Contents
sggev - compute for a pair of N-by-N real nonsymmetric
matrices (A,B)
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);
sggev computes for a pair of N-by-N real 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 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).
JOBVL (input)
= 'N': do not compute the left generalized eigen-
vectors;
= 'V': compute the left generalized eigenvectors.
JOBVR (input)
= 'N': do not compute the right generalized
eigenvectors;
= 'V': compute the right generalized eigenvec-
tors.
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 (input)
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 (input)
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 gen-
erally 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 ille-
gal value.
= 1,...,N: The QZ iteration failed. No eigenvec-
tors 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 itera-
tion failed in SHGEQZ.
=N+2: error return from STGEVC.