NAME

       spteqr.f -

SYNOPSIS

   Functions/Subroutines
       subroutine spteqr (COMPZ, N, D, E, Z, LDZ, WORK, INFO)
           SPTEQR

Function/Subroutine Documentation

   subroutine spteqr (characterCOMPZ, integerN, real, dimension( * )D, real, dimension( * )E,
       real, dimension( ldz, * )Z, integerLDZ, real, dimension( * )WORK, integerINFO)
       SPTEQR

       Purpose:

            SPTEQR computes all eigenvalues and, optionally, eigenvectors of a
            symmetric positive definite tridiagonal matrix by first factoring the
            matrix using SPTTRF, and then calling SBDSQR 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 SSYTRD, SSPTRD, or SSBTRD 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.)

       Parameters:
           COMPZ

                     COMPZ is 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

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

           D

                     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

                     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

                     Z is REAL 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

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

           WORK

                     WORK is REAL array, dimension (4*N)

           INFO

                     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.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       Definition at line 146 of file spteqr.f.

Author

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