# slasd5.f man page

slasd5.f

## Synopsis

### Functions/Subroutines

subroutine **slasd5** (I, D, Z, DELTA, RHO, DSIGMA, WORK)**SLASD5** computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc.

## Function/Subroutine Documentation

### subroutine slasd5 (integer I, real, dimension( 2 ) D, real, dimension( 2 ) Z, real, dimension( 2 ) DELTA, real RHO, real DSIGMA, real, dimension( 2 ) WORK)

**SLASD5** computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc.

**Purpose:**

This subroutine computes the square root of the I-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) * diag( D ) + RHO * Z * transpose(Z) . The diagonal entries in the array D are assumed to satisfy 0 <= D(i) < D(j) for i < j . We also assume RHO > 0 and that the Euclidean norm of the vector Z is one.

**Parameters:**-
*I*I is INTEGER The index of the eigenvalue to be computed. I = 1 or I = 2.

*D*D is REAL array, dimension (2) The original eigenvalues. We assume 0 <= D(1) < D(2).

*Z*Z is REAL array, dimension (2) The components of the updating vector.

*DELTA*DELTA is REAL array, dimension (2) Contains (D(j) - sigma_I) in its j-th component. The vector DELTA contains the information necessary to construct the eigenvectors.

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

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

*WORK*WORK is REAL array, dimension (2) WORK contains (D(j) + sigma_I) in its j-th component.

**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 118 of file slasd5.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page slasd5(3) is an alias of slasd5.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK