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ctgex2.f(3) | LAPACK | ctgex2.f(3) |
NAME¶
ctgex2.f -SYNOPSIS¶
Functions/Subroutines¶
subroutine ctgex2 (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, INFO)
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 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
WANTQ
WANTZ
N
A
LDA
B
LDB
Q
LDQ
Z
LDZ
J1
INFO
Author:
WANTQ is LOGICAL .TRUE. : update the left transformation matrix Q; .FALSE.: do not update Q.
WANTZ is LOGICAL .TRUE. : update the right transformation matrix Z; .FALSE.: do not update Z.
N is INTEGER The order of the matrices A and B. N >= 0.
A is COMPLEX arrays, dimensions (LDA,N) On entry, the matrix A in the pair (A, B). On exit, the updated matrix A.
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
B is COMPLEX arrays, dimensions (LDB,N) On entry, the matrix B in the pair (A, B). On exit, the updated matrix B.
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
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 is INTEGER The leading dimension of the array Q. LDQ >= 1; If WANTQ = .TRUE., LDQ >= N.
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 is INTEGER The leading dimension of the array Z. LDZ >= 1; If WANTZ = .TRUE., LDZ >= N.
J1 is INTEGER The index to the first block (A11, B11).
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.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
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.
[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.
Author¶
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