DLARTGS(3)     LAPACK routine of NEC Numeric Library Collection     DLARTGS(3)



NAME
       DLARTGS

SYNOPSIS
       SUBROUTINE DLARTGS (X, Y, SIGMA, CS, SN)



PURPOSE
            DLARTGS generates a plane rotation designed to introduce a bulge in
            Golub-Reinsch-style implicit QR iteration for the bidiagonal SVD
            problem. X and Y are the top-row entries, and SIGMA is the shift.
            The computed CS and SN define a plane rotation satisfying

               [  CS  SN  ]  .  [ X^2 - SIGMA ]  =  [ R ],
               [ -SN  CS  ]     [    X * Y    ]     [ 0 ]

            with R nonnegative.  If X^2 - SIGMA and X * Y are 0, then the
            rotation is by PI/2.




ARGUMENTS
           X         (input)
                     X is DOUBLE PRECISION
                     The (1,1) entry of an upper bidiagonal matrix.

           Y         (input)
                     Y is DOUBLE PRECISION
                     The (1,2) entry of an upper bidiagonal matrix.

           SIGMA     (input)
                     SIGMA is DOUBLE PRECISION
                     The shift.

           CS        (output)
                     CS is DOUBLE PRECISION
                     The cosine of the rotation.

           SN        (output)
                     SN is DOUBLE PRECISION
                     The sine of the rotation.



LAPACK routine                  31 October 2017                     DLARTGS(3)