indexing a matrix

I have a matrix MATRIX with values that I want to rearrange. I also
have another matrix INDEX that is the same shape of MATRIX that has
the order of the columns for the rearrangement.

for example, if MATRIX is 1 2 3
4 5 6
7 8 9
10 11 12

and INDEX is: 3 2 1
2 1 3
1 2 3
2 3 1

then my final matrix I want to have look like: 3 2 1
5 4
6
7 8
9
11 12 10

Is there any succinct way of creating this new matrix using MATRIX and
INDEX?

Lance

On Jun 13, 10:47*am, Lance <lanc...@gmail.com> wrote:
> I have a matrix MATRIX with values that I want to rearrange. *I also
> have another matrix INDEX that is the same shape of MATRIX that has
> the order of the columns for the rearrangement.
>
> for example, if MATRIX is 1 *2 *3
> * * * * * * * * * * * * * * * * * * *4 *5 *6
> * * * * * * * * * * * * * * * * * * *7 *8 *9
> * * * * * * * * * * * * * * * * * *10 11 12
>
> and INDEX is: * 3 *2 *1
> * * * * * * * * * * * * * * * * 2 *1 *3
> * * * * * * * * * * * * * * * * 1 *2 *3
> * * * * * * * * * * * * * * * * 2 *3 *1
>
> then my final matrix I want to have look like: *3 *2 *1
> * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *5 *4
> 6
> * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *7 *8
> 9
> * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *11 12 *10
>
> Is there any succinct way of creating this new matrix using MATRIX and
> INDEX?
>
> Lance

Please excuse the poor formatting. It looked fine before I submitted.

Hopefully this formats better:

for example, if MATRIX
1 2 3
4 5 6
7 8 9
10 11 12

and INDEX is:
3 2 1
2 1 3
1 2 3
2 3 1

then my final matrix I want to have look like:
3 2 1
5 4 6
7 8 9
11 12 10

On 6/13/2012 11:47 AM, Lance wrote:
> I have a matrix MATRIX with values that I want to rearrange. I also
> have another matrix INDEX that is the same shape of MATRIX that has
> the order of the columns for the rearrangement.
>
> for example, if MATRIX is 1 2 3
> 4 5 6
> 7 8 9
> 10 11 12
>
> and INDEX is: 3 2 1
> 2 1 3
> 1 2 3
> 2 3 1
>
> then my final matrix I want to have look like: 3 2 1
> 5 4
> 6
> 7 8
> 9
> 11 12 10
>
> Is there any succinct way of creating this new matrix using MATRIX and
> INDEX?

⊃(⊂¨⊂[2]INDEX)⌷¨⊂[2]MATRIX

--
_________________________________________
Bob Smith -- bsmith@sudleydeplacespam.com

To reply to me directly, delete "despam".

>
> ⊃(⊂¨⊂[2]INDEX)⌷¨⊂[2]MATRIX
>
> --
> _________________________________________
> Bob Smith -- bsm...@sudleydeplacespam.com
>
Thanks for the reply. Unfortunately this isn't working for me. I'm
working with APL+Win 2.0. Could it be my version of APL?

On 6/13/2012 12:11 PM, Lance wrote:
>>
>> ⊃(⊂¨⊂[2]INDEX)⌷¨⊂[2]MATRIX
>>
> Thanks for the reply. Unfortunately this isn't working for me. I'm
> working with APL+Win 2.0. Could it be my version of APL?

That's a very old version -- apparently it doesn't have an indexing
function (⌷).

If it supports axis operator on scalar dyadics, try

(,MATRIX)[INDEX+[1](1↓�MATRIX)ׯ1+�1↑�MATRIX]

If not, try

(,MATRIX)[INDEX+�(⌽�INDEX)�(1↓�MATRIX)ׯ1+�1 ↑�MATRIX]

For a more modern APL, try NARS2000 -- it's free at nars200.org.

--
_________________________________________
Bob Smith -- bsmith@sudleydeplacespam.com

To reply to me directly, delete "despam".

On Thursday, 14 June 2012 03:52:17 UTC+12, Lance wrote:
> Hopefully this formats better:
>
> for example, if MATRIX
> 1 2 3
> 4 5 6
> 7 8 9
> 10 11 12
>
> and INDEX is:
> 3 2 1
> 2 1 3
> 1 2 3
> 2 3 1
>
> then my final matrix I want to have look like:
> 3 2 1
> 5 4 6
> 7 8 9
> 11 12 10

The following shows (in J) how the concept of rank can be used to solve this problem. (needs INDEX-1 because J uses Index Origin 0).

(INDEX-1) {"1 MATRIX
3 2 1
5 4 6
7 8 9
11 12 10

On Wed, 13 Jun 2012 08:47:13 -0700, Lance wrote:

> I have a matrix MATRIX with values that I want to rearrange. I also
> have another matrix INDEX that is the same shape of MATRIX that has the
> order of the columns for the rearrangement.

This is what I would do in Dyalog:

M�4 3��12
I�4 3�3 2 1 2 1 3 1 2 3 2 3 1
M[(�3 4��4),¨I]
3 2 1
5 4 6
7 8 9
11 12 10



--
Aaron W. Hsu | arcfide@sacrideo.us | http://www.sacrideo.us
Programming is just another word for the lost art of thinking.

On Jun 14, 5:16Â*pm, "Aaron W. Hsu" <arcf...@sacrideo.us> wrote:
> On Wed, 13 Jun 2012 08:47:13 -0700, Lance wrote:
> > I have a matrix MATRIX with values that I want to rearrange. Â*I also
> > have another matrix INDEX that is the same shape of MATRIX that has the
> > order of the columns for the rearrangement.
>
> This is what I would do in Dyalog:
>
> Â* Â* Â* Â* Mâ†�4 3â�´â�³12
> Â* Â* Â* Â* Iâ†�4 3â�´3 2 1 2 1 3 1 2 3 2 3 1
> Â* Â* Â* Â* M[(â�‰3 4â�´â�³4),¨I]
> Â*3 Â*2 Â*1
> Â*5 Â*4 Â*6
> Â*7 Â*8 Â*9
> 11 12 10
>
> --
> Aaron W. Hsu | arcf...@sacrideo.us |http://www.sacrideo.us
> Programming is just another word for the lost art of thinking.

That is nice. I wasn't aware of that form of indexing.
Glad I had the free copy of Dyalog to check it out.

On Fri, 15 Jun 2012 14:17:57 -0700, Gary Logan wrote:

> That is nice. I wasn't aware of that form of indexing.
> Glad I had the free copy of Dyalog to check it out.

Personally I would prefer a non-nested indexing solution like this, but
the nested solutions works well enough in practice, and can be remarkably
efficient, despite its nested nature.

--
Aaron W. Hsu | arcfide@sacrideo.us | http://www.sacrideo.us
Programming is just another word for the lost art of thinking.

"Lance" <lancemd@gmail.com> wrote in message news:8e5359cc-af72-4a7d-9943-aac2d1f55e12@b1g2000vbb.googlegroups.com...
> Hopefully this formats better:
>
> for example, if MATRIX
> 1 2 3
> 4 5 6
> 7 8 9
> 10 11 12
>
> and INDEX is:
> 3 2 1
> 2 1 3
> 1 2 3
> 2 3 1
>
> then my final matrix I want to have look like:
> 3 2 1
> 5 4 6
> 7 8 9
> 11 12 10

Try this:

(�MATRIX)�(,MATRIX)[(,INDEX)+n×(n�¯1↑�INDEX)/¯1+�↑�INDEX]

Graham.

On 7/2/2012 4:02 PM, Graham wrote:
> "Lance" <lancemd@gmail.com> wrote in message news:8e5359cc-af72-4a7d-9943-aac2d1f55e12@b1g2000vbb.googlegroups.com...
>> Hopefully this formats better:
>>
>> for example, if MATRIX
>> 1 2 3
>> 4 5 6
>> 7 8 9
>> 10 11 12
>>
>> and INDEX is:
>> 3 2 1
>> 2 1 3
>> 1 2 3
>> 2 3 1
>>
>> then my final matrix I want to have look like:
>> 3 2 1
>> 5 4 6
>> 7 8 9
>> 11 12 10
> Try this:
>
> (�MATRIX)�(,MATRIX)[(,INDEX)+n×(n�¯1↑�INDEX)/¯1+�↑�INDEX]
>
> Graham.

That may work, I'm not familiar with APL+Win2.0, but
there are a couple of constructs which could cause an
older interpreter to burp. Namely, the use of ↑ for 1↑
and using an extended definition of /.

Bob Smith gave three solutions to the problem and his
third solution should work as far back as APL\360.

"Gary Logan" <glogan1513@gmail.com> wrote in message news:jt38av$k9v$1@dont-email.me...
> On 7/2/2012 4:02 PM, Graham wrote:
>> "Lance" <lancemd@gmail.com> wrote in message news:8e5359cc-af72-4a7d-9943-aac2d1f55e12@b1g2000vbb.googlegroups.com...
>>> Hopefully this formats better:
>>>
>>> for example, if MATRIX
>>> 1 2 3
>>> 4 5 6
>>> 7 8 9
>>> 10 11 12
>>>
>>> and INDEX is:
>>> 3 2 1
>>> 2 1 3
>>> 1 2 3
>>> 2 3 1
>>>
>>> then my final matrix I want to have look like:
>>> 3 2 1
>>> 5 4 6
>>> 7 8 9
>>> 11 12 10
>> Try this:
>>
>> (�MATRIX)�(,MATRIX)[(,INDEX)+n×(n�¯1↑�INDEX)/¯1+�↑�INDEX]
>>
>> Graham.
>
> That may work, I'm not familiar with APL+Win2.0, but
> there are a couple of constructs which could cause an
> older interpreter to burp. Namely, the use of ↑ for 1↑
> and using an extended definition of /.

I have been a life long user of APL+WIN and I have tested it as far back as APL*PLUS III which was a precursor to the APL+WIN family and it works fine.

Graham.

On Wednesday, 13 June 2012 12:47:13 UTC-3, Lance wrote:
> I have a matrix MATRIX with values that I want to rearrange. I also
>
> have another matrix INDEX that is the same shape of MATRIX that has
>
> the order of the columns for the rearrangement.
....
> Is there any succinct way of creating this new matrix using MATRIX and
>
> INDEX?
>
> Lance

Dyalog APL, and 'AssertEq' does a check for equality....

MATRIX�4 3��12
INDEX�4 3�3 2 1 2 1 3 1 2 3 2 3 1
RESULT�4 3 � 3 2 1 5 4 6 7 8 9 11 12 10
AssertEq RESULT on 4 3�MATRIX[↑(�4),¨¨↓INDEX]

I hope I matched your data correctly.