ssteqr(3S)

NAME
     SSTEQR - compute all eigenvalues and, optionally, eigenvectors of a
     symmetric tridiagonal matrix using the implicit QL or QR method

SYNOPSIS
     SUBROUTINE SSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )

         CHARACTER      COMPZ

         INTEGER        INFO, LDZ, N

         REAL           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
     SSTEQR computes all eigenvalues and, optionally, eigenvectors of a
     symmetric tridiagonal matrix using the implicit QL or QR method. The
     eigenvectors of a full or band symmetric matrix can also be found if
     SSYTRD or SSPTRD or SSBTRD has been used to reduce this matrix to
     tridiagonal form.


ARGUMENTS
     COMPZ   (input) CHARACTER*1
             = 'N':  Compute eigenvalues only.
             = 'V':  Compute eigenvalues and eigenvectors of the original
             symmetric matrix.  On entry, Z must contain the orthogonal matrix
             used to reduce the original matrix to tridiagonal form.  = 'I':
             Compute eigenvalues and eigenvectors of the tridiagonal matrix.
             Z is initialized to the identity matrix.

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

     D       (input/output) REAL array, dimension (N)
             On entry, the diagonal elements of the tridiagonal matrix.  On
             exit, if INFO = 0, the eigenvalues in ascending order.
     E       (input/output) REAL array, dimension (N-1)
             On entry, the (n-1) subdiagonal elements of the tridiagonal
             matrix.  On exit, E has been destroyed.

     Z       (input/output) REAL array, dimension (LDZ, N)
             On entry, if  COMPZ = 'V', then Z contains the orthogonal matrix
             used in the reduction to tridiagonal form.  On exit, if INFO = 0,
             then if  COMPZ = 'V', Z contains the orthonormal eigenvectors of
             the original symmetric matrix, and if COMPZ = 'I', Z contains the
             orthonormal eigenvectors of the symmetric tridiagonal matrix.  If
             COMPZ = 'N', then Z is not referenced.

     LDZ     (input) INTEGER
             The leading dimension of the array Z.  LDZ >= 1, and if
             eigenvectors are desired, then  LDZ >= max(1,N).

     WORK    (workspace) REAL array, dimension (max(1,2*N-2))
             If COMPZ = 'N', then WORK is not referenced.

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value
             > 0:  the algorithm has failed to find all the eigenvalues in a
             total of 30*N iterations; if INFO = i, then i elements of E have
             not converged to zero; on exit, D and E contain the elements of a
             symmetric tridiagonal matrix which is orthogonally similar to the
             original matrix.

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

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