NAME

       stgexc.f -

SYNOPSIS

   Functions/Subroutines
       subroutine stgexc (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, IFST, ILST, WORK,
           LWORK, INFO)
           STGEXC

Function/Subroutine Documentation

   subroutine stgexc (logicalWANTQ, logicalWANTZ, integerN, real, dimension( lda, * )A,
       integerLDA, real, dimension( ldb, * )B, integerLDB, real, dimension( ldq, * )Q,
       integerLDQ, real, dimension( ldz, * )Z, integerLDZ, integerIFST, integerILST, real,
       dimension( * )WORK, integerLWORK, integerINFO)
       STGEXC

       Purpose:

            STGEXC reorders the generalized real Schur decomposition of a real
            matrix pair (A,B) using an orthogonal equivalence transformation

                           (A, B) = Q * (A, B) * Z**T,

            so that the diagonal block of (A, B) with row index IFST is moved
            to row ILST.

            (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

       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 REAL array, dimension (LDA,N)
                     On entry, the matrix A in generalized real Schur canonical
                     form.
                     On exit, the updated matrix A, again in generalized
                     real Schur canonical form.

           LDA

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

           B

                     B is REAL array, dimension (LDB,N)
                     On entry, the matrix B in generalized real Schur canonical
                     form (A,B).
                     On exit, the updated matrix B, again in generalized
                     real Schur canonical form (A,B).

           LDB

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

           Q

                     Q is REAL array, dimension (LDZ,N)
                     On entry, if WANTQ = .TRUE., the orthogonal matrix Q.
                     On exit, the updated matrix Q.
                     If WANTQ = .FALSE., Q is not referenced.

           LDQ

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

           Z

                     Z is REAL array, dimension (LDZ,N)
                     On entry, if WANTZ = .TRUE., the orthogonal matrix Z.
                     On exit, the updated matrix Z.
                     If WANTZ = .FALSE., Z is not referenced.

           LDZ

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

           IFST

                     IFST is INTEGER

           ILST

                     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.
                     On exit, if IFST pointed on entry to the second row of
                     a 2-by-2 block, it is changed to point to the first row;
                     ILST always points to the first row of the block in its
                     final position (which may differ from its input value by
                     +1 or -1). 1 <= IFST, ILST <= N.

           WORK

                     WORK is REAL array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     LWORK is INTEGER
                     The dimension of the array WORK.
                     LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16.

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal size of the WORK array, returns
                     this value as the first entry of the WORK array, and no error
                     message related to LWORK is issued by XERBLA.

           INFO

                     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.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

       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.

       Definition at line 220 of file stgexc.f.

Author

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