slasd5.f (3) - Linux Manuals

NAME

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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