ZSTEQR (3lapack)

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.