n维数组中唯一值的索引 [英] Indices of unique values in n-dimensional array
问题描述
我有一个二维Numpy数组,包含从0到n的值. 我想得到一个长度为n的列表,以使该列表的第i个元素是值i + 1(不包括0)的所有索引的数组.
I have a 2D Numpy array containing values from 0 to n. I want to get a list of length n, such that the i'th element of that list is an array of all the indices with value i+1 (0 is excluded).
例如,对于输入
array([[1, 0, 1],
[2, 2, 0]])
我希望得到
[array([[0, 0], [0, 2]]), array([[1,0], [1,1]])]
我发现了以下相关问题: 获取所有索引的列表numpy数组中重复元素的数量 这可能会有所帮助,但是我希望找到一个更直接的解决方案,该解决方案不需要对数组进行展平和排序,并且尽可能高效.
I found this related question: Get a list of all indices of repeated elements in a numpy array which may be helpful, but I hoped to find a more direct solution that doesn't require flattening and sorting the array and that is as efficient as possible.
推荐答案
这是一种矢量化方法,适用于任意维数的数组.此解决方案的想法是扩展
Here's a vectorized approach, which works for arrays of an arbitrary amount of dimensions. The idea of this solution is to extend the functionality of the return_index
method in np.unique
, and return an array of arrays, each containing the N-dimensional indices of unique values in a numpy array.
对于更紧凑的解决方案,我在以下各个步骤中定义了以下功能以及一些解释:
For a more compact solution, I've defined the following function along with some explanations throughout the different steps:
def ndix_unique(x):
"""
Returns an N-dimensional array of indices
of the unique values in x
----------
x: np.array
Array with arbitrary dimensions
Returns
-------
- 1D-array of sorted unique values
- Array of arrays. Each array contains the indices where a
given value in x is found
"""
x_flat = x.ravel()
ix_flat = np.argsort(x_flat)
u, ix_u = np.unique(x_flat[ix_flat], return_index=True)
ix_ndim = np.unravel_index(ix_flat, x.shape)
ix_ndim = np.c_[ix_ndim] if x.ndim > 1 else ix_flat
return u, np.split(ix_ndim, ix_u[1:])
检查问题数组-
Checking with the array from the question -
a = np.array([[1, 0, 1],[2, 2, 0]])
vals, ixs = ndix_unique(a)
print(vals)
array([0, 1, 2])
print(ixs)
[array([[0, 1],
[1, 2]]),
array([[0, 0],
[0, 2]]),
array([[1, 0],
[1, 1]])]
让我们尝试其他情况:
a = np.array([[1,1,4],[2,2,1],[3,3,1]])
vals, ixs = ndix_unique(a)
print(vals)
array([1, 2, 3, 4])
print(ixs)
array([array([[0, 0],
[0, 1],
[1, 2],
[2, 2]]),
array([[1, 0],
[1, 1]]),
array([[2, 0],
[2, 1]]),
array([[0, 2]])], dtype=object)
对于 1D 阵列:
a = np.array([1,5,4,3,3])
vals, ixs = ndix_unique(a)
print(vals)
array([1, 3, 4, 5])
print(ixs)
array([array([0]), array([3, 4]), array([2]), array([1])], dtype=object)
最后一个带有 3D ndarray的示例:
Finally another example with a 3D ndarray:
a = np.array([[[1,1,2]],[[2,3,4]]])
vals, ixs = ndix_unique(a)
print(vals)
array([1, 2, 3, 4])
print(ixs)
array([array([[0, 0, 0],
[0, 0, 1]]),
array([[0, 0, 2],
[1, 0, 0]]),
array([[1, 0, 1]]),
array([[1, 0, 2]])], dtype=object)
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