SRC/cpteqr.f(3)

NAME
SRC/cpteqr.f

SYNOPSIS

  Functions/Subroutines
subroutine cpteqr (compz, n, d, e, z, ldz, work, info)
CPTEQR

Function/Subroutine Documentation

  subroutine cpteqr (character compz, integer n, real, dimension( * ) d, real, dimension( * ) e, complex, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer info)

CPTEQR

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.)
    !>

Parameters
    COMPZ

    !>          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

    !>          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 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

    !>          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 leading principal
    !>                      minor of order i was not positive.
    !>                > 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.

Definition at line 144 of file cpteqr.f.

Author

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