SSYGV(3)       LAPACK routine of NEC Numeric Library Collection       SSYGV(3)



NAME
       SSYGV

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



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

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

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

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

           B         (input/output)
                     B is REAL array, dimension (LDB, N)
                     On entry, the symmetric positive definite 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)
                     LDB is INTEGER
                     The leading dimension of the array B.  LDB >= max(1,N).

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

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

           LWORK     (input)
                     LWORK is 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.

                     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)
                     INFO is 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.



LAPACK routine                  31 October 2017                       SSYGV(3)