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 (integerI, real, dimension( 2 )D, real, dimension( 2 )Z, real, dimension( 2 )DELTA, realRHO, realDSIGMA, 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:

September 2012

Contributors:

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

Definition at line 117 of file slasd5.f.

Author

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Referenced By

slasd5(3) is an alias of slasd5.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK