NAME

ctgexc - reorder the generalized Schur decomposition of a complex matrix pair (A,B), using an unitary equivalence transformation (A, B) := Q * (A, B) * Z', so that the diagonal block of (A, B) with row index IFST is moved to row ILST

SYNOPSIS

  SUBROUTINE CTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, 
 *      IFST, ILST, INFO)
  COMPLEX A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*)
  INTEGER N, LDA, LDB, LDQ, LDZ, IFST, ILST, INFO
  LOGICAL WANTQ, WANTZ

  SUBROUTINE CTGEXC_64( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, 
 *      LDZ, IFST, ILST, INFO)
  COMPLEX A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*)
  INTEGER*8 N, LDA, LDB, LDQ, LDZ, IFST, ILST, INFO
  LOGICAL*8 WANTQ, WANTZ

F95 INTERFACE

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

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

C INTERFACE

#include <sunperf.h>

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

void ctgexc_64(logical wantq, logical wantz, long n, complex *a, long lda, complex *b, long ldb, complex *q, long ldq, complex *z, long ldz, long *ifst, long *ilst, long *info);

PURPOSE

ctgexc reorders the generalized Schur decomposition of a complex matrix pair (A,B), using an unitary equivalence transformation (A, B) := Q * (A, B) * Z', so that the diagonal block of (A, B) with row index IFST is moved to row ILST.

(A, B) must be in generalized Schur canonical form, that is, A and B are both 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 upper triangular matrix A in the pair (A, B). On exit, the updated matrix A.
LDA (input)
The leading dimension of the array A. LDA > = max(1,N).
B (input/output)
On entry, the upper triangular matrix B in the pair (A, B). On exit, the updated matrix B.
LDB (input)
The leading dimension of the array B. LDB > = max(1,N).
Q (input/output)
On entry, if WANTQ = .TRUE., the unitary 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 unitary 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.
ILST (input/output)
See the description of IFST.

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.

[2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified Eigenvalues of a Regular Matrix Pair (A, B) and Condition Estimation: Theory, Algorithms and Software, Report

    UMINF - 94.04, Department of Computing Science, Umea University,
    S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87.
    To appear in Numerical Algorithms, 1996.

[3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software for Solving the Generalized Sylvester Equation and Estimating the Separation between Regular Matrix Pairs, Report UMINF - 93.23, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, December 1993, Revised April 1994, Also as LAPACK working Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1, 1996.