
NAMEztgex2.f SYNOPSISFunctions/Subroutinessubroutine ztgex2 (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, INFO) Function/Subroutine Documentationsubroutine ztgex2 (logicalWANTQ, logicalWANTZ, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( ldq, * )Q, integerLDQ, complex*16, dimension( ldz, * )Z, integerLDZ, integerJ1, integerINFO)ZTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation. Purpose:ZTGEX2 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
Author:
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*16 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*16 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*16 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*16 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. 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.
Definition at line 190 of file ztgex2.f.
[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 UMINF94.04, Department of Computing Science, Umea University, S901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87. To appear in Numerical Algorithms, 1996. AuthorGenerated automatically by Doxygen for LAPACK from the source code.
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