Previous: zstein Up: ../lapack-z.html Next: zsycon

zsteqr

 NAME
      ZSTEQR - compute all eigenvalues and, optionally, eigenvec-
      tors 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, eigenvec-
      tors 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 ZSYTRD or ZSPTRD or
      ZSBTRD 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 eigen-
              values 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 tri-
              diagonal 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 uni-
              tary matrix used in the reduction to tridiagonal
              form.  On exit, if  COMPZ = 'V', Z contains the

              orthonormal eigenvectors of the original Hermitian
              matrix, and if COMPZ = 'I', Z contains the orthonor-
              mal eigenvectors of the symmetric tridiagonal
              matrix.  If an error exit is made, Z contains the
              eigenvectors associated with the stored eigenvalues.
              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).

 (max(1,2*N-2))
      WORK    (workspace) DOUBLE PRECISION array, dimension
              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.