dlasd9(3S)

NAME
     DLASD9 - find the square roots of the roots of the secular equation,

SYNOPSIS
     SUBROUTINE DLASD9( ICOMPQ, LDU, K, D, Z, VF, VL, DIFL, DIFR, DSIGMA,
                        WORK, INFO )

         INTEGER        ICOMPQ, INFO, K, LDU

         DOUBLE         PRECISION D( * ), DIFL( * ), DIFR( LDU, * ), DSIGMA( *
                        ), VF( * ), VL( * ), WORK( * ), Z( * )

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
     DLASD9 finds the square roots of the roots of the secular equation, as
     defined by the values in DSIGMA and Z.  It makes the
     appropriate calls to DLASD4, and stores, for each  element in D, the
     distance to its two nearest poles (elements in DSIGMA). It also updates
     the arrays VF and VL, the first and last components of all the right
     singular vectors of the original bidiagonal matrix.

     DLASD9 is called from DLASD7.


ARGUMENTS
     ICOMPQ  (input) INTEGER
             Specifies whether singular vectors are to be computed in factored
             form in the calling routine:

             ICOMPQ = 0             Compute singular values only.

             ICOMPQ = 1             Compute singular vector matrices in
             factored form also.

     K       (input) INTEGER
             The number of terms in the rational function to be solved by
             DLASD4.  K >= 1.
     D       (output) DOUBLE PRECISION array, dimension(K)
             D(I) contains the updated singular values.

     DSIGMA  (input) DOUBLE PRECISION array, dimension(K)
             The first K elements of this array contain the old roots of the
             deflated updating problem.  These are the poles of the secular
             equation.

     Z       (input) DOUBLE PRECISION array, dimension (K)
             The first K elements of this array contain the components of the
             deflation-adjusted updating row vector.

     VF      (input/output) DOUBLE PRECISION array, dimension(K)
             On entry, VF contains  information passed through SBEDE8.f On
             exit, VF contains the first K components of the first components
             of all right singular vectors of the bidiagonal matrix.

     VL      (input/output) DOUBLE PRECISION array, dimension(K)
             On entry, VL contains  information passed through SBEDE8.f On
             exit, VL contains the first K components of the last components
             of all right singular vectors of the bidiagonal matrix.

     DIFL    (output) DOUBLE PRECISION array, dimension (K).
             On exit, DIFL(I) = D(I) - DSIGMA(I).

     DIFR    (output) DOUBLE PRECISION array,
             dimension (LDU, 2) if ICOMPQ =1 and dimension (K) if ICOMPQ = 0.
             On exit, DIFR(I, 1) = D(I) - DSIGMA(I+1), DIFR(K, 1) is not
             defined and will not be referenced.

             If ICOMPQ = 1, DIFR(1:K, 2) is an array containing the
             normalizing factors for the right singular vector matrix.

     LDU     (input) INTEGER
             The leading dimension of DIFR if ICOMPQ = 1.  LDU >= 1.

     WORK    (workspace) DOUBLE PRECISION array,
             dimension at least (3 * K) Workspace.

     INFO    (output) INTEGER
             = 0:  successful exit.
             < 0:  if INFO = -i, the i-th argument had an illegal value.
             > 0:  if INFO = 1, an singular value did not converge

FURTHER DETAILS
     Based on contributions by
        Ming Gu and Huan Ren, Computer Science Division, University of
        California at Berkeley, USA

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

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