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.