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RedHat 9 (Linux i386) - man page for zhpevd (redhat section l)

ZHPEVD(l)					)					ZHPEVD(l)

NAME
       ZHPEVD  - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian
       matrix A in packed storage

SYNOPSIS
       SUBROUTINE ZHPEVD( JOBZ, UPLO, N, AP, W,  Z,  LDZ,  WORK,  LWORK,  RWORK,  LRWORK,  IWORK,
			  LIWORK, INFO )

	   CHARACTER	  JOBZ, UPLO

	   INTEGER	  INFO, LDZ, LIWORK, LRWORK, LWORK, N

	   INTEGER	  IWORK( * )

	   DOUBLE	  PRECISION RWORK( * ), W( * )

	   COMPLEX*16	  AP( * ), WORK( * ), Z( LDZ, * )

PURPOSE
       ZHPEVD  computes  all the eigenvalues and, optionally, eigenvectors of a complex Hermitian
       matrix A in packed storage. If eigenvectors are desired, it  uses  a  divide  and  conquer
       algorithm.

       The  divide  and conquer algorithm makes very mild assumptions about floating point arith-
       metic. 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.

       AP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
	       On entry, the upper or lower triangle of the Hermitian 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  diago-
	       nal and first subdiagonal of T overwrite the corresponding elements of A.

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

       Z       (output) COMPLEX*16 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.

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

       WORK    (workspace/output) COMPLEX*16 array, dimension (LWORK)
	       On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
	       The dimension of 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.

	       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) DOUBLE PRECISION array,
	       dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

       LRWORK  (input) 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	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 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 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.

LAPACK version 3.0			   15 June 2000 				ZHPEVD(l)


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