ssygv(3F)

NAME
     SSYGV - compute all the eigenvalues, and optionally, the eigenvectors of
     a real generalized symmetric-definite eigenproblem, of the form
     A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

SYNOPSIS
     SUBROUTINE SSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK,
                       INFO )

         CHARACTER     JOBZ, UPLO

         INTEGER       INFO, ITYPE, LDA, LDB, LWORK, N

         REAL          A( LDA, * ), B( LDB, * ), W( * ), WORK( * )

PURPOSE
     SSYGV computes all the eigenvalues, and optionally, the eigenvectors of a
     real generalized symmetric-definite eigenproblem, of the form
     A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.  Here A and B
     are assumed to be symmetric and B is also
     positive definite.


ARGUMENTS
     ITYPE   (input) INTEGER
             Specifies the problem type to be solved:
             = 1:  A*x = (lambda)*B*x
             = 2:  A*B*x = (lambda)*x
             = 3:  B*A*x = (lambda)*x

     JOBZ    (input) CHARACTER*1
             = 'N':  Compute eigenvalues only;
             = 'V':  Compute eigenvalues and eigenvectors.

     UPLO    (input) CHARACTER*1
             = 'U':  Upper triangles of A and B are stored;
             = 'L':  Lower triangles of A and B are stored.

     N       (input) INTEGER
             The order of the matrices A and B.  N >= 0.

     A       (input/output) REAL array, dimension (LDA, N)
             On entry, the symmetric matrix A.  If UPLO = 'U', the leading N-
             by-N upper triangular part of A contains the upper triangular
             part of the matrix A.  If UPLO = 'L', the leading N-by-N lower
             triangular part of A contains the lower triangular part of the
             matrix A.

             On exit, if JOBZ = 'V', then if INFO = 0, A contains the matrix Z
             of eigenvectors.  The eigenvectors are normalized as follows:  if
             ITYPE = 1 or 2, Z**T*B*Z = I; if ITYPE = 3, Z**T*inv(B)*Z = I.
             If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') or
             the lower triangle (if UPLO='L') of A, including the diagonal, is
             destroyed.

     LDA     (input) INTEGER
             The leading dimension of the array A.  LDA >= max(1,N).

     B       (input/output) REAL array, dimension (LDB, N)
             On entry, the symmetric matrix B.  If UPLO = 'U', the leading N-
             by-N upper triangular part of B contains the upper triangular
             part of the matrix B.  If UPLO = 'L', the leading N-by-N lower
             triangular part of B contains the lower triangular part of the
             matrix B.

             On exit, if INFO <= N, the part of B containing the matrix is
             overwritten by the triangular factor U or L from the Cholesky
             factorization B = U**T*U or B = L*L**T.

     LDB     (input) INTEGER
             The leading dimension of the array B.  LDB >= max(1,N).

     W       (output) REAL array, dimension (N)
             If INFO = 0, the eigenvalues in ascending order.

     WORK    (workspace/output) REAL array, dimension (LWORK)
             On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

     LWORK   (input) INTEGER
             The length of the array WORK.  LWORK >= max(1,3*N-1).  For
             optimal efficiency, LWORK >= (NB+2)*N, where NB is the blocksize
             for SSYTRD returned by ILAENV.

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value
             > 0:  SPOTRF or SSYEV returned an error code:
             <= N:  if INFO = i, SSYEV failed to converge; i off-diagonal
             elements of an intermediate tridiagonal form did not converge to
             zero; > N:   if INFO = N + i, for 1 <= i <= N, then the leading
             minor of order i of B is not positive definite.  The
             factorization of B could not be completed and no eigenvalues or
             eigenvectors were computed.