ctgexc(3)

NAME

CTGEXC - reorder the generalized Schur decomposition of a

complex matrix pair (A,B), using an unitary equivalence transfor

mation (A, B) := Q * (A, B) * Z', so that the diagonal block of

(A, B) with row index IFST is moved to row ILST

SYNOPSIS

SUBROUTINE  CTGEXC(  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         A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
Z( LDZ, * )

PURPOSE

CTGEXC reorders the generalized Schur decomposition of a

complex matrix pair (A,B), using an unitary equivalence transfor

mation (A, B) := Q * (A, B) * Z', 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 vec

tors are updated.

Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'

ARGUMENTS

WANTQ (input) LOGICAL

WANTZ (input) LOGICAL

N (input) INTEGER

The order of the matrices A and B. N >= 0.

A (input/output) COMPLEX 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 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 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 ref

erenced.

LDQ (input) INTEGER

The leading dimension of the array Q. LDQ >= 1; If

WANTQ = .TRUE., LDQ >= N.

Z (input/output) COMPLEX 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 ref

erenced.

LDZ (input) INTEGER

The leading dimension of the array Z. LDZ >= 1; If

WANTZ = .TRUE., LDZ >= N.

IFST (input/output) INTEGER

ILST (input/output) INTEGER Specify the re

ordering of the diagonal blocks of (A, B). The block with row

index IFST is moved to row ILST, by a sequence of swapping be

tween adjacent blocks.

INFO (output) INTEGER

=0: Successful exit.
<0: if INFO = -i, the i-th argument had an ille

gal value.
=1: The transformed matrix pair (A, B) would be

too far from generalized Schur form; the problem is ill- condi

tioned. (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 Eigenval

ues 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 Condi

tion
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 Es

timating 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 LA

PACK working
Note 75. To appear in ACM Trans. on Math. Software,

Vol 22, No 1,
1996.

LAPACK version 3.0 15 June 2000

CTGEXC(3)