stgex2.f.html

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      SUBROUTINE <a name="STGEX2.1"></a><a href="stgex2.f.html#STGEX2.1">STGEX2</a>( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
     $                   LDZ, J1, N1, N2, WORK, LWORK, 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, LWORK, N, N1, N2
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      REAL               A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
     $                   WORK( * ), 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="STGEX2.20"></a><a href="stgex2.f.html#STGEX2.1">STGEX2</a> swaps adjacent diagonal blocks (A11, B11) and (A22, B22)
</span><span class="comment">*</span><span class="comment">  of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair
</span><span class="comment">*</span><span class="comment">  (A, B) by an orthogonal equivalence transformation.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  (A, B) must be in generalized real Schur canonical form (as returned
</span><span class="comment">*</span><span class="comment">  by <a name="SGGES.25"></a><a href="sgges.f.html#SGGES.1">SGGES</a>), i.e. A is block upper triangular with 1-by-1 and 2-by-2
</span><span class="comment">*</span><span class="comment">  diagonal blocks. B is 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) REAL 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) REAL 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) REAL array, dimension (LDZ,N)
</span><span class="comment">*</span><span class="comment">          On entry, if WANTQ = .TRUE., the orthogonal matrix Q.
</span><span class="comment">*</span><span class="comment">          On exit, 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) REAL array, dimension (LDZ,N)
</span><span class="comment">*</span><span class="comment">          On entry, if WANTZ =.TRUE., the orthogonal matrix Z.
</span><span class="comment">*</span><span class="comment">          On exit, 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). 1 &lt;= J1 &lt;= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N1      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the first block (A11, B11). N1 = 0, 1 or 2.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N2      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the second block (A22, B22). N2 = 0, 1 or 2.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace) REAL array, dimension (MAX(1,LWORK)).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LWORK   (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The dimension of the array WORK.
</span><span class="comment">*</span><span class="comment">          LWORK &gt;=  MAX( N*(N2+N1), (N2+N1)*(N2+N1)*2 )
</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">            &gt;0: If INFO = 1, the transformed matrix (A, B) would be
</span><span class="comment">*</span><span class="comment">                too far from generalized Schur form; the blocks are
</span><span class="comment">*</span><span class="comment">                not swapped and (A, B) and (Q, Z) are unchanged.
</span><span class="comment">*</span><span class="comment">                The problem of swapping is too ill-conditioned.
</span><span class="comment">*</span><span class="comment">            &lt;0: If INFO = -16: LWORK is too small. Appropriate value
</span><span class="comment">*</span><span class="comment">                for LWORK is returned in WORK(1).
</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,
</span><span class="comment">*</span><span class="comment">      Report UMINF - 94.04, Department of Computing Science, Umea
</span><span class="comment">*</span><span class="comment">      University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working
</span><span class="comment">*</span><span class="comment">      Note 87. To appear in 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">  Replaced various illegal calls to SCOPY by calls to <a name="SLASET.130"></a><a href="slaset.f.html#SLASET.1">SLASET</a>, or by DO
</span><span class="comment">*</span><span class="comment">  loops. Sven Hammarling, 1/5/02.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
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