R help - Apr 2010 - reordering of matrix rows to maximize the sum of the diagonal

Hi r-help community,
    This question isn't so much a syntax/coding one, but here goes:

Let's say I have matrix of arbitrary dimensions and I'd like to
reorder the rows in such a way that I could maximize the sum of the
entries along the diagonal.

For example, for this 3x3 matrix:


     [,1] [,2] [,3]
[1,]    3    4   13
[2,]    9    1    2
[3,]    2   11    1

rearranging the rows to maximize the sum along the diagonal would
produce this matrix:

     [,1] [,2] [,3]
[1,]    9    1    2
[2,]    2   11    1
[3,]    3    4   13


I've been experimenting with some scripts of my own, but I figured I'd
ask if one of you R-ninjas might know of an existing function (or
algorithm I could look up and then code) that can do this somewhat
efficiently (or even just correctly!).

Best,
Jonathan

Can you specify how you would re-order this matrix:

matrix(1:16, 4,4)

 > apply(mtx, 2, which.max)
[1] 4 4 4 4

-- 
David.
On Apr 23, 2010, at 4:10 PM, Jonathan wrote:
> Hi r-help community,
>    This question isn't so much a syntax/coding one, but here goes:
>
> Let's say I have matrix of arbitrary dimensions and I'd like to
> reorder the rows in such a way that I could maximize the sum of the
> entries along the diagonal.
>
> For example, for this 3x3 matrix:
>
>
>     [,1] [,2] [,3]
> [1,]    3    4   13
> [2,]    9    1    2
> [3,]    2   11    1
>
> rearranging the rows to maximize the sum along the diagonal would
> produce this matrix:
>
>     [,1] [,2] [,3]
> [1,]    9    1    2
> [2,]    2   11    1
> [3,]    3    4   13
>
>
> I've been experimenting with some scripts of my own, but I figured
I'd
> ask if one of you R-ninjas might know of an existing function (or
> algorithm I could look up and then code) that can do this somewhat
> efficiently (or even just correctly!).
>
> Best,
> Jonathan
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
David Winsemius, MD
West Hartford, CT

one way is:

M <- matrix(sample(13, 9, TRUE), 3, 3)

n <- ncol(M)
ind <- apply(M, 2, which.max)
maxs <- M[cbind(ind, 1:n)]
diags <- diag(M)
diag(M) <- M[cbind(ind, 1:n)]
M[cbind(ind, 1:n)] <- diags
M


I hope it helps.

Best,
Dimitris


On 4/23/2010 10:10 PM, Jonathan wrote:
> Hi r-help community,
>      This question isn't so much a syntax/coding one, but here goes:
>
> Let's say I have matrix of arbitrary dimensions and I'd like to
> reorder the rows in such a way that I could maximize the sum of the
> entries along the diagonal.
>
> For example, for this 3x3 matrix:
>
>
>       [,1] [,2] [,3]
> [1,]    3    4   13
> [2,]    9    1    2
> [3,]    2   11    1
>
> rearranging the rows to maximize the sum along the diagonal would
> produce this matrix:
>
>       [,1] [,2] [,3]
> [1,]    9    1    2
> [2,]    2   11    1
> [3,]    3    4   13
>
>
> I've been experimenting with some scripts of my own, but I figured
I'd
> ask if one of you R-ninjas might know of an existing function (or
> algorithm I could look up and then code) that can do this somewhat
> efficiently (or even just correctly!).
>
> Best,
> Jonathan
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
-- 
Dimitris Rizopoulos
Assistant Professor
Department of Biostatistics
Erasmus University Medical Center

Address: PO Box 2040, 3000 CA Rotterdam, the Netherlands
Tel: +31/(0)10/7043478
Fax: +31/(0)10/7043014

Hi:

How about this? Calling your matrix a,

a[order(rowSums(a)), ]
     [,1] [,2] [,3]
[1,]    9    1    2
[2,]    2   11    1
[3,]    3    4   13

HTH,
Dennis


On Fri, Apr 23, 2010 at 1:10 PM, Jonathan <jonsleepy@gmail.com> wrote:
> Hi r-help community,
>    This question isn't so much a syntax/coding one, but here goes:
>
> Let's say I have matrix of arbitrary dimensions and I'd like to
> reorder the rows in such a way that I could maximize the sum of the
> entries along the diagonal.
>
> For example, for this 3x3 matrix:
>
>
>     [,1] [,2] [,3]
> [1,]    3    4   13
> [2,]    9    1    2
> [3,]    2   11    1
>
> rearranging the rows to maximize the sum along the diagonal would
> produce this matrix:
>
>     [,1] [,2] [,3]
> [1,]    9    1    2
> [2,]    2   11    1
> [3,]    3    4   13
>
>
> I've been experimenting with some scripts of my own, but I figured
I'd
> ask if one of you R-ninjas might know of an existing function (or
> algorithm I could look up and then code) that can do this somewhat
> efficiently (or even just correctly!).
>
> Best,
> Jonathan
>
> ______________________________________________
> R-help@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
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