
NAMEztgexc.f SYNOPSISFunctions/Subroutinessubroutine ztgexc (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, IFST, ILST, INFO) Function/Subroutine Documentationsubroutine ztgexc (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, integerIFST, integerILST, integerINFO)ZTGEXC Purpose:ZTGEXC reorders the generalized Schur decomposition of a complex matrix pair (A,B), using an unitary equivalence transformation (A, B) := Q * (A, B) * Z**H, so that the diagonal block of (A, B) with row index IFST is moved to row ILST. (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 array, dimension (LDA,N) On entry, the upper triangular 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 array, dimension (LDB,N) On entry, the upper triangular 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) On entry, if WANTQ = .TRUE., the unitary matrix Q. On exit, the updated matrix Q. If WANTQ = .FALSE., Q is not referenced.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) On entry, if WANTZ = .TRUE., the unitary matrix Z. On exit, the updated matrix Z. If WANTZ = .FALSE., Z is not referenced.LDZ LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1; If WANTZ = .TRUE., LDZ >= N.IFST IFST is INTEGERILST ILST is INTEGER Specify the reordering of the diagonal blocks of (A, B). The block with row index IFST is moved to row ILST, by a sequence of swapping between adjacent blocks.INFO INFO is INTEGER =0: Successful exit. <0: if INFO = i, the ith argument had an illegal value. =1: The transformed matrix pair (A, B) would be too far from generalized Schur form; the problem is ill conditioned. (A, B) may have been partially reordered, and ILST points to the first row of the current position of the block being moved. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
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 200 of file ztgexc.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 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. [3] B. Kagstrom and P. Poromaa, LAPACKStyle Algorithms and Software for Solving the Generalized Sylvester Equation and Estimating the Separation between Regular Matrix Pairs, Report UMINF  93.23, Department of Computing Science, Umea University, S901 87 Umea, Sweden, December 1993, Revised April 1994, Also as LAPACK working Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1, 1996. AuthorGenerated automatically by Doxygen for LAPACK from the source code.
Visit the GSP FreeBSD Man Page Interface. 