ztgexc.f

          SUBROUTINE ZTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
         $                   LDZ, IFST, ILST, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          LOGICAL            WANTQ, WANTZ
          INTEGER            IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N
    *     ..
    *     .. Array Arguments ..
          COMPLEX*16         A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
         $                   Z( LDZ, * )
    *     ..
    *
    *  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', 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)' = Q(out) * A(out) * Z(out)'
    *         Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
    *
    *  Arguments
    *  =========
    *
    *  WANTQ   (input) LOGICAL
    *          .TRUE. : update the left transformation matrix Q;
    *          .FALSE.: do not update Q.
    *
    *  WANTZ   (input) LOGICAL
    *          .TRUE. : update the right transformation matrix Z;
    *          .FALSE.: do not update Z.
    *
    *  N       (input) INTEGER
    *          The order of the matrices A and B. N >= 0.
    *
    *  A       (input/output) 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)  INTEGER
    *          The leading dimension of the array A. LDA >= max(1,N).
    *
    *  B       (input/output) 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)  INTEGER
    *          The leading dimension of the array B. LDB >= max(1,N).
    *
    *  Q       (input/output) 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) INTEGER
    *          The leading dimension of the array Q. LDQ >= 1;
    *          If WANTQ = .TRUE., LDQ >= N.
    *
    *  Z       (input/output) 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) INTEGER
    *          The leading dimension of the array Z. LDZ >= 1;
    *          If WANTZ = .TRUE., LDZ >= N.
    *
    *  IFST    (input) INTEGER
    *  ILST    (input/output) 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) 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.
    *
    *
    *  Further Details
    *  ===============
    *
    *  Based on contributions by
    *     Bo Kagstrom and Peter Poromaa, Department of Computing Science,
    *     Umea University, S-901 87 Umea, Sweden.
    *
    *  [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.
    *
    *  =====================================================================
    *
    *     .. Local Scalars ..
          INTEGER            HERE
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           XERBLA, ZTGEX2
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX
    *     ..
    *     .. Executable Statements ..
    *
    *     Decode and test input arguments.
          INFO = 0
          IF( N.LT.0 ) THEN
             INFO = -3
          ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
             INFO = -5
          ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
             INFO = -7
          ELSE IF( LDQ.LT.1 .OR. WANTQ .AND. ( LDQ.LT.MAX( 1, N ) ) ) THEN
             INFO = -9
          ELSE IF( LDZ.LT.1 .OR. WANTZ .AND. ( LDZ.LT.MAX( 1, N ) ) ) THEN
             INFO = -11
          ELSE IF( IFST.LT.1 .OR. IFST.GT.N ) THEN
             INFO = -12
          ELSE IF( ILST.LT.1 .OR. ILST.GT.N ) THEN
             INFO = -13
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'ZTGEXC', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.LE.1 )
         $   RETURN
          IF( IFST.EQ.ILST )
         $   RETURN
    *
          IF( IFST.LT.ILST ) THEN
    *
             HERE = IFST
    *
       10    CONTINUE
    *
    *        Swap with next one below
    *
             CALL ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
         $                HERE, INFO )
             IF( INFO.NE.0 ) THEN
                ILST = HERE
                RETURN
             END IF
             HERE = HERE + 1
             IF( HERE.LT.ILST )
         $      GO TO 10
             HERE = HERE - 1
          ELSE
             HERE = IFST - 1
    *
       20    CONTINUE
    *
    *        Swap with next one above
    *
             CALL ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
         $                HERE, INFO )
             IF( INFO.NE.0 ) THEN
                ILST = HERE
                RETURN
             END IF
             HERE = HERE - 1
             IF( HERE.GE.ILST )
         $      GO TO 20
             HERE = HERE + 1
          END IF
          ILST = HERE
          RETURN
    *
    *     End of ZTGEXC
    *
          END