Question

When I use Python to model a 3-Dimensional matrix, I first make a multi-array of zeros. Then, I can easily overwrite each element by referencing its index. The problem is, the order of indices change when trying to reference multiple elements using [:]. I’m going to speak in matrix math jargon, so bear with me.

In the example below, I want to model the position of an object in the 2-D plane per time level. So for each time level, I have an X (row) and Y (column) coordinate. In the example below, I use two time levels with 3 rows and 4 columns.

    >>> Simple = numpy.zeros([2,3,4],float)
    >>> print Simple
    [[[ 0.  0.  0.  0.]
    [ 0.  0.  0.  0.]
    [ 0.  0.  0.  0.]]

    [[ 0.  0.  0.  0.]
    [ 0.  0.  0.  0.]
    [ 0.  0.  0.  0.]]]

Looks good. I have two 3×4 matrices. Now I want to change the value of the 2nd matrix (2nd time level), 3rd row, 4th column to be equal to 9.

    >>> Simple[1][2][3] = 9
    >>> print Simple
    [[[ 0.  0.  0.  0.]
    [ 0.  0.  0.  0.]
    [ 0.  0.  0.  0.]]

    [[ 0.  0.  0.  0.]
    [ 0.  0.  0.  0.]
    [ 0.  0.  0.  9.]]]

So far so good. From this, I can tell that the order of indices is Simple[TimeLevel,X,Y]. So now, for each time level, I want the element in the first row, second column (timelevel = both,x=0,y=1) to be the number “4”.

   >>> Simple[:][0][1] = 4
   >>> print Simple
   [[[ 0.  0.  0.  0.]
   [ 4.  4.  4.  4.]
   [ 0.  0.  0.  0.]]

   [[ 0.  0.  0.  0.]
   [ 0.  0.  0.  0.]
   [ 0.  0.  0.  9.]]]

So as you can see, the order of indices is no longer the same. It switched from Simple[TimeLevel,row,column] to Simple[column,TimeLevel,row].

My question is: WHY?

Answer 1

All [:] does is return a copy of the sequence. This is not what you want.

>>> Simple[:,0,1] = 4
>>> Simple
array([[[ 0.,  4.,  0.,  0.],
        [ 0.,  0.,  0.,  0.],
        [ 0.,  0.,  0.,  0.]],

       [[ 0.,  4.,  0.,  0.],
        [ 0.,  0.,  0.,  0.],
        [ 0.,  0.,  0.,  0.]]])