rebin 1.0.1

Rationale

The input array, a is assumed to be strided. In other words, if

a.strides = (s0, s1, ...),

then

a[i0, i1, ...] = a[[s0*i0 + s1*i1 + ...]],

where [[...]] denotes the offset operator. To compute the output array, we first create a tiled version of a. The number of dimensions of tiled is twice that of a: for each index in a, tiled has one slow index and one fast index

tiled[i0, i1, ..., j0, j1, ...] = a[f0*i0 + j0, f1*i1 + j1, ...],

where factor=(f0, f1, ...) is the binning factor (size of the tiles). Upon using the strides of a

tiled[i0, i1, ..., j0, j1, ...] = a[[s0*f0*i0 + s1*f1*i1 + ... +
                                     s0*j0 + s1*j1 + ...]],

which shows that the strides of tiled are

tiled.strides = (s0*f0, s1*f1, ..., s0, s1, ...).

In other words, tiled is a view of a with modified strides. Restriding an array can be done with the as_strided function from numpy.lib.stride_tricks. Then, the output array is readily computed as follows

out = func(tiled, axis = tuple(range(-a.ndim, 0)))

where reduction is carried out on the fast indices.

Boundary cases

When the dimensions of the input array are not integer multiples of the dimensions of the tiles, the remainding rows/columns are simply discarded. For example

+--------+--------+--------+--------+----+
|  1   1 |  2   2 |  3   3 |  4   4 |  5 |
|  1   1 |  2   2 |  3   3 |  4   4 |  5 |
+--------+--------+--------+--------+----+
|  6   6 |  7   7 |  8   8 |  9   9 | 10 |
|  6   6 |  7   7 |  8   8 |  9   9 | 10 |
+--------+--------+--------+--------+----+
| 11  11 | 12  12 | 13  13 | 14  14 | 15 |
+--------+--------+--------+--------+----+

will produce

+----+----+----+----+
|  4 |  8 | 12 | 16 |
+----+----+----+----+
| 24 | 28 | 32 | 36 |
+----+----+----+----+

for (2, 2) tiles and a sum reduction.