sggev(3P) Sun Performance Library sggev(3P)NAMEsggev - compute for a pair of N-by-N real nonsymmetric matrices (A,B)
SYNOPSIS
SUBROUTINE SGGEV(JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI,
BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO)
CHARACTER * 1 JOBVL, JOBVR
INTEGER N, LDA, LDB, LDVL, LDVR, LWORK, INFO
REAL A(LDA,*), B(LDB,*), ALPHAR(*), ALPHAI(*), BETA(*), VL(LDVL,*),
VR(LDVR,*), WORK(*)
SUBROUTINE SGGEV_64(JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI,
BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO)
CHARACTER * 1 JOBVL, JOBVR
INTEGER*8 N, LDA, LDB, LDVL, LDVR, LWORK, INFO
REAL A(LDA,*), B(LDB,*), ALPHAR(*), ALPHAI(*), BETA(*), VL(LDVL,*),
VR(LDVR,*), WORK(*)
F95 INTERFACE
SUBROUTINE GGEV(JOBVL, JOBVR, [N], A, [LDA], B, [LDB], ALPHAR,
ALPHAI, BETA, VL, [LDVL], VR, [LDVR], [WORK], [LWORK], [INFO])
CHARACTER(LEN=1) :: JOBVL, JOBVR
INTEGER :: N, LDA, LDB, LDVL, LDVR, LWORK, INFO
REAL, DIMENSION(:) :: ALPHAR, ALPHAI, BETA, WORK
REAL, DIMENSION(:,:) :: A, B, VL, VR
SUBROUTINE GGEV_64(JOBVL, JOBVR, [N], A, [LDA], B, [LDB], ALPHAR,
ALPHAI, BETA, VL, [LDVL], VR, [LDVR], [WORK], [LWORK], [INFO])
CHARACTER(LEN=1) :: JOBVL, JOBVR
INTEGER(8) :: N, LDA, LDB, LDVL, LDVR, LWORK, INFO
REAL, DIMENSION(:) :: ALPHAR, ALPHAI, BETA, WORK
REAL, DIMENSION(:,:) :: A, B, VL, VR
C INTERFACE
#include <sunperf.h>
void sggev(char jobvl, char jobvr, int n, float *a, int lda, float *b,
int ldb, float *alphar, float *alphai, float *beta, float
*vl, int ldvl, float *vr, int ldvr, int *info);
void sggev_64(char jobvl, char jobvr, long n, float *a, long lda, float
*b, long ldb, float *alphar, float *alphai, float *beta,
float *vl, long ldvl, float *vr, long ldvr, long *info);
PURPOSEsggev computes for a pair of N-by-N real nonsymmetric matrices (A,B)
the generalized eigenvalues, and optionally, the left and/or right gen‐
eralized 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 singu‐
lar. 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 eigenvector v(j) corresponding to the eigenvalue lambda(j) of
(A,B) satisfies
A * v(j) = lambda(j) * B * v(j).
The left eigenvector u(j) corresponding to the eigenvalue 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).
ARGUMENTS
JOBVL (input)
= 'N': do not compute the left generalized eigenvectors;
= 'V': compute the left generalized eigenvectors.
JOBVR (input)
= 'N': do not compute the right generalized eigenvectors;
= 'V': compute the right generalized eigenvectors.
N (input) The order of the matrices A, B, VL, and VR. N >= 0.
A (input/output)
On entry, the matrix A in the pair (A,B). On exit, A has
been overwritten.
LDA (input)
The leading dimension of A. LDA >= max(1,N).
B (input/output)
On entry, the matrix B in the pair (A,B). On exit, B has
been overwritten.
LDB (input)
The leading dimension of B. LDB >= max(1,N).
ALPHAR (output)
On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
be the generalized eigenvalues. 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) negative.
Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(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, ALPHAR and ALPHAI will be always less
than and usually comparable with norm(A) in magnitude, and
BETA always less than and usually comparable with norm(B).
ALPHAI (output)
See the description for ALPHAR.
BETA (output)
See the description for ALPHAR.
VL (output)
If JOBVL = 'V', the left eigenvectors u(j) are stored one
after another in the columns of VL, in the same order as
their eigenvalues. If the j-th eigenvalue is real, then u(j)
= VL(:,j), the j-th column of VL. If the j-th and (j+1)-th
eigenvalues form a complex conjugate pair, then u(j) =
VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1). Each
eigenvector will be scaled so the largest component have
abs(real part)+abs(imag. part)=1. Not referenced if JOBVL =
'N'.
LDVL (input)
The leading dimension of the matrix VL. LDVL >= 1, and if
JOBVL = 'V', LDVL >= N.
VR (output)
If JOBVR = 'V', the right eigenvectors v(j) are stored one
after another in the columns of VR, in the same order as
their eigenvalues. If the j-th eigenvalue is real, then v(j)
= VR(:,j), the j-th column of VR. If the j-th and (j+1)-th
eigenvalues form a complex conjugate pair, then v(j) =
VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1). Each
eigenvector will be scaled so the largest component have
abs(real part)+abs(imag. part)=1. Not referenced if JOBVR =
'N'.
LDVR (input)
The leading dimension of the matrix VR. LDVR >= 1, and if
JOBVR = 'V', LDVR >= N.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
The dimension of the array WORK. LWORK >= max(1,8*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.
INFO (output)
= 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 ALPHAR(j), ALPHAI(j), and BETA(j) should
be correct for j=INFO+1,...,N. > N: =N+1: other than QZ
iteration failed in SHGEQZ.
=N+2: error return from STGEVC.
6 Mar 2009 sggev(3P)
