SRC/cstedc.f(3)

NAME
SRC/cstedc.f

SYNOPSIS

  Functions/Subroutines
subroutine cstedc (compz, n, d, e, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
CSTEDC

Function/Subroutine Documentation

  subroutine cstedc (character compz, integer n, real, dimension( * ) d, real, dimension( * ) e, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info)

CSTEDC

Purpose:

    !>
    !> CSTEDC computes all eigenvalues and, optionally, eigenvectors of a
    !> symmetric tridiagonal matrix using the divide and conquer method.
    !> The eigenvectors of a full or band complex Hermitian matrix can also
    !> be found if CHETRD or CHPTRD or CHBTRD has been used to reduce this
    !> matrix to tridiagonal form.
    !>
    !>

Parameters
    COMPZ

    !>          COMPZ is CHARACTER*1
    !>          = 'N':  Compute eigenvalues only.
    !>          = 'I':  Compute eigenvectors of tridiagonal matrix also.
    !>          = 'V':  Compute eigenvectors of original Hermitian matrix
    !>                  also.  On entry, Z contains the unitary matrix used
    !>                  to reduce the original matrix to tridiagonal form.
    !>

    N

    !>          N is INTEGER
    !>          The dimension of the symmetric tridiagonal matrix.  N >= 0.
    !>

    D

    !>          D is REAL array, dimension (N)
    !>          On entry, the diagonal elements of the tridiagonal matrix.
    !>          On exit, if INFO = 0, the eigenvalues in ascending order.
    !>

    E

    !>          E is REAL array, dimension (N-1)
    !>          On entry, the 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', then Z contains the unitary
    !>          matrix used in the reduction to tridiagonal form.
    !>          On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
    !>          orthonormal eigenvectors of the original Hermitian matrix,
    !>          and if COMPZ = 'I', Z contains the orthonormal eigenvectors
    !>          of the symmetric tridiagonal matrix.
    !>          If  COMPZ = 'N', then Z is not referenced.
    !>

    LDZ

    !>          LDZ is INTEGER
    !>          The leading dimension of the array Z.  LDZ >= 1.
    !>          If eigenvectors are desired, then LDZ >= max(1,N).
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK.
    !>          If COMPZ = 'N' or 'I', or N <= 1, LWORK must be at least 1.
    !>          If COMPZ = 'V' and N > 1, LWORK must be at least N*N.
    !>          Note that for COMPZ = 'V', then if N is less than or
    !>          equal to the minimum divide size, usually 25, then LWORK need
    !>          only be 1.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the optimal sizes of the WORK, RWORK and
    !>          IWORK arrays, returns these values as the first entries of
    !>          the WORK, RWORK and IWORK arrays, and no error message
    !>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
    !>

    RWORK

    !>          RWORK is REAL array, dimension (MAX(1,LRWORK))
    !>          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
    !>

    LRWORK

    !>          LRWORK is INTEGER
    !>          The dimension of the array RWORK.
    !>          If COMPZ = 'N' or N <= 1, LRWORK must be at least 1.
    !>          If COMPZ = 'V' and N > 1, LRWORK must be at least
    !>                         1 + 3*N + 2*N*lg N + 4*N**2 ,
    !>                         where lg( N ) = smallest integer k such
    !>                         that 2**k >= N.
    !>          If COMPZ = 'I' and N > 1, LRWORK must be at least
    !>                         1 + 4*N + 2*N**2 .
    !>          Note that for COMPZ = 'I' or 'V', then if N is less than or
    !>          equal to the minimum divide size, usually 25, then LRWORK
    !>          need only be max(1,2*(N-1)).
    !>
    !>          If LRWORK = -1, then a workspace query is assumed; the
    !>          routine only calculates the optimal sizes of the WORK, RWORK
    !>          and IWORK arrays, returns these values as the first entries
    !>          of the WORK, RWORK and IWORK arrays, and no error message
    !>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
    !>          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
    !>

    LIWORK

    !>          LIWORK is INTEGER
    !>          The dimension of the array IWORK.
    !>          If COMPZ = 'N' or N <= 1, LIWORK must be at least 1.
    !>          If COMPZ = 'V' or N > 1,  LIWORK must be at least
    !>                                    6 + 6*N + 5*N*lg N.
    !>          If COMPZ = 'I' or N > 1,  LIWORK must be at least
    !>                                    3 + 5*N .
    !>          Note that for COMPZ = 'I' or 'V', then if N is less than or
    !>          equal to the minimum divide size, usually 25, then LIWORK
    !>          need only be 1.
    !>
    !>          If LIWORK = -1, then a workspace query is assumed; the
    !>          routine only calculates the optimal sizes of the WORK, RWORK
    !>          and IWORK arrays, returns these values as the first entries
    !>          of the WORK, RWORK and IWORK arrays, and no error message
    !>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit.
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>          > 0:  The algorithm failed to compute an eigenvalue while
    !>                working on the submatrix lying in rows and columns
    !>                INFO/(N+1) through mod(INFO,N+1).
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Definition at line 204 of file cstedc.f.

Author

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