SYNOPSIS
 SUBROUTINE SGGEV(
 JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO )
 CHARACTER JOBVL, JOBVR
 INTEGER INFO, LDA, LDB, LDVL, LDVR, LWORK, N
 REAL A( LDA, * ), ALPHAI( * ), ALPHAR( * ), B( LDB, * ), BETA( * ), VL( LDVL, * ), VR( LDVR, * ), WORK( * )
PURPOSE
SGGEV computes for a pair of NbyN 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 conjugatetranspose of u(j).
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) REAL 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) REAL 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).
 ALPHAR (output) REAL array, dimension (N)
 ALPHAI (output) REAL array, dimension (N) BETA (output) REAL array, dimension (N) On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will be the generalized eigenvalues. If ALPHAI(j) is zero, then the jth eigenvalue is real; if positive, then the jth 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).
 VL (output) REAL array, dimension (LDVL,N)
 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 jth eigenvalue is real, then u(j) = VL(:,j), the jth column of VL. If the jth 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 is scaled so the largest component has 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) REAL array, dimension (LDVR,N)
 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 jth eigenvalue is real, then v(j) = VR(:,j), the jth column of VR. If the jth 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 is scaled so the largest component has 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) 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(1,8*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) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith 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.