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NAME
     dsbgv - compute 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 DSBGV( 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

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



     #include <sunperf.h>

     void dsbgv(char jobz, char uplo, int n, int ka, int kb, dou-
               ble  *dab,  int ldab, double *bb, int ldbb, double
               *w, double *dz, int ldz, int *info) ;

PURPOSE
     DSBGV 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) DOUBLE PRECISION  array,  dimension
               (LDAB, N)
               On entry, the upper or lower triangle of the  sym-
               metric  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) DOUBLE PRECISION  array,  dimension
               (LDBB, N)
               On entry, the upper or lower triangle of the  sym-
               metric  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 fac-
               torization B = S**T*S, as returned by DPBSTF.

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

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

     Z         (output) DOUBLE PRECISION 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)  DOUBLE  PRECISION  array,   dimension
               (3*N)

     INFO      (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value
               > 0:  if INFO = i, and i is:
               <= N:  the algorithm 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 DPBSTF
               returned INFO = i: B  is  not  positive  definite.
               The  factorization of B could not be completed and
               no eigenvalues or eigenvectors were computed.

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