NAME

       lasd5 - lasd5: D&C step: secular equation, 2x2

SYNOPSIS

   Functions
       subroutine dlasd5 (i, d, z, delta, rho, dsigma, work)
           DLASD5 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.
       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.

Detailed Description

Function Documentation

   subroutine dlasd5 (integer i, double precision, dimension( 2 ) d, double precision, dimension(
       2 ) z, double precision, dimension( 2 ) delta, double precision rho, double precision
       dsigma, double precision, dimension( 2 ) work)
       DLASD5 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 DOUBLE PRECISION array, dimension ( 2 )
                    The original eigenvalues.  We assume 0 <= D(1) < D(2).

           Z

                     Z is DOUBLE PRECISION array, dimension ( 2 )
                    The components of the updating vector.

           DELTA

                     DELTA is DOUBLE PRECISION 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 DOUBLE PRECISION
                    The scalar in the symmetric updating formula.

           DSIGMA

                     DSIGMA is DOUBLE PRECISION
                    The computed sigma_I, the I-th updated eigenvalue.

           WORK

                     WORK is DOUBLE PRECISION 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.

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

   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.

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

Author

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