使用元组列表作为二维 Numpy 数组中列乘积的索引

Question

I have a 2D numpy array A and a list of tuples tup that look like:

A = np.array(range(1,11)).reshape(-3,2)
A
array([[ 1,  2],
       [ 3,  4],
       [ 5,  6],
       [ 7,  8],
       [ 9, 10]])

tup = [(0,),
 (1,),
 (0, 1),
 (0, 0),
 (1, 1),
 (0, 1, 1),
 (1, 1, 1),
 (0, 0, 0),
 (0, 0, 1)]

I'm looking to create a new np.array as result whose columns are products of the columns of A: the indices of the columns to be used in the products are given by the values in the tuples. For example, the above should yield:

[[1,3,5,7,9],
[2,4,6,8,10],
[2,12,30,56,90],
[1,9,25,49,81],
[4,16,36,64,100],
[4,48,180,448,900],
...]]

Where the rows above correspond to:

[A[0],
A[1],
A[0]*A[1],
A[0]*A[0],
A[1]*A[1],
A[0]*A[1]*A[1],
A[1]*A[1]*A[1],
...]

The tuples can be of any length >= 1. So far I've tried iterating through each index of tup and looping through the number of entries of each tuple, but I'm having difficulty writing out the product given the number of terms per product varies for different iterations. Any help or direction is much appreciated! Slight preference towards base Python and/or Numpy solutions.

Answer 1

In [135]: A = np.array(range(1,11)).reshape(-3,2)
In [136]: tup = [(0,),
     ...:  (1,),
     ...:  (0, 1),
     ...:  (0, 0),
     ...:  (1, 1),
     ...:  (0, 1, 1),
     ...:  (1, 1, 1),
     ...:  (0, 0, 0),
     ...:  (0, 0, 1)]

Let's try some indexing

In [137]: A[0,tup[0]]
Out[137]: array([1])
In [138]: A[0,tup[1]]
Out[138]: array([2])
In [141]: A[0,tup[2]]
Out[141]: array([1, 2])

or for all rows of A :

In [142]: A[:,tup[2]]
Out[142]: 
array([[ 1,  2],
       [ 3,  4],
       [ 5,  6],
       [ 7,  8],
       [ 9, 10]])

and the desired product:

In [143]: np.prod(A[:,tup[2]],axis=1)
Out[143]: array([ 2, 12, 30, 56, 90])

Now do this for a elements of tup .

[np.prod(A[:,k],axis=1) for k in tup]