LAPACK 3.11.0
LAPACK: Linear Algebra PACKage

◆ ctgex2()

subroutine ctgex2 ( logical  WANTQ,
logical  WANTZ,
integer  N,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( ldb, * )  B,
integer  LDB,
complex, dimension( ldq, * )  Q,
integer  LDQ,
complex, dimension( ldz, * )  Z,
integer  LDZ,
integer  J1,
integer  INFO 
)

CTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation.

Download CTGEX2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 CTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)
 in an upper triangular matrix pair (A, B) by an unitary equivalence
 transformation.

 (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
[in]WANTQ
          WANTQ is LOGICAL
          .TRUE. : update the left transformation matrix Q;
          .FALSE.: do not update Q.
[in]WANTZ
          WANTZ is LOGICAL
          .TRUE. : update the right transformation matrix Z;
          .FALSE.: do not update Z.
[in]N
          N is INTEGER
          The order of the matrices A and B. N >= 0.
[in,out]A
          A is COMPLEX array, dimension (LDA,N)
          On entry, the matrix A in the pair (A, B).
          On exit, the updated matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A. LDA >= max(1,N).
[in,out]B
          B is COMPLEX array, dimension (LDB,N)
          On entry, the matrix B in the pair (A, B).
          On exit, the updated matrix B.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B. LDB >= max(1,N).
[in,out]Q
          Q is COMPLEX array, dimension (LDQ,N)
          If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit,
          the updated matrix Q.
          Not referenced if WANTQ = .FALSE..
[in]LDQ
          LDQ is INTEGER
          The leading dimension of the array Q. LDQ >= 1;
          If WANTQ = .TRUE., LDQ >= N.
[in,out]Z
          Z is COMPLEX array, dimension (LDZ,N)
          If WANTZ = .TRUE, on entry, the unitary matrix Z. On exit,
          the updated matrix Z.
          Not referenced if WANTZ = .FALSE..
[in]LDZ
          LDZ is INTEGER
          The leading dimension of the array Z. LDZ >= 1;
          If WANTZ = .TRUE., LDZ >= N.
[in]J1
          J1 is INTEGER
          The index to the first block (A11, B11).
[out]INFO
          INFO is INTEGER
           =0:  Successful exit.
           =1:  The transformed matrix pair (A, B) would be too far
                from generalized Schur form; the problem is ill-
                conditioned.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
In the current code both weak and strong stability tests are performed. The user can omit the strong stability test by changing the internal logical parameter WANDS to .FALSE.. See ref. [2] for details.
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.