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

NAME

       LAPACK-3  - computes all the eigenvalues and, optionally, eigenvectors of a real symmetric
       band matrix A

SYNOPSIS

       SUBROUTINE SSBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,  WORK,  LWORK,  IWORK,  LIWORK,
                          INFO )

           CHARACTER      JOBZ, UPLO

           INTEGER        INFO, KD, LDAB, LDZ, LIWORK, LWORK, N

           INTEGER        IWORK( * )

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

PURPOSE

       SSBEVD computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band
       matrix A. 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 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.

        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 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 during 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) 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 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).

        WORK    (workspace/output) REAL array,
                dimension (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 must be at least 1.
                If JOBZ  = 'N' and N > 2, LWORK must be at least 2*N.
                If JOBZ  = 'V' and N > 2, LWORK must be at least
                ( 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 INFO = 0, IWORK(1) returns the optimal LIWORK.

        LIWORK  (input) INTEGER
                The dimension of the array LIWORK.
                If JOBZ  = 'N' or N <= 1, LIWORK must be at least 1.
                If JOBZ  = 'V' and N > 2, LIWORK must be at least 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, the algorithm failed to converge; i
                off-diagonal elements of an intermediate tridiagonal
                form did not converge to zero.

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