DTGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22)


 of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair


 (A, B) by an orthogonal equivalence transformation.


 (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

WANTQ

          WANTQ is LOGICAL


          .TRUE. : update the left transformation matrix Q;


          .FALSE.: do not update Q.

WANTZ

          WANTZ is LOGICAL


          .TRUE. : update the right transformation matrix Z;


          .FALSE.: do not update Z.

N

          N is INTEGER


          The order of the matrices A and B. N >= 0.

A

          A is DOUBLE PRECISION array, dimensions (LDA,N)


          On entry, the matrix A in the pair (A, B).


          On exit, the updated matrix A.

LDA

          LDA is INTEGER


          The leading dimension of the array A. LDA >= max(1,N).

B

          B is DOUBLE PRECISION array, dimensions (LDB,N)


          On entry, the matrix B in the pair (A, B).


          On exit, the updated matrix B.

LDB

          LDB is INTEGER


          The leading dimension of the array B. LDB >= max(1,N).

Q

          Q is DOUBLE PRECISION array, dimension (LDQ,N)


          On entry, if WANTQ = .TRUE., the orthogonal matrix Q.


          On exit, the updated matrix Q.


          Not referenced if WANTQ = .FALSE..

LDQ

          LDQ is INTEGER


          The leading dimension of the array Q. LDQ >= 1.


          If WANTQ = .TRUE., LDQ >= N.

Z

          Z is DOUBLE PRECISION array, dimension (LDZ,N)


          On entry, if WANTZ =.TRUE., the orthogonal matrix Z.


          On exit, the updated matrix Z.


          Not referenced if WANTZ = .FALSE..

LDZ

          LDZ is INTEGER


          The leading dimension of the array Z. LDZ >= 1.


          If WANTZ = .TRUE., LDZ >= N.

J1

          J1 is INTEGER


          The index to the first block (A11, B11). 1 <= J1 <= N.

N1

          N1 is INTEGER


          The order of the first block (A11, B11). N1 = 0, 1 or 2.

N2

          N2 is INTEGER


          The order of the second block (A22, B22). N2 = 0, 1 or 2.

WORK

          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)).

LWORK

          LWORK is INTEGER


          The dimension of the array WORK.


          LWORK >=  MAX( 1, N*(N2+N1), (N2+N1)*(N2+N1)*2 )

INFO

          INFO is INTEGER


            =0: Successful exit


            >0: If INFO = 1, the transformed matrix (A, B) would be


                too far from generalized Schur form; the blocks are


                not swapped and (A, B) and (Q, Z) are unchanged.


                The problem of swapping is too ill-conditioned.


            <0: If INFO = -16: LWORK is too small. Appropriate value


                for LWORK is returned in WORK(1).

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016

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.

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.