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



NAME
       ZTGEXC

SYNOPSIS
       SUBROUTINE ZTGEXC (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
           IFST, ILST, INFO)



PURPOSE
            ZTGEXC reorders the generalized Schur decomposition of a complex
            matrix pair (A,B), using an unitary equivalence transformation
            (A, B) := Q * (A, B) * Z**H, 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)**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 array, dimension (LDA,N)
                     On entry, the upper triangular 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 array, dimension (LDB,N)
                     On entry, the upper triangular 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)
                     On entry, if WANTQ = .TRUE., the unitary matrix Q.
                     On exit, the updated matrix Q.
                     If WANTQ = .FALSE., Q is not referenced.

           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)
                     On entry, if WANTZ = .TRUE., the unitary matrix Z.
                     On exit, the updated matrix Z.
                     If WANTZ = .FALSE., Z is not referenced.

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

           IFST      (input)
                     IFST is INTEGER

           ILST      (input/output)
                     ILST is INTEGER
                     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.

           INFO      (output)
                     INFO is INTEGER
                      =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.



LAPACK routine                  31 October 2017                      ZTGEXC(3)