slasd5.f(3)

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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