CPTEQR(3)      LAPACK routine of NEC Numeric Library Collection      CPTEQR(3)



NAME
       CPTEQR

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



PURPOSE
            CPTEQR computes all eigenvalues and, optionally, eigenvectors of a
            symmetric positive definite tridiagonal matrix by first factoring the
            matrix using SPTTRF and then calling CBDSQR to compute the singular
            values of the bidiagonal factor.

            This routine computes the eigenvalues of the positive definite
            tridiagonal matrix to high relative accuracy.  This means that if the
            eigenvalues range over many orders of magnitude in size, then the
            small eigenvalues and corresponding eigenvectors will be computed
            more accurately than, for example, with the standard QR method.

            The eigenvectors of a full or band positive definite Hermitian matrix
            can also be found if CHETRD, CHPTRD, or CHBTRD has been used to
            reduce this matrix to tridiagonal form.  (The reduction to
            tridiagonal form, however, may preclude the possibility of obtaining
            high relative accuracy in the small eigenvalues of the original
            matrix, if these eigenvalues range over many orders of magnitude.)




ARGUMENTS
           COMPZ     (input)
                     COMPZ is CHARACTER*1
                     = 'N':  Compute eigenvalues only.
                     = 'V':  Compute eigenvectors of original Hermitian
                             matrix also.  Array Z contains the unitary matrix
                             used to reduce the original matrix to tridiagonal
                             form.
                     = 'I':  Compute eigenvectors of tridiagonal matrix also.

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

           D         (input/output)
                     D is REAL array, dimension (N)
                     On entry, the n diagonal elements of the tridiagonal matrix.
                     On normal exit, D contains the eigenvalues, in descending
                     order.

           E         (input/output)
                     E is 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)
                     Z is COMPLEX array, dimension (LDZ, N)
                     On entry, if COMPZ = 'V', the unitary matrix used in the
                     reduction to tridiagonal form.
                     On exit, if COMPZ = 'V', the orthonormal eigenvectors of the
                     original Hermitian matrix;
                     if COMPZ = 'I', the orthonormal eigenvectors of the
                     tridiagonal matrix.
                     If INFO > 0 on exit, Z contains the eigenvectors associated
                     with only the stored eigenvalues.
                     If  COMPZ = 'N', then Z is not referenced.

           LDZ       (input)
                     LDZ is INTEGER
                     The leading dimension of the array Z.  LDZ >= 1, and if
                     COMPZ = 'V' or 'I', LDZ >= max(1,N).

           WORK      (output)
                     WORK is REAL array, dimension (4*N)

           INFO      (output)
                     INFO is INTEGER
                     = 0:  successful exit.
                     < 0:  if INFO = -i, the i-th argument had an illegal value.
                     > 0:  if INFO = i, and i is:
                           <= N  the Cholesky factorization of the matrix could
                                 not be performed because the i-th principal minor
                                 was not positive definite.
                           > N   the SVD algorithm failed to converge;
                                 if INFO = N+i, i off-diagonal elements of the
                                 bidiagonal factor did not converge to zero.



LAPACK routine                  31 October 2017                      CPTEQR(3)