ZTGEX2(3)      LAPACK routine of NEC Numeric Library Collection      ZTGEX2(3)



NAME
       ZTGEX2

SYNOPSIS
       SUBROUTINE ZTGEX2 (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1,
           INFO)



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




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

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

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

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

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

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

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

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

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

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

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

           INFO      (output)
                     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.






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..



LAPACK routine                  31 October 2017                      ZTGEX2(3)