dtgex2 (3)  Linux Manuals
NAME
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 1by1 or 2by2 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 1by1 and 2by2 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.
WANTZWANTZ is LOGICAL .TRUE. : update the right transformation matrix Z; .FALSE.: do not update Z.
NN is INTEGER The order of the matrices A and B. N >= 0.
AA is DOUBLE PRECISION array, dimensions (LDA,N) On entry, the matrix A in the pair (A, B). On exit, the updated matrix A.
LDALDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
BB is DOUBLE PRECISION array, dimensions (LDB,N) On entry, the matrix B in the pair (A, B). On exit, the updated matrix B.
LDBLDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
QQ 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..
LDQLDQ is INTEGER The leading dimension of the array Q. LDQ >= 1. If WANTQ = .TRUE., LDQ >= N.
ZZ 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..
LDZLDZ is INTEGER The leading dimension of the array Z. LDZ >= 1. If WANTZ = .TRUE., LDZ >= N.
J1J1 is INTEGER The index to the first block (A11, B11). 1 <= J1 <= N.
N1N1 is INTEGER The order of the first block (A11, B11). N1 = 0, 1 or 2.
N2N2 is INTEGER The order of the second block (A22, B22). N2 = 0, 1 or 2.
WORKWORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)).
LWORKLWORK is INTEGER The dimension of the array WORK. LWORK >= MAX( 1, N*(N2+N1), (N2+N1)*(N2+N1)*2 )
INFOINFO 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 illconditioned. <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, S901 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 RealTime Applications, Kluwer Academic Publ. 1993, pp 195218. [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, S901 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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