---
name: "slasd4"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/slasd4/3lapack"
---

# slasd4(3lapack)

subroutine compute 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

## NAME

SLASD4 - subroutine compute 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 SLASD4(

  N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )

- INTEGER

  I, INFO, N

- REAL

  RHO, SIGMA

- REAL

  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 diagonal matrix whose entries are given as the squares of the corresponding entries in the array d, and that 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) REAL array, dimension ( N )

  The original eigenvalues.  It is assumed that they are in order, 0 \<= 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) - 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) REAL

  The scalar in the symmetric updating formula.

- SIGMA (output) REAL

  The computed sigma\_I, the I-th updated eigenvalue.

- WORK (workspace) REAL 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