spteqr.f(3)

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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