DTGEX2 (3) Linux Manual Page

dtgex2.f –

Synopsis

Functions/Subroutines

subroutine dtgex2 (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, N1, N2, WORK, LWORK, INFO)
DTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an orthogonal equivalence transformation.

Function/Subroutine Documentation

subroutine dtgex2 (logicalWANTQ, logicalWANTZ, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( ldq, * )Q, integerLDQ, double precision, dimension( ldz, * )Z, integerLDZ, integerJ1, integerN1, integerN2, double precision, dimension( * )WORK, integerLWORK, integerINFO)

DTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an orthogonal equivalence transformation.

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 matrix pair

 (A, B) by an orthogonal equivalence transformation.

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

 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 vectors are

 updated.

 Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T

 Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T

 

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 DOUBLE PRECISION array, 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 DOUBLE PRECISION array, 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 DOUBLE PRECISION array, dimension (LDQ,N)

 On entry, if WANTQ = .TRUE., the orthogonal 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 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

 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). 1 <= J1 <= N.

N1

 N1 is INTEGER

 The order of the first block (A11, B11). N1 = 0, 1 or 2.

N2

 N2 is INTEGER

 The order of the second block (A22, B22). N2 = 0, 1 or 2.

WORK

 WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)).

LWORK

 LWORK is INTEGER

 The dimension of the array WORK.

 LWORK >= MAX( 1, N*(N2+N1), (N2+N1)*(N2+N1)*2 )

INFO

 INFO is 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).

 

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 221 of file dtgex2.f.

Author

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