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CGEGS

Section: LAPACK driver routine (version 3.2) (1)
Updated: April 2011
Index

NAME

LAPACK-3 - routine i deprecated and has been replaced by routine CGGES

SYNOPSIS

SUBROUTINE CGEGS(: JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA,VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK,INFO )
: CHARACTERJOBVSL, JOBVSR
: INTEGERINFO, LDA, LDB, LDVSL, LDVSR, LWORK, N
: REALRWORK( * )
: COMPLEXA( LDA, * ), ALPHA( * ), B( LDB, * ),BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ),WORK( * )

PURPOSE

This routine is deprecated and has been replaced by routine CGGES.
CGEGS computes the eigenvalues, Schur form, and, optionally, the
left and or/right Schur vectors of a complex matrix pair (A,B).
Given two square matrices A and B, the generalized Schur

factorization has the form

A = Q*S*Z**H, B = Q*T*Z**H

where Q and Z are unitary matrices and S and T are upper triangular.
The columns of Q are the left Schur vectors

and the columns of Z are the right Schur vectors.

If only the eigenvalues of (A,B) are needed, the driver routine
CGEGV should be used instead. See CGEGV for a description of the
eigenvalues of the generalized nonsymmetric eigenvalue problem
(GNEP).

ARGUMENTS

JOBVSL (input) CHARACTER*1: = aqNaq: do not compute the left Schur vectors;

= aqVaq: compute the left Schur vectors (returned in VSL).
JOBVSR (input) CHARACTER*1: = aqNaq: do not compute the right Schur vectors;

= aqVaq: compute the right Schur vectors (returned in VSR).
N (input) INTEGER: The order of the matrices A, B, VSL, and VSR. N >= 0.
A (input/output) COMPLEX array, dimension (LDA, N): On entry, the matrix A.
On exit, the upper triangular matrix S from the generalized
Schur factorization.
LDA (input) INTEGER: The leading dimension of A. LDA >= max(1,N).
B (input/output) COMPLEX array, dimension (LDB, N): On entry, the matrix B.
On exit, the upper triangular matrix T from the generalized
Schur factorization.
LDB (input) INTEGER: The leading dimension of B. LDB >= max(1,N).
ALPHA (output) COMPLEX array, dimension (N): The complex scalars alpha that define the eigenvalues of
GNEP. ALPHA(j) = S(j,j), the diagonal element of the Schur
form of A.
BETA (output) COMPLEX array, dimension (N): The non-negative real scalars beta that define the
eigenvalues of GNEP. BETA(j) = T(j,j), the diagonal element
of the triangular factor T.
Together, the quantities alpha = ALPHA(j) and beta = BETA(j)
represent the j-th eigenvalue of the matrix pair (A,B), in
one of the forms lambda = alpha/beta or mu = beta/alpha.
Since either lambda or mu may overflow, they should not,
in general, be computed.
VSL (output) COMPLEX array, dimension (LDVSL,N): If JOBVSL = aqVaq, the matrix of left Schur vectors Q.
Not referenced if JOBVSL = aqNaq.
LDVSL (input) INTEGER: The leading dimension of the matrix VSL. LDVSL >= 1, and
if JOBVSL = aqVaq, LDVSL >= N.
VSR (output) COMPLEX array, dimension (LDVSR,N): If JOBVSR = aqVaq, the matrix of right Schur vectors Z.
Not referenced if JOBVSR = aqNaq.
LDVSR (input) INTEGER: The leading dimension of the matrix VSR. LDVSR >= 1, and
if JOBVSR = aqVaq, LDVSR >= N.
WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)): On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER: The dimension of the array WORK.  LWORK >= max(1,2*N).
For good performance, LWORK must generally be larger.
To compute the optimal value of LWORK, call ILAENV to get
blocksizes (for CGEQRF, CUNMQR, and CUNGQR.)  Then compute:
NB  -- MAX of the blocksizes for CGEQRF, CUNMQR, and CUNGQR;
the optimal LWORK is N*(NB+1).
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
RWORK (workspace) REAL array, dimension (3*N)
INFO (output) INTEGER: = 0:  successful exit

< 0:  if INFO = -i, the i-th argument had an illegal value.

=1,...,N:
The QZ iteration failed.  (A,B) are not in Schur
form, but ALPHA(j) and BETA(j) should be correct for
j=INFO+1,...,N.
> N:  errors that usually indicate LAPACK problems:

=N+1: error return from CGGBAL

=N+2: error return from CGEQRF

=N+3: error return from CUNMQR

=N+4: error return from CUNGQR

=N+5: error return from CGGHRD

=N+6: error return from CHGEQZ (other than failed
iteration)
=N+7: error return from CGGBAK (computing VSL)

=N+8: error return from CGGBAK (computing VSR)

=N+9: error return from CLASCL (various places)

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