Rearranging Matrix Elements with Numpy

matrix, numpy, python

Solution

edit: I just stumbled across a NumPy solution that uses advanced indexing:

#                 a  b  c  d  e  f
A = numpy.array([[0, 1, 2, 3, 4, 5],
                 [1, 0, 3, 4, 5, 6],
                 [2, 3, 0, 5, 6, 7],
                 [3, 4, 5, 0, 7, 8],
                 [4, 5, 6, 7, 0, 9],
                 [5, 6, 7, 8, 9, 0]])

#            a  d  b  e  c  f
new_order = [0, 3, 1, 4, 2, 5]
A1 = A[:, new_order][new_order]

Here is a pure Python solution which may be transferable to NumPy:

#     a  b  c  d  e  f
A = [[0, 1, 2, 3, 4, 5],
     [1, 0, 3, 4, 5, 6],
     [2, 3, 0, 5, 6, 7],
     [3, 4, 5, 0, 7, 8],
     [4, 5, 6, 7, 0, 9],
     [5, 6, 7, 8, 9, 0]]

#            a  d  b  e  c  f
new_order = [0, 3, 1, 4, 2, 5]    # maps previous index to new index
A1 = [[A[i][j] for j in new_order] for i in new_order]

Result:

>>> pprint.pprint(A1)
[[0, 3, 1, 4, 2, 5],
 [3, 0, 4, 7, 5, 8],
 [1, 4, 0, 5, 3, 6],
 [4, 7, 5, 0, 6, 9],
 [2, 5, 3, 6, 0, 7],
 [5, 8, 6, 9, 7, 0]]

Here is a version that modifies `A` in place:

A[:] = [A[i] for i in new_order]
for row in A:
    row[:] = [row[i] for i in new_order]

Problem

I have a NumPy matrix which I've simplified to exemplify: ``` a b c d e f A = [[0, 1, 2, 3, 4, 5], b [1, 0, 3, 4, 5, 6], c [2, 3, 0, 5, 6, 7], d [3, 4, 5, 0, 7, 8], e [4, 5, 6, 7, 0, 9], f [5, 6, 7, 8, 9, 0]] ``` where the number at the "intersections" is important, but their order is not right. I want to re-arrange the rows and columns such that the new order is [a, d, b, e, c, f] but this value that I'm calling "the intersection" is the same. Below I have started to transform the matrix how I want. Filling the 'e' row involves looking at the intersections above for (e,a) (= 4), then (e,d) (=7) , then (e,b) (=5), (e,e), (e,c), and (e,f) ``` a d b e c f A1= [[0, 3, 1, 4, 2, 5], d [3, 0, 4, 7, 5, 8], b [1, 4, 0, 5, 3, 6], e [4, 7, 5, ``` Can anyone please suggest how to re-arrange my matrix in this manner?

Original source

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