ztgex2()

subroutine ztgex2	(	logical	wantq,
		logical	wantz,
		integer	n,
		complex*16, dimension( lda, * )	a,
		integer	lda,
		complex*16, dimension( ldb, * )	b,
		integer	ldb,
		complex*16, dimension( ldq, * )	q,
		integer	ldq,
		complex*16, dimension( ldz, * )	z,
		integer	ldz,
		integer	j1,
		integer	info )

ZTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation.

Download ZTGEX2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> ZTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)
!> in an upper triangular matrix pair (A, B) by an unitary equivalence
!> transformation.
!>
!> (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)**H = Q(out) * A(out) * Z(out)**H
!>        Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H
!>
!> 

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 COMPLEX*16 array, dimensions (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 COMPLEX*16 array, dimensions (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 COMPLEX*16 array, dimension (LDQ,N) !> If WANTQ = .TRUE, on entry, the unitary 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 COMPLEX*16 array, dimension (LDZ,N) !> If WANTZ = .TRUE, on entry, the unitary 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). !>
[out]	INFO	!> INFO is INTEGER !> =0: Successful exit. !> =1: The transformed matrix pair (A, B) would be too far !> from generalized Schur form; the problem is ill- !> conditioned. !>

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.