chbev(3S)

NAME
     CHBEV - compute all the eigenvalues and, optionally, eigenvectors of a
     complex Hermitian band matrix A

SYNOPSIS
     SUBROUTINE CHBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, RWORK,
                       INFO )

         CHARACTER     JOBZ, UPLO

         INTEGER       INFO, KD, LDAB, LDZ, N

         REAL          RWORK( * ), W( * )

         COMPLEX       AB( LDAB, * ), WORK( * ), Z( LDZ, * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     CHBEV computes all the eigenvalues and, optionally, eigenvectors of a
     complex Hermitian band matrix A.

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) COMPLEX 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.  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) COMPLEX 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) COMPLEX array, dimension (N)

     RWORK   (workspace) REAL array, dimension (max(1,3*N-2))

     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.

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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