SSPGV(3)              LAPACK driver routine (version 3.1)             SSPGV(3)



NAME
       SSPGV - 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 SSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, INFO )

           CHARACTER     JOBZ, UPLO

           INTEGER       INFO, ITYPE, LDZ, N

           REAL          AP( * ), BP( * ), W( * ), WORK( * ), Z( LDZ, * )

PURPOSE
       SSPGV 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, stored in packed format, 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.

       AP      (input/output) REAL array, dimension
               (N*(N+1)/2) On entry, the upper or lower triangle of  the  sym-
               metric matrix A, packed columnwise in a linear array.  The j-th
               column of A is stored in the array AP as  follows:  if  UPLO  =
               'U',  AP(i  +  (j-1)*j/2)  = A(i,j) for 1<=i<=j; if UPLO = 'L',
               AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

               On exit, the contents of AP are destroyed.

       BP      (input/output) REAL array, dimension (N*(N+1)/2)
               On entry, the upper or lower triangle of the  symmetric  matrix
               B,  packed  columnwise in a linear array.  The j-th column of B
               is stored in the array BP as follows: if UPLO  =  'U',  BP(i  +
               (j-1)*j/2)  =  B(i,j)  for  1<=i<=j;  if  UPLO  =  'L',  BP(i +
               (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.

               On exit, the triangular factor U or L from the Cholesky factor-
               ization B = U**T*U or B = L*L**T, in the same storage format as
               B.

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

       Z       (output) REAL array, dimension (LDZ, N)
               If JOBZ = 'V', then if INFO = 0, Z 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 Z is not referenced.

       LDZ     (input) INTEGER
               The  leading dimension of the array Z.  LDZ >= 1, and if JOBZ =
               'V', LDZ >= max(1,N).

       WORK    (workspace) REAL array, dimension (3*N)

       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an illegal value
               > 0:  SPPTRF or SSPEV returned an error code:
               <= N:  if INFO = i, SSPEV 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 driver routine (version 3.N1o)vember 2006                        SSPGV(3)