ztgex2.f(3) LAPACK ztgex2.f(3)
NAME
ztgex2.f -
SYNOPSIS
Functions/Subroutines
subroutine ztgex2 (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, INFO)
ZTGEX2
Function/Subroutine Documentation
subroutine ztgex2 (logicalWANTQ, logicalWANTZ, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B,
integerLDB, complex*16, dimension( ldq, * )Q, integerLDQ, complex*16, dimension( ldz, * )Z, integerLDZ, integerJ1, integerINFO)
ZTGEX2
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:
WANTQ
WANTQ is LOGICAL
.TRUE. : update the left transformation matrix Q;
.FALSE.: do not update Q.
WANTZ
WANTZ is LOGICAL
.TRUE. : update the right transformation matrix Z;
.FALSE.: do not update Z.
N
N is INTEGER
The order of the matrices A and B. N >= 0.
A
A is COMPLEX*16 arrays, dimensions (LDA,N)
On entry, the matrix A in the pair (A, B).
On exit, the updated matrix A.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B
B is COMPLEX*16 arrays, dimensions (LDB,N)
On entry, the matrix B in the pair (A, B).
On exit, the updated matrix B.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
Q
Q is COMPLEX*16 array, dimension (LDZ,N)
If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit,
the updated matrix Q.
Not referenced if WANTQ = .FALSE..
LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= 1;
If WANTQ = .TRUE., LDQ >= N.
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..
LDZ
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1;
If WANTZ = .TRUE., LDZ >= N.
J1
J1 is INTEGER
The index to the first block (A11, B11).
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.
Date:
November 2011
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.
Definition at line 190 of file ztgex2.f.
Author
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