ztgexc (l) - Linux Manuals

ztgexc: reorders the generalized Schur decomposition of a complex matrix pair (A,B), using an unitary equivalence transformation (A, B) := Q * (A, B) * Zaq, so that the diagonal block of (A, B) with row index IFST is moved to row ILST

NAME

ZTGEXC - reorders the generalized Schur decomposition of a complex matrix pair (A,B), using an unitary equivalence transformation (A, B) := Q * (A, B) * Zaq, so that the diagonal block of (A, B) with row index IFST is moved to row ILST

SYNOPSIS

SUBROUTINE ZTGEXC(
WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, IFST, ILST, INFO )

    
LOGICAL WANTQ, WANTZ

    
INTEGER IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N

    
COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ, * )

PURPOSE

ZTGEXC reorders the generalized Schur decomposition of a complex matrix pair (A,B), using an unitary equivalence transformation (A, B) := Q * (A, B) * Zaq, so that the diagonal block of (A, B) with row index IFST is moved to row ILST. (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)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) COMPLEX*16 array, dimension (LDA,N)
On entry, the upper triangular 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) COMPLEX*16 array, dimension (LDB,N)
On entry, the upper triangular 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) COMPLEX*16 array, dimension (LDZ,N)
On entry, if WANTQ = .TRUE., the unitary matrix Q. On exit, the updated matrix Q. If WANTQ = .FALSE., Q is not referenced.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= 1; If WANTQ = .TRUE., LDQ >= N.
Z (input/output) COMPLEX*16 array, dimension (LDZ,N)
On entry, if WANTZ = .TRUE., the unitary matrix Z. On exit, the updated matrix Z. If WANTZ = .FALSE., Z is not referenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1; If WANTZ = .TRUE., LDZ >= N.
IFST (input) INTEGER
ILST (input/output) INTEGER Specify the reordering of the diagonal blocks of (A, B). The block with row index IFST is moved to row ILST, by a sequence of swapping between adjacent blocks.
INFO (output) INTEGER
=0: Successful exit.
<0: if INFO = -i, the i-th argument had an illegal value.
=1: The transformed matrix pair (A, B) would be too far from generalized Schur form; the problem is ill- conditioned. (A, B) may have been partially reordered, and ILST points to the first row of the current position of the block being moved.

FURTHER DETAILS

Based on contributions by

Bo Kagstrom and Peter Poromaa, Department of Computing Science,
Umea University, S-901 87 Umea, Sweden.
[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.
[3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
 for Solving the Generalized Sylvester Equation and Estimating the
 Separation between Regular Matrix Pairs, Report UMINF - 93.23,
 Department of Computing Science, Umea University, S-901 87 Umea,
 Sweden, December 1993, Revised April 1994, Also as LAPACK working
 Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,
 1996.

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