# slaed4.f(3) [centos man page]

slaed4.f(3) LAPACK slaed4.f(3)NAME

slaed4.f-SYNOPSIS

Functions/Subroutines subroutine slaed4 (N, I, D, Z, DELTA, RHO, DLAM, INFO) SLAED4 used by sstedc. Finds a single root of the secular equation.Function/Subroutine Documentation subroutine slaed4 (integerN, integerI, real, dimension( * )D, real, dimension( * )Z, real, dimension( * )DELTA, realRHO, realDLAM, integerINFO) SLAED4 used by sstedc. Finds a single root of the secular equation. Purpose: This subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that 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 ) + 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 REAL array, dimension (N) The original eigenvalues. It is assumed that they are in order, D(I) < D(J) for I < J. Z Z is REAL array, dimension (N) The components of the updating vector. DELTA DELTA is REAL array, dimension (N) If N .GT. 2, DELTA contains (D(j) - lambda_I) in its j-th component. If N = 1, then DELTA(1) = 1. If N = 2, see SLAED5 for detail. The vector DELTA contains the information necessary to construct the eigenvectors by SLAED3 and SLAED9. RHO RHO is REAL The scalar in the symmetric updating formula. DLAM DLAM is REAL The computed lambda_I, the I-th updated eigenvalue. 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: September 2012 Contributors: Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA Definition at line 146 of file slaed4.f.AuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 slaed4.f(3)

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SLAED4(l)) SLAED4(l)NAME

SLAED4 - subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0SYNOPSIS

SUBROUTINE SLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO ) INTEGER I, INFO, N REAL DLAM, RHO REAL D( * ), DELTA( * ), Z( * )PURPOSE

This subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that 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 ) + 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) REAL array, dimension (N) The original eigenvalues. It is assumed that they are in order, D(I) < D(J) for I < J. Z (input) REAL array, dimension (N) The components of the updating vector. DELTA (output) REAL array, dimension (N) If N .ne. 1, DELTA contains (D(j) - lambda_I) in its j-th component. If N = 1, then DELTA(1) = 1. The vector DELTA contains the information necessary to construct the eigenvectors. RHO (input) REAL The scalar in the symmetric updating formula. DLAM (output) REAL The computed lambda_I, the I-th updated eigenvalue. 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, USALAPACK version 3.015 June 2000 SLAED4(l)