LAPACK 3.11.0
LAPACK: Linear Algebra PACKage

◆ dtgexc()

subroutine dtgexc ( logical  WANTQ,
logical  WANTZ,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( ldq, * )  Q,
integer  LDQ,
double precision, dimension( ldz, * )  Z,
integer  LDZ,
integer  IFST,
integer  ILST,
double precision, dimension( * )  WORK,
integer  LWORK,
integer  INFO 
)

DTGEXC

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

Purpose:
 DTGEXC reorders the generalized real Schur decomposition of a real
 matrix pair (A,B) using an orthogonal equivalence transformation

                (A, B) = Q * (A, B) * Z**T,

 so that the diagonal block of (A, B) with row index IFST is moved
 to row ILST.

 (A, B) must be in generalized real Schur canonical form (as returned
 by DGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2
 diagonal blocks. B is upper triangular.

 Optionally, the matrices Q and Z of generalized Schur vectors are
 updated.

        Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T
        Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T
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 DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the matrix A in generalized real Schur canonical
          form.
          On exit, the updated matrix A, again in generalized
          real Schur canonical form.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A. LDA >= max(1,N).
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,N)
          On entry, the matrix B in generalized real Schur canonical
          form (A,B).
          On exit, the updated matrix B, again in generalized
          real Schur canonical form (A,B).
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B. LDB >= max(1,N).
[in,out]Q
          Q is DOUBLE PRECISION array, dimension (LDQ,N)
          On entry, if WANTQ = .TRUE., the orthogonal matrix Q.
          On exit, the updated matrix Q.
          If WANTQ = .FALSE., Q is not referenced.
[in]LDQ
          LDQ is INTEGER
          The leading dimension of the array Q. LDQ >= 1.
          If WANTQ = .TRUE., LDQ >= N.
[in,out]Z
          Z is DOUBLE PRECISION array, dimension (LDZ,N)
          On entry, if WANTZ = .TRUE., the orthogonal matrix Z.
          On exit, the updated matrix Z.
          If WANTZ = .FALSE., Z is not referenced.
[in]LDZ
          LDZ is INTEGER
          The leading dimension of the array Z. LDZ >= 1.
          If WANTZ = .TRUE., LDZ >= N.
[in,out]IFST
          IFST is INTEGER
[in,out]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.
          On exit, if IFST pointed on entry to the second row of
          a 2-by-2 block, it is changed to point to the first row;
          ILST always points to the first row of the block in its
          final position (which may differ from its input value by
          +1 or -1). 1 <= IFST, ILST <= N.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK.
          LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.
[out]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.
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.