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RedHat 9 (Linux i386) - man page for ztgexc (redhat section l)

ZTGEXC(l)					)					ZTGEXC(l)

NAME
       ZTGEXC - 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 ZTGEXC( 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*16	  A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ, * )

PURPOSE
       ZTGEXC  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 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 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*16 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*16 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*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     (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 				ZTGEXC(l)


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