DSBGV (3lapack)

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 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) DOUBLE PRECISION 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 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 illegal 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.