stgexc()

subroutine stgexc	(	logical	wantq,
		logical	wantz,
		integer	n,
		real, dimension( lda, * )	a,
		integer	lda,
		real, dimension( ldb, * )	b,
		integer	ldb,
		real, dimension( ldq, * )	q,
		integer	ldq,
		real, dimension( ldz, * )	z,
		integer	ldz,
		integer	ifst,
		integer	ilst,
		real, dimension( * )	work,
		integer	lwork,
		integer	info )

STGEXC

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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

[in]	WANTQ	!> WANTQ is LOGICAL !> .TRUE. : update the left transformation matrix Q; !> .FALSE.: do not update Q. !>
[in]	WANTZ	!> WANTZ is LOGICAL !> .TRUE. : update the right transformation matrix Z; !> .FALSE.: do not update Z. !>
[in]	N	!> N is INTEGER !> The order of the matrices A and B. N >= 0. !>
[in,out]	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. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[in,out]	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). !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !>
[in,out]	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. !>
[in]	LDQ	!> LDQ is INTEGER !> The leading dimension of the array Q. LDQ >= 1. !> If WANTQ = .TRUE., LDQ >= N. !>
[in,out]	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. !>
[in]	LDZ	!> LDZ is INTEGER !> The leading dimension of the array Z. LDZ >= 1. !> If WANTZ = .TRUE., LDZ >= N. !>
[in,out]	IFST	!> IFST is INTEGER !>
[in,out]	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. !>
[out]	WORK	!> WORK is REAL array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !>
[in]	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. !>
[out]	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.

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.
!>