!>
!> CTGEXC reorders the generalized Schur decomposition of a complex
!> matrix pair (A,B), using an unitary equivalence transformation
!> (A, B) := Q * (A, B) * Z**H, so that the diagonal block of (A, B) with
!> row index IFST is moved to row ILST.
!>
!> (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 upper triangular 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 upper triangular 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)
!>          On entry, if WANTQ = .TRUE., the unitary matrix Q.
!>          On exit, the updated matrix Q.
!>          If WANTQ = .FALSE., Q is not referenced.
!> 

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)
!>          On entry, if WANTZ = .TRUE., the unitary matrix Z.
!>          On exit, the updated matrix Z.
!>          If WANTZ = .FALSE., Z is not referenced.
!> 

LDZ

!>          LDZ is INTEGER
!>          The leading dimension of the array Z. LDZ >= 1;
!>          If WANTZ = .TRUE., LDZ >= N.
!> 

IFST

!>          IFST is INTEGER
!> 

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.
!> 

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.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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.
[3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software for Solving the Generalized Sylvester Equation and Estimating the Separation between Regular Matrix Pairs, Report UMINF - 93.23, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, December 1993, Revised April 1994, Also as LAPACK working Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1, 1996.

!>
!> 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
!>
!> 

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, 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.
!> 

LDA

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

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).
!> 

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.
!>          If WANTQ = .FALSE., Q is not referenced.
!> 

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.
!>          If WANTZ = .FALSE., Z is not referenced.
!> 

LDZ

!>          LDZ is INTEGER
!>          The leading dimension of the array Z. LDZ >= 1.
!>          If WANTZ = .TRUE., LDZ >= N.
!> 

IFST

!>          IFST is INTEGER
!> 

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.
!> 

WORK

!>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!> 

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.
!> 

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.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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.
!> 

!>
!> STGEXC 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 SGGES), 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 REAL 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.
!> 

LDA

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

B

!>          B is REAL 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).
!> 

LDB

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

Q

!>          Q is REAL 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.
!> 

LDQ

!>          LDQ is INTEGER
!>          The leading dimension of the array Q. LDQ >= 1.
!>          If WANTQ = .TRUE., LDQ >= N.
!> 

Z

!>          Z is REAL 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.
!> 

LDZ

!>          LDZ is INTEGER
!>          The leading dimension of the array Z. LDZ >= 1.
!>          If WANTZ = .TRUE., LDZ >= N.
!> 

IFST

!>          IFST is INTEGER
!> 

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.
!> 

WORK

!>          WORK is REAL array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!> 

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.
!> 

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.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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.
!> 

!>
!> ZTGEXC reorders the generalized Schur decomposition of a complex
!> matrix pair (A,B), using an unitary equivalence transformation
!> (A, B) := Q * (A, B) * Z**H, so that the diagonal block of (A, B) with
!> row index IFST is moved to row ILST.
!>
!> (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*16 array, dimension (LDA,N)
!>          On entry, the upper triangular 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*16 array, dimension (LDB,N)
!>          On entry, the upper triangular 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*16 array, dimension (LDQ,N)
!>          On entry, if WANTQ = .TRUE., the unitary matrix Q.
!>          On exit, the updated matrix Q.
!>          If WANTQ = .FALSE., Q is not referenced.
!> 

LDQ

!>          LDQ is INTEGER
!>          The leading dimension of the array Q. LDQ >= 1;
!>          If WANTQ = .TRUE., LDQ >= N.
!> 

Z

!>          Z is COMPLEX*16 array, dimension (LDZ,N)
!>          On entry, if WANTZ = .TRUE., the unitary matrix Z.
!>          On exit, the updated matrix Z.
!>          If WANTZ = .FALSE., Z is not referenced.
!> 

LDZ

!>          LDZ is INTEGER
!>          The leading dimension of the array Z. LDZ >= 1;
!>          If WANTZ = .TRUE., LDZ >= N.
!> 

IFST

!>          IFST is INTEGER
!> 

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.
!> 

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.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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.
[3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software for Solving the Generalized Sylvester Equation and Estimating the Separation between Regular Matrix Pairs, Report UMINF - 93.23, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, December 1993, Revised April 1994, Also as LAPACK working Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1, 1996.