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## dspevd()

subroutine dspevd | ( | character | jobz,
|  | character | uplo,
|  | integer | n,
|  | double precision, dimension( * ) | ap,
|  | double precision, dimension( * ) | w,
|  | double precision, dimension( ldz, * ) | z,
|  | integer | ldz,
|  | double precision, dimension( * ) | work,
|  | integer | lwork,
|  | integer, dimension( * ) | iwork,
|  | integer | liwork,
|  | integer | info )

DSPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

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

Purpose:

      !>
      !> DSPEVD computes all the eigenvalues and, optionally, eigenvectors
      !> of a real symmetric matrix A in packed storage. If eigenvectors are
      !> desired, it uses a divide and conquer algorithm.
      !>
      !>

Parameters

  [in]

  JOBZ

      !>          JOBZ is CHARACTER*1
      !>          = 'N':  Compute eigenvalues only;
      !>          = 'V':  Compute eigenvalues and eigenvectors.
      !>

  [in]

  UPLO

      !>          UPLO is CHARACTER*1
      !>          = 'U':  Upper triangle of A is stored;
      !>          = 'L':  Lower triangle of A is stored.
      !>

  [in]

  N

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

  [in,out]

  AP

      !>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
      !>          On entry, the upper or lower triangle of the symmetric matrix
      !>          A, packed columnwise in a linear array.  The j-th column of A
      !>          is stored in the array AP as follows:
      !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
      !>          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
      !>
      !>          On exit, AP is overwritten by values generated during the
      !>          reduction to tridiagonal form.  If UPLO = 'U', the diagonal
      !>          and first superdiagonal of the tridiagonal matrix T overwrite
      !>          the corresponding elements of A, and if UPLO = 'L', the
      !>          diagonal and first subdiagonal of T overwrite the
      !>          corresponding elements of A.
      !>

  [out]

  W

      !>          W is DOUBLE PRECISION array, dimension (N)
      !>          If INFO = 0, the eigenvalues in ascending order.
      !>

  [out]

  Z

      !>          Z is DOUBLE PRECISION array, dimension (LDZ, N)
      !>          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
      !>          eigenvectors of the matrix A, with the i-th column of Z
      !>          holding the eigenvector associated with W(i).
      !>          If JOBZ = 'N', then Z is not referenced.
      !>

  [in]

  LDZ

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

  [out]

  WORK

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

  [in]

  LWORK

      !>          LWORK is INTEGER
      !>          The dimension of the array WORK.
      !>          If N <= 1,               LWORK must be at least 1.
      !>          If JOBZ = 'N' and N > 1, LWORK must be at least 2*N.
      !>          If JOBZ = 'V' and N > 1, LWORK must be at least
      !>                                                 1 + 6*N + N**2.
      !>
      !>          If LWORK = -1, then a workspace query is assumed; the routine
      !>          only calculates the required sizes of the WORK and IWORK
      !>          arrays, returns these values as the first entries of the WORK
      !>          and IWORK arrays, and no error message related to LWORK 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 required LIWORK.
      !>

  [in]

  LIWORK

      !>          LIWORK is INTEGER
      !>          The dimension of the array IWORK.
      !>          If JOBZ  = 'N' or N <= 1, LIWORK must be at least 1.
      !>          If JOBZ  = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
      !>
      !>          If LIWORK = -1, then a workspace query is assumed; the
      !>          routine only calculates the required sizes of the WORK and
      !>          IWORK arrays, returns these values as the first entries of
      !>          the WORK and IWORK arrays, and no error message related to
      !>          LWORK 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:  if INFO = i, the algorithm failed to converge; i
      !>                off-diagonal elements of an intermediate tridiagonal
      !>                form did not converge to zero.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.