SRC/ztgex2.f(3)            Library Functions Manual            SRC/ztgex2.f(3)

NAME
       SRC/ztgex2.f

SYNOPSIS
   Functions/Subroutines
       subroutine ztgex2 (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, j1,
           info)
           ZTGEX2 swaps adjacent diagonal blocks in an upper (quasi)
           triangular matrix pair by an unitary equivalence transformation.

Function/Subroutine Documentation
   subroutine ztgex2 (logical wantq, logical wantz, integer n, complex*16,
       dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b,
       integer ldb, complex*16, dimension( ldq, * ) q, integer ldq,
       complex*16, dimension( ldz, * ) z, integer ldz, integer j1, integer
       info)
       ZTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular
       matrix pair by an unitary equivalence transformation.

       Purpose:


            ZTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)
            in an upper triangular matrix pair (A, B) by an unitary equivalence
            transformation.

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

       Parameters
           WANTQ

                     WANTQ is LOGICAL
                     .TRUE. : update the left transformation matrix Q;
                     .FALSE.: do not update Q.

           WANTZ

                     WANTZ is LOGICAL
                     .TRUE. : update the right transformation matrix Z;
                     .FALSE.: do not update Z.

           N

                     N is INTEGER
                     The order of the matrices A and B. N >= 0.

           A

                     A is COMPLEX*16 array, dimensions (LDA,N)
                     On entry, the matrix A in the pair (A, B).
                     On exit, the updated matrix A.

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A. LDA >= max(1,N).

           B

                     B is COMPLEX*16 array, dimensions (LDB,N)
                     On entry, the matrix B in the pair (A, B).
                     On exit, the updated matrix B.

           LDB

                     LDB is INTEGER
                     The leading dimension of the array B. LDB >= max(1,N).

           Q

                     Q is COMPLEX*16 array, dimension (LDQ,N)
                     If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit,
                     the updated matrix Q.
                     Not referenced if WANTQ = .FALSE..

           LDQ

                     LDQ is INTEGER
                     The leading dimension of the array Q. LDQ >= 1;
                     If WANTQ = .TRUE., LDQ >= N.

           Z

                     Z is COMPLEX*16 array, dimension (LDZ,N)
                     If WANTZ = .TRUE, on entry, the unitary matrix Z. On exit,
                     the updated matrix Z.
                     Not referenced if WANTZ = .FALSE..

           LDZ

                     LDZ is INTEGER
                     The leading dimension of the array Z. LDZ >= 1;
                     If WANTZ = .TRUE., LDZ >= N.

           J1

                     J1 is INTEGER
                     The index to the first block (A11, B11).

           INFO

                     INFO is INTEGER
                      =0:  Successful exit.
                      =1:  The transformed matrix pair (A, B) would be too far
                           from generalized Schur form; the problem is ill-
                           conditioned.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Further Details:
           In the current code both weak and strong stability tests are
           performed. The user can omit the strong stability test by changing
           the internal logical parameter WANDS to .FALSE.. See ref. [2] for
           details.

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

       References:
           [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.

       Definition at line 188 of file ztgex2.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/ztgex2.f(3)