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I only managed to extract one diagonal using Numpy einsum. How do I get the other diagonals like [6, 37, 68, 99] with help of einsum?

x =  np.arange(1, 26 ).reshape(5,5)
y =  np.arange(26, 51).reshape(5,5)
z =  np.arange(51, 76).reshape(5,5)
t =  np.arange(76, 101).reshape(5,5)
p =  np.arange(101, 126).reshape(5,5)

a4 = np.array([x, y, z, t, p]

Extracting one diagonal:

>>>np.einsum('iii->i', a4)
>>>[  1  32  63  94 125]
Johan Blomquist
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2 Answers2

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I don't have any "easy" solution using einsum but it is quite simple with a for loop:

import numpy as np

# Generation of a 3x3x3 matrix
x =  np.arange(1 , 10).reshape(3,3)
y =  np.arange(11, 20).reshape(3,3)
z =  np.arange(21, 30).reshape(3,3)

M = np.array([x, y, z])

# Generation of the index
I = np.arange(0,len(M))

# Generation of all the possible diagonals
for ii in [1,-1]:
    for jj in [1,-1]:
        print(M[I[::ii],I[::jj],I])

# OUTPUT:
# [ 1 15 29]
# [ 7 15 23]
# [21 15  9]
# [27 15  3]

We fix the index of the last dimension and we find all the possible combinations of backward and forward indexing for the other dimensions.

obchardon
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0

Do you realize that this einsum is the same as:

In [64]: a4=np.arange(1,126).reshape(5,5,5)
In [65]: i=np.arange(5)
In [66]: a4[i,i,i]
Out[66]: array([  1,  32,  63,  94, 125])

It should be easy to tweak the indices to get other diagonals.

In [73]: a4[np.arange(4),np.arange(1,5),np.arange(4)]
Out[73]: array([ 6, 37, 68, 99])

That `iii->i' producing the main diagonal is more of an happy accident than a designed feature. Don't try to push it.

hpaulj
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