stgex2()

subroutine stgex2	(	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	j1,
		integer	n1,
		integer	n2,
		real, dimension( * )	work,
		integer	lwork,
		integer	info )

STGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an orthogonal equivalence transformation.

Download STGEX2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> STGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22)
!> of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair
!> (A, B) by an orthogonal equivalence transformation.
!>
!> (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 the pair (A, B). !> On exit, the updated matrix A. !>
[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 the pair (A, B). !> On exit, the updated matrix 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. !> Not referenced if WANTQ = .FALSE.. !>
[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. !> Not referenced if WANTZ = .FALSE.. !>
[in]	LDZ	!> LDZ is INTEGER !> The leading dimension of the array Z. LDZ >= 1. !> If WANTZ = .TRUE., LDZ >= N. !>
[in]	J1	!> J1 is INTEGER !> The index to the first block (A11, B11). 1 <= J1 <= N. !>
[in]	N1	!> N1 is INTEGER !> The order of the first block (A11, B11). N1 = 0, 1 or 2. !>
[in]	N2	!> N2 is INTEGER !> The order of the second block (A22, B22). N2 = 0, 1 or 2. !>
[out]	WORK	!> WORK is REAL array, dimension (MAX(1,LWORK)). !>
[in]	LWORK	!> LWORK is INTEGER !> The dimension of the array WORK. !> LWORK >= MAX( N*(N2+N1), (N2+N1)*(N2+N1)*2 ) !>
[out]	INFO	!> INFO is INTEGER !> =0: Successful exit !> >0: If INFO = 1, the transformed matrix (A, B) would be !> too far from generalized Schur form; the blocks are !> not swapped and (A, B) and (Q, Z) are unchanged. !> The problem of swapping is too ill-conditioned. !> <0: If INFO = -16: LWORK is too small. Appropriate value !> for LWORK is returned in WORK(1). !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

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

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.
!>
!>  [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.
!>