NAME

       lasq3 - lasq3: dqds step

SYNOPSIS

   Functions
       subroutine dlasq3 (i0, n0, z, pp, dmin, sigma, desig, qmax, nfail, iter, ndiv, ieee,
           ttype, dmin1, dmin2, dn, dn1, dn2, g, tau)
           DLASQ3 checks for deflation, computes a shift and calls dqds. Used by sbdsqr.
       subroutine slasq3 (i0, n0, z, pp, dmin, sigma, desig, qmax, nfail, iter, ndiv, ieee,
           ttype, dmin1, dmin2, dn, dn1, dn2, g, tau)
           SLASQ3 checks for deflation, computes a shift and calls dqds. Used by sbdsqr.

Detailed Description

Function Documentation

   subroutine dlasq3 (integer i0, integer n0, double precision, dimension( * ) z, integer pp,
       double precision dmin, double precision sigma, double precision desig, double precision
       qmax, integer nfail, integer iter, integer ndiv, logical ieee, integer ttype, double
       precision dmin1, double precision dmin2, double precision dn, double precision dn1, double
       precision dn2, double precision g, double precision tau)
       DLASQ3 checks for deflation, computes a shift and calls dqds. Used by sbdsqr.

       Purpose:

            DLASQ3 checks for deflation, computes a shift (TAU) and calls dqds.
            In case of failure it changes shifts, and tries again until output
            is positive.

       Parameters
           I0

                     I0 is INTEGER
                    First index.

           N0

                     N0 is INTEGER
                    Last index.

           Z

                     Z is DOUBLE PRECISION array, dimension ( 4*N0 )
                    Z holds the qd array.

           PP

                     PP is INTEGER
                    PP=0 for ping, PP=1 for pong.
                    PP=2 indicates that flipping was applied to the Z array
                    and that the initial tests for deflation should not be
                    performed.

           DMIN

                     DMIN is DOUBLE PRECISION
                    Minimum value of d.

           SIGMA

                     SIGMA is DOUBLE PRECISION
                    Sum of shifts used in current segment.

           DESIG

                     DESIG is DOUBLE PRECISION
                    Lower order part of SIGMA

           QMAX

                     QMAX is DOUBLE PRECISION
                    Maximum value of q.

           NFAIL

                     NFAIL is INTEGER
                    Increment NFAIL by 1 each time the shift was too big.

           ITER

                     ITER is INTEGER
                    Increment ITER by 1 for each iteration.

           NDIV

                     NDIV is INTEGER
                    Increment NDIV by 1 for each division.

           IEEE

                     IEEE is LOGICAL
                    Flag for IEEE or non IEEE arithmetic (passed to DLASQ5).

           TTYPE

                     TTYPE is INTEGER
                    Shift type.

           DMIN1

                     DMIN1 is DOUBLE PRECISION

           DMIN2

                     DMIN2 is DOUBLE PRECISION

           DN

                     DN is DOUBLE PRECISION

           DN1

                     DN1 is DOUBLE PRECISION

           DN2

                     DN2 is DOUBLE PRECISION

           G

                     G is DOUBLE PRECISION

           TAU

                     TAU is DOUBLE PRECISION

                    These are passed as arguments in order to save their values
                    between calls to DLASQ3.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

   subroutine slasq3 (integer i0, integer n0, real, dimension( * ) z, integer pp, real dmin, real
       sigma, real desig, real qmax, integer nfail, integer iter, integer ndiv, logical ieee,
       integer ttype, real dmin1, real dmin2, real dn, real dn1, real dn2, real g, real tau)
       SLASQ3 checks for deflation, computes a shift and calls dqds. Used by sbdsqr.

       Purpose:

            SLASQ3 checks for deflation, computes a shift (TAU) and calls dqds.
            In case of failure it changes shifts, and tries again until output
            is positive.

       Parameters
           I0

                     I0 is INTEGER
                    First index.

           N0

                     N0 is INTEGER
                    Last index.

           Z

                     Z is REAL array, dimension ( 4*N0 )
                    Z holds the qd array.

           PP

                     PP is INTEGER
                    PP=0 for ping, PP=1 for pong.
                    PP=2 indicates that flipping was applied to the Z array
                    and that the initial tests for deflation should not be
                    performed.

           DMIN

                     DMIN is REAL
                    Minimum value of d.

           SIGMA

                     SIGMA is REAL
                    Sum of shifts used in current segment.

           DESIG

                     DESIG is REAL
                    Lower order part of SIGMA

           QMAX

                     QMAX is REAL
                    Maximum value of q.

           NFAIL

                     NFAIL is INTEGER
                    Increment NFAIL by 1 each time the shift was too big.

           ITER

                     ITER is INTEGER
                    Increment ITER by 1 for each iteration.

           NDIV

                     NDIV is INTEGER
                    Increment NDIV by 1 for each division.

           IEEE

                     IEEE is LOGICAL
                    Flag for IEEE or non IEEE arithmetic (passed to SLASQ5).

           TTYPE

                     TTYPE is INTEGER
                    Shift type.

           DMIN1

                     DMIN1 is REAL

           DMIN2

                     DMIN2 is REAL

           DN

                     DN is REAL

           DN1

                     DN1 is REAL

           DN2

                     DN2 is REAL

           G

                     G is REAL

           TAU

                     TAU is REAL

                    These are passed as arguments in order to save their values
                    between calls to SLASQ3.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

Author

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