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## slartgs()

subroutine slartgs | ( | real | x,
|  | real | y,
|  | real | sigma,
|  | real | cs,
|  | real | sn )

SLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem.

Download SLARTGS + dependencies [TGZ] [ZIP] [TXT]

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.
      !>

Parameters

  [in]

  X

      !>          X is REAL
      !>          The (1,1) entry of an upper bidiagonal matrix.
      !>

  [in]

  Y

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

  [in]

  SIGMA

      !>          SIGMA is REAL
      !>          The shift.
      !>

  [out]

  CS

      !>          CS is REAL
      !>          The cosine of the rotation.
      !>

  [out]

  SN

      !>          SN is REAL
      !>          The sine of the rotation.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.