Python单元素元组

Question

Suppose I have a matrix M and an indexing set idx=[(0,1),(2,3),(3,2)] and I want to create two sets of tuples, idx_leq1 consisting of those tuples whose first and second elements are both less than or equal to 1 and idx_geq2 consisting of those tuples whose first and second elements are both greater than or equal to 2.

I want to access the elements M[idx_leq1] and M[idx_geq2] cleanly. I have tried idx_leq1 = tuple([e for e in idx if e[0]<=1 and e[1]<=1]) , but this returns idx_leq1 = ((0,1),) which I can't use to index M . On the other hand, idx_geq2 = tuple([e for e in idx if e[0]>=2 and e[1]>=2]) = ((2,3),(3,2)) works.

How can I solve this for the case where my first index set consists of only one coordinate pair? I don't want to do M[idx_leq1[0]] .

I can do: list(chain(*[(e,) for e in idx if e[0]<=1 and e[1]<=1])) and list(chain(*[(e,) for e in idx if e[0]>=2 and e[1]>=2])) , but then I still have to grab the first element for idx_leq1 whereas I can pass idx_geq2 to M and grab the appropriate elements.

Thanks!

Answer 1

[Tested with numpy.mat ]

[M[0, 1]] should be fetched as in M[[0], [1]] . When indexing matrix, Multidimensional list-of-locations indexing requires k lists of index each working with one dimension.

For example, in order to fetch M[0, 3], M[1, 4], M[2, 5] , one should use M[[0, 1, 2], [3, 4, 5]] . In other word, the index that you give to M should not be considered lists of coordinates. Rather, they are lists of "coordinates on each dimension".
In your case, a M[[0, 1]] (or its equivalent in tuple type) fetches M[0], M[1] as [0, 1] is considered to work on the first dimension, and the second dimension is broadcasted.

Ref: http://scipy-cookbook.readthedocs.io/items/Indexing.html#Multidimensional-list-of-locations-indexing
This reference believes that the reason to use "list of dims" rather than "list of coordinates" is to save number of instances, as unpacking many tuples might be expensive.