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NAME
     dlasq3 - DLASQ3 is the workhorse of the whole bidiagonal SVD
     algorithm

SYNOPSIS
     SUBROUTINE DLASQ3( N, Q, E, QQ, EE, SUP, SIGMA,  KEND,  OFF,
               IPHASE, ICONV, EPS, TOL2, SMALL2 )

     INTEGER ICONV, IPHASE, KEND, N, OFF

     DOUBLE PRECISION EPS, SIGMA, SMALL2, SUP, TOL2

     DOUBLE PRECISION E( * ), EE( * ), Q( * ), QQ( * )



     #include <sunperf.h>

     void dlasq3(int *n, double *q, double *e, double *qq, double
               *ee,  double  *sup,  double *sigma, int *kend, int
               *off, int *iphase, int iconv, double  eps,  double
               tol2, double small2) ;

PURPOSE
        DLASQ3 is the workhorse of the whole bidiagonal SVD algo-
     rithm.
        This can be described as the differential qd with shifts.


ARGUMENTS
     N         (input/output) INTEGER
               On entry, N  specifies  the  number  of  rows  and
               columns  in  the matrix. N must be at least 3.  On
               exit N is non-negative and  less  than  the  input
               value.

     Q         (input/output) DOUBLE PRECISION  array,  dimension
               (N)
               Q array in ping (see IPHASE below)

     E         (input/output) DOUBLE PRECISION  array,  dimension
               (N)
               E array in ping (see IPHASE below)

     QQ        (input/output) DOUBLE PRECISION  array,  dimension
               (N)
               Q array in pong (see IPHASE below)

     EE        (input/output) DOUBLE PRECISION  array,  dimension
               (N)
               E array in pong (see IPHASE below)

     SUP       (input/output) DOUBLE PRECISION
               Upper bound for the smallest eigenvalue

     SIGMA     (input/output) DOUBLE PRECISION
               Accumulated shift for the present submatrix

     KEND      (input/output) INTEGER
               Index where minimum D(i) occurs in recurrence  for
               splitting criterion

     OFF       (input/output) INTEGER
               Offset for arrays

     IPHASE    (input/output) INTEGER
               If IPHASE = 1 (ping) then  data  is  in  Q  and  E
               arrays If IPHASE = 2 (pong) then data is in QQ and
               EE arrays

     ICONV     (input) INTEGER
               If ICONV = 0 a bottom part of  a  matrix  (with  a
               split) If ICONV =-3 a top part of a matrix (with a
               split)

     EPS       (input) DOUBLE PRECISION
               Machine epsilon

     TOL2      (input) DOUBLE PRECISION
               Square of the relative tolerance TOL as defined in
               DLASQ1

     SMALL2    (input) DOUBLE PRECISION
               A threshold value as defined in DLASQ1

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