ztgex2.f.html

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      SUBROUTINE <a name="ZTGEX2.1"></a><a href="ztgex2.f.html#ZTGEX2.1">ZTGEX2</a>( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
     $                   LDZ, J1, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      LOGICAL            WANTQ, WANTZ
      INTEGER            INFO, J1, LDA, LDB, LDQ, LDZ, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      COMPLEX*16         A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
     $                   Z( LDZ, * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="ZTGEX2.20"></a><a href="ztgex2.f.html#ZTGEX2.1">ZTGEX2</a> swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)
</span><span class="comment">*</span><span class="comment">  in an upper triangular matrix pair (A, B) by an unitary equivalence
</span><span class="comment">*</span><span class="comment">  transformation.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  (A, B) must be in generalized Schur canonical form, that is, A and
</span><span class="comment">*</span><span class="comment">  B are both upper triangular.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Optionally, the matrices Q and Z of generalized Schur vectors are
</span><span class="comment">*</span><span class="comment">  updated.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">         Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
</span><span class="comment">*</span><span class="comment">         Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WANTQ   (input) LOGICAL
</span><span class="comment">*</span><span class="comment">          .TRUE. : update the left transformation matrix Q;
</span><span class="comment">*</span><span class="comment">          .FALSE.: do not update Q.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WANTZ   (input) LOGICAL
</span><span class="comment">*</span><span class="comment">          .TRUE. : update the right transformation matrix Z;
</span><span class="comment">*</span><span class="comment">          .FALSE.: do not update Z.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrices A and B. N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input/output) COMPLEX*16 arrays, dimensions (LDA,N)
</span><span class="comment">*</span><span class="comment">          On entry, the matrix A in the pair (A, B).
</span><span class="comment">*</span><span class="comment">          On exit, the updated matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA     (input)  INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array A. LDA &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  B       (input/output) COMPLEX*16 arrays, dimensions (LDB,N)
</span><span class="comment">*</span><span class="comment">          On entry, the matrix B in the pair (A, B).
</span><span class="comment">*</span><span class="comment">          On exit, the updated matrix B.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDB     (input)  INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array B. LDB &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Q       (input/output) COMPLEX*16 array, dimension (LDZ,N)
</span><span class="comment">*</span><span class="comment">          If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit,
</span><span class="comment">*</span><span class="comment">          the updated matrix Q.
</span><span class="comment">*</span><span class="comment">          Not referenced if WANTQ = .FALSE..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDQ     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array Q. LDQ &gt;= 1;
</span><span class="comment">*</span><span class="comment">          If WANTQ = .TRUE., LDQ &gt;= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Z       (input/output) COMPLEX*16 array, dimension (LDZ,N)
</span><span class="comment">*</span><span class="comment">          If WANTZ = .TRUE, on entry, the unitary matrix Z. On exit,
</span><span class="comment">*</span><span class="comment">          the updated matrix Z.
</span><span class="comment">*</span><span class="comment">          Not referenced if WANTZ = .FALSE..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDZ     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array Z. LDZ &gt;= 1;
</span><span class="comment">*</span><span class="comment">          If WANTZ = .TRUE., LDZ &gt;= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  J1      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The index to the first block (A11, B11).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">           =0:  Successful exit.
</span><span class="comment">*</span><span class="comment">           =1:  The transformed matrix pair (A, B) would be too far
</span><span class="comment">*</span><span class="comment">                from generalized Schur form; the problem is ill-
</span><span class="comment">*</span><span class="comment">                conditioned. 
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Further Details
</span><span class="comment">*</span><span class="comment">  ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Based on contributions by
</span><span class="comment">*</span><span class="comment">     Bo Kagstrom and Peter Poromaa, Department of Computing Science,
</span><span class="comment">*</span><span class="comment">     Umea University, S-901 87 Umea, Sweden.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  In the current code both weak and strong stability tests are
</span><span class="comment">*</span><span class="comment">  performed. The user can omit the strong stability test by changing
</span><span class="comment">*</span><span class="comment">  the internal logical parameter WANDS to .FALSE.. See ref. [2] for
</span><span class="comment">*</span><span class="comment">  details.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
</span><span class="comment">*</span><span class="comment">      Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
</span><span class="comment">*</span><span class="comment">      M.S. Moonen et al (eds), Linear Algebra for Large Scale and
</span><span class="comment">*</span><span class="comment">      Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
</span><span class="comment">*</span><span class="comment">      Eigenvalues of a Regular Matrix Pair (A, B) and Condition
</span><span class="comment">*</span><span class="comment">      Estimation: Theory, Algorithms and Software, Report UMINF-94.04,
</span><span class="comment">*</span><span class="comment">      Department of Computing Science, Umea University, S-901 87 Umea,
</span><span class="comment">*</span><span class="comment">      Sweden, 1994. Also as LAPACK Working Note 87. To appear in
</span><span class="comment">*</span><span class="comment">      Numerical Algorithms, 1996.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      COMPLEX*16         CZERO, CONE
      PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ),
     $                   CONE = ( 1.0D+0, 0.0D+0 ) )
      DOUBLE PRECISION   TEN
      PARAMETER          ( TEN = 10.0D+0 )
      INTEGER            LDST
      PARAMETER          ( LDST = 2 )
      LOGICAL            WANDS
      PARAMETER          ( WANDS = .TRUE. )
<span class="comment">*</span><span class="comment">     ..
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