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

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

     CHARACTER JOBZ, UPLO

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

     DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * )



     #include <sunperf.h>

     void dsygv(int itype, char jobz, char uplo,  int  n,  double
               *da,  int lda, double *db, int ldb, double *w, int
               *info) ;

PURPOSE
     DSYGV computes all  the  eigenvalues,  and  optionally,  the
     eigenvectors of a real generalized symmetric-definite eigen-
     problem, 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) DOUBLE PRECISION  array,  dimension
               (LDA, N)
               On entry, the symmetric matrix A.  If UPLO =  'U',
               the leading N-by-N upper triangular part of A con-
               tains 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  con-
               tains the matrix Z of eigenvectors.  The eigenvec-
               tors 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) DOUBLE PRECISION  array,  dimension
               (LDB, N)
               On entry, the symmetric matrix B.  If UPLO =  'U',
               the leading N-by-N upper triangular part of B con-
               tains 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) DOUBLE PRECISION array, dimension (N)
               If INFO = 0, the eigenvalues in ascending order.

     WORK      (workspace/output) DOUBLE PRECISION array,  dimen-
               sion (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  DSYTRD
               returned by ILAENV.

     INFO      (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value
               > 0:  DPOTRF or DSYEV returned an error code:
               <= N:  if INFO = i, DSYEV failed  to  converge;  i
               off-diagonal elements of an intermediate tridiago-
               nal 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.

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