dstevd(3S)

NAME
     DSTEVD - compute all eigenvalues and, optionally, eigenvectors of a real
     symmetric tridiagonal matrix

SYNOPSIS
     SUBROUTINE DSTEVD( JOBZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK,
                        INFO )

         CHARACTER      JOBZ

         INTEGER        INFO, LDZ, LIWORK, LWORK, N

         INTEGER        IWORK( * )

         DOUBLE         PRECISION D( * ), E( * ), 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
     DSTEVD computes all eigenvalues and, optionally, eigenvectors of a real
     symmetric tridiagonal matrix. 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.

     N       (input) INTEGER
             The order of the matrix.  N >= 0.

     D       (input/output) DOUBLE PRECISION array, dimension (N)
             On entry, the n diagonal elements of the tridiagonal matrix A.
             On exit, if INFO = 0, the eigenvalues in ascending order.

     E       (input/output) DOUBLE PRECISION array, dimension (N)
             On entry, the (n-1) subdiagonal elements of the tridiagonal
             matrix A, stored in elements 1 to N-1 of E; E(N) need not be set,
             but is used by the routine.  On exit, the contents of E are
             destroyed.

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

     LWORK   (input) INTEGER
             The dimension of the array WORK.  If JOBZ  = 'N' or N <= 1 then
             LWORK must be at least 1.  If JOBZ  = 'V' and N > 1 then LWORK
             must be at least ( 1 + 4*N + N**2 ).

             If LWORK = -1, then a workspace query is assumed; the routine
             only calculates the optimal size of the WORK array, returns this
             value as the first entry of the WORK array, and no error message
             related to LWORK is issued by XERBLA.

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

     LIWORK  (input) INTEGER
             The dimension of the array IWORK.  If JOBZ  = 'N' or N <= 1 then
             LIWORK must be at least 1.  If JOBZ  = 'V' and N > 1 then LIWORK
             must be at least 3+5*N.

             If LIWORK = -1, then a workspace query is assumed; the routine
             only calculates the optimal size of the IWORK array, returns this
             value as the first entry of the IWORK array, and no error message
             related to 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 E did not converge to zero.
SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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