DGEGS(1) LAPACK driver routine (version 3.2) DGEGS(1)NAME
DGEGS - routine i deprecated and has been replaced by routine DGGES
SYNOPSIS
SUBROUTINE DGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR, ALPHAI,
BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, INFO )
CHARACTER JOBVSL, JOBVSR
INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N
DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ), B(
LDB, * ), BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, *
), WORK( * )
PURPOSE
This routine is deprecated and has been replaced by routine DGGES.
DGEGS computes the eigenvalues, real Schur form, and, optionally, left
and or/right Schur vectors of a real matrix pair (A,B). Given two
square matrices A and B, the generalized real Schur factorization has
the form
A = Q*S*Z**T, B = Q*T*Z**T
where Q and Z are orthogonal matrices, T is upper triangular, and S is
an upper quasi-triangular matrix with 1-by-1 and 2-by-2 diagonal
blocks, the 2-by-2 blocks corresponding to complex conjugate pairs of
eigenvalues of (A,B). 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 DGEGV
should be used instead. See DGEGV for a description of the eigenvalues
of the generalized nonsymmetric eigenvalue problem (GNEP).
ARGUMENTS
JOBVSL (input) CHARACTER*1
= 'N': do not compute the left Schur vectors;
= 'V': compute the left Schur vectors (returned in VSL).
JOBVSR (input) CHARACTER*1
= 'N': do not compute the right Schur vectors;
= 'V': 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) DOUBLE PRECISION array, dimension (LDA, N)
On entry, the matrix A. On exit, the upper quasi-triangular
matrix S from the generalized real Schur factorization.
LDA (input) INTEGER
The leading dimension of A. LDA >= max(1,N).
B (input/output) DOUBLE PRECISION array, dimension (LDB, N)
On entry, the matrix B. On exit, the upper triangular matrix T
from the generalized real Schur factorization.
LDB (input) INTEGER
The leading dimension of B. LDB >= max(1,N).
ALPHAR (output) DOUBLE PRECISION array, dimension (N)
The real parts of each scalar alpha defining an eigenvalue of
GNEP.
ALPHAI (output) DOUBLE PRECISION array, dimension (N)
The imaginary parts of each scalar alpha defining an eigenvalue
of GNEP. If ALPHAI(j) is zero, then the j-th eigenvalue is
real; if positive, then the j-th and (j+1)-st eigenvalues are a
complex conjugate pair, with ALPHAI(j+1) = -ALPHAI(j).
BETA (output) DOUBLE PRECISION array, dimension (N)
The scalars beta that define the eigenvalues of GNEP.
Together, the quantities alpha = (ALPHAR(j),ALPHAI(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) DOUBLE PRECISION array, dimension (LDVSL,N)
If JOBVSL = 'V', the matrix of left Schur vectors Q. Not ref‐
erenced if JOBVSL = 'N'.
LDVSL (input) INTEGER
The leading dimension of the matrix VSL. LDVSL >=1, and if JOB‐
VSL = 'V', LDVSL >= N.
VSR (output) DOUBLE PRECISION array, dimension (LDVSR,N)
If JOBVSR = 'V', the matrix of right Schur vectors Z. Not ref‐
erenced if JOBVSR = 'N'.
LDVSR (input) INTEGER
The leading dimension of the matrix VSR. LDVSR >= 1, and if
JOBVSR = 'V', LDVSR >= N.
WORK (workspace/output) DOUBLE PRECISION 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(1,4*N). For
good performance, LWORK must generally be larger. To compute
the optimal value of LWORK, call ILAENV to get blocksizes (for
DGEQRF, DORMQR, and DORGQR.) Then compute: NB -- MAX of the
blocksizes for DGEQRF, DORMQR, and DORGQR The optimal LWORK is
2*N + 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.
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 ALPHAR(j), ALPHAI(j), and BETA(j) should be correct
for j=INFO+1,...,N. > N: errors that usually indicate LAPACK
problems:
=N+1: error return from DGGBAL
=N+2: error return from DGEQRF
=N+3: error return from DORMQR
=N+4: error return from DORGQR
=N+5: error return from DGGHRD
=N+6: error return from DHGEQZ (other than failed iteration)
=N+7: error return from DGGBAK (computing VSL)
=N+8: error return from DGGBAK (computing VSR)
=N+9: error return from DLASCL (various places)
LAPACK driver routine (version 3November 2008 DGEGS(1)