CGGEV(3S)CGGEV(3S)NAMECGGEV - compute for a pair of N-by-N complex nonsymmetric matrices (A,B),
the generalized eigenvalues, and optionally, the left and/or right
generalized eigenvectors
SYNOPSIS
SUBROUTINE CGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, VL, LDVL,
VR, LDVR, WORK, LWORK, RWORK, INFO )
CHARACTER JOBVL, JOBVR
INTEGER INFO, LDA, LDB, LDVL, LDVR, LWORK, N
REAL RWORK( * )
COMPLEX A( LDA, * ), ALPHA( * ), B( LDB, * ), BETA( * ), VL(
LDVL, * ), VR( LDVR, * ), WORK( * )
IMPLEMENTATION
These routines are part of the SCSL Scientific Library and can be loaded
using either the -lscs or the -lscs_mp option. The -lscs_mp option
directs the linker to use the multi-processor version of the library.
When linking to SCSL with -lscs or -lscs_mp, the default integer size is
4 bytes (32 bits). Another version of SCSL is available in which integers
are 8 bytes (64 bits). This version allows the user access to larger
memory sizes and helps when porting legacy Cray codes. It can be loaded
by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
only one of the two versions; 4-byte integer and 8-byte integer library
calls cannot be mixed.
PURPOSECGGEV computes for a pair of N-by-N complex nonsymmetric matrices (A,B),
the generalized eigenvalues, and optionally, the left and/or right
generalized eigenvectors. A generalized eigenvalue for a pair of matrices
(A,B) is a scalar lambda or a ratio alpha/beta = lambda, such that A -
lambda*B is singular. It is usually represented as the pair (alpha,beta),
as there is a reasonable interpretation for beta=0, and even for both
being zero.
The right generalized eigenvector v(j) corresponding to the generalized
eigenvalue lambda(j) of (A,B) satisfies
A * v(j) = lambda(j) * B * v(j).
The left generalized eigenvector u(j) corresponding to the generalized
eigenvalues lambda(j) of (A,B) satisfies
u(j)**H * A = lambda(j) * u(j)**H * B
where u(j)**H is the conjugate-transpose of u(j).
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CGGEV(3S)CGGEV(3S)ARGUMENTS
JOBVL (input) CHARACTER*1
= 'N': do not compute the left generalized eigenvectors;
= 'V': compute the left generalized eigenvectors.
JOBVR (input) CHARACTER*1
= 'N': do not compute the right generalized eigenvectors;
= 'V': compute the right generalized eigenvectors.
N (input) INTEGER
The order of the matrices A, B, VL, and VR. N >= 0.
A (input/output) COMPLEX array, dimension (LDA, N)
On entry, the matrix A in the pair (A,B). On exit, A has been
overwritten.
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 in the pair (A,B). On exit, B has been
overwritten.
LDB (input) INTEGER
The leading dimension of B. LDB >= max(1,N).
ALPHA (output) COMPLEX array, dimension (N)
BETA (output) COMPLEX array, dimension (N) On exit,
ALPHA(j)/BETA(j), j=1,...,N, will be the generalized eigenvalues.
Note: the quotients ALPHA(j)/BETA(j) may easily over- or
underflow, and BETA(j) may even be zero. Thus, the user should
avoid naively computing the ratio alpha/beta. However, ALPHA
will be always less than and usually comparable with norm(A) in
magnitude, and BETA always less than and usually comparable with
norm(B).
VL (output) COMPLEX array, dimension (LDVL,N)
If JOBVL = 'V', the left generalized eigenvectors u(j) are stored
one after another in the columns of VL, in the same order as
their eigenvalues. Each eigenvector will be scaled so the
largest component will have abs(real part) + abs(imag. part) = 1.
Not referenced if JOBVL = 'N'.
LDVL (input) INTEGER
The leading dimension of the matrix VL. LDVL >= 1, and if JOBVL =
'V', LDVL >= N.
VR (output) COMPLEX array, dimension (LDVR,N)
If JOBVR = 'V', the right generalized eigenvectors v(j) are
stored one after another in the columns of VR, in the same order
as their eigenvalues. Each eigenvector will be scaled so the
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CGGEV(3S)CGGEV(3S)
largest component will have abs(real part) + abs(imag. part) = 1.
Not referenced if JOBVR = 'N'.
LDVR (input) INTEGER
The leading dimension of the matrix VR. LDVR >= 1, and if JOBVR =
'V', LDVR >= N.
WORK (workspace/output) COMPLEX array, dimension (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.
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/output) REAL array, dimension (8*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. No eigenvectors have been
calculated, but ALPHA(j) and BETA(j) should be correct for
j=INFO+1,...,N. > N: =N+1: other then QZ iteration failed in
SHGEQZ,
=N+2: error return from STGEVC.
SEE ALSOINTRO_LAPACK(3S), INTRO_SCSL(3S)
This man page is available only online.
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