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

NAME

       LAPACK-3  -  computes  selected  eigenvalues  and,  optionally,  eigenvectors of a complex
       Hermitian band matrix A

SYNOPSIS

       SUBROUTINE ZHBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL, VU, IL, IU, ABSTOL,  M,
                          W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO )

           CHARACTER      JOBZ, RANGE, UPLO

           INTEGER        IL, INFO, IU, KD, LDAB, LDQ, LDZ, M, N

           DOUBLE         PRECISION ABSTOL, VL, VU

           INTEGER        IFAIL( * ), IWORK( * )

           DOUBLE         PRECISION RWORK( * ), W( * )

           COMPLEX*16     AB( LDAB, * ), Q( LDQ, * ), WORK( * ), Z( LDZ, * )

PURPOSE

       ZHBEVX  computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian
       band matrix A.  Eigenvalues and eigenvectors
        can be selected by specifying either a range of values or a range of
        indices for the desired eigenvalues.

ARGUMENTS

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

        RANGE   (input) CHARACTER*1
                = 'A': all eigenvalues will be found;
                = 'V': all eigenvalues in the half-open interval (VL,VU]
                will be found;
                = 'I': the IL-th through IU-th eigenvalues will be found.

        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) COMPLEX*16 array, dimension (LDAB, N)
                On entry, the upper or lower triangle of the Hermitian 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.

        LDAB    (input) INTEGER
                The leading dimension of the array AB.  LDAB >= KD + 1.

        Q       (output) COMPLEX*16 array, dimension (LDQ, N)
                If JOBZ = 'V', the N-by-N unitary matrix used in the
                reduction to tridiagonal form.
                If JOBZ = 'N', the array Q is not referenced.

        LDQ     (input) INTEGER
                The leading dimension of the array Q.  If JOBZ = 'V', then
                LDQ >= max(1,N).

        VL      (input) DOUBLE PRECISION
                VU      (input) DOUBLE PRECISION
                If RANGE='V', the lower and upper bounds of the interval to
                be searched for eigenvalues. VL < VU.
                Not referenced if RANGE = 'A' or 'I'.

        IL      (input) INTEGER
                IU      (input) INTEGER
                If RANGE='I', the indices (in ascending order) of the
                smallest and largest eigenvalues to be returned.
                1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
                Not referenced if RANGE = 'A' or 'V'.

        ABSTOL  (input) DOUBLE PRECISION
                The absolute error tolerance for the eigenvalues.
                An approximate eigenvalue is accepted as converged
                when it is determined to lie in an interval [a,b]
                of width less than or equal to
                ABSTOL + EPS *   max( |a|,|b| ) ,
                where EPS is the machine precision.  If ABSTOL is less than
                or equal to zero, then  EPS*|T|  will be used in its place,
                where |T| is the 1-norm of the tridiagonal matrix obtained
                by reducing AB to tridiagonal form.
                Eigenvalues will be computed most accurately when ABSTOL is
                set to twice the underflow threshold 2*DLAMCH('S'), not zero.
                If this routine returns with INFO>0, indicating that some
                eigenvectors did not converge, try setting ABSTOL to
                2*DLAMCH('S').
                See "Computing Small Singular Values of Bidiagonal Matrices
                with Guaranteed High Relative Accuracy," by Demmel and
                Kahan, LAPACK Working Note #3.

        M       (output) INTEGER
                The total number of eigenvalues found.  0 <= M <= N.
                If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.

        W       (output) DOUBLE PRECISION array, dimension (N)
                The first M elements contain the selected eigenvalues in
                ascending order.

        Z       (output) COMPLEX*16 array, dimension (LDZ, max(1,M))
                If JOBZ = 'V', then if INFO = 0, the first M columns of Z
                contain the orthonormal eigenvectors of the matrix A
                corresponding to the selected eigenvalues, with the i-th
                column of Z holding the eigenvector associated with W(i).
                If an eigenvector fails to converge, then that column of Z
                contains the latest approximation to the eigenvector, and the
                index of the eigenvector is returned in IFAIL.
                If JOBZ = 'N', then Z is not referenced.
                Note: the user must ensure that at least max(1,M) columns are
                supplied in the array Z; if RANGE = 'V', the exact value of M
                is not known in advance and an upper bound must be used.

        LDZ     (input) INTEGER
                The leading dimension of the array Z.  LDZ >= 1, and if
                JOBZ = 'V', LDZ >= max(1,N).

        WORK    (workspace) COMPLEX*16 array, dimension (N)

        RWORK   (workspace) DOUBLE PRECISION array, dimension (7*N)

        IWORK   (workspace) INTEGER array, dimension (5*N)

        IFAIL   (output) INTEGER array, dimension (N)
                If JOBZ = 'V', then if INFO = 0, the first M elements of
                IFAIL are zero.  If INFO > 0, then IFAIL contains the
                indices of the eigenvectors that failed to converge.
                If JOBZ = 'N', then IFAIL is not referenced.

        INFO    (output) INTEGER
                = 0:  successful exit
                < 0:  if INFO = -i, the i-th argument had an illegal value
                > 0:  if INFO = i, then i eigenvectors failed to converge.
                Their indices are stored in array IFAIL.

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