NAME

dtgexc - reorder the generalized real Schur decomposition of a real matrix pair (A,B) using an orthogonal equivalence transformation (A, B) = Q * (A, B) * Z',

SYNOPSIS

  SUBROUTINE DTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, 
 *      IFST, ILST, WORK, LWORK, INFO)
  INTEGER N, LDA, LDB, LDQ, LDZ, IFST, ILST, LWORK, INFO
  LOGICAL WANTQ, WANTZ
  DOUBLE PRECISION A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*), WORK(*)

  SUBROUTINE DTGEXC_64( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, 
 *      LDZ, IFST, ILST, WORK, LWORK, INFO)
  INTEGER*8 N, LDA, LDB, LDQ, LDZ, IFST, ILST, LWORK, INFO
  LOGICAL*8 WANTQ, WANTZ
  DOUBLE PRECISION A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*), WORK(*)

F95 INTERFACE

  SUBROUTINE TGEXC( WANTQ, WANTZ, N, A, [LDA], B, [LDB], Q, [LDQ], Z, 
 *       [LDZ], IFST, ILST, [WORK], [LWORK], [INFO])
  INTEGER :: N, LDA, LDB, LDQ, LDZ, IFST, ILST, LWORK, INFO
  LOGICAL :: WANTQ, WANTZ
  REAL(8), DIMENSION(:) :: WORK
  REAL(8), DIMENSION(:,:) :: A, B, Q, Z

  SUBROUTINE TGEXC_64( WANTQ, WANTZ, N, A, [LDA], B, [LDB], Q, [LDQ], 
 *       Z, [LDZ], IFST, ILST, [WORK], [LWORK], [INFO])
  INTEGER(8) :: N, LDA, LDB, LDQ, LDZ, IFST, ILST, LWORK, INFO
  LOGICAL(8) :: WANTQ, WANTZ
  REAL(8), DIMENSION(:) :: WORK
  REAL(8), DIMENSION(:,:) :: A, B, Q, Z

C INTERFACE

#include <sunperf.h>

void dtgexc(logical wantq, logical wantz, int n, double *a, int lda, double *b, int ldb, double *q, int ldq, double *z, int ldz, int *ifst, int *ilst, int *info);

void dtgexc_64(logical wantq, logical wantz, long n, double *a, long lda, double *b, long ldb, double *q, long ldq, double *z, long ldz, long *ifst, long *ilst, long *info);

PURPOSE

dtgexc reorders the generalized real Schur decomposition of a real matrix pair (A,B) using an orthogonal equivalence transformation

so that the diagonal block of (A, B) with row index IFST is moved to row ILST.

(A, B) must be in generalized real Schur canonical form (as returned by SGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2 diagonal blocks. B is upper triangular.

Optionally, the matrices Q and Z of generalized Schur vectors are updated.

       Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
       Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'

ARGUMENTS

WANTQ (input)
.TRUE. : update the left transformation matrix Q;
.FALSE.: do not update Q.
WANTZ (input)
.TRUE. : update the right transformation matrix Z;
.FALSE.: do not update Z.
N (input)
The order of the matrices A and B. N > = 0.
A (input/output)
On entry, the matrix A in generalized real Schur canonical form. On exit, the updated matrix A, again in generalized real Schur canonical form.
LDA (input)
The leading dimension of the array A. LDA > = max(1,N).
B (input/output)
On entry, the matrix B in generalized real Schur canonical form (A,B). On exit, the updated matrix B, again in generalized real Schur canonical form (A,B).
LDB (input)
The leading dimension of the array B. LDB > = max(1,N).
Q (input/output)
On entry, if WANTQ = .TRUE., the orthogonal matrix Q. On exit, the updated matrix Q. If WANTQ = .FALSE., Q is not referenced.
LDQ (input)
The leading dimension of the array Q. LDQ > = 1. If WANTQ = .TRUE., LDQ > = N.
Z (input/output)
On entry, if WANTZ = .TRUE., the orthogonal matrix Z. On exit, the updated matrix Z. If WANTZ = .FALSE., Z is not referenced.
LDZ (input)
The leading dimension of the array Z. LDZ > = 1. If WANTZ = .TRUE., LDZ > = N.
IFST (input/output)
Specify the reordering of the diagonal blocks of (A, B). The block with row index IFST is moved to row ILST, by a sequence of swapping 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, ILST < = N.
ILST (input/output)
See the description of IFST.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
The dimension of the array WORK. LWORK > = 4*N + 16.
If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

INFO (output)

 =0:  successful exit.

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

 =1:  The transformed matrix pair (A, B) would be too far
from generalized Schur form; the problem is ill-
conditioned. (A, B) may have been partially reordered,
and ILST points to the first row of the current
position of the block being moved.

FURTHER DETAILS

Based on contributions by

   Bo Kagstrom and Peter Poromaa, Department of Computing Science,
   Umea University, S-901 87 Umea, Sweden.

[1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the Generalized Real Schur Form of a Regular Matrix Pair (A, B), in M.S. Moonen et al (eds), Linear Algebra for Large Scale and Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.