NAME

       ctgexc.f -

SYNOPSIS

   Functions/Subroutines
       subroutine ctgexc (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, IFST, ILST, INFO)
           CTGEXC

Function/Subroutine Documentation

   subroutine ctgexc (logicalWANTQ, logicalWANTZ, integerN, complex, dimension( lda, * )A,
       integerLDA, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldq, * )Q,
       integerLDQ, complex, dimension( ldz, * )Z, integerLDZ, integerIFST, integerILST,
       integerINFO)
       CTGEXC

       Purpose:

            CTGEXC 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

       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 array, dimension (LDA,N)
                     On entry, the upper triangular 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 array, dimension (LDB,N)
                     On entry, the upper triangular 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 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

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

           Z

                     Z is COMPLEX 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

                     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.

           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.
            [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.
            [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software for Solving the
           Generalized Sylvester Equation and Estimating the Separation between Regular Matrix
           Pairs, Report UMINF - 93.23, Department of Computing Science, Umea University, S-901
           87 Umea, Sweden, December 1993, Revised April 1994, Also as LAPACK working Note 75. To
           appear in ACM Trans. on Math. Software, Vol 22, No 1, 1996.

       Definition at line 200 of file ctgexc.f.

Author

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