# cgegs.f - Man Page

SRC/DEPRECATED/cgegs.f

## Synopsis

### Functions/Subroutines

subroutine cgegs (jobvsl, jobvsr, n, a, lda, b, ldb, alpha, beta, vsl, ldvsl, vsr, ldvsr, work, lwork, rwork, info)
CGEGS computes the eigenvalues, Schur form, and, optionally, the left and or/right Schur vectors of a complex matrix pair (A,B)

## Function/Subroutine Documentation

### subroutine cgegs (character jobvsl, character jobvsr, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) alpha, complex, dimension( * ) beta, complex, dimension( ldvsl, * ) vsl, integer ldvsl, complex, dimension( ldvsr, * ) vsr, integer ldvsr, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer info)

CGEGS computes the eigenvalues, Schur form, and, optionally, the left and or/right Schur vectors of a complex matrix pair (A,B)

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This routine is deprecated and has been replaced by routine CGGES.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).
Parameters

JOBVSL

JOBVSL is CHARACTER*1
= 'N':  do not compute the left Schur vectors;
= 'V':  compute the left Schur vectors (returned in VSL).

JOBVSR

JOBVSR is CHARACTER*1
= 'N':  do not compute the right Schur vectors;
= 'V':  compute the right Schur vectors (returned in VSR).

N

N is INTEGER
The order of the matrices A, B, VSL, and VSR.  N >= 0.

A

A is COMPLEX array, dimension (LDA, N)
On entry, the matrix A.
On exit, the upper triangular matrix S from the generalized
Schur factorization.

LDA

LDA is INTEGER
The leading dimension of A.  LDA >= max(1,N).

B

B is COMPLEX array, dimension (LDB, N)
On entry, the matrix B.
On exit, the upper triangular matrix T from the generalized
Schur factorization.

LDB

LDB is INTEGER
The leading dimension of B.  LDB >= max(1,N).

ALPHA

ALPHA is 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

BETA is 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

VSL is COMPLEX array, dimension (LDVSL,N)
If JOBVSL = 'V', the matrix of left Schur vectors Q.
Not referenced if JOBVSL = 'N'.

LDVSL

LDVSL is INTEGER
The leading dimension of the matrix VSL. LDVSL >= 1, and
if JOBVSL = 'V', LDVSL >= N.

VSR

VSR is COMPLEX array, dimension (LDVSR,N)
If JOBVSR = 'V', the matrix of right Schur vectors Z.
Not referenced if JOBVSR = 'N'.

LDVSR

LDVSR is INTEGER
The leading dimension of the matrix VSR. LDVSR >= 1, and
if JOBVSR = 'V', LDVSR >= N.

WORK

WORK is COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is 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

RWORK is REAL array, dimension (3*N)

INFO

INFO is 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)
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 222 of file cgegs.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cgegs(3) is an alias of cgegs.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK