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

CSTEDC(l)					)					CSTEDC(l)

NAME
       CSTEDC  - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal
       matrix using the divide and conquer method

SYNOPSIS
       SUBROUTINE CSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO
			  )

	   CHARACTER	  COMPZ

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

	   INTEGER	  IWORK( * )

	   REAL 	  D( * ), E( * ), RWORK( * )

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

PURPOSE
       CSTEDC  computes  all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal
       matrix using the divide and conquer method. The eigenvectors of a  full	or  band  complex
       Hermitian  matrix  can also be found if CHETRD or CHPTRD or CHBTRD has been used to reduce
       this matrix to tridiagonal form.

       This code 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  con-
       ceivably  fail  on  hexadecimal	or  decimal machines without guard digits, but we know of
       none.  See SLAED3 for details.

ARGUMENTS
       COMPZ   (input) CHARACTER*1
	       = 'N':  Compute eigenvalues only.
	       = 'I':  Compute eigenvectors of tridiagonal matrix also.
	       = 'V':  Compute eigenvectors of original Hermitian matrix also.	On entry, Z  con-
	       tains the unitary matrix used to reduce the original matrix to tridiagonal form.

       N       (input) INTEGER
	       The dimension of the symmetric tridiagonal matrix.  N >= 0.

       D       (input/output) REAL array, dimension (N)
	       On  entry, the diagonal elements of the tridiagonal matrix.  On exit, if INFO = 0,
	       the eigenvalues in ascending order.

       E       (input/output) REAL array, dimension (N-1)
	       On entry, the subdiagonal elements of the tridiagonal matrix.  On exit, E has been
	       destroyed.

       Z       (input/output) COMPLEX array, dimension (LDZ,N)
	       On entry, if COMPZ = 'V', then Z contains the unitary matrix used in the reduction
	       to tridiagonal form.  On exit, if INFO = 0, then if COMPZ = 'V',  Z  contains  the
	       orthonormal  eigenvectors  of the original Hermitian matrix, and if COMPZ = 'I', Z
	       contains the orthonormal eigenvectors of the  symmetric	tridiagonal  matrix.   If
	       COMPZ = 'N', then Z is not referenced.

       LDZ     (input) INTEGER
	       The  leading  dimension	of  the array Z.  LDZ >= 1.  If eigenvectors are desired,
	       then 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 COMPZ = 'N' or 'I', or N <= 1, LWORK must  be
	       at least 1.  If COMPZ = 'V' and N > 1, LWORK must be at least N*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) 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 COMPZ = 'N' or N <= 1, LRWORK must be at
	       least 1.  If COMPZ = 'V' and N > 1, LRWORK must be at least 1 + 3*N + 2*N*lg  N	+
	       3*N**2  ,  where lg( N ) = smallest integer k such that 2**k >= N.  If COMPZ = 'I'
	       and N > 1, LRWORK must be at least 1 + 4*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 COMPZ = 'N' or N <= 1,  LIWORK  must  be  at
	       least  1.   If  COMPZ = 'V' or N > 1,  LIWORK must be at least 6 + 6*N + 5*N*lg N.
	       If COMPZ = 'I' or 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:  The algorithm failed to compute an eigenvalue while working on the submatrix
	       lying in rows and columns INFO/(N+1) through mod(INFO,N+1).

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

LAPACK version 3.0			   15 June 2000 				CSTEDC(l)


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