Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  computes  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 SSBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB,  W,  Z,  LDZ,  WORK,  LWORK,
                          IWORK, LIWORK, INFO )

           CHARACTER      JOBZ, UPLO

           INTEGER        INFO, KA, KB, LDAB, LDBB, LDZ, LIWORK, LWORK, N

           INTEGER        IWORK( * )

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

PURPOSE

       SSBGVD  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.  If eigenvectors are
        desired, it uses a divide and conquer algorithm.
        The divide and conquer algorithm makes very mild assumptions about
        floating point arithmetic. It will work on machines with a guard
        digit in add/subtract, or on those binary machines without guard
        digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
        Cray-2. It could conceivably fail on hexadecimal or decimal machines
        without guard digits, but we know of none.

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) REAL 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) REAL 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(ka+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 SPBSTF.

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

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

        Z       (output) REAL 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 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 >= max(1,N).

        WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
                On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

        LWORK   (input) INTEGER
                The dimension of the array WORK.
                If N <= 1,               LWORK >= 1.
                If JOBZ = 'N' and N > 1, LWORK >= 3*N.
                If JOBZ = 'V' and N > 1, LWORK >= 1 + 5*N + 2*N**2.
                If LWORK = -1, then a workspace query is assumed; the routine
                only calculates the optimal sizes of the WORK and IWORK
                arrays, returns these values as the first entries of the WORK
                and IWORK arrays, and no error message related to LWORK or
                LIWORK is issued by XERBLA.

        IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
                On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.

        LIWORK  (input) INTEGER
                The dimension of the array IWORK.
                If JOBZ  = 'N' or N <= 1, LIWORK >= 1.
                If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.
                If LIWORK = -1, then a workspace query is assumed; the
                routine only calculates the optimal sizes of the WORK and
                IWORK arrays, returns these values as the first entries of
                the WORK and IWORK arrays, and no error message related to
                LWORK or LIWORK is issued by XERBLA.

        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 SPBSTF
                returned INFO = i: B is not positive definite.
                The factorization of B could not be completed and
                no eigenvalues or eigenvectors were computed.

FURTHER DETAILS

        Based on contributions by
           Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

 LAPACK driver routine (version 3.2)        April 2011                            SSBGVD(3lapack)