NAME

       laed5 - laed5: D&C step: secular equation, 2x2

SYNOPSIS

   Functions
       subroutine dlaed5 (i, d, z, delta, rho, dlam)
           DLAED5 used by DSTEDC. Solves the 2-by-2 secular equation.
       subroutine slaed5 (i, d, z, delta, rho, dlam)
           SLAED5 used by SSTEDC. Solves the 2-by-2 secular equation.

Detailed Description

Function Documentation

   subroutine dlaed5 (integer i, double precision, dimension( 2 ) d, double precision, dimension( 2 ) z, double
       precision, dimension( 2 ) delta, double precision rho, double precision dlam)
       DLAED5 used by DSTEDC. Solves the 2-by-2 secular equation.

       Purpose:

            This subroutine computes the I-th eigenvalue of a symmetric rank-one
            modification of a 2-by-2 diagonal matrix

                       diag( D )  +  RHO * Z * transpose(Z) .

            The diagonal elements in the array D are assumed to satisfy

                       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 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)
                    The vector DELTA contains the information necessary
                    to construct the eigenvectors.

           RHO

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

           DLAM

                     DLAM is DOUBLE PRECISION
                    The computed lambda_I, the I-th updated eigenvalue.

       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 slaed5 (integer i, real, dimension( 2 ) d, real, dimension( 2 ) z, real, dimension( 2 ) delta,
       real rho, real dlam)
       SLAED5 used by SSTEDC. Solves the 2-by-2 secular equation.

       Purpose:

            This subroutine computes the I-th eigenvalue of a symmetric rank-one
            modification of a 2-by-2 diagonal matrix

                       diag( D )  +  RHO * Z * transpose(Z) .

            The diagonal elements in the array D are assumed to satisfy

                       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 D(1) < D(2).

           Z

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

           DELTA

                     DELTA is REAL array, dimension (2)
                    The vector DELTA contains the information necessary
                    to construct the eigenvectors.

           RHO

                     RHO is REAL
                    The scalar in the symmetric updating formula.

           DLAM

                     DLAM is REAL
                    The computed lambda_I, the I-th updated eigenvalue.

       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

       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.12.0                              Tue Jan 28 2025 00:54:31                                    laed5(3)