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



NAME
       SLARTGS

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



PURPOSE
            SLARTGS 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 REAL
                     The (1,1) entry of an upper bidiagonal matrix.

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

           SIGMA     (input)
                     SIGMA is REAL
                     The shift.

           CS        (output)
                     CS is REAL
                     The cosine of the rotation.

           SN        (output)
                     SN is REAL
                     The sine of the rotation.



LAPACK routine                  31 October 2017                     SLARTGS(3)