clarrv man page on IRIX

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



CLARRV(3S)							    CLARRV(3S)

NAME
     CLARRV - compute the eigenvectors of the tridiagonal matrix T = L D L^T
     given L, D and the eigenvalues of L D L^T

SYNOPSIS
     SUBROUTINE CLARRV( N, D, L, ISPLIT, M, W, IBLOCK, GERSCH, TOL, Z, LDZ,
			ISUPPZ, WORK, IWORK, INFO )

	 INTEGER	INFO, LDZ, M, N

	 REAL		TOL

	 INTEGER	IBLOCK( * ), ISPLIT( * ), ISUPPZ( * ), IWORK( * )

	 REAL		D( * ), GERSCH( * ), L( * ), W( * ), WORK( * )

	 COMPLEX	Z( LDZ, * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     CLARRV computes the eigenvectors of the tridiagonal matrix T = L D L^T
     given L, D and the eigenvalues of L D L^T. The input eigenvalues should
     have high relative accuracy with respect to the entries of L and D. The
     desired accuracy of the output can be specified by the input parameter
     TOL.

ARGUMENTS
     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 diagonal matrix D.  On
	     exit, D may be overwritten.

     L	     (input/output) REAL array, dimension (N-1)
	     On entry, the (n-1) subdiagonal elements of the unit bidiagonal
	     matrix L in elements 1 to N-1 of L. L(N) need not be set. On
	     exit, L is overwritten.

									Page 1

CLARRV(3S)							    CLARRV(3S)

     ISPLIT  (input) INTEGER array, dimension (N)
	     The splitting points, at which T breaks up into submatrices.  The
	     first submatrix consists of rows/columns 1 to ISPLIT( 1 ), the
	     second of rows/columns ISPLIT( 1 )+1 through ISPLIT( 2 ), etc.

     TOL     (input) REAL
	     The absolute error tolerance for the eigenvalues/eigenvectors.
	     Errors in the input eigenvalues must be bounded by TOL.  The
	     eigenvectors output have residual norms bounded by TOL, and the
	     dot products between different eigenvectors are bounded by TOL.
	     TOL must be at least N*EPS*|T|, where EPS is the machine
	     precision and |T| is the 1-norm of the tridiagonal matrix.

     M	     (input) INTEGER
	     The total number of eigenvalues found.  0 <= M <= N.  If RANGE =
	     'A', M = N, and if RANGE = 'I', M = IU-IL+1.

     W	     (input) REAL array, dimension (N)
	     The first M elements of W contain the eigenvalues for which
	     eigenvectors are to be computed.  The eigenvalues should be
	     grouped by split-off block and ordered from smallest to largest
	     within the block ( The output array W from SLARRE is expected
	     here ).  Errors in W must be bounded by TOL (see above).

     IBLOCK  (input) INTEGER array, dimension (N)
	     The submatrix indices associated with the corresponding
	     eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to the
	     first submatrix from the top, =2 if W(i) belongs to the second
	     submatrix, etc.

     Z	     (output) COMPLEX array, dimension (LDZ, max(1,M) )
	     If JOBZ = 'V', then if INFO = 0, the first M columns of Z contain
	     the orthonormal eigenvectors of the matrix T corresponding to the
	     selected eigenvalues, with the i-th column of Z holding the
	     eigenvector associated with W(i).	If JOBZ = 'N', then Z is not
	     referenced.  Note: the user must ensure that at least max(1,M)
	     columns are supplied in the array Z; if RANGE = 'V', the exact
	     value of M is not known in advance and an upper bound must be
	     used.

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

     ISUPPZ  (output) INTEGER ARRAY, dimension ( 2*max(1,M) )
	     The support of the eigenvectors in Z, i.e., the indices
	     indicating the nonzero elements in Z. The i-th eigenvector is
	     nonzero only in elements ISUPPZ( 2*i-1 ) through ISUPPZ( 2*i ).

     GERSCH  (workspace) REAL array, dimension (2*N)

									Page 2

CLARRV(3S)							    CLARRV(3S)

     WORK    (workspace) REAL array, dimension (13*N)

     IWORK   (workspace) INTEGER array, dimension (6*N)

     INFO    (output) INTEGER
	     = 0:  successful exit
	     < 0:  if INFO = -i, the i-th argument had an illegal value
	     > 0:  if INFO = 1, internal error in SLARRB if INFO = 2, internal
	     error in CSTEIN

FURTHER DETAILS
     Based on contributions by
	Inderjit Dhillon, IBM Almaden, USA
	Osni Marques, LBNL/NERSC, USA
	Ken Stanley, Computer Science Division, University of
	  California at Berkeley, USA

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

     This man page is available only online.

									Page 3

[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