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

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 COMPLEX array, dimension (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 COMPLEX array, dimension (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 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..

LDQ

          LDQ is INTEGER


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


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

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..

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).

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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

June 2017

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.