CTGEX2 (3) Linux Manual Page

ctgex2.f –

Synopsis

Functions/Subroutines

subroutine ctgex2 (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, INFO)
CTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation.

Function/Subroutine Documentation

subroutine ctgex2 (logicalWANTQ, logicalWANTZ, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldq, * )Q, integerLDQ, complex, dimension( ldz, * )Z, integerLDZ, integerJ1, integerINFO)

CTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation.

Purpose:

 CTGEX2 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 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 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 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 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:

September 2012

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 ctgex2.f.

Author

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