Loading...
Searching...
No Matches

## chbevd()

subroutine chbevd | ( | character | jobz,
|  | character | uplo,
|  | integer | n,
|  | integer | kd,
|  | complex, dimension( ldab, * ) | ab,
|  | integer | ldab,
|  | real, dimension( * ) | w,
|  | complex, dimension( ldz, * ) | z,
|  | integer | ldz,
|  | complex, dimension( * ) | work,
|  | integer | lwork,
|  | real, dimension( * ) | rwork,
|  | integer | lrwork,
|  | integer, dimension( * ) | iwork,
|  | integer | liwork,
|  | integer | info )

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

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

Purpose:

      !>
      !> CHBEVD computes all the eigenvalues and, optionally, eigenvectors of
      !> a complex Hermitian band matrix A.  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]

  KD

      !>          KD is INTEGER
      !>          The number of superdiagonals of the matrix A if UPLO = 'U',
      !>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
      !>

  [in,out]

  AB

      !>          AB is COMPLEX array, dimension (LDAB, N)
      !>          On entry, the upper or lower triangle of the Hermitian band
      !>          matrix A, stored in the first KD+1 rows of the array.  The
      !>          j-th column of A is stored in the j-th column of the array AB
      !>          as follows:
      !>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
      !>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
      !>
      !>          On exit, AB is overwritten by values generated during the
      !>          reduction to tridiagonal form.  If UPLO = 'U', the first
      !>          superdiagonal and the diagonal of the tridiagonal matrix T
      !>          are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
      !>          the diagonal and first subdiagonal of T are returned in the
      !>          first two rows of AB.
      !>

  [in]

  LDAB

      !>          LDAB is INTEGER
      !>          The leading dimension of the array AB.  LDAB >= KD + 1.
      !>

  [out]

  W

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

  [out]

  Z

      !>          Z is COMPLEX 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 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 N <= 1,               LWORK must be at least 1.
      !>          If JOBZ = 'N' and N > 1, LWORK must be at least N.
      !>          If JOBZ = 'V' and N > 1, LWORK must be at least 2*N**2.
      !>
      !>          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 (LRWORK)
      !>          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
      !>

  [in]

  LRWORK

      !>          LRWORK is INTEGER
      !>          The dimension of array RWORK.
      !>          If N <= 1,               LRWORK must be at least 1.
      !>          If JOBZ = 'N' and N > 1, LRWORK must be at least N.
      !>          If JOBZ = 'V' and N > 1, LRWORK must be at least
      !>                        1 + 5*N + 2*N**2.
      !>
      !>          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 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 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:  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.