zsteqr(3F)

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

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

         CHARACTER      COMPZ

         INTEGER        INFO, LDZ, N

         DOUBLE         PRECISION D( * ), E( * ), WORK( * )

         COMPLEX*16     Z( LDZ, * )

PURPOSE
     ZSTEQR 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 complex Hermitian matrix can also be found
     if ZHETRD or ZHPTRD or ZHBTRD 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
             Hermitian matrix.  On entry, Z must contain the unitary 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (N-1)
             On entry, the (n-1) subdiagonal elements of the tridiagonal
             matrix.  On exit, E has been destroyed.

     Z       (input/output) COMPLEX*16 array, dimension (LDZ, N)
             On entry, if  COMPZ = 'V', then Z contains the unitary 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 Hermitian 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) DOUBLE PRECISION 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 unitarily similar to the
             original matrix.