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



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

SYNOPSIS
       SUBROUTINE SSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ,
                         WORK, INFO )

           CHARACTER     JOBZ, UPLO

           INTEGER       INFO, KA, KB, LDAB, LDBB, LDZ, N

           REAL          AB( LDAB, * ), BB( LDBB, * ), W( * ), WORK( *  ),  Z(
                         LDZ, * )

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


ARGUMENTS
       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.

       KA      (input) INTEGER
               The number of superdiagonals of the matrix A if UPLO = 'U',  or
               the number of subdiagonals if UPLO = 'L'. KA >= 0.

       KB      (input) INTEGER
               The  number of superdiagonals of the matrix B if UPLO = 'U', or
               the number of subdiagonals if UPLO = 'L'. KB >= 0.

       AB      (input/output) REAL array, dimension (LDAB, N)
               On entry, the upper or lower triangle  of  the  symmetric  band
               matrix A, stored in the first ka+1 rows of the array.  The j-th
               column of A is stored in the j-th column of  the  array  AB  as
               follows:  if  UPLO  = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-
               ka)<=i<=j;  if  UPLO  =  'L',  AB(1+i-j,j)     =   A(i,j)   for
               j<=i<=min(n,j+ka).

               On exit, the contents of AB are destroyed.

       LDAB    (input) INTEGER
               The leading dimension of the array AB.  LDAB >= KA+1.

       BB      (input/output) REAL array, dimension (LDBB, N)
               On  entry,  the  upper  or lower triangle of the symmetric band
               matrix B, stored in the first kb+1 rows of the array.  The j-th
               column  of  B  is  stored in the j-th column of the array BB as
               follows: if UPLO = 'U', BB(kb+1+i-j,j) =  B(i,j)  for  max(1,j-
               kb)<=i<=j;   if   UPLO  =  'L',  BB(1+i-j,j)     =  B(i,j)  for
               j<=i<=min(n,j+kb).

               On exit, the factor S from the split Cholesky factorization B =
               S**T*S, as returned by SPBSTF.

       LDBB    (input) INTEGER
               The leading dimension of the array BB.  LDBB >= KB+1.

       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, with the i-th column of Z holding the eigenvector
               associated  with  W(i). The eigenvectors are normalized so that
               Z**T*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 >= 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:  if INFO = i, and i is:
               <=  N:   the  algorithm failed to converge: i off-diagonal ele-
               ments of an intermediate tridiagonal form did not  converge  to
               zero; > N:   if INFO = N + i, for 1 <= i <= N, then SPBSTF
               returned  INFO = i: B is not positive definite.  The factoriza-
               tion of B could not be completed and no eigenvalues  or  eigen-
               vectors were computed.



 LAPACK driver routine (version 3.N1o)vember 2006                        SSBGV(3)