STGEX2(3)      LAPACK routine of NEC Numeric Library Collection      STGEX2(3)



NAME
       STGEX2

SYNOPSIS
       SUBROUTINE STGEX2 (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1,
           N1, N2, WORK, LWORK, INFO)



PURPOSE
            STGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22)
            of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair
            (A, B) by an orthogonal equivalence transformation.

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




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 REAL 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 REAL 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 REAL array, dimension (LDZ,N)
                     On entry, if WANTQ = .TRUE., the orthogonal 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 REAL array, dimension (LDZ,N)
                     On entry, if WANTZ =.TRUE., the orthogonal 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). 1 <= J1 <= N.

           N1        (input)
                     N1 is INTEGER
                     The order of the first block (A11, B11). N1 = 0, 1 or 2.

           N2        (input)
                     N2 is INTEGER
                     The order of the second block (A22, B22). N2 = 0, 1 or 2.

           WORK      (output)
                     WORK is REAL array, dimension (MAX(1,LWORK)).

           LWORK     (input)
                     LWORK is INTEGER
                     The dimension of the array WORK.
                     LWORK >=  MAX( N*(N2+N1), (N2+N1)*(N2+N1)*2 )

           INFO      (output)
                     INFO is INTEGER
                       =0: Successful exit
                       >0: If INFO = 1, the transformed matrix (A, B) would be
                           too far from generalized Schur form; the blocks are
                           not swapped and (A, B) and (Q, Z) are unchanged.
                           The problem of swapping is too ill-conditioned.
                       <0: If INFO = -16: LWORK is too small. Appropriate value
                           for LWORK is returned in WORK(1).






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                      STGEX2(3)