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

CHBEVD(l)					)					CHBEVD(l)

NAME
       CHBEVD  - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian
       band matrix A

SYNOPSIS
       SUBROUTINE CHBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,  WORK,  LWORK,  RWORK,  LRWORK,
			  IWORK, LIWORK, INFO )

	   CHARACTER	  JOBZ, UPLO

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

	   INTEGER	  IWORK( * )

	   REAL 	  RWORK( * ), W( * )

	   COMPLEX	  AB( LDAB, * ), WORK( * ), Z( LDZ, * )

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.

       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.

       KD      (input) INTEGER
	       The number of superdiagonals of the matrix A if UPLO = 'U', or the number of  sub-
	       diagonals if UPLO = 'L'.  KD >= 0.

       AB      (input/output) 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 col-
	       umn  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.

       LDAB    (input) INTEGER
	       The leading dimension of the array AB.  LDAB >= KD + 1.

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

       Z       (output) 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.

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

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

       LWORK   (input) 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	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 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 				CHBEVD(l)


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