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, * )


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)


               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



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