dsbgv.f

          SUBROUTINE DSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
         $                  LDZ, WORK, INFO )
    *
    *  -- LAPACK driver routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          JOBZ, UPLO
          INTEGER            INFO, KA, KB, LDAB, LDBB, LDZ, N
    *     ..
    *     .. Array Arguments ..
          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.
    *
    *  =====================================================================
    *
    *     .. Local Scalars ..
          LOGICAL            UPPER, WANTZ
          CHARACTER          VECT
          INTEGER            IINFO, INDE, INDWRK
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           DPBSTF, DSBGST, DSBTRD, DSTEQR, DSTERF, XERBLA
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          WANTZ = LSAME( JOBZ, 'V' )
          UPPER = LSAME( UPLO, 'U' )
    *
          INFO = 0
          IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
             INFO = -1
          ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
             INFO = -2
          ELSE IF( N.LT.0 ) THEN
             INFO = -3
          ELSE IF( KA.LT.0 ) THEN
             INFO = -4
          ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
             INFO = -5
          ELSE IF( LDAB.LT.KA+1 ) THEN
             INFO = -7
          ELSE IF( LDBB.LT.KB+1 ) THEN
             INFO = -9
          ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
             INFO = -12
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'DSBGV ', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 )
         $   RETURN
    *
    *     Form a split Cholesky factorization of B.
    *
          CALL DPBSTF( UPLO, N, KB, BB, LDBB, INFO )
          IF( INFO.NE.0 ) THEN
             INFO = N + INFO
             RETURN
          END IF
    *
    *     Transform problem to standard eigenvalue problem.
    *
          INDE = 1
          INDWRK = INDE + N
          CALL DSBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
         $             WORK( INDWRK ), IINFO )
    *
    *     Reduce to tridiagonal form.
    *
          IF( WANTZ ) THEN
             VECT = 'U'
          ELSE
             VECT = 'N'
          END IF
          CALL DSBTRD( VECT, UPLO, N, KA, AB, LDAB, W, WORK( INDE ), Z, LDZ,
         $             WORK( INDWRK ), IINFO )
    *
    *     For eigenvalues only, call DSTERF.  For eigenvectors, call SSTEQR.
    *
          IF( .NOT.WANTZ ) THEN
             CALL DSTERF( N, W, WORK( INDE ), INFO )
          ELSE
             CALL DSTEQR( JOBZ, N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ),
         $                INFO )
          END IF
          RETURN
    *
    *     End of DSBGV
    *
          END