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## cstedc()

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

Download CSTEDC + dependencies [TGZ] [ZIP] [TXT]

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

  [in]

  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.
      !>

  [in]

  N

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

  [in,out]

  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.
      !>

  [in,out]

  E

      !>          E is REAL array, dimension (N-1)
      !>          On entry, the subdiagonal elements of the tridiagonal matrix.
      !>          On exit, E has been destroyed.
      !>

  [in,out]

  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.
      !>

  [in]

  LDZ

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

  [out]

  WORK

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

  [in]

  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.
      !>

  [out]

  RWORK

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

  [in]

  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.
      !>

  [out]

  IWORK

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

  [in]

  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.
      !>

  [out]

  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