Sorting the columns of a matrix

[Alexander Koplenig]

Dear Statalisters,
I'm just getting started with Mata, so apologies upfront: I have, I think, a very simple question: I'm calculating eigenvectors and eigenvalues of square matrix Cmat. Here's an example for 3x3 matrix:

: Cmat = (2,2,3\1,2,2\1,2,0)

:
: // Eigenvalues and Eigenvectors
: eigenvalues = .

: eigenvectors = .

:
: eigensystem(Cmat, eigenvectors, eigenvalues,)


: // Extract real part of eigenvalues and eigenvectors
: eigenvectors = Re(eigenvectors)

: eigenvalues = Re(eigenvalues')

:
:
: eigenvectors
                  1              2              3
    +----------------------------------------------+
  1 |  -.7621332906   -.5136120346   -.8772027338  |
  2 |  -.5282854667   -.3152370696    .4686056046  |
  3 |  -.3742556787    .7980152053     .104518664  |
    +----------------------------------------------+

: eigenvalues
                 1
    +---------------+
  1 |  4.859523389  |
  2 |  -1.43366463  |
  3 |  .5741412412  |
    +---------------+

The eigenvectors are sorted by their absolute eigenvalues in descending order (the default), but I'd like to have the eigenvectors sorted by their actual eigenvalues, e.g.:

: sort(eigenvalues,-1)
                 1
    +---------------+
  1 |  4.859523389  |
  2 |  .5741412412  |
  3 |  -1.43366463  |
    +---------------+

The first column of the eigenvector matrix should therefore represent the eigenvector with the largest value (4.86), the second column the eigenvector with the second largest value (.57) and so on.

Thank you for your help!

Best,
Ali

[Alexander Koplenig]

PS: Here's my current workaround, which gets the job done, but feels a bit clumsy

: Re_sort=sort((eigenvalues' \ eigenvectors)',-1)
:
: ncols = cols(Re_sort)

:
: eigenvectors = (Re_sort[1..., 2..ncols])'

:
: eigenvectors
                  1              2              3
    +----------------------------------------------+
  1 |  -.7621332906   -.8772027338   -.5136120346  |
  2 |  -.5282854667    .4686056046   -.3152370696  |
  3 |  -.3742556787     .104518664    .7980152053  |
    +----------------------------------------------+

[daniel klein]

If I understand your request, this may help

order = order(eigenvalues,-1)
eigenvalues[order]
eigenvectors[,order]

[Scott Merryman]

Would this work in all cases?

mata:
    Cmat = (2,2,3\1,2,2\1,2,0)
    // Eigenvalues and Eigenvectors
    eigenvalues = .
    eigenvectors = .
    eigensystem(Cmat, eigenvectors, eigenvalues,)
    // Extract real part of eigenvalues and eigenvectors
    eigenvectors = Re(eigenvectors)
    eigenvalues = Re(eigenvalues')
    ev = eigenvectors'[order(eigenvalues,-1),.]'
    ev
end

[Alexander Koplenig]

Both suggestions work. Thanks Daniel and Scott!

Best
Ali

[jose felix sanz]

Hi, when I sort a matrix, I would like to keep the original names of columns and rows. How can I do that?

Example:

I have the matrix A:

	TME	PTME	PC	PRR
Andalucia	.15656199	.12322447	2.033e-06	1.2705429	.96197714
Aragón	.15951484	.12407515	1.779e-06	1.2856308	.95954026
Asturias	.16233983	.12742271	1.720e-06	1.2740259	.95998392
Islas Bale~s	.16614045	.13165379	1.666e-06	1.2619496	.96028466
Canarias	.15917927	.12188039	2.159e-06	1.3060285	.95752415
Cantabria	.16459393	.12626319	1.923e-06	1.3035782	.9561301
Castilla-L~n	.15245961	.11823103	1.836e-06	1.2895059	.96118192
Castilla-L~a	.15460907	.12151381	1.948e-06	1.2723581	.96232693
Cataluña	.17575781	.14004542	1.471e-06	1.2550058	.95847177
Valenciana	.16774078	.12685677	2.257e-06	1.3222849	.95317605
Extremadura	.16042142	.11391964	3.243e-06	1.4081982	.94751967
Galicia	.15425344	.11935986	1.923e-06	1.2923393	.96037703
Madrid	.15994971	.12654823	1.213e-06	1.2639427	.96175922
Murcia	.14988071	.11888892	1.805e-06	1.2606785	.96482648
La Rioja	.16039163	.12129363	2.036e-06	1.3223417	.95550505
Ceuta y Me~a	.16838468	.1297451	1.713e-06	1.2978115	.9555997
Total Régi~n	.16263953	.12735901	1.723e-06	1.2770163	.95957041

I compute the following:

mata: st_matrix("B", sort(st_matrix("A"), -1))

The work is done, but I lost the original names of rows during the process. How can I avoid that? The names of the rows should be the same as the new order of the columns.

[daniel klein]

Something along these lines should do:

A = st_matrix("A")
rownames = st_matrixrowstripe("A")
order = order(A, -1)
st_matrix("B",A[order,])
st_matrixrowstripe("B",rownames[order,])

[jose felix sanz]

Thanks, Daniel, for the advice. I will try it.