cpteqr man page on YellowDog

Man page or keyword search:  
man Server   18644 pages
apropos Keyword Search (all sections)
Output format
YellowDog logo
[printable version]

CPTEQR(l)			       )			     CPTEQR(l)

NAME
       CPTEQR  -  compute  all	eigenvalues and, optionally, eigenvectors of a
       symmetric positive definite tridiagonal matrix by first	factoring  the
       matrix  using  SPTTRF  and  then calling CBDSQR to compute the singular
       values of the bidiagonal factor

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

	   CHARACTER	  COMPZ

	   INTEGER	  INFO, LDZ, N

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

	   COMPLEX	  Z( LDZ, * )

PURPOSE
       CPTEQR computes all eigenvalues and, optionally, eigenvectors of a sym‐
       metric  positive	 definite  tridiagonal	matrix	by first factoring the
       matrix using SPTTRF and then calling CBDSQR  to	compute	 the  singular
       values of the bidiagonal factor.	 This routine computes the eigenvalues
       of the positive definite tridiagonal matrix to high relative  accuracy.
       This  means that if the eigenvalues range over many orders of magnitude
       in size, then the small eigenvalues and corresponding eigenvectors will
       be  computed  more  accurately  than, for example, with the standard QR
       method.

       The eigenvectors of a full or band positive definite  Hermitian	matrix
       can  also be found if CHETRD, CHPTRD, or CHBTRD has been used to reduce
       this matrix to tridiagonal form.	 (The reduction to  tridiagonal	 form,
       however,	 may preclude the possibility of obtaining high relative accu‐
       racy in the small eigenvalues of the original matrix, if	 these	eigen‐
       values range over many orders of magnitude.)

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

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

       D       (input/output) REAL array, dimension (N)
	       On entry, the n diagonal elements of  the  tridiagonal  matrix.
	       On  normal  exit,  D  contains  the  eigenvalues, in descending
	       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', the unitary matrix used in the reduc‐
	       tion to tridiagonal  form.   On	exit,  if  COMPZ  =  'V',  the
	       orthonormal  eigenvectors  of the original Hermitian matrix; if
	       COMPZ = 'I', the orthonormal eigenvectors  of  the  tridiagonal
	       matrix.	If INFO > 0 on exit, Z contains the eigenvectors asso‐
	       ciated with only the stored eigenvalues.	 If  COMPZ = 'N', then
	       Z is not referenced.

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

       WORK    (workspace) REAL array, dimension (4*N)

       INFO    (output) INTEGER
	       = 0:  successful exit.
	       < 0:  if INFO = -i, the i-th argument had an illegal value.
	       > 0:  if INFO = i, and i is: <= N  the  Cholesky	 factorization
	       of the matrix could not be performed because the i-th principal
	       minor was not positive  definite.   >  N	   the	SVD  algorithm
	       failed  to  converge; if INFO = N+i, i off-diagonal elements of
	       the bidiagonal factor did not converge to zero.

LAPACK version 3.0		 15 June 2000			     CPTEQR(l)
[top]

List of man pages available for YellowDog

Copyright (c) for man pages and the logo by the respective OS vendor.

For those who want to learn more, the polarhome community provides shell access and support.

[legal] [privacy] [GNU] [policy] [cookies] [netiquette] [sponsors] [FAQ]
Tweet
Polarhome, production since 1999.
Member of Polarhome portal.
Based on Fawad Halim's script.
....................................................................
Vote for polarhome
Free Shell Accounts :: the biggest list on the net