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.

X

          X is REAL


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

Y

          Y is REAL


          The (1,2) entry of an upper bidiagonal matrix.

SIGMA

          SIGMA is REAL


          The shift.

CS

          CS is REAL


          The cosine of the rotation.

SN

          SN is REAL


          The sine of the rotation.

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NAG Ltd.

September 2012