DPTEQR man page on IRIX

Man page or keyword search:  
man Server   31559 pages
apropos Keyword Search (all sections)
Output format
IRIX logo
[printable version]



DPTEQR(3F)							    DPTEQR(3F)

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

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

	 CHARACTER	COMPZ

	 INTEGER	INFO, LDZ, N

	 DOUBLE		PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )

PURPOSE
     DPTEQR computes all eigenvalues and, optionally, eigenvectors of a
     symmetric positive definite tridiagonal matrix by first factoring the
     matrix using DPTTRF, and then calling DBDSQR 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 symmetric positive definite matrix can
     also be found if DSYTRD, DSPTRD, or DSBTRD has been used to reduce this
     matrix to tridiagonal form. (The reduction to tridiagonal form, however,
     may preclude the possibility of obtaining high relative accuracy in the
     small eigenvalues of the original matrix, if these eigenvalues range over
     many orders of magnitude.)

ARGUMENTS
     COMPZ   (input) CHARACTER*1
	     = 'N':  Compute eigenvalues only.
	     = 'V':  Compute eigenvectors of original symmetric matrix also.
	     Array Z contains the orthogonal 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) DOUBLE PRECISION array, dimension (N)
	     On entry, the n diagonal elements of the tridiagonal matrix.  On
	     normal exit, D contains the eigenvalues, in descending order.

									Page 1

DPTEQR(3F)							    DPTEQR(3F)

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

     Z	     (input/output) DOUBLE PRECISION array, dimension (LDZ, N)
	     On entry, if COMPZ = 'V', the orthogonal matrix used in the
	     reduction to tridiagonal form.  On exit, if COMPZ = 'V', the
	     orthonormal eigenvectors of the original symmetric matrix; if
	     COMPZ = 'I', the orthonormal eigenvectors of the tridiagonal
	     matrix.  If INFO > 0 on exit, Z contains the eigenvectors
	     associated 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) DOUBLE PRECISION array, dimension (LWORK)
	     If	 COMPZ = 'N', then LWORK = 2*N If  COMPZ = 'V' or 'I', then
	     LWORK = MAX(1,4*N-4)

     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.

									Page 2

[top]

List of man pages available for IRIX

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