For practical reasons the items of a vector are listed horizontally but the
items of higher dimensional arrays are listed vertically. You must
remember this when you interpret displays.
To illustrate, in
i. 3 2 4
0 1 2 3
4 5 6 7
8 9 10 11
12 13 14 15
16 17 18 19
20 21 22 23
the items (three tables) are listed vertically, and the items of each table
(two vectors) are listed vertically, but the items of each vector (four
numbers) are listed horizontally.
On Thursday, September 11, 2014, George Dallas <[email protected]>
wrote:
> Let’s say we have a rank 3 array A like so:
>
>
>
> ]A=.i.2 4 7
>
> 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
>
>
>
> And we would like to add the rows. The rank conjunction along the second
> dimension seems to work fine in this case.
>
>
>
> +/"2 A
>
> 42 46 50 54 58 62 66
>
> 154 158 162 166 170 174 178
>
>
>
> Now let’s say we’d like to add the columns. The rank conjunction along the
> first dimension is employed in this case to produce the result.
>
>
>
> +/"1 A
>
> 21 70 119 168
>
> 217 266 315 364
>
>
>
> It is this result where I, being a J novice, perceive that an unexpected
> transposition has taken place. I’ll explain what formed my expectations.
> Coming from a Matlab background I’m used to expect the results in a certain
> spatial location. For example, if I wanted to replicate the same results in
> Matlab I would do something like the following with A being a 4 by 7 by 2
> array (as opposed to a 2 by 4 by 7 in J, but this is a very minor
> difference and one can adjust to it easily).
>
>
>
> >> A
>
> A(:,:,1) =
>
> 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
>
> A(:,:,2) =
>
> 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
>
>
>
> >> sum(A,1)
>
> ans(:,:,1) =
>
> 42 46 50 54 58 62 66
>
> ans(:,:,2) =
>
> 154 158 162 166 170 174 178
>
>
>
> >> sum(A,2)
>
> ans(:,:,1) =
>
> 21
>
> 70
>
> 119
>
> 168
>
> ans(:,:,2) =
>
> 217
>
> 266
>
> 315
>
> 364
>
>
>
> So Matlab’s sum(A,1) corresponds to J’s +/”2 A, but Matlab’s sum(A,2)
> corresponds to a visually transposed form of J’s +/”1 A. In other words,
> the shape of the result of adding columns in Matlab carries a spatial
> resemblance to performing the addition of the columns of A on a chalkboard
> and writing the result in a vertical manner for each successive row.
>
>
>
> I suspect there are good reasons for this behavior in J that allow for easy
> scaling of the results in higher dimensions. I think my fear is that this
> behavior might lead me to erroneous indexing due to not having the proper
> visualization of the results. For example in Matlab I could find result of
> the sum of the columns of A for the third row of the first 2D slice at the
> position (3,1,1) of the result of sum(A,2). Whereas I’m not sure about the
> proper way of indexing on the results of +/”1 A.
>
>
>
> I have observed this behavior elsewhere in J as well. For example using the
> dyad ,. (stitch) on i.5 and 1+i.5, seems to first transpose the row vectors
> and then appending to the right, whereas I was expecting the row vector 0 1
> 2 3 4 1 2 3 4 5 as output.
>
>
>
> i.5
>
> 0 1 2 3 4
>
> 1+i.5
>
> 1 2 3 4 5
>
> (i.5),.(1+i.5)
>
> 0 1
>
> 1 2
>
> 2 3
>
> 3 4
>
> 4 5
>
>
>
> My question to the J community then is with regards to the appropriate way
> to think about arrays in J so that I can correctly anticipate vector
> transposition when applying the rank conjunction and how to properly index
> on its result.
>
>
>
> Thank you,
>
> George
> ----------------------------------------------------------------------
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--
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