slasd5(3S)

NAME
     SLASD5 - 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)

SYNOPSIS
     SUBROUTINE SLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK )

         INTEGER        I

         REAL           DSIGMA, RHO

         REAL           D( 2 ), DELTA( 2 ), WORK( 2 ), Z( 2 )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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.


ARGUMENTS
     I      (input) INTEGER
            The index of the eigenvalue to be computed.  I = 1 or I = 2.

     D      (input) REAL array, dimension ( 2 )
            The original eigenvalues.  We assume 0 <= D(1) < D(2).

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

     DELTA  (output) REAL array, dimension ( 2 )
            Contains (D(j) - lambda_I) in its  j-th component.  The vector
            DELTA contains the information necessary to construct the
            eigenvectors.

     RHO    (input) REAL
            The scalar in the symmetric updating formula.

            DSIGMA (output) REAL The computed lambda_I, the I-th updated
            eigenvalue.

     WORK   (workspace) REAL array, dimension ( 2 )
            WORK contains (D(j) + sigma_I) in its  j-th component.

FURTHER DETAILS
     Based on contributions by
        Ren-Cang Li, Computer Science Division, University of California
        at Berkeley, USA


SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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