Re: new array indexing in lush2

That's cool. Sure beats nested selects in unverbosity.

  -- Yann


On Saturday 18 October 2008, Ralf Juengling wrote:
> Good afternoon,
>
> We briefly talked about the need for more powerful
> ways of indexing Lush arrays in the past. I finally
> took the time to implement some ideas in Lush2 (rev 93).
>
> I added two new indexing modes and left the old
> one in place, so this extension is backwards compatible.
> Let me demonstrate briefly how it works.
>
> ? m  ;; a matrix
> = [d[d   1.0000   2.0000   3.0000   4.0000   5.0000]
>      [d   6.0000   7.0000   8.0000   9.0000  10.0000]
>      [d  11.0000  12.0000  13.0000  14.0000  15.0000]
>      [d  16.0000  17.0000  18.0000  19.0000  20.0000]]
>
> ? img  ;; an RGB image
> = ::INDEX:<512x512x3>
>
> The old-style indexing uses numbers as subscripts--
> as many numbers as dimensions--and gives the indexed
> element as a number or the updated array as result.
>
> ? ; element (1,2) of m
> ? (m 1 2)
> = 8
> ? ; updating element (1,2) of m
> ? (m 1 2 -8)
> = [d[d   1.0000   2.0000   3.0000   4.0000   5.0000]
>      [d   6.0000   7.0000  -8.0000   9.0000  10.0000]
>      [d  11.0000  12.0000  13.0000  14.0000  15.0000]
>      [d  16.0000  17.0000  18.0000  19.0000  20.0000]]
>
> Both new indexing modes use arrays as subscripts and
> give an array of indexed elements or the updated array
> as result.
>
> In the first mode, the subscript is a vector, and its
> contents are used to do a (partial) select:
>
> ? ; element (1,2) of m
> ? (m [1 2])
> = [d@ -8]
>
> ? ; row 1 of m
> ? (m [1])
> = [d   6.0000   7.0000  -8.0000   9.0000  10.0000]
>
> ? ; all of m
> ? (m [])
> = [d[d   1.0000   2.0000   3.0000   4.0000   5.0000]
>      [d   6.0000   7.0000  -8.0000   9.0000  10.0000]
>      [d  11.0000  12.0000  13.0000  14.0000  15.0000]
>      [d  16.0000  17.0000  18.0000  19.0000  20.0000]]
>
> ? ; updating all of m
> ? (m [] 0)
> = [d[d   0.0000   0.0000   0.0000   0.0000   0.0000]
>      [d   0.0000   0.0000   0.0000   0.0000   0.0000]
>      [d   0.0000   0.0000   0.0000   0.0000   0.0000]
>      [d   0.0000   0.0000   0.0000   0.0000   0.0000]]
>
> ? ; updating row 1 of m
> ? (m [1] 1)
> = [d[d   0.0000   0.0000   0.0000   0.0000   0.0000]
>      [d   1.0000   1.0000   1.0000   1.0000   1.0000]
>      [d   0.0000   0.0000   0.0000   0.0000   0.0000]
>      [d   0.0000   0.0000   0.0000   0.0000   0.0000]]
>
> ? ; pixel (100, 100) of img
> ? (img [100 100])
> = [u   182    74    87]
>
> In the second mode, the subscript argument is an array
> of subscript vectors, that is, the extent in the
> last dimension equals the rank of the array to be
> indexed.
>
> ? ; subscripts of diagonal elements of m
> ? (setq ss [[0 0] [1 1] [2 2] [3 3]])
> = [d[d   0.0000   0.0000]
>      [d   1.0000   1.0000]
>      [d   2.0000   2.0000]
>      [d   3.0000   3.0000]]
> ? (m ss)
> = [d   0.0000   1.0000   0.0000   0.0000]
>
> ? ; updating diagonal elements of m
> ? (m ss [10 20 30 40])
> = [d[d  10.0000   0.0000   0.0000   0.0000   0.0000]
>      [d   1.0000  20.0000   1.0000   1.0000   1.0000]
>      [d   0.0000   0.0000  30.0000   0.0000   0.0000]
>      [d   0.0000   0.0000   0.0000  40.0000   0.0000]]
>
> ? ; updating diagonal elements of m
> ? (m ss (/ (m ss) 10))
> = [d[d   1.0000   0.0000   0.0000   0.0000   0.0000]
>      [d   1.0000   2.0000   1.0000   1.0000   1.0000]
>      [d   0.0000   0.0000   3.0000   0.0000   0.0000]
>      [d   0.0000   0.0000   0.0000   4.0000   0.0000]]
>
> This second mode is in particular handy in combination
> with 'where', which gives you the indices of all nonzero
> entries in an array (the function that used to be
> called 'where' in lush is called 'btrace' in lush2):
>
> ? (where m)
> = [i[i     0     0]
>      [i     1     0]
>      [i     1     1]
>      [i     1     2]
>      [i     1     3]
>      [i     1     4]
>      [i     2     2]
>      [i     3     3]]
>
> ? ; start with a fresh m
> ? (setq m (reshape (arange 20) '(4 5)))
> = [d[d   1.0000   2.0000   3.0000   4.0000   5.0000]
>      [d   6.0000   7.0000   8.0000   9.0000  10.0000]
>      [d  11.0000  12.0000  13.0000  14.0000  15.0000]
>      [d  16.0000  17.0000  18.0000  19.0000  20.0000]]
>
> ? ; change all odd entries
> ? (mod m 2)
> = [d[d   1.0000   0.0000   1.0000   0.0000   1.0000]
>      [d   0.0000   1.0000   0.0000   1.0000   0.0000]
>      [d   1.0000   0.0000   1.0000   0.0000   1.0000]
>      [d   0.0000   1.0000   0.0000   1.0000   0.0000]]
>
> ? (let ((ss (where (mod m 2))))
>      (m ss (* (m ss) 10)) )
> = [d[d  10.0000   2.0000  30.0000   4.0000  50.0000]
>      [d   6.0000  70.0000   8.0000  90.0000  10.0000]
>      [d 110.0000  12.0000 130.0000  14.0000 150.0000]
>      [d  16.0000 170.0000  18.0000 190.0000  20.0000]]
>
>
> The indexing stuff if very new and the compiler does
> not support the new indexing modes yet. But before I
> put more work into it, I thought you should take a
> look at this.
>
> Cheers,
> Ralf
>
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