csteqr(l) [redhat man page]

CSTEQR(l)								 )								 CSTEQR(l)

NAME

       CSTEQR - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method

SYNOPSIS

       SUBROUTINE CSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )

	   CHARACTER	  COMPZ

	   INTEGER	  INFO, LDZ, N

	   REAL 	  D( * ), E( * ), WORK( * )

	   COMPLEX	  Z( LDZ, * )

PURPOSE

       CSTEQR  computes  all  eigenvalues  and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR 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.

ARGUMENTS

       COMPZ   (input) CHARACTER*1
	       = 'N':  Compute eigenvalues only.
	       = 'V':  Compute eigenvalues and eigenvectors of the original Hermitian matrix.  On entry, Z must contain the unitary matrix used to
	       reduce the original matrix to tridiagonal form.	= 'I':	Compute eigenvalues and eigenvectors of the tridiagonal matrix.  Z is ini-
	       tialized to the identity matrix.

       N       (input) INTEGER
	       The order of the 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 (n-1) 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, and if eigenvectors are desired, then  LDZ >= max(1,N).

       WORK    (workspace) REAL array, dimension (max(1,2*N-2))
	       If COMPZ = 'N', then WORK is not referenced.

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value
	       >  0:   the  algorithm has failed to find all the eigenvalues in a total of 30*N iterations; if INFO = i, then i elements of E have
	       not converged to zero; on exit, D and E contain the elements of a symmetric tridiagonal matrix which is unitarily  similar  to  the
	       original matrix.

LAPACK version 3.0						   15 June 2000 							 CSTEQR(l)

ssteqr.f(3)							      LAPACK							       ssteqr.f(3)

NAME

       ssteqr.f -

SYNOPSIS

   Functions/Subroutines
       subroutine ssteqr (COMPZ, N, D, E, Z, LDZ, WORK, INFO)
	   SSTEQR

Function/Subroutine Documentation
   subroutine ssteqr (characterCOMPZ, integerN, real, dimension( * )D, real, dimension( * )E, real, dimension( ldz, * )Z, integerLDZ, real,
       dimension( * )WORK, integerINFO)
       SSTEQR

       Purpose:

	    SSTEQR computes all eigenvalues and, optionally, eigenvectors of a
	    symmetric tridiagonal matrix using the implicit QL or QR method.
	    The eigenvectors of a full or band symmetric matrix can also be found
	    if SSYTRD or SSPTRD or SSBTRD has been used to reduce this matrix to
	    tridiagonal form.

       Parameters:
	   COMPZ

		     COMPZ is CHARACTER*1
		     = 'N':  Compute eigenvalues only.
		     = 'V':  Compute eigenvalues and eigenvectors of the original
			     symmetric matrix.	On entry, Z must contain the
			     orthogonal matrix used to reduce the original matrix
			     to tridiagonal form.
		     = 'I':  Compute eigenvalues and eigenvectors of the
			     tridiagonal matrix.  Z is initialized to the identity
			     matrix.

	   N

		     N is INTEGER
		     The order of the matrix.  N >= 0.

	   D

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

	   E

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

	   Z

		     Z is REAL array, dimension (LDZ, N)
		     On entry, if  COMPZ = 'V', then Z contains the orthogonal
		     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 symmetric matrix,
		     and if COMPZ = 'I', Z contains the orthonormal eigenvectors
		     of the symmetric tridiagonal matrix.
		     If COMPZ = 'N', then Z is not referenced.

	   LDZ

		     LDZ is INTEGER
		     The leading dimension of the array Z.  LDZ >= 1, and if
		     eigenvectors are desired, then  LDZ >= max(1,N).

	   WORK

		     WORK is REAL array, dimension (max(1,2*N-2))
		     If COMPZ = 'N', then WORK is not referenced.

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit
		     < 0:  if INFO = -i, the i-th argument had an illegal value
		     > 0:  the algorithm has failed to find all the eigenvalues in
			   a total of 30*N iterations; if INFO = i, then i
			   elements of E have not converged to zero; on exit, D
			   and E contain the elements of a symmetric tridiagonal
			   matrix which is orthogonally similar to the original
			   matrix.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 132 of file ssteqr.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       ssteqr.f(3)