LAPACK

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 is INTEGER


         The index of the eigenvalue to be computed.  I = 1 or I = 2.



          D is DOUBLE PRECISION array, dimension (2)


         The original eigenvalues.  We assume D(1) < D(2).



          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.