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dsbev

 NAME
      DSBEV - compute all the eigenvalues and, optionally, eigen-
      vectors of a real symmetric band matrix A

 SYNOPSIS
      SUBROUTINE DSBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,
                        WORK, INFO )

          CHARACTER     JOBZ, UPLO

          INTEGER       INFO, KD, LDAB, LDZ, N

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

 PURPOSE
      DSBEV computes all the eigenvalues and, optionally, eigen-
      vectors of a real symmetric band matrix A.

 ARGUMENTS
      JOBZ    (input) CHARACTER*1
              = 'N':  Compute eigenvalues only;
              = 'V':  Compute eigenvalues and eigenvectors.

      UPLO    (input) CHARACTER*1
              = 'U':  Upper triangle of A is stored;
              = 'L':  Lower triangle of A is stored.

      N       (input) INTEGER
              The order of the matrix A.  N >= 0.

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

 N)
      AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,
              On entry, the upper or lower triangle of the sym-
              metric band matrix A, stored in the first KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
              if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for
              j<=i<=min(n,j+kd).

              On exit, AB is overwritten by values generated dur-
              ing the reduction to tridiagonal form.  If UPLO =
              'U', the first superdiagonal and the diagonal of the
              tridiagonal matrix T are returned in rows KD and
              KD+1 of AB, and if UPLO = 'L', the diagonal and

              first subdiagonal of T are returned in the first two
              rows of AB.

      LDAB    (input) INTEGER
              The leading dimension of the array AB.  LDAB >= KD +
              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
              orthonormal eigenvectors of the matrix A, with the
              i-th column of Z holding the eigenvector associated
              with W(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).

 (max(1,3*N-2))
      WORK    (workspace) DOUBLE PRECISION array, dimension

      INFO    (output) INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal
              value
              > 0:  if INFO = i, the algorithm failed to converge;
              i off-diagonal elements of an intermediate tridiago-
              nal form did not converge to zero.