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stgexc.f(3)				      LAPACK				      stgexc.f(3)

NAME
       stgexc.f -

SYNOPSIS
   Functions/Subroutines
       subroutine stgexc (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, IFST, ILST, WORK,
	   LWORK, INFO)
	   STGEXC

Function/Subroutine Documentation
   subroutine stgexc (logicalWANTQ, logicalWANTZ, integerN, real, dimension( lda, * )A,
       integerLDA, real, dimension( ldb, * )B, integerLDB, real, dimension( ldq, * )Q,
       integerLDQ, real, dimension( ldz, * )Z, integerLDZ, integerIFST, integerILST, real,
       dimension( * )WORK, integerLWORK, integerINFO)
       STGEXC

       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**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

       Parameters:
	   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 (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

		     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.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Contributors:
	   Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901
	   87 Umea, Sweden.

       References:

	     [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.

       Definition at line 220 of file stgexc.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      stgexc.f(3)
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