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dtrexc(3P)		    Sun Performance Library		    dtrexc(3P)

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 trans‐
       formation 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-diag‐
       onal 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-triangu‐
		 lar matrix, again in Schur canonical form.

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

       Q (input) 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  dif‐
		 fer  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.

				  6 Mar 2009			    dtrexc(3P)
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