[Numpy-discussion] interleaved indexing

[Stéfan van der Walt]

Hi Amir

2008/7/18 Amir <amirnntp@gmail.com>:
> A very beginner question about indexing: let x be an array where n =
> len(x). I would like to create a view y of x such that:
>
> y[i] = x[i:i+m,...]  for each i and a fixed m << n
>
> so I can do things like numpy.cov(y). With n large, allocating y is a
> problem for me. Currently, I either do for loops in cython or
> translate operations into correlate() but am hoping there is an easier
> way, maybe using fancy indexing or broadcasting. Memory usage is
> secondary to speed, though.

Robert Kern's recently added numpy.lib.stride_tricks should help:

In [84]: x = np.arange(100).reshape(10,-1)

In [85]: x
Out[85]:
array([[ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14, 15, 16, 17, 18, 19],
       [20, 21, 22, 23, 24, 25, 26, 27, 28, 29],
       [30, 31, 32, 33, 34, 35, 36, 37, 38, 39],
       [40, 41, 42, 43, 44, 45, 46, 47, 48, 49],
       [50, 51, 52, 53, 54, 55, 56, 57, 58, 59],
       [60, 61, 62, 63, 64, 65, 66, 67, 68, 69],
       [70, 71, 72, 73, 74, 75, 76, 77, 78, 79],
       [80, 81, 82, 83, 84, 85, 86, 87, 88, 89],
       [90, 91, 92, 93, 94, 95, 96, 97, 98, 99]])

In [86]: x.stridesOut[86]: (40, 4)

In [87]: xx = np.lib.stride_tricks.as_strided(x, shape=(8, 3, 10),
strides=(40, 40, 4))

In [88]: xx
Out[88]:
array([[[ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9],
        [10, 11, 12, 13, 14, 15, 16, 17, 18, 19],
        [20, 21, 22, 23, 24, 25, 26, 27, 28, 29]],

       [[10, 11, 12, 13, 14, 15, 16, 17, 18, 19],
        [20, 21, 22, 23, 24, 25, 26, 27, 28, 29],
        [30, 31, 32, 33, 34, 35, 36, 37, 38, 39]],

       [[20, 21, 22, 23, 24, 25, 26, 27, 28, 29],
        [30, 31, 32, 33, 34, 35, 36, 37, 38, 39],
        [40, 41, 42, 43, 44, 45, 46, 47, 48, 49]],

[...]

Cheers
Stéfan