r, c = np.tril_indices_from(B2[0, 0])
B2[:, :, r, c] = B2[:, :, r, r - c]
print(repr(B2[100, 10]))
# array([[ 1.  ,  0.  ,  0.  ,  0.  ],
#        [ 0.75,  0.25,  0.  ,  0.  ],
#        [ 0.7 ,  0.2 ,  0.1 ,  0.  ],
#        [ 0.1 ,  0.4 ,  0.3 ,  0.2 ]])

对于上三角矩阵,您可以简单地从c中减去r,例如:

r, c = np.triu_indices_from(B.T)
B.T[r, c] = B.T[c - r, c]

这里有一种2D数组情况的方法-

mask = np.tril(np.ones((4,4),dtype=bool))
out = np.zeros_like(B)
out[mask] = B[:,::-1][mask[:,::-1]]

您可以使用相同的2D掩码将其扩展到3D阵列情况,masking使用它的最后两个轴,如so-

out = np.zeros_like(B)
out[:,mask] = B[:,:,::-1][:,mask[:,::-1]]

类似地,对于4D阵列情况,如so-

out = np.zeros_like(B)
out[:,:,mask] = B[:,:,:,::-1][:,:,mask[:,::-1]]

可以看出,我们将掩模过程保持在(4,4)的最后两个轴,并且解决方案基本保持不变。

样品运行-

In [95]: B
Out[95]: 
array([[ 1.  ,  0.  ,  0.  ,  0.  ],
       [ 0.25,  0.75,  0.  ,  0.  ],
       [ 0.1 ,  0.2 ,  0.7 ,  0.  ],
       [ 0.2 ,  0.3 ,  0.4 ,  0.1 ]])
In [96]: mask = np.tril(np.ones((4,4),dtype=bool))
    ...: out = np.zeros_like(B)
    ...: out[mask] = B[:,::-1][mask[:,::-1]]
    ...: 
In [97]: out
Out[97]: 
array([[ 1.  ,  0.  ,  0.  ,  0.  ],
       [ 0.75,  0.25,  0.  ,  0.  ],
       [ 0.7 ,  0.2 ,  0.1 ,  0.  ],
       [ 0.1 ,  0.4 ,  0.3 ,  0.2 ]])

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