PERMA

Permutes the rows or columns of a matrix.

Required Arguments

A — NRA by NCA matrix to be permuted. (Input)

IPERMU — Vector of length K containing a permutation IPERMU(1), …, IPERMU(K) of the integers 1, …, K where K = NRA if the rows of A are to be permuted and K = NCA if the columns of A are to be permuted. (Input)

APER — NRA by NCA matrix containing the permuted matrix. (Output)
If A is not needed, A and APER can share the same storage locations.

Optional Arguments

NRA — Number of rows. (Input)
Default: NRA = size (A,1).

NCA — Number of columns. (Input)
Default: NCA = size (A,2).

LDA — Leading dimension of A exactly as specified in the dimension statement of the calling program. (Input)
Default: LDA = size (A,1).

IPATH — Option parameter. (Input)
IPATH = 1 means the rows of A will be permuted. IPATH = 2 means the columns of A will be permuted.
Default: IPATH = 1.

LDAPER — Leading dimension of APER exactly as specified in the dimension statement of the calling program. (Input)
Default: LDAPER = size (APER,1).

FORTRAN 90 Interface

Generic: CALL PERMA (A, IPERMU, APER [, …])

Specific: The specific interface names are S_PERMA and D_PERMA.

FORTRAN 77 Interface

Single: CALL PERMA (NRA, NCA, A, LDA, IPERMU, IPATH, APER, LDAPER)

Double: The double precision name is DPERMA.

Description

Routine PERMA interchanges the rows or columns of a matrix using a permutation vector such as the one obtained from routines SVRBP (see the Utilities chapter in Math Library manual) or SVRGP.

The routine PERMA permutes a column (row) at a time by calling PERMU. This process is continued until all the columns (rows) are permuted. On completion, let B = APER and pi = IPERMU(I), then

 

for all i, j.

Comments

1. Workspace may be explicitly provided, if desired, by use of P2RMA/DP2RMA. The reference is:

CALL P2RMA (NRA, NCA, A, LDA, IPERMU, IPATH, APER, LDAPER, WORK)

The additional argument is:

WORK — Real work vector of length NCA.

Example

This example permutes the columns of a matrix A.

 

USE PERMA_INT

USE UMACH_INT

 

IMPLICIT NONE

! Declare variables

INTEGER IPATH, LDA, LDAPER, NCA, NRA

PARAMETER (IPATH=2, LDA=3, LDAPER=3, NCA=5, NRA=3)

!

INTEGER I, IPERMU(5), J, NOUT

REAL A(LDA,NCA), APER(LDAPER,NCA)

! Set values for A, IPERMU

! A = ( 3.0 5.0 1.0 2.0 4.0 )

! ( 3.0 5.0 1.0 2.0 4.0 )

! ( 3.0 5.0 1.0 2.0 4.0 )

!

! IPERMU = ( 3 4 1 5 2 )

!

DATA A/3*3.0, 3*5.0, 3*1.0, 3*2.0, 3*4.0/, IPERMU/3, 4, 1, 5, 2/

! Perform column permutation on A,

! giving APER

CALL PERMA (A, IPERMU, APER, IPATH=IPATH)

! Get output unit number

CALL UMACH (2, NOUT)

! Print results

WRITE (NOUT,99999) ((APER(I,J),J=1,NCA),I=1,NRA)

!

99999 FORMAT (' The output matrix is:', /, 3(5F8.1,/))

END

Output

 

The Output matrix is:

1.0 2.0 3.0 4.0 5.0

1.0 2.0 3.0 4.0 5.0

1.0 2.0 3.0 4.0 5.0