NAME

SLASQ3 - SLASQ3 is the workhorse of the whole bidiagonal SVD algorithm

SYNOPSIS

SUBROUTINE SLASQ3(
N, Q, E, QQ, EE, SUP, SIGMA, KEND, OFF, IPHASE, ICONV, EPS, TOL2, SMALL2 )

INTEGER ICONV, IPHASE, KEND, N, OFF

REAL EPS, SIGMA, SMALL2, SUP, TOL2

REAL E( ∗ ), EE( ∗ ), Q( ∗ ), QQ( ∗ )

PURPOSE

   SLASQ3 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) REAL array, dimension (N)
Q array in ping (see IPHASE below)

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

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

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

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

SIGMA   (input/output) REAL
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) REAL
Machine epsilon

TOL2    (input) REAL
Square of the relative tolerance TOL as defined in SLASQ1

SMALL2  (input) REAL
A threshold value as defined in SLASQ1

  —  LAPACK version 2.0  —  08 October 1994