dtgex2 (l) - Linux Manuals

dtgex2: 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

NAME

DTGEX2 - 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

SYNOPSIS

SUBROUTINE DTGEX2(
WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, N1, N2, WORK, LWORK, INFO )

    
LOGICAL WANTQ, WANTZ

    
INTEGER INFO, J1, LDA, LDB, LDQ, LDZ, LWORK, N, N1, N2

    
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), Q( LDQ, * ), WORK( * ), Z( LDZ, * )

PURPOSE

DTGEX2 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 DGGES), 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)aq = Q(out) * A(out) * Z(out)aq
 Q(in) * B(in) * Z(in)aq = Q(out) * B(out) * Z(out)aq

ARGUMENTS

WANTQ (input) LOGICAL .TRUE. : update the left transformation matrix Q;

WANTZ (input) LOGICAL


N (input) INTEGER
The order of the matrices A and B. N >= 0.
A (input/output) DOUBLE PRECISION arrays, dimensions (LDA,N)
On entry, the matrix A in the pair (A, B). On exit, the updated matrix A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B (input/output) DOUBLE PRECISION arrays, dimensions (LDB,N)
On entry, the matrix B in the pair (A, B). On exit, the updated matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
Q (input/output) DOUBLE PRECISION array, dimension (LDZ,N)
On entry, if WANTQ = .TRUE., the orthogonal matrix Q. On exit, the updated matrix Q. Not referenced if WANTQ = .FALSE..
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= 1. If WANTQ = .TRUE., LDQ >= N.
Z (input/output) DOUBLE PRECISION array, dimension (LDZ,N)
On entry, if WANTZ =.TRUE., the orthogonal matrix Z. On exit, the updated matrix Z. Not referenced if WANTZ = .FALSE..
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1. If WANTZ = .TRUE., LDZ >= N.
J1 (input) INTEGER
The index to the first block (A11, B11). 1 <= J1 <= N.
N1 (input) INTEGER
The order of the first block (A11, B11). N1 = 0, 1 or 2.
N2 (input) INTEGER
The order of the second block (A22, B22). N2 = 0, 1 or 2.
WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)).
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= MAX( 1, N*(N2+N1), (N2+N1)*(N2+N1)*2 )
INFO (output) 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).

FURTHER DETAILS

Based on contributions by

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

Pages related to dtgex2

  • dtgex2 (3)
  • dtgexc (l) - reorders the generalized real Schur decomposition of a real matrix pair (A,B) using an orthogonal equivalence transformation (A, B) = Q * (A, B) * Zaq,
  • dtgevc (l) - computes some or all of the right and/or left eigenvectors of a pair of real matrices (S,P), where S is a quasi-triangular matrix and P is upper triangular
  • dtgsen (l) - reorders the generalized real Schur decomposition of a real matrix pair (A, B) (in terms of an orthonormal equivalence trans- formation Qaq * (A, B) * Z), so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix A and the upper triangular B
  • dtgsja (l) - computes the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B
  • dtgsna (l) - estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a matrix pair (A, B) in generalized real Schur canonical form (or of any matrix pair (Q*A*Zaq, Q*B*Zaq) with orthogonal matrices Q and Z, where Zaq denotes the transpose of Z
  • dtgsy2 (l) - solves the generalized Sylvester equation
  • dtgsyl (l) - solves the generalized Sylvester equation