使用 Numpy 从基于向量的 3D 矩阵中选择列

Question

So I am trying to select some columns from a 3D matrix based on the values in a vector using Numpy. I have already solved the problem using a list comprehension, but I figured that there might be a better way using Numpy's builtin methods. Does anyone know if such a method or combination of methods exist?

matrix1 = np.array([[1, 2, 3],
                    [4, 5, 6],
                    [7, 8, 9]])
matrix2 = np.array([[10, 11, 12],
                    [13, 14, 15],
                    [16, 17, 18]])
total_matrix = np.array([matrix1, matrix2])
vector = [0,1,1]

# Retrieve the first column from the first matrix, second and third from the second matrix.
result = np.array([total_matrix[index2,: , index1] for index1, index2 in enumerate(vector)]).transpose()

# result:
np.array([[1, 11, 12],
          [4, 14, 15],
          [7, 15, 18]])

Answer 1

In [58]: total_matrix[vector, np.arange(3)[:,None], np.arange(3)]
Out[58]: 
array([[ 1, 11, 12],
       [ 4, 14, 15],
       [ 7, 17, 18]])

vector indexes the first dimension. The other 2 broadcast with it to select the required (3,3). While I knew the general principle, I tried a number of variations (about 9) before getting the right one.

The use of diagonal in the other answer is equivalent to doing:

In [61]: total_matrix[vector][:,np.arange(3),np.arange(3)]
Out[61]: 
array([[ 1,  5,  9],
       [10, 14, 18],
       [10, 14, 18]])

Answer 2

You can slice the total_matrix using your vector and then select appropriate diagonal elements of it:

>>> np.diagonal(total_matrix[vector], axis1=0, axis2=2)
array([[ 1, 11, 12],
       [ 4, 14, 15],
       [ 7, 17, 18]])