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

STGEXC(l)					)					STGEXC(l)

NAME
       STGEXC  -  reorder  the	generalized  real Schur decomposition of a real matrix pair (A,B)
       using an orthogonal equivalence transformation  (A, B) = Q * (A, B) * Z',

SYNOPSIS
       SUBROUTINE STGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ,  Z,	LDZ,  IFST,  ILST,  WORK,
			  LWORK, INFO )

	   LOGICAL	  WANTQ, WANTZ

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

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

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

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

       Q       (input/output) REAL array, dimension (LDZ,N)
	       On entry, if WANTQ = .TRUE., the orthogonal 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) 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     (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.  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    (workspace/output) REAL array, dimension (LWORK)
	       On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
	       The dimension of the array WORK. 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    (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.

LAPACK version 3.0			   15 June 2000 				STGEXC(l)


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