dlasq3(3F)

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( * )

PURPOSE
        DLASQ3 is the workhorse of the whole bidiagonal SVD algorithm.
        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