从给定的 numpy 数组创建块对角线 numpy 数组 [英] Create block diagonal numpy array from a given numpy array

问题描述

我有一个列数和行数相等的二维 numpy 数组.我想将它们排列成一个更大的阵列，在对角线上有更小的阵列.应该可以指定起始矩阵在对角线上的频率.例如:

I have a 2-dimensional numpy array with an equal number of columns and rows. I would like to arrange them into a bigger array having the smaller ones on the diagonal. It should be possible to specify how often the starting matrix should be on the diagonal. For example:

a = numpy.array([[5, 7], 
                 [6, 3]])

因此，如果我想在对角线上使用该数组 2 次，则所需的输出将是:

So if I wanted this array 2 times on the diagonal the desired output would be:

array([[5, 7, 0, 0], 
       [6, 3, 0, 0], 
       [0, 0, 5, 7], 
       [0, 0, 6, 3]])

3 次:

array([[5, 7, 0, 0, 0, 0], 
       [6, 3, 0, 0, 0, 0], 
       [0, 0, 5, 7, 0, 0], 
       [0, 0, 6, 3, 0, 0],
       [0, 0, 0, 0, 5, 7],
       [0, 0, 0, 0, 6, 3]])

是否有一种使用 numpy 方法和任意大小的起始数组(仍然考虑起始数组具有相同的行数和列数)来实现这一点的快速方法?

Is there a fast way to implement this with numpy methods and for arbitrary sizes of the starting array (still considering the starting array to have the same number of rows and columns)?

推荐答案

方法 #1

numpy.kron -

np.kron(np.eye(r,dtype=int),a) # r is number of repeats

样品运行 -

In [184]: a
Out[184]: 
array([[1, 2, 3],
       [3, 4, 5]])

In [185]: r = 3 # number of repeats

In [186]: np.kron(np.eye(r,dtype=int),a)
Out[186]: 
array([[1, 2, 3, 0, 0, 0, 0, 0, 0],
       [3, 4, 5, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 1, 2, 3, 0, 0, 0],
       [0, 0, 0, 3, 4, 5, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 1, 2, 3],
       [0, 0, 0, 0, 0, 0, 3, 4, 5]])

方法#2

另一个高效的diagonal-viewed-array-assignment -

def repeat_along_diag(a, r):
    m,n = a.shape
    out = np.zeros((r,m,r,n), dtype=a.dtype)
    diag = np.einsum('ijik->ijk',out)
    diag[:] = a
    return out.reshape(-1,n*r)

样品运行 -

In [188]: repeat_along_diag(a,3)
Out[188]: 
array([[1, 2, 3, 0, 0, 0, 0, 0, 0],
       [3, 4, 5, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 1, 2, 3, 0, 0, 0],
       [0, 0, 0, 3, 4, 5, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 1, 2, 3],
       [0, 0, 0, 0, 0, 0, 3, 4, 5]])

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