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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