Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  - computes all eigenvalues and, optionally, eigenvectors of a symmetric positive
       definite tridiagonal matrix by first factoring the matrix using DPTTRF, and  then  calling
       DBDSQR to compute the singular values of the bidiagonal factor

SYNOPSIS

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

           CHARACTER      COMPZ

           INTEGER        INFO, LDZ, N

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

PURPOSE

       DPTEQR  computes  all  eigenvalues  and,  optionally, eigenvectors of a symmetric positive
       definite tridiagonal matrix by first factoring the matrix using DPTTRF, and  then  calling
       DBDSQR 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 symmetric positive definite matrix
        can also be found if DSYTRD, DSPTRD, or DSBTRD 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) CHARACTER*1
                = 'N':  Compute eigenvalues only.
                = 'V':  Compute eigenvectors of original symmetric
                matrix also.  Array Z contains the orthogonal
                matrix used to reduce the original matrix to
                tridiagonal form.
                = 'I':  Compute eigenvectors of tridiagonal matrix also.

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

        D       (input/output) DOUBLE PRECISION 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) 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) DOUBLE PRECISION array, dimension (LDZ, N)
                On entry, if COMPZ = 'V', the orthogonal matrix used in the
                reduction to tridiagonal form.
                On exit, if COMPZ = 'V', the orthonormal eigenvectors of the
                original symmetric 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) INTEGER
                The leading dimension of the array Z.  LDZ >= 1, and if
                COMPZ = 'V' or 'I', LDZ >= max(1,N).

        WORK    (workspace) DOUBLE PRECISION array, dimension (4*N)

        INFO    (output) 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 (version 3.2)               April 2011                            DPTEQR(3lapack)