dlasd4(l) [redhat man page]
DLASD4(l) ) DLASD4(l) NAME
DLASD4 - subroutine computes the square root of the I-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix whose entries are given as the squares of the corresponding entries in the array d, and that 0 <= D(i) < D(j) for i < j and that RHO > 0 SYNOPSIS
SUBROUTINE DLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO ) INTEGER I, INFO, N DOUBLE PRECISION RHO, SIGMA DOUBLE PRECISION D( * ), DELTA( * ), WORK( * ), Z( * ) PURPOSE
This subroutine computes the square root of the I-th updated eigenvalue of a positive symmetric rank-one modification to a positive diago- nal matrix whose entries are given as the squares of the corresponding entries in the array d, and that 0 <= D(i) < D(j) for i < j and that RHO > 0. This is arranged by the calling routine, and is no loss in generality. The rank-one modified system is thus diag( D ) * diag( D ) + RHO * Z * Z_transpose. where we assume the Euclidean norm of Z is 1. The method consists of approximating the rational functions in the secular equation by simpler interpolating rational functions. ARGUMENTS
N (input) INTEGER The length of all arrays. I (input) INTEGER The index of the eigenvalue to be computed. 1 <= I <= N. D (input) DOUBLE PRECISION array, dimension ( N ) The original eigenvalues. It is assumed that they are in order, 0 <= D(I) < D(J) for I < J. Z (input) DOUBLE PRECISION array, dimension ( N ) The components of the updating vector. DELTA (output) DOUBLE PRECISION array, dimension ( N ) If N .ne. 1, DELTA contains (D(j) - sigma_I) in its j-th component. If N = 1, then DELTA(1) = 1. The vector DELTA contains the information necessary to construct the (singular) eigenvectors. RHO (input) DOUBLE PRECISION The scalar in the symmetric updating formula. SIGMA (output) DOUBLE PRECISION The computed lambda_I, the I-th updated eigenvalue. WORK (workspace) DOUBLE PRECISION array, dimension ( N ) If N .ne. 1, WORK contains (D(j) + sigma_I) in its j-th component. If N = 1, then WORK( 1 ) = 1. INFO (output) INTEGER = 0: successful exit > 0: if INFO = 1, the updating process failed. PARAMETERS
Logical variable ORGATI (origin-at-i?) is used for distinguishing whether D(i) or D(i+1) is treated as the origin. ORGATI = .true. origin at i ORGATI = .false. origin at i+1 Logical variable SWTCH3 (switch-for-3-poles?) is for noting if we are working with THREE poles! MAXIT is the maximum number of iterations allowed for each eigenvalue. Further Details =============== Based on contributions by Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA LAPACK version 3.0 15 June 2000 DLASD4(l)
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dlasd4.f(3) LAPACK dlasd4.f(3) NAME
dlasd4.f - SYNOPSIS
Functions/Subroutines subroutine dlasd4 (N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO) DLASD4 Function/Subroutine Documentation subroutine dlasd4 (integerN, integerI, double precision, dimension( * )D, double precision, dimension( * )Z, double precision, dimension( * )DELTA, double precisionRHO, double precisionSIGMA, double precision, dimension( * )WORK, integerINFO) DLASD4 Purpose: This subroutine computes the square root of the I-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix whose entries are given as the squares of the corresponding entries in the array d, and that 0 <= D(i) < D(j) for i < j and that RHO > 0. This is arranged by the calling routine, and is no loss in generality. The rank-one modified system is thus diag( D ) * diag( D ) + RHO * Z * Z_transpose. where we assume the Euclidean norm of Z is 1. The method consists of approximating the rational functions in the secular equation by simpler interpolating rational functions. Parameters: N N is INTEGER The length of all arrays. I I is INTEGER The index of the eigenvalue to be computed. 1 <= I <= N. D D is DOUBLE PRECISION array, dimension ( N ) The original eigenvalues. It is assumed that they are in order, 0 <= D(I) < D(J) for I < J. Z Z is DOUBLE PRECISION array, dimension ( N ) The components of the updating vector. DELTA DELTA is DOUBLE PRECISION array, dimension ( N ) If N .ne. 1, DELTA contains (D(j) - sigma_I) in its j-th component. If N = 1, then DELTA(1) = 1. The vector DELTA contains the information necessary to construct the (singular) eigenvectors. RHO RHO is DOUBLE PRECISION The scalar in the symmetric updating formula. SIGMA SIGMA is DOUBLE PRECISION The computed sigma_I, the I-th updated eigenvalue. WORK WORK is DOUBLE PRECISION array, dimension ( N ) If N .ne. 1, WORK contains (D(j) + sigma_I) in its j-th component. If N = 1, then WORK( 1 ) = 1. INFO INFO is INTEGER = 0: successful exit > 0: if INFO = 1, the updating process failed. Internal Parameters: Logical variable ORGATI (origin-at-i?) is used for distinguishing whether D(i) or D(i+1) is treated as the origin. ORGATI = .true. origin at i ORGATI = .false. origin at i+1 Logical variable SWTCH3 (switch-for-3-poles?) is for noting if we are working with THREE poles! MAXIT is the maximum number of iterations allowed for each eigenvalue. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 Contributors: Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA Definition at line 154 of file dlasd4.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 dlasd4.f(3)