# slasd4.f man page

slasd4.f

## Synopsis

### Functions/Subroutines

subroutine **slasd4** (**N**, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO)**SLASD4** computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by sbdsdc.

## Function/Subroutine Documentation

### subroutine slasd4 (integer N, integer I, real, dimension( * ) D, real, dimension( * ) Z, real, dimension( * ) DELTA, real RHO, real SIGMA, real, dimension( * ) WORK, integer INFO)

**SLASD4** computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by sbdsdc.

**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 REAL 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 REAL array, dimension ( N ) The components of the updating vector.

*DELTA*DELTA is 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*RHO is REAL The scalar in the symmetric updating formula.

*SIGMA*SIGMA is REAL The computed sigma_I, the I-th updated eigenvalue.

*WORK*WORK is 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*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 155 of file slasd4.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page slasd4(3) is an alias of slasd4.f(3).