# dlaed4.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **dlaed4** (**N**, I, D, Z, DELTA, RHO, DLAM, INFO)**DLAED4** used by sstedc. Finds a single root of the secular equation.

## Function/Subroutine 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 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 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 .GT. 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.

**Date:**December 2016

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

Definition at line 147 of file dlaed4.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dlaed4(3) is an alias of dlaed4.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK