dtgex2(3)

NAME

DTGEX2 - swap adjacent diagonal blocks (A11, B11) and

(A22, B22) of size 1-by-1 or 2-by-2 in an upper (quasi) triangu

lar matrix pair (A, B) by an orthogonal equivalence transforma

tion

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 ma

trix pair (A, B) by an orthogonal equivalence transformation.

(A, B) must be in generalized real Schur canonical form (as re

turned 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 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) DOUBLE PRECISION arrays, dimensions

(LDA,N)

On entry, the matrix A in the pair (A, B). On ex

it, 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 ex

it, 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

(LWORK).

LWORK (input) INTEGER

The dimension of the array WORK. LWORK >= MAX(

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 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 LA

PACK Working
Note 87. To appear in Numerical Algorithms, 1996.

LAPACK version 3.0 15 June 2000

DTGEX2(3)