ztgex2(l) [redhat man page]

ZTGEX2(l)								 )								 ZTGEX2(l)

NAME

       ZTGEX2 - swap adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)

SYNOPSIS

       SUBROUTINE ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, INFO )

	   LOGICAL	  WANTQ, WANTZ

	   INTEGER	  INFO, J1, LDA, LDB, LDQ, LDZ, N

	   COMPLEX*16	  A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ, * )

PURPOSE

       ZTGEX2  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)' = Q(out) * A(out) * Z(out)'
	      Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'

ARGUMENTS

       WANTQ   (input) LOGICAL

       WANTZ   (input) LOGICAL

       N       (input) INTEGER
	       The order of the matrices A and B. N >= 0.

       A       (input/output) COMPLEX*16 arrays, dimensions (LDA,N)
	       On entry, the matrix A in the pair (A, B).  On exit, the updated matrix A.

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

       B       (input/output) COMPLEX*16 arrays, dimensions (LDB,N)
	       On entry, the matrix B in the pair (A, B).  On exit, the updated matrix B.

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

       Q       (input/output) COMPLEX*16 array, dimension (LDZ,N)
	       If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit, the updated matrix Q.  Not referenced if WANTQ = .FALSE..

       LDQ     (input) INTEGER
	       The leading dimension of the array Q. LDQ >= 1; If WANTQ = .TRUE., LDQ >= N.

       Z       (input/output) COMPLEX*16 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     (input) INTEGER
	       The leading dimension of the array Z. LDZ >= 1; If WANTZ = .TRUE., LDZ >= N.

       J1      (input) INTEGER
	       The index to the first block (A11, B11).

       INFO    (output) INTEGER
	       =0:  Successful exit.
	       =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.

FURTHER DETAILS

       Based on contributions by
	  Bo Kagstrom and Peter Poromaa, Department of Computing Science,
	  Umea University, S-901 87 Umea, Sweden.

       In  the current code both weak and strong stability tests are performed. The user can omit the strong stability test by changing the inter-
       nal logical parameter WANDS to .FALSE.. See ref. [2] for details.

       [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.

LAPACK version 3.0						   15 June 2000 							 ZTGEX2(l)

CTGEXC(l)								 )								 CTGEXC(l)

NAME

       CTGEXC  - reorder the generalized Schur decomposition of a complex matrix pair (A,B), using an unitary equivalence transformation (A, B) :=
       Q * (A, B) * Z', so that the diagonal block of (A, B) with row index IFST is moved to row ILST

SYNOPSIS

       SUBROUTINE CTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, IFST, ILST, INFO )

	   LOGICAL	  WANTQ, WANTZ

	   INTEGER	  IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N

	   COMPLEX	  A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ, * )

PURPOSE

       CTGEXC reorders the generalized Schur decomposition of a complex matrix pair (A,B), using an unitary equivalence transformation (A, B) := Q
       *  (A, B) * Z', so that the diagonal block of (A, B) with row index IFST is moved to row ILST.  (A, B) must be in generalized Schur canoni-
       cal 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)' = Q(out) * A(out) * Z(out)'
	      Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'

ARGUMENTS

       WANTQ   (input) LOGICAL

       WANTZ   (input) LOGICAL

       N       (input) INTEGER
	       The order of the matrices A and B. N >= 0.

       A       (input/output) COMPLEX array, dimension (LDA,N)
	       On entry, the upper triangular matrix A in the pair (A, B).  On exit, the updated matrix A.

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

       B       (input/output) COMPLEX array, dimension (LDB,N)
	       On entry, the upper triangular matrix B in the pair (A, B).  On exit, the updated matrix B.

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

       Q       (input/output) COMPLEX array, dimension (LDZ,N)
	       On entry, if WANTQ = .TRUE., the unitary matrix Q.  On exit, the updated matrix Q.  If WANTQ = .FALSE., Q is not referenced.

       LDQ     (input) INTEGER
	       The leading dimension of the array Q. LDQ >= 1; If WANTQ = .TRUE., LDQ >= N.

       Z       (input/output) 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     (input) INTEGER
	       The leading dimension of the array Z. LDZ >= 1; If WANTZ = .TRUE., LDZ >= N.

       IFST    (input/output) INTEGER
	       ILST    (input/output) 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    (output) 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.

FURTHER DETAILS

       Based on contributions by
	  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.

LAPACK version 3.0						   15 June 2000 							 CTGEXC(l)