CXML
        	    
LAPACK version 3.0
cheevd(3)

PURPOSE
  CHEEVD - compute all eigenvalues and, optionally, eigenvectors of a complex
  Hermitian matrix A

SYNTAX
  SUBROUTINE CHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, LRWORK,
		     IWORK, LIWORK, INFO )

      CHARACTER	     JOBZ, UPLO

      INTEGER	     INFO, LDA, LIWORK, LRWORK, LWORK, N

      INTEGER	     IWORK( * )

      REAL	     RWORK( * ), W( * )

      COMPLEX	     A( LDA, * ), WORK( * )

DESCRIPTION
  CHEEVD computes all eigenvalues and, optionally, eigenvectors of a complex
  Hermitian matrix A. If eigenvectors are desired, it uses a divide and
  conquer algorithm.

  The divide and conquer algorithm makes very mild assumptions about floating
  point arithmetic. It will work on machines with a guard digit in
  add/subtract, or on those binary machines without guard digits which
  subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
  conceivably fail on hexadecimal or decimal machines without guard digits,
  but we know of none.

ARGUMENTS
  JOBZ	  (input) CHARACTER*1
	  = 'N':  Compute eigenvalues only;
	  = 'V':  Compute eigenvalues and eigenvectors.

  UPLO	  (input) CHARACTER*1
	  = 'U':  Upper triangle of A is stored;
	  = 'L':  Lower triangle of A is stored.

  N	  (input) INTEGER
	  The order of the matrix A.  N >= 0.

  A	  (input/output) COMPLEX array, dimension (LDA, N)
	  On entry, the Hermitian matrix A.  If UPLO = 'U', the leading N-
	  by-N upper triangular part of A contains the upper triangular part
	  of the matrix A.  If UPLO = 'L', the leading N-by-N lower
	  triangular part of A contains the lower triangular part of the
	  matrix A.  On exit, if JOBZ = 'V', then if INFO = 0, A contains the
	  orthonormal eigenvectors of the matrix A.  If JOBZ = 'N', then on
	  exit the lower triangle (if UPLO='L') or the upper triangle (if
	  UPLO='U') of A, including the diagonal, is destroyed.

  LDA	  (input) INTEGER
	  The leading dimension of the array A.	 LDA >= max(1,N).

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

  WORK	  (workspace/output) COMPLEX array, dimension (LWORK)
	  On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

  LWORK	  (input) INTEGER
	  The length 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
	  + 1.	If JOBZ	 = 'V' and N > 1, LWORK must be at least 2*N + N**2.

	  If LWORK = -1, then a workspace query is assumed; the routine only
	  calculates the optimal size of the WORK array, returns this value
	  as the first entry of the WORK array, and no error message related
	  to LWORK is issued by XERBLA.

  RWORK	  (workspace/output) REAL array,
	  dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the
	  optimal LRWORK.

  LRWORK  (input) INTEGER
	  The dimension of the 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 size of the RWORK array, returns this value
	  as the first entry of the RWORK array, and no error message related
	  to LRWORK is issued by XERBLA.

  IWORK	  (workspace/output) INTEGER array, dimension (LIWORK)
	  On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

  LIWORK  (input) INTEGER
	  The dimension of the array IWORK.  If N <= 1,		       LIWORK
	  must be at least 1.  If JOBZ	= 'N' and 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 size of the IWORK array, returns this value
	  as the first entry of the IWORK array, and no error message related
	  to LIWORK is issued by XERBLA.

  INFO	  (output) 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.

FURTHER DETAILS
  Based on contributions by
     Jeff Rutter, Computer Science Division, University of California
     at Berkeley, USA