SGEGS(1) LAPACK driver routine (version 3.2) SGEGS(1)NAME
SGEGS - routine i deprecated and has been replaced by routine SGGES
SYNOPSIS
SUBROUTINE SGEGS( 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
REAL A( LDA, * ), ALPHAI( * ), ALPHAR( * ), B( LDB, * ),
BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ), WORK( *
)
PURPOSE
This routine is deprecated and has been replaced by routine SGGES.
SGEGS 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 SGEGV
should be used instead. See SGEGV 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) REAL 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) REAL 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) REAL array, dimension (N)
The real parts of each scalar alpha defining an eigenvalue of
GNEP.
ALPHAI (output) REAL 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) REAL 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) REAL 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) REAL 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) REAL 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
SGEQRF, SORMQR, and SORGQR.) Then compute: NB -- MAX of the
blocksizes for SGEQRF, SORMQR, and SORGQR 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 SGGBAL
=N+2: error return from SGEQRF
=N+3: error return from SORMQR
=N+4: error return from SORGQR
=N+5: error return from SGGHRD
=N+6: error return from SHGEQZ (other than failed iteration)
=N+7: error return from SGGBAK (computing VSL)
=N+8: error return from SGGBAK (computing VSR)
=N+9: error return from SLASCL (various places)
LAPACK driver routine (version 3November 2008 SGEGS(1)
