SRC/dsbevd.f(3)            Library Functions Manual            SRC/dsbevd.f(3)

NAME
       SRC/dsbevd.f

SYNOPSIS
   Functions/Subroutines
       subroutine dsbevd (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork,
           iwork, liwork, info)
            DSBEVD computes the eigenvalues and, optionally, the left and/or
           right eigenvectors for OTHER matrices

Function/Subroutine Documentation
   subroutine dsbevd (character jobz, character uplo, integer n, integer kd,
       double precision, dimension( ldab, * ) ab, integer ldab, double
       precision, dimension( * ) w, double precision, dimension( ldz, * ) z,
       integer ldz, double precision, dimension( * ) work, integer lwork,
       integer, dimension( * ) iwork, integer liwork, integer info)
        DSBEVD computes the eigenvalues and, optionally, the left and/or right
       eigenvectors for OTHER matrices

       Purpose:


            DSBEVD 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.

       Parameters
           JOBZ

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

           UPLO

                     UPLO is CHARACTER*1
                     = 'U':  Upper triangle of A is stored;
                     = 'L':  Lower triangle of A is stored.

           N

                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           KD

                     KD is INTEGER
                     The number of superdiagonals of the matrix A if UPLO = 'U',
                     or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

           AB

                     AB is DOUBLE PRECISION 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

                     LDAB is INTEGER
                     The leading dimension of the array AB.  LDAB >= KD + 1.

           W

                     W is DOUBLE PRECISION array, dimension (N)
                     If INFO = 0, the eigenvalues in ascending order.

           Z

                     Z is DOUBLE PRECISION 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

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

           WORK

                     WORK is DOUBLE PRECISION array,
                                                    dimension (LWORK)
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     LWORK is 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

                     IWORK is INTEGER array, dimension (MAX(1,LIWORK))
                     On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

           LIWORK

                     LIWORK is INTEGER
                     The dimension of the array IWORK.
                     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

                     INFO is 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.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 185 of file dsbevd.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/dsbevd.f(3)