3-dimensional array in numpy

Question

New at Python and Numpy, trying to create 3-dimensional arrays. My problem is that the order of the dimensions are off compared to Matlab. In fact the order doesn\'t make se

Answer 1

As much as people like to say "order doesn't matter its just convention" this breaks down when entering cross domain interfaces, IE transfer from C ordering to Fortran ordering or some other ordering scheme. There, precisely how your data is layed out and how shape is represented in numpy is very important.

By default, numpy uses C ordering, which means contiguous elements in memory are the elements stored in rows. You can also do FORTRAN ordering ("F"), this instead orders elements based on columns, indexing contiguous elements.

Numpy's shape further has its own order in which it displays the shape. In numpy, shape is largest stride first, ie, in a 3d vector, it would be the least contiguous dimension, Z, or pages, 3rd dim etc... So when executing:

np.zeros((2,3,4)).shape

you will get

(2,3,4)

which is actually (frames, rows, columns). doing np.zeros((2,2,3,4)).shape instead would mean (metaframs, frames, rows, columns). This makes more sense when you think of creating multidimensional arrays in C like langauges. For C++, creating a non contiguously defined 4D array results in an array [ of arrays [ of arrays [ of elements ]]]. This forces you to de reference the first array that holds all the other arrays (4th dimension) then the same all the way down (3rd, 2nd, 1st) resulting in syntax like:

double element = array4d[w][z][y][x];

In fortran, this indexed ordering is reversed (x is instead first array4d[x][y][z][w]), most contiguous to least contiguous and in matlab, it gets all weird.

Matlab tried to preserve both mathematical default ordering (row, column) but also use column major internally for libraries, and not follow C convention of dimensional ordering. In matlab, you order this way:

double element = array4d[y][x][z][w];

which deifies all convention and creates weird situations where you are sometimes indexing as if row ordered and sometimes column ordered (such as with matrix creation).

In reality, Matlab is the unintuitive one, not Numpy.