• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

dtrexc - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that the diagonal block of T with row index IFST is moved to row ILST

SYNOPSIS

  SUBROUTINE DTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO)
  CHARACTER * 1 COMPQ
  INTEGER N, LDT, LDQ, IFST, ILST, INFO
  DOUBLE PRECISION T(LDT,*), Q(LDQ,*), WORK(*)

  SUBROUTINE DTREXC_64( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, 
 *      INFO)
  CHARACTER * 1 COMPQ
  INTEGER*8 N, LDT, LDQ, IFST, ILST, INFO
  DOUBLE PRECISION T(LDT,*), Q(LDQ,*), WORK(*)

F95 INTERFACE

  SUBROUTINE TREXC( COMPQ, [N], T, [LDT], Q, [LDQ], IFST, ILST, [WORK], 
 *       [INFO])
  CHARACTER(LEN=1) :: COMPQ
  INTEGER :: N, LDT, LDQ, IFST, ILST, INFO
  REAL(8), DIMENSION(:) :: WORK
  REAL(8), DIMENSION(:,:) :: T, Q

  SUBROUTINE TREXC_64( COMPQ, [N], T, [LDT], Q, [LDQ], IFST, ILST, 
 *       [WORK], [INFO])
  CHARACTER(LEN=1) :: COMPQ
  INTEGER(8) :: N, LDT, LDQ, IFST, ILST, INFO
  REAL(8), DIMENSION(:) :: WORK
  REAL(8), DIMENSION(:,:) :: T, Q

C INTERFACE

#include <sunperf.h>

void dtrexc(char compq, int n, double *t, int ldt, double *q, int ldq, int *ifst, int *ilst, int *info);

void dtrexc_64(char compq, long n, double *t, long ldt, double *q, long ldq, long *ifst, long *ilst, long *info);

PURPOSE

dtrexc reorders the real Schur factorization of a real matrix A = Q*T*Q**T, so that the diagonal block of T with row index IFST is moved to row ILST.

The real Schur form T is reordered by an orthogonal similarity transformation Z**T*T*Z, and optionally the matrix Q of Schur vectors is updated by postmultiplying it with Z.

T must be in Schur canonical form (as returned by SHSEQR), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign.

ARGUMENTS

• COMPQ (input)
  

   = 'V':  update the matrix Q of Schur vectors;

   = 'N':  do not update Q.

• N (input)
  The order of the matrix T. N > = 0.

• T (input/output)
  On entry, the upper quasi-triangular matrix T, in Schur Schur canonical form. On exit, the reordered upper quasi-triangular matrix, again in Schur canonical form.

• LDT (input)
  The leading dimension of the array T. LDT > = max(1,N).

• Q (input/output)
  On entry, if COMPQ = 'V', the matrix Q of Schur vectors. On exit, if COMPQ = 'V', Q has been postmultiplied by the orthogonal transformation matrix Z which reorders T. If COMPQ = 'N', Q is not referenced.

• LDQ (input)
  The leading dimension of the array Q. LDQ > = max(1,N).

• IFST (input/output)
  Specify the reordering of the diagonal blocks of T. The block with row index IFST is moved to row ILST, by a sequence of transpositions between adjacent blocks. On exit, if IFST pointed on entry to the second row of a 2-by-2 block, it is changed to point to the first row; ILST always points to the first row of the block in its final position (which may differ from its input value by +1 or -1). 1 < = IFST < = N; 1 < = ILST < = N.

• ILST (input/output)
  See the description of IFST.

• WORK (workspace)
  dimension(N)

• INFO (output)
  

   = 0:  successful exit

   < 0:  if INFO  = -i, the i-th argument had an illegal value

   = 1:  two adjacent blocks were too close to swap (the problem
  is very ill-conditioned); T may have been partially
  reordered, and ILST points to the first row of the
  current position of the block being moved.