Man page - laed4(3)

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laed4

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine dlaed4 (integer n, integer i, double precision, dimension( * )d, double precision, dimension( * ) z, double precision, dimension( * )delta, double precision rho, double precision dlam, integer info)
subroutine slaed4 (integer n, integer i, real, dimension( * ) d, real,dimension( * ) z, real, dimension( * ) delta, real rho, real dlam,integer info)
Author

NAME

laed4 - laed4: D&C step: secular equation nonlinear solver

SYNOPSIS

Functions

subroutine dlaed4 (n, i, d, z, delta, rho, dlam, info)
DLAED4 used by DSTEDC. Finds a single root of the secular equation.
subroutine slaed4 (n, i, d, z, delta, rho, dlam, info)
SLAED4 used by SSTEDC. Finds a single root of the secular equation.

Detailed Description

Function Documentation

subroutine dlaed4 (integer n, integer i, double precision, dimension( * )d, double precision, dimension( * ) z, double precision, dimension( * )delta, double precision rho, double precision dlam, integer info)

DLAED4 used by DSTEDC. 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 DOUBLE PRECISION array, dimension (N)
The original eigenvalues. It is assumed that they are in
order, 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 > 2, DELTA contains (D(j) - lambda_I) in its j-th
component. If N = 1, then DELTA(1) = 1. If N = 2, see DLAED5
for detail. The vector DELTA contains the information necessary
to construct the eigenvectors by DLAED3 and DLAED9.

RHO

RHO is DOUBLE PRECISION
The scalar in the symmetric updating formula.

DLAM

DLAM is DOUBLE PRECISION
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.

Contributors:

Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

subroutine slaed4 (integer n, integer i, real, dimension( * ) d, real,dimension( * ) z, real, dimension( * ) delta, real rho, real dlam,integer info)

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 > 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.

Contributors:

Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

Author

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