Joshua Wiley jwiley.psych at gmail.com
Mon Nov 8 01:33:50 CET 2010

```On Sat, Nov 6, 2010 at 7:38 AM, Stephen Liu <satimis at yahoo.com> wrote:
> Hi Joshua,
>
>
> 1)
>> a3d
> , , 1 <--- this is the first position of the third dimension ***THIS IS THE THIRD DIMENSION***
>
>     [,1] [,2] [,3] [,4]  <--- positions 1, 2, 3, 4 of the second dimension
> [1,]    1    4    7   10
> [2,]    2    5    8   11
> [3,]    3    6    9   12
> ^  the first dimension
>
> , , 2 <--- the second position of the third dimension ***THIS IS THE THIRD DIMENSION***
> ...
> [/quote]
>
> Where is the third dimension?

I pointed to the third dimension above.  You can think of a 3d array
kind of like a journal (I don't know if this is helpful, but I kind of
like the analogy so...).  Each page holds a two dimensional table, so
I could tell you to look at row 4, column 3 on page 16.  Nevertheless,
at any given point, it is just a flat page.

>
> 2)
> so you can think that in the original vector "a":
> 1 maps to a[1, 1, 1] in the 3d array
> 2 maps to a[2, 1, 1].
> 3 maps to a[3, 1, 1]
> 4 maps to a[1, 2, 1]
> 12 maps to a[3, 4, 1]
> 20 maps to a[2, 3, 2]
> 24 maps to a[3, 4, 2]
> [/quote]
>
> My finding;
>
> # 1 maps to a[1, 1, 1] in the 3d array
>> a3d <- array(a, dim = c(1, 1, 1))
>> a3d
> , , 1
>
>     [,1]
> [1,]    1
>
> Correct
>
> # 2 maps to a[2, 1, 1].
>> a3d <- array(a, dim = c(2, 1, 1))
>> a3d
> , , 1
>
>     [,1]
> [1,]    1
> [2,]    2
>
> Correct
>
> # 3 maps to a[3, 1, 1]
>> a3d <- array(a, dim = c(3, 1, 1))
>> a3d
> , , 1
>
>     [,1]
> [1,]    1
> [2,]    2
> [3,]    3
>
> Correct
>
> # 4 maps to a[1, 2, 1]
>> a3d <- array(a, dim = c(1, 2, 1))
>> a3d
> , , 1
>
>     [,1] [,2]
> [1,]    1    2
>
> Incorrect.  It is "2"

No, it is correct.  You cannot assume that you may use the same
indices to access an array when you have created it with different
dimensions.  Consider:

> array(1:24, dim = c(3, 4, 2))[1, 2, 1]
[1] 4
> array(1:24, dim = c(1, 2, 1))[1, 2, 1]
[1] 2

>
>
> # 12 maps to a[3, 4, 1]
>> a3d <- array(a, dim = c(3, 4, 1))
>> a3d
> , , 1
>
>     [,1] [,2] [,3] [,4]
> [1,]    1    4    7   10
> [2,]    2    5    8   11
> [3,]    3    6    9   12
>
> Correct
>
> # 20 maps to a[2, 3, 2]
>> a3d <- array(a, dim = c(2, 3, 2))
>> a3d
> , , 1
>
>     [,1] [,2] [,3]
> [1,]    1    3    5
> [2,]    2    4    6
>
> , , 2
>
>     [,1] [,2] [,3]
> [1,]    7    9   11
> [2,]    8   10   12
>
> Incorrect.  It is "12"

See my above comment about not expecting things in the same location
when you change the space they live in.

Sorry this was so slow in coming, I missed the email somehow.

Cheers,

Josh

[snip]

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